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Even though we focus on +periodic systems, the code and techniques presented here can be directly +transferred to molecules. +""" + +# %% +# First, import the necessary packages +# + +import os +import warnings +import zipfile + +import matplotlib.image as mpimg +import matplotlib.pyplot as plt +import numpy as np +import requests +import torch +from matplotlib.animation import FuncAnimation +from mlelec.data.derived_properties import compute_eigenvalues +from mlelec.data.mldataset import MLDataset +from mlelec.data.qmdataset import QMDataset +from mlelec.models.equivariant_lightning import LitEquivariantModel, MSELoss +from mlelec.utils.pbc_utils import blocks_to_matrix +from mlelec.utils.plot_utils import plot_bands_frame + + +warnings.filterwarnings("ignore") +torch.set_default_dtype(torch.float64) + +# sphinx_gallery_thumbnail_number = 3 + + +# %% +# Get Data and Prepare Data Set +# ----------------------------- +# + + +# %% +# The data set contains 35 distorted graphene unit cells containing 2 +# atoms. The reference density functional theory (DFT) calculations are +# performed with `CP2K `__ using a minimal +# `STO-3G `__ basis and +# the `PBE `__ functional. +# The Kohn-Sham equations are solved on a Monkhorst-Pack grid of +# :math:`15\times 15\times 1` points in the Brillouin zone of the crystal. +# + + +# %% +# Obtain structures and DFT data +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# Generating training structures requires running a suitable DFT code, +# and converting the output data in a format that can be processed by +# the ML library ``mlelec``. Given that it takes some time to run even +# these small calculations, we provide pre-computed data, but you can +# also find instructions on how to generate data from scratch. + +# %% +# Run your own cp2k calculations +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# If you have computational resources, you can run the DFT calculations +# needed to produce the data set. `This other +# tutorial `__ in the atomistic cookbook can +# help you set up the CP2K calculations for this data set, using the +# ``reftraj_hamiltonian.cp2k`` file provided in ``data/``. To do the same +# for another data set, adapt the reftraj file. +# We will provide here some of the functions in the `batch-cp2k +# tutorial `__ that need to be adapted to the +# current data set. Note however you will have to modify these and combine +# them with other tutorials to actually generate the data. + + +# %% +# Start by importing all the modules from the `batch-cp2k +# tutorial `__ and run the cell to install +# CP2K. Run also the cells up to the one defining ``write_cp2k_in``. +# The following code snippet defines a slighly modified version of that function, +# allowing for non-orthorombic supercell, and accounting for the reftraj file +# name change. +# + +# %% +# .. code:: python +# +# def write_cp2k_in( +# fname: str, +# project_name: str, +# last_snapshot: int, +# cell_a: List[float], +# cell_b: List[float], +# cell_c: List[float], +# ) -> None: +# """Writes a cp2k input file from a template. +# +# Importantly, it writes the location of the basis set definitions, +# determined from the path of the system CP2K install to the input file. +# """ +# +# cp2k_in = open("reftraj_hamiltonian.cp2k", "r").read() +# +# cp2k_in = cp2k_in.replace("//PROJECT//", project_name) +# cp2k_in = cp2k_in.replace("//LAST_SNAPSHOT//", str(last_snapshot)) +# cp2k_in = cp2k_in.replace("//CELL_A//", " ".join([f"{c:.6f}" for c in cell_a])) +# cp2k_in = cp2k_in.replace("//CELL_B//", " ".join([f"{c:.6f}" for c in cell_b])) +# cp2k_in = cp2k_in.replace("//CELL_C//", " ".join([f"{c:.6f}" for c in cell_c])) +# +# with open(fname, "w") as f: +# f.write(cp2k_in) +# + + +# %% +# Unlike the `batch-cp2k tutorial `__, the +# current data set includes a single stoichiometry, :math:`\mathrm{C_2}`. +# Therefore, you can run this cell to set the calculation scripts up. +# + +# %% +# .. code:: python +# +# project_name = 'graphene' +# frames = ase_read('C2.xyz', index=':') +# os.makedirs(project_name, exist_ok=True) +# os.makedirs(f"{project_name}/FOCK", exist_ok=True) +# os.makedirs(f"{project_name}/OVER", exist_ok=True) +# +# write_cp2k_in( +# f"{project_name}/in.cp2k", +# project_name=project_name, +# last_snapshot=len(frames), +# cell_a=frames[0].cell.array[0], +# cell_b=frames[0].cell.array[1], +# cell_c=frames[0].cell.array[2], +# ) +# +# ase_write(f"{project_name}/init.xyz", frames[0]) +# write_reftraj(f"{project_name}/reftraj.xyz", frames) +# write_cellfile(f"{project_name}/reftraj.cell", frames) +# + + +# %% +# The CP2K calculations can be simply run using: +# + + +# %% +# .. code:: python +# +# subprocess.run(( +# f"cp2k.ssmp -i {project_name}/in.cp2k " +# "> {project_name}/out.cp2k" +# ), +# shell=True) +# + + +# %% +# Once the calculations are done, we can parse the results with: +# + + +# %% +# .. code:: python +# +# from scipy.sparse import csr_matrix +# +# nao = 10 +# ifr = 1 +# fock = [] +# over = [] +# with open(f"{project_name}/out.cp2k", "r") as outfile: +# T_lists = [] # List to hold all T_list instances +# while True: +# line = outfile.readline() +# if not line: +# break +# if line.strip().split()[:3] != ["KS", "CSR", "write|"]: +# continue +# else: +# nT = int(line.strip().split()[3]) +# outfile.readline() # Skip the next line if necessary +# T_list = [] # Initialize a new T_list for this block +# for _ in range(nT): +# line = outfile.readline() +# if not line: +# break +# T_list.append([np.int32(j) for j in line.strip().split()[1:4]]) +# T_list = np.array(T_list) +# T_lists.append(T_list) # Append the T_list to T_lists +# fock_ = {} +# over_ = {} +# for iT, T in enumerate( +# T_list +# ): # Loop through the translations and load matrices +# T = T.tolist() +# r, c, data = np.loadtxt( +# ( +# f"{project_name}/FOCK/{project_name}" +# f"-KS_SPIN_1_R_{iT+1}-1_{ifr}.csr" +# ), +# unpack=True, +# ) +# r = np.int32(r - 1) +# c = np.int32(c - 1) +# fock_[tuple(T)] = csr_matrix( +# (data, (r, c)), shape=(nao, nao) +# ).toarray() +# +# r, c, data = np.loadtxt( +# ( +# f"{project_name}/OVER/{project_name}" +# f"-S_SPIN_1_R_{iT+1}-1_{ifr}.csr" +# ), +# unpack=True, +# ) +# r = np.int32(r - 1) +# c = np.int32(c - 1) +# over_[tuple(T)] = csr_matrix( +# (data, (r, c)), shape=(nao, nao) +# ).toarray() +# fock.append(fock_) +# over.append(over_) +# ifr += 1 +# + + +# %% +# You can now save the matrices to ``.npy`` files, and a file with the +# k-grids used in the calculations. +# + + +# %% +# .. code:: python +# +# os.makedirs("data", exist_ok=True) +# # Save the Hamiltonians +# np.save("data/graphene_fock.npy", fock) +# # Save the overlaps +# np.save("data/graphene_ovlp.npy", over) +# # Write a file with the k-grids, one line per structure +# np.savetxt('data/kmesh.dat', [[15,15,1]]*len(frames), fmt='%d') +# + + +# %% +# Download precomputed data +# ^^^^^^^^^^^^^^^^^^^^^^^^^ +# + + +# %% +# For the sake of simplicity, you can also download precomputed data and +# run just the machine learning part of the notebook using these data. +# + +filename = "precomputed.zip" +if not os.path.exists(filename): + url = ( + "https://github.com/curiosity54/mlelec/raw/" + "tutorial_periodic/examples/periodic_tutorial/precomputed.zip" + ) + response = requests.get(url) + response.raise_for_status() + with open(filename, "wb") as f: + f.write(response.content) + +with zipfile.ZipFile(filename, "r") as zip_ref: + zip_ref.extractall("./") + + +# %% +# Periodic Hamiltonians in real and reciprocal space +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# The DFT calculations for the dataset above were performed using a +# *minimal* STO-3G basis. The basis set is specified for each species +# using three quantum numbers, :math:`n`, :math:`l`, :math:`m`. :math:`n` +# is usually a natural number relating to the *radial* extent or +# resolution whereas :math:`l` and :math:`m` specify the *angular +# components* determining the shape of the orbital and its orientation in +# space. For example, :math:`1s` orbitals correspond to :math:`n=1`, +# :math:`l=0` and :math:`m=0`, while a :math:`2p_z` orbital corresponds to +# :math:`n=2`, :math:`l=1` and :math:`m=0`. For the STO-3G basis-set, +# these quantum numbers for Carbon (identified by its atomic number) are +# given as follows. +# + +basis = "sto-3g" +orbitals = { + "sto-3g": {6: [[1, 0, 0], [2, 0, 0], [2, 1, -1], [2, 1, 0], [2, 1, 1]]}, +} + + +# %% +# For each *frame* which of either train and test structures, the QM data +# comprises the configuration, along with the corresponding *overlap* and +# *Hamiltonian* (used interchangeably with *Fock*) matrices in the basis +# specified above, as well as the :math:`k`-point grid that was used for the +# calculation. +# +# Note that we are currently specifying these matrices in *real-space*, +# :math:`\mathbf{H}(\mathbf{t})` , such that the element +# :math:`\langle \mathbf{0} i nlm| \hat{H}| \mathbf{t} i' n'l'm'\rangle` +# indicates the interaction between orbital :math:`nlm` on atom :math:`i` +# in the undisplaced cell (denoted by the null lattice translation, +# :math:`\mathbf{t}=\mathbf{0}`) and orbital :math:`n'l'm'` on atom +# :math:`i'` in a periodic copy of the unit cell translated by +# :math:`\mathbf{t}`. A short-hand notation for +# :math:`\langle \mathbf{0} i nlm| \hat{H}| \mathbf{t} i' n'l'm'\rangle` +# is :math:`H_{\small\substack{i,nlm\\i',n'l'm'}}(\mathbf{t})` +# + +# %% +# .. figure:: graphene_lattice.png +# :alt: Representation of a graphene unit cell and some replicas. +# :width: 600px +# +# Representation of a graphene unit cell and its +# :math:`3 \times 3 \times 1` replicas in real space. The central cell +# is denoted by :math:`\mathbf{t}=(0,0,0)`, while the cells translated +# by a single lattice vector along directions 1 and 2 are denoted by +# :math:`\mathbf{t}=(1,0,0)` and :math:`\mathbf{t}=(0,1,0)`, +# respectively. The Hamiltonian matrix element between the :math:`1s` +# orbital on atom :math:`i` in the central unit cell and the +# :math:`2p_z` orbital on atom :math:`i'` in the +# :math:`\mathbf{t}=(1,0,0)` cell is schematically represented. +# + + +# %% +# Alternatively, we can provide the matrices in *reciprocal* (or +# Fourier, :math:`k`) space. These are related to the real-space matrices +# by a *Bloch sum*, +# +# .. math:: +# +# \mathbf{H}(\mathbf{k})=\sum_{\mathbf{t}}\ +# e^{i\mathbf{k}\cdot\mathbf{t}} \mathbf{H}(\mathbf{t}). +# +# +# In the case the input matrices are in reciprocal space, there should be +# one matrix per :math:`k`-point in the grid. +# + +# %% +# A ``QMDataset`` to store the DFT data +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# The ``QMDataset`` class holds all the relevant data +# obtained from a quantum-mechanical (in this case, DFT) calculation, +# combining information from the files containing structures, +# Hamiltonians and overlap matrices, and :math:`k`-point mesh. + +qmdata = QMDataset.from_file( + # File containing the atomistic structures + frames_path="data/C2.xyz", + # File containing the Hamiltonian (of Fock) matrices + fock_realspace_path="graphene_fock.npy", + # File containing the overlap matrices + overlap_realspace_path="graphene_ovlp.npy", + # File containing the k-point grids used for the DFT calculations + kmesh_path="kmesh.dat", + # Physical dimensionality of the system. Graphene is a 2D material + dimension=2, + # Device where to run the calculations + # (can be 'cpu' or 'cuda', if GPUs are available) + device="cpu", + # Name of the basis set used for the calculations + orbs_name=basis, + # List of quantum numbers associated with the basis set orbitals + orbs=orbitals[basis], +) + + +# %% +# Quantities stored in ``QMDataset`` can be accessed as attributes, +# e.g. ``qmdata.fock_realspace`` is a list (one element per structure) of +# dictionaries labeled by the indices of the unit cell real-space +# translations containing ``torch.Tensor``. +# + +structure_idx = 0 +realspace_translation = 0, 0, 0 +print(f"The real-space Hamiltonian matrix for structure {structure_idx} labeled by") +print(f"translation T={realspace_translation} is:") +print(f"{qmdata.fock_realspace[structure_idx][realspace_translation]}") + + +# %% +# Machine learning data set +# ~~~~~~~~~~~~~~~~~~~~~~~~~ +# + + +# %% +# Symmetries of the Hamiltonian matrix +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# + + +# %% +# The data stored in ``QMDataset`` can be transformed into a format that +# is optimal for machine learning modeling by leveraging the underlying +# *physical symmetries* that characterize the atomistic structure, the +# basis set, and their associated matrices. +# +# The Hamiltonian matrix is a complex learning target, indexed by two +# atoms and the orbitals centered on them. Each +# :math:`\mathbf{H}(\mathbf{k})` is a *Hermitian* matrix, while in real +# space, periodicity introduces a *symmetry over translation pairs* such +# that :math:`\mathbf{H}(-\mathbf{t}) = \mathbf{H}(\mathbf{t})^\dagger`, +# where the dagger, :math:`\dagger`, denotes Hermitian conjugation. +# +# To address the symmetries associated with swapping atomic indices or +# orbital labels, we divide the matrix into *blocks labeled by pairs of +# atom types*. +# +# - ``block_type = 0``, or *on-site* blocks, consist of elements +# corresponding to the interaction of orbitals on the same atom, +# :math:`i = i'`. +# +# - ``block_type = 2``, or *cross-species* blocks, consist of elements +# corresponding to orbitals centered on atoms of distinct species. +# Since the two atoms can be distinguished, they can be consistently +# arranged in a predetermined order. +# +# - ``block_type = 1, -1``, or *same-species* blocks, consist of +# elements corresponding to orbitals centered on distinct atoms of the +# same species. As these atoms are indistinguishable and cannot be +# ordered definitively, the pair must be symmetrized for permutations. +# We construct symmetric and antisymmetric combinations +# :math:`(\mathbf{H}_{\small\substack{i,nlm\\i',n'l'm'}}(\mathbf{t})\pm\ +# \mathbf{H}_{\small\substack{i',nlm\\i,n'l'm'}}(\mathbf{-t}))` +# that correspond to ``block_type`` :math:`+1` and :math:`-1`, +# respectively. +# + + +# %% +# Equivariant structure of the Hamiltonians +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# + + +# %% +# Even though the Hamiltonian operator under consideration is invariant, +# *its representation transforms under the action of structural rotations +# and inversions* due to the choice of the basis functions. Each of the +# blocks has elements of the form +# :math:`\langle\mathbf{0}inlm|\hat{H}|\mathbf{t}i'n'l'm'\rangle`, which +# are in an *uncoupled* representation and transform as a product of +# (real) spherical harmonics, :math:`Y_l^m \otimes Y_{l'}^{m'}`. +# +# This product can be decomposed into a direct sum of irreducible +# representations (irreps) of :math:`\mathrm{SO(3)}`, +# +# .. math:: \lambda \mu:\lambda \in [|l_1-l_2|,l_1+l_2],\mu \in [-\lambda,\lambda], +# +# which express the Hamiltonian blocks in terms of contributions that +# rotate independently and can be modeled using a feature that +# geometrically describes the pair of atoms under consideration and shares +# the same symmetry. We use the notation +# :math:`H_{ii';nn'll'}^{\lambda\mu}` to indicate the elements of the +# Hamiltonian in this coupled basis. +# +# The resulting irreps form a *coupled* representation, each of which +# transforms as a spherical harmonic :math:`Y^\mu_\lambda` under +# :math:`\mathrm{SO(3)}` rotations, but may exhibit more complex behavior +# under inversions. For example, spherical harmonics transform under +# inversion, :math:`\hat{i}`, as polar tensors: +# +# .. math:: \hat{i}Y^\mu_\lambda = (-1)^\lambda Y^\mu_\lambda. +# +# Some of the coupled basis terms transform like :math:`Y^\mu_\lambda`, +# while others instead transform as pseudotensors, +# +# .. math:: \hat{i}H^{\lambda\mu}=(-1)^{\lambda+1}H^{\lambda\mu} +# +# where we omit for simplicity the indices that are not directly associated +# with inversion and rotation symmetry. For more details about the block +# decomposition, please refer to `Nigam et al., J. Chem. Phys. 156, 014115 +# (2022) `__. +# +# The following is an animation of a trajectory along a `Lissajous +# curve `__ in 3D space, +# alongside a colormap representing the values of the real-space +# Hamiltonian matrix elements of the graphene unit cell in a minimal +# STO-3G basis. From the animation, it is evident how invariant elements, +# such as those associated with interactions between :math:`s` orbitals, +# do not change under structural rotations. On the other hand, +# interactions allowing for equivariant components, such as the +# :math:`s`-:math:`p` block, change under rotations. +# + +image_files = sorted( + [ + f"frames/{f}" + for f in os.listdir("./frames") + if f.startswith("rot_") and f.endswith(".png") + ] +) +images = [mpimg.imread(img) for img in image_files] +fig, ax = plt.subplots() +img_display = ax.imshow(images[0]) +ax.axis("off") + + +def update(frame): + img_display.set_data(images[frame]) + return [img_display] + + +ani = FuncAnimation(fig, update, frames=len(images), interval=20, blit=True) + + +# %% +# .. code:: python +# +# from IPython.display import HTML +# HTML(ani.to_jshtml()) +# + + +# %% +# Mapping geometric features to Hamiltonian targets +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# + + +# %% +# Each Hamiltonian block obtained from the procedure `described +# above <#symmetries-of-the-hamiltonian-matrix>`__ can be modeled using +# symmetrized features. +# +# Elements of ``block_type=0`` are indexed by a single atom and are best +# described by a symmetrized atom-centered density correlation +# (`ACDC `__), denoted by +# :math:`|\overline{\rho_{i}^{\otimes \nu}; \sigma; \lambda\mu }\rangle`, +# where :math:`\nu` refers to the correlation (body)-order, and—just as +# for the blocks—:math:`\lambda \mu` indicate the :math:`\mathrm{SO(3)}` +# irrep to which the feature is symmetrized. The symbol :math:`\sigma` +# denotes the inversion parity. +# +# For other blocks, such as ``block_type=2``, which explicitly reference +# two atoms, we use `two-center `__ +# ACDCs, :math:`|\overline{\rho_{ii'}^{\otimes \nu}; \lambda\mu }\rangle`. +# +# For ``block_type=1, -1``, we ensure equivariance with respect to atom +# index permutation by constructing symmetric and antisymmetric pair +# features: +# :math:`(|\overline{\rho_{ii'}^{\otimes \nu};\lambda\mu }\rangle\pm\ +# |\overline{\rho_{i'i}^{\otimes \nu};\lambda\mu }\rangle)`. +# + + +# %% +# The features are discretized on a basis of radial functions and +# spherical harmonics, and their performance may depend on the +# *resolution* of the functions included in the model. There are +# additional hyperparameters, such as the *cutoff* radius, which +# controls the extent of the atomic environment, and Gaussian widths. In +# the following, we allow for flexibility in discretizing the +# atom-centered and two-centered ACDCs by defining the hyperparameters for +# the single-center (SC) :math:`\lambda`-SOAP and two-center (TC) ACDC +# descriptors. +# +# The single and two-center descriptors have very similar hyperparameters, +# except for the cutoff radius, which is larger for the two-center +# descriptors to explicitly include distant pairs of atoms. +# +# Note that the descriptors of pairs of atoms separated by distances +# greater than the cutoff radius are identically zero. Thus, any model +# based on these descriptors would predict an identically zero value for +# these pairs. +# + +SC_HYPERS = { + "cutoff": 3.0, + "max_radial": 6, + "max_angular": 6, + "atomic_gaussian_width": 0.5, + "center_atom_weight": 1, + "radial_basis": {"Gto": {}}, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, +} + +TC_HYPERS = { + "cutoff": 6.0, + "max_radial": 6, + "max_angular": 6, + "atomic_gaussian_width": 0.3, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {}}, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, +} + + +# %% +# We then use the above defined hyperparameters to compute the descriptor +# and initialize a ``MLDataset`` instance, which contains, among other +# things, the Hamiltonian block decomposition and the geometric features +# described above. +# +# In addition to computing the descriptors, ``MLDataset`` takes the data +# stored in the ``QMDataset`` instance and puts it in a form required to +# train a ML model. +# + + +# %% +# The ``item_names`` argument is a list of names of the quantities we want +# to compute and target in the ML model training, or that we want to be +# able to access later. +# +# For example, ``fock_blocks`` is a +# `metatensor.Tensormap `__ containing the +# Hamiltonian coupled blocks. We also want to access the overlap matrices +# in :math:`k`-space (``overlap_kspace``) to be able to compute the +# Hamiltonian eigenvalues in the :math:`k`-grid. +# + + +mldata = MLDataset( + # A QMDataset instance + qmdata, + # The names of the quantities to compute/initialize for the training + item_names=["fock_blocks", "overlap_kspace"], + # Hypers for the SC descriptors + hypers_atom=SC_HYPERS, + # Hypers for the TC descriptors + hypers_pair=TC_HYPERS, + # Cutoff for the angular quantum number to use in the Clebsh-Gordan iterations + lcut=4, + # Fraction of structures in the training set + train_frac=0.7, + # Fraction of structures in the validation set + val_frac=0.2, + # Fraction of structures in the test set + test_frac=0.1, + # Whether to shuffle or not the structure indices before splitting the data set + shuffle=True, +) + + +# %% +# The matrix decomposition into blocks and the calculations of geometric +# features is performed by the ``MLDataset`` class. +# + + +# %% +# ``mldata.features`` is ``metatensor.TensorMap`` containing the +# stuctures’ descriptors +# + +mldata.features + + +# %% +# ``mldata.items`` is a ``namedtuple`` containing the quantities defined +# in ``item_names``. e.g. the coupled Hamiltonian blocks: +# + +print("The TensorMap containing the Hamiltonian coupled blocks is") +mldata.items.fock_blocks + + +# %% +# Or the overlap matrices: +# + +structure_idx = 0 +k_idx = 0 +print(f"The overlap matrix for structure {structure_idx} at the {k_idx}-th k-point is") +mldata.items.overlap_kspace[structure_idx][k_idx] + + +# %% +# A machine learning model for the electronic Hamiltonian of graphene +# ------------------------------------------------------------------- +# + + +# %% +# Linear model +# ~~~~~~~~~~~~ +# +# In simple cases, such as the present one, it is convenient to start with +# a linear model that directly maps the geometric descriptors to the +# target coupled blocks. This can be achieved using `Ridge regression +# `__ +# as implemented in `scikit-learn `__. +# +# The linear regression model is expressed as +# +# .. math:: +# +# +# H_{ii',\mathbf{Q}}^{\lambda\mu}(\mathbf{t}) = \ +# \sum_\mathbf{q} w_{\mathbf{q}}^{\mathbf{Q},\lambda} \ +# (\rho_{ii'}^{\otimes \nu}(\mathbf{t}))_{\mathbf{q}}^{\lambda\mu}, +# +# where a shorthand notation for the features has been introduced. Here, +# :math:`\mathbf{Q}` includes all labels indicating the involved orbitals, +# atomic species, and permutation symmetry, while :math:`\mathbf{q}` +# represents the feature dimension. The quantities +# :math:`w_{\mathbf{q}}^{\mathbf{Q},\lambda}` are the model’s weights. +# Note that different weights are associated with different values of +# :math:`\mathbf{Q}` and :math:`\lambda`, but not with specific atom pairs +# or the translation vector, whose dependence arises only through the +# descriptors. +# + + +# %% +# In ``mlelec``, a linear model can be trained through the +# ``LitEquivariantModel`` class, which accepts an ``init_from_ridge`` +# keyword. When set to ``True``, this initializes the weights of a more +# general ``torch.nn.Module`` with the weights provided by Ridge +# regression. +# + + +# %% +# We will pass other keyword arguments to ``LitEquivariantModel``, to be +# able to further train the weights on top to the initial Ridge +# regression. +# + +model = LitEquivariantModel( + mldata=mldata, # a MLDataset instance + nlayers=0, # The number of hidden layers + nhidden=1, # The number of neurons in each hidden layer + init_from_ridge=True, # If True, initialize the weights and biases of the + # purely linear model from Ridge regression + optimizer="LBFGS", # Type of optimizer. Adam is likely better for + # a more general neural network + activation="SiLU", # The nonlinear activation function + learning_rate=1e-3, # Initial learning rate (LR) + lr_scheduler_patience=10, + lr_scheduler_factor=0.7, + lr_scheduler_min_lr=1e-6, + loss_fn=MSELoss(), # Use the mean square error as loss function +) + + +# %% +# Model’s accuracy in reproducing derived properties +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# + + +# %% +# The Hamiltonian coupled blocks predicted by the ML model can be accessed +# from ``model.forward()`` +# + +predicted_blocks = model.forward(mldata.features) + + +# %% +# The real-space blocks can be transformed to Hamiltonian matrices via the +# ``mlelec.utils.pbc_utils.blocks_to_matrix`` function. The resulting +# real-space Hamiltonians can be Fourier transformed to give the +# :math:`k`-space ones. +# + +HT = blocks_to_matrix( + predicted_blocks, + orbitals["sto-3g"], + {A: qmdata.structures[A] for A in range(len(qmdata))}, + detach=True, +) +Hk = qmdata.bloch_sum(HT, is_tensor=True) + + +# %% +# Kohn-Sham eigenvalues +# ''''''''''''''''''''' +# + + +# %% +# We can then compute the eigenvalues on the :math:`k`-grid used for the +# calculation to assess the model accuracy in predicting band energies. +# + +target_eigenvalues = compute_eigenvalues(qmdata.fock_kspace, qmdata.overlap_kspace) +predicted_eigenvalues = compute_eigenvalues(Hk, qmdata.overlap_kspace) + +Hartree = 27.211386024367243 # eV + +plt.rcParams["font.size"] = 14 +fig, ax = plt.subplots() +ax.set_aspect("equal") + +x_text = 0.38 +y_text = 0.2 +d = 0.06 + +for i, (idx, label) in enumerate( + zip( + [mldata.train_idx, mldata.val_idx, mldata.test_idx], + ["train", "validation", "test"], + ) +): + + target = ( + torch.stack([target_eigenvalues[i] for i in idx]).flatten().detach() * Hartree + ) + prediction = ( + torch.stack([predicted_eigenvalues[i] for i in idx]).flatten().detach() + * Hartree + ) + + non_core_states = target > -100 + rmse = np.sqrt( + np.mean( + (target.numpy()[non_core_states] - prediction.numpy()[non_core_states]) ** 2 + ) + ) + ax.scatter(target, prediction, marker=".", label=label, alpha=0.5) + ax.text( + x=x_text, + y=y_text - d * i, + s=rf"$\mathrm{{RMSE_{{{label}}}={rmse:.2f}\,eV}}$", + transform=ax.transAxes, + ) + +xmin, xmax = ax.get_xlim() +ax.plot([xmin, xmax], [xmin, xmax], "--k") +ax.set_xlim(xmin, xmax) +ax.set_ylim(xmin, xmax) +ax.legend() +ax.set_xlabel("Target eigenvalues (eV)") +ax.set_ylabel("Predicted eigenvalues (eV)") + + +# %% +# Graphene band structure +# ''''''''''''''''''''''' +# + + +# %% +# Apart from the eigenvalues on a mesh in the Brillouin zone, we can use +# the real-space Hamiltonians predicted by the model to compute the band +# structure along high-symmetry paths. +# + +fig, ax = plt.subplots(figsize=(8, 4.8)) + +idx = 0 + +handles = [] + +with warnings.catch_warnings(): + warnings.filterwarnings("ignore", category=DeprecationWarning) + + # Plot reference + ax, h_ref = plot_bands_frame( + qmdata.fock_realspace[idx], idx, qmdata, ax=ax, color="blue", lw=2 + ) + + # Plot prediction + ax, h_pred = plot_bands_frame( + HT[idx], idx, qmdata, ax=ax, color="lime", ls="--", lw=2 + ) + +ax.set_ylim(-30, 30) +ax.legend( + [h_ref, h_pred], + ["Reference", "Prediction"], + loc="center left", + bbox_to_anchor=(1, 0.5), +) +fig.tight_layout() + + +# %% +# Adding nonlinearities +# --------------------- +# + + +# %% +# The model used above consists of several submodels, one for each Hamiltonian +# coupled block. Each submodel can be extended to a `multilayer +# perceptron `__ +# (MLP) that maps the corresponding set of geometric features to the +# Hamiltonian coupled block. Nonlinearities are applied to the invariants +# constructed from each equivariant feature block using the +# ``EquivariantNonlinearity`` module. This section outlines the process to +# modify the model to introduce non-linear terms. Given that the time +# to train and evaluate the model would then increase, this section +# includes snippets of code, but is not a complete implementation and +# is not executed when running this example. + + +# %% +# The architecture of ``EquivariantNonlinearity`` can be visualized with +# ``torchviz`` with the following snippet: +# +# .. code:: python +# +# import torch +# from mlelec.models.equivariant_model import EquivariantNonLinearity +# from torchviz import make_dot +# m = EquivariantNonLinearity(torch.nn.SiLU(), layersize = 10) +# y = m.forward(torch.randn(3,3,10)) +# dot = make_dot(y, dict(m.named_parameters())) +# dot.graph_attr.update(size='150,150') +# dot.render("equivariantnonlinear", format="png") +# dot +# + + +# %% +# .. figure:: equivariantnonlinear.png +# :alt: Graph representing the architecture of EquivariantNonLinearity +# :width: 300px +# +# Graph representing the architecture of EquivariantNonLinearity +# + + +# %% +# The global architecture of the MLP, implemented in ``simpleMLP``, can be +# visualized with +# +# .. code:: python +# +# import torch +# from mlelec.models.equivariant_model import simpleMLP +# from torchviz import make_dot +# mlp = simpleMLP( +# nin=10, +# nout=1, +# nhidden=1, +# nlayers=1, +# bias=True, +# activation='SiLU', +# apply_layer_norm=True +# ) +# y = mlp.forward(torch.randn(1,1,10)) +# dot = make_dot(y, dict(mlp.named_parameters())) +# dot.graph_attr.update(size='150,150') +# dot.render("simpleMLP", format="png") +# dot +# + + +# %% +# .. figure:: simpleMLP.png +# :alt: Graph representing the architecture of simpleMLP +# :width: 600px +# +# Graph representing the architecture of simpleMLP +# + + +# %% +# Set up the training loop for stochastic gradient descent +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# + + +# %% +# Import additional modules needed to monitor the training. +# + + +# %% +# .. code:: python +# +# import lightning.pytorch as pl +# from lightning.pytorch.callbacks import EarlyStopping +# from mlelec.callbacks.logging import LoggingCallback +# from mlelec.models.equivariant_lightning import MLDatasetDataModule +# + + +# %% +# We set up a callback for logging training information such as the +# training and validation losses. +# + + +# %% +# .. code:: python +# +# logger_callback = LoggingCallback(log_every_n_epochs=5) +# + + +# %% +# We set up an early stopping criterion to stop the training when the +# validation loss function stops decreasing. +# + + +# %% +# .. code:: python +# +# early_stopping = EarlyStopping( +# monitor="val_loss", min_delta=1e-3, patience=10, verbose=False, mode="min" +# ) +# + + +# %% +# We define a ``lighting.pytorch.Trainer`` instance to handle the training +# loop. For example, we can further optimize the weights for 50 epochs using +# the `LBFGS `__ +# optimizer. +# +# Note that PyTorch Lightning requires the definition of a data module to +# instantiate DataLoaders to be used during the training. +# + + +# %% +# .. code:: python +# +# data_module = MLDatasetDataModule(mldata, batch_size=16, num_workers=0) +# +# trainer = pl.Trainer( +# max_epochs=50, +# accelerator="cpu", +# check_val_every_n_epoch=10, +# callbacks=[early_stopping, logger_callback], +# logger=False, +# enable_checkpointing=False, +# ) +# +# trainer.fit(model, data_module) +# + + +# %% +# We compute the test set loss to assess the model accuracy on an unseen +# set of structures +# + + +# %% +# .. code:: python +# +# trainer.test(model, data_module) +# + + +# %% +# In this case, Ridge regression already provides good accuracy, so +# further optimizing the weights offers limited improvement. However, for +# more complex datasets, the benefits of additional optimization can be +# significant. +# diff --git a/_downloads/09625016882c3624ff36e3486ce6c8c2/dos-align.zip b/_downloads/09625016882c3624ff36e3486ce6c8c2/dos-align.zip new file mode 100644 index 00000000..0cc89b62 Binary files /dev/null and b/_downloads/09625016882c3624ff36e3486ce6c8c2/dos-align.zip differ diff --git a/_downloads/184bee2944e6bfa0af8580936f246718/thermostats.zip b/_downloads/184bee2944e6bfa0af8580936f246718/thermostats.zip new file mode 100644 index 00000000..eb53c8ab Binary files /dev/null and b/_downloads/184bee2944e6bfa0af8580936f246718/thermostats.zip differ diff --git a/_downloads/2c684432538bab3d8a6f8db14f3827bf/heat-capacity.ipynb b/_downloads/2c684432538bab3d8a6f8db14f3827bf/heat-capacity.ipynb new file mode 100644 index 00000000..d938c757 --- /dev/null +++ b/_downloads/2c684432538bab3d8a6f8db14f3827bf/heat-capacity.ipynb @@ -0,0 +1,208 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Quantum heat capacity of water\n\n:Authors:\n Filippo Bigi [@frostedoyster](https://github.com/frostedoyster/);\n Michele Ceriotti [@ceriottm](https://github.com/ceriottm/)\n\nThis example shows how to estimate the heat capacity of liquid water\nfrom a path integral molecular dynamics simulation. The dynamics are\nrun with [i-PI](http://ipi-code.org), and\n[LAMMPS](http://lammps.org) is used\nas the driver to simulate the [q-TIP4P/f water\nmodel](http://doi.org/10.1063/1.3167790).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import os\nimport subprocess\nimport time\nimport xml.etree.ElementTree as ET\n\nimport ipi\nimport matplotlib.pyplot as plt\nimport numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A non-trivial energy estimator\n\nAs introduced in the\n[path-integrals example](http://lab-cosmo.github.io/atomistic-cookbook/latest/examples/path-integrals),\npath-integral estimators\nfor observables that depend on momenta are generally not trivial to compute.\n\nIn this example, we will focus on the constant-volume heat capacity,\n$c_V$, which is one such\nobservable, and we will calculate it for liquid water at room temperature.\nBecause of the presence of high-frequency vibrations, many of the nuclear\ndegrees of freedom are trapped in the vibrational ground state, which reduces\nsubstantially the heat capacity from the value that would be obtained\nin the classical limit. See [this review](http://doi.org/10.1021/acs.chemrev.5b00674)\nfor an overview of the impact of quantum nuclei on the properties of water.\nFrom a computational perspective, this means that it is necessary to use\nspecialized simulations and estimators to evaluate the correct value.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running the PIMD calculation\n\nThis follows the same steps as the ``path-integrals`` example. One important\ndifference is that we will request the ``scaledcoords`` output to the relevant\nsection of the ``i-PI`` input XML file, which\ncontains estimators that can be used to calculate the total energy and\nheat capacity as following\n[Yamamoto, J. Chem. Phys. (2005)](https://arxiv.org/abs/physics/0505109).\n\nThe input file is shown below. It should be noted that ``scaledcoords``\nis given a finite differences displacement as a parameter. This is necessary\nas the estimators require higher order derivatives of the potential energy,\nwhich are calculated using finite differences. This also means that\nevaluating the estimator adds substantial overhead (so it is wise to only\ncompute it every few simulation steps, to eliminate correlations between\nsnapshots) and that one should be careful to use well-converged simulation\nparameters to avoid discontinuities and noise (for instance, we increase\nthe accuracy of the particle-mesh electrostatic calculation, and use a\nshifted Lennard-Jones potential to avoid a discontinuity at the cutoff).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Open and show the relevant part of the input\nxmlroot = ET.parse(\"data/input.xml\").getroot()\nprint(\" \" + ET.tostring(xmlroot.find(\".//properties\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We launch the i-PI and LAMMPS processes, exactly as in the\n``path-integrals`` example.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# don't rerun if the outputs already exist\nipi_process = None\nif not os.path.exists(\"water-cv.out\"):\n ipi_process = subprocess.Popen([\"i-pi\", \"data/input.xml\"])\n time.sleep(2) # wait for i-PI to start\n lmp_process = [subprocess.Popen([\"lmp\", \"-in\", \"data/in.lmp\"]) for i in range(2)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Skip this cell if you want to run in the background\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "if ipi_process is not None:\n ipi_process.wait()\n lmp_process[0].wait()\n lmp_process[1].wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analyzing the results\nLet's plot the potential and conserved energy as a function of time,\njust to check that the simulation ran sensibly.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "output_data, output_desc = ipi.read_output(\"water-cv.out\")\nfix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"potential\"] - output_data[\"potential\"][0],\n \"b-\",\n label=\"Potential, $V$\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"conserved\"] - output_data[\"conserved\"][0],\n \"r-\",\n label=\"Conserved, $H$\",\n)\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"energy / a.u.\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As described in the [i-PI documentation](https://ipi-code.org/i-pi/output-tags.html),\nthe two quantities returned by the ``scaledcoords`` output are ``eps_v``\nand ``eps_v'``, defined in the aforementioned\n[paper](https://arxiv.org/abs/physics/0505109).\n\nThese estimators ($\\epsilon_v$ and $\\epsilon_v'$) are derived in the\n\"scaled coordinates\" formalism, which is a useful trick to avoid the\ngrowth of the error in the instantaneous values of the estimators with\nthe number of beads used in the path integral simulation.\n\nThe same paper contains the formulas to calculate the total energy and\nheat capacity from these estimators:\n\n\\begin{align}E = \\langle \\epsilon_v \\rangle \\quad\n C_V = k_B \\beta^2 \\left( \\langle \\epsilon_v^2 \\rangle - \\langle\n \\epsilon_v \\rangle^2 - \\langle \\epsilon_v' \\rangle \\right)\\end{align}\n\nFirst the energy, whose estimator will be compared to the total energy\ncalculated as the sum of the potential and kinetic energy estimators.\nSince the kinetic energy is itself calculated from a scaled-coordinates\nestimator (the \"centroid virial\" estimator), the two total energies are\nthe same.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "eps_v = output_data[\"scaledcoords(fd_delta=5e-3)\"][:, 0]\neps_v_prime = output_data[\"scaledcoords(fd_delta=5e-3)\"][:, 1]\n\nenergy_estimator = eps_v # first formula\n\nfix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n energy_estimator - energy_estimator[0],\n \"b-\",\n label=\"scaled coordinates estimator\",\n)\nax.plot(\n output_data[\"time\"][:],\n (\n output_data[\"potential\"]\n - output_data[\"potential\"][0]\n + output_data[\"kinetic_cv\"]\n - output_data[\"kinetic_cv\"][0]\n ),\n \"r.\",\n label=\"potential + virial kinetic\",\n)\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"total energy / a.u.\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And, finally, the heat capacity. Note that normally the simulation\nrequires a few ps for equilibration. Here we discard a few dozen steps\nto eliminate the initial jump, which is due to the relaxation of the\nring polymers starting from a single atomic configuration.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# i-PI scaledcoords outputs are in atomic units (see docs)\nkB = 3.16681e-6 # Boltzmann constant in atomic units\nT = 298.0 # temperature in K, as defined in the input file\nbeta = 1.0 / (kB * T)\n\nskip = 20\nheat_capacity = ( # second formula\n kB\n * (beta**2)\n * (\n np.mean(eps_v[skip:] ** 2)\n - np.mean(eps_v[skip:]) ** 2\n - np.mean(eps_v_prime[skip:])\n )\n)\nheat_capacity_per_molecule = heat_capacity / 32 # 32 molecules in the simulation\nprint(f\"Heat capacity (per water molecule): {(heat_capacity_per_molecule/kB):.2f} kB\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You may recognize that the first part of the estimator is reminiscent\nof the classical estimator for the heat capacity as the fluctuations of the\n(quantum) total energy, which in this case however requires a correction given\nby the mean of the second part of the scaled-coordinates estimator.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Estimating the statistical error\n\nEspecially with such an underconverged simulation, it is important to\nestimate the statistical error in the heat capacity.\n\nGenerally, errors on measurements are computed\nas \"standard errors\", i.e. the standard deviation of a series of data points\ndivided by the square root of the number of data points. In our case,\nhowever, this is made more complicated by the correlation between\nclose steps in the molecular dynamics trajectory, which would lead to an\noverestimation of the number of independent samples. To fix this, we can\ncalculate the autocorrelation time of the estimators whose errors we\nwant to estimate, and apply a correction factor to the number of samples.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def autocorrelate(x):\n n = len(x)\n xo = x - x.mean() # remove mean\n acov = (np.correlate(xo, xo, \"full\"))[n - 1 :]\n return acov[: len(acov) // 2]\n\n\ndef autocorrelation_time(x):\n acov = autocorrelate(x)\n return 1.0 + np.sum(acov) / acov[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using these helper functions, we can now calculate the error on the various\nparts of the heat capacity estimator. Note also the autocorrelation times, that\nare just a little larger than one, indicating that the stride used to print out\nthe estimators is appropriate (as there is little correlation between the samples).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Autocorrelation times (i.e. number of steps needed to have independent samples)\nautocorr_time_error_delta_eps_v = autocorrelation_time(\n (eps_v[skip:] - eps_v[skip:].mean()) ** 2\n)\nautocorr_time_error_eps_v_prime = autocorrelation_time(eps_v_prime[skip:])\n\nprint(\n f\"\"\"\nAutocorrelation times (in number of samples):\n(eps-)^2: {autocorr_time_error_delta_eps_v:.2f}\neps': {autocorr_time_error_eps_v_prime:.2f}\n\"\"\"\n)\n\n# Effective number of samples\neffective_samples_delta_eps_v = len(eps_v[skip:]) / autocorr_time_error_delta_eps_v\neffective_samples_eps_v_prime = len(eps_v[skip:]) / autocorr_time_error_eps_v_prime\n\n# Standard errors using the effective number of samples\nerror_delta_eps_v = np.std((eps_v[skip:] - eps_v[skip:].mean()) ** 2) / np.sqrt(\n effective_samples_delta_eps_v\n)\nerror_eps_v_prime = np.std(eps_v_prime[skip:]) / np.sqrt(effective_samples_eps_v_prime)\n\n# Error on the heat capacity (assuming quadrature sum)\nerror_heat_capacity = (\n kB * (beta**2) * np.sqrt(error_delta_eps_v**2 + error_eps_v_prime**2)\n)\n\nerror_heat_capacity_per_molecule = (\n error_heat_capacity / 32\n) # 32 molecules in the simulation\n\nprint(\n \"Error on the heat capacity (per water molecule): \"\n f\"{(error_heat_capacity_per_molecule/kB):.2f} kB\"\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The obtained heat capacity is consistent with the values from the literature\n(see e.g. [Ceriotti et al., J. Chem. Phys. (2011)](http://doi.org/10.1063/1.3556661)\nwhere the convergence of the heat capacity with number of beads is shown for the same\nwater model used in this example).\nHowever, the error is quite large, which is expected given the short simulation time.\nTo reduce the error, one would need to run a longer simulation. Other important error\nsources, which are not accounted for in the error estimate, are the finite size of the\nsystem and number of beads. Both of these are too small in this example to give\nreliable results.\n\nIn a realistic simulation, up to a few 100s of picoseconds might be needed to reduce\nthe sampling error to a small value (1-2% of the heat capacity). For water at room\ntemperature, you will need 32 beads at the very least (8 were used in this example).\nIt is more difficult to give a general rule for the system size: (quantum) energy\nfluctuations are usually localized, but to guarantee accurate sampling of the\nliquid structure, a few hundred water molecules would be a reasonable guess\n(32 were used in this example).\n\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/3237a57d8246eaec10a69b4e251f623d/environment.yml b/_downloads/3237a57d8246eaec10a69b4e251f623d/environment.yml new file mode 100644 index 00000000..fafbc008 --- /dev/null +++ b/_downloads/3237a57d8246eaec10a69b4e251f623d/environment.yml @@ -0,0 +1,8 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - pip: + - ase + - matplotlib diff --git a/_downloads/328f2a3eeccb4e902f81e5646c33e2e8/environment.yml b/_downloads/328f2a3eeccb4e902f81e5646c33e2e8/environment.yml new file mode 100644 index 00000000..b436b4a5 --- /dev/null +++ b/_downloads/328f2a3eeccb4e902f81e5646c33e2e8/environment.yml @@ -0,0 +1,14 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - rust >=1.65 + - pip: + - ase==3.22.1 + - chemiscope>=0.7 + - matplotlib + - metatensor + - rascaline @ git+https://github.com/Luthaf/rascaline@ca957642f512e141c7570e987aadc05c7ac71983 + - skmatter + - equisolve @ git+https://github.com/lab-cosmo/equisolve.git@c858bedef4b2799eb445e4c92535ee387224089a diff --git a/_downloads/360e0a4751205a155ce4949942081de0/pi-metad.ipynb b/_downloads/360e0a4751205a155ce4949942081de0/pi-metad.ipynb new file mode 100644 index 00000000..96464d3d --- /dev/null +++ b/_downloads/360e0a4751205a155ce4949942081de0/pi-metad.ipynb @@ -0,0 +1,589 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Path integral metadynamics\n\n:Authors: Michele Ceriotti [@ceriottm](https://github.com/ceriottm/)\n\nThis example shows how to run a free-energy sampling calculation that\ncombines path integral molecular dynamics to model nuclear quantum effects\nand metadynamics to accelerate sampling of the high-free-energy regions.\n\nThe rather complicated setup combines [i-PI](http://ipi-code.org)\nto perform path integral\nMD, its built-in driver to compute energy and forces for the Zundel\n$\\mathrm{H_5O_2^+}$ cation, and [PLUMED](http://plumed.org/)\nto perform metadynamics.\nIf you want to see an example in a more realistic scenario, you can look at\n[this paper (Rossi et al., JCTC (2020))](http://doi.org/10.1021/acs.jctc.0c00362),\nin which this\nmethodology is used to simulate the decomposition of methanesulphonic\nacid in a solution of phenol and hydrogen peroxide.\n\nNote also that, in order to keep the execution time of this example as\nlow as possible, several parameters are set to values that would not be\nsuitable for an accurate, converged simulation.\nThey will be highlighted and more reasonable values will be provided.\n\"High-quality\" runs can also be realized substituting the input files\nused in this example with those labeled with the ``_hiq`` suffix, that\nare also provided in the ``data/`` folder.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import bz2\nimport os\nimport subprocess\nimport time\nimport xml.etree.ElementTree as ET\n\nimport ase\nimport ase.io\nimport chemiscope\nimport ipi\nimport matplotlib.pyplot as plt\nimport numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Metadynamics for the Zundel cation\n\nMetadynamics is a method to accelerate sampling of rare events - microscopic processes\nthat are too infrequent to be observed over the time scale (ns-\u00b5s) accessible to\nmolecular dynamics simulations. You can read one of the many excellent reviews\non metadynamics (see e.g.\n[Bussi and Branduardi (2015)](https://doi.org/10.1002/9781118889886.ch1)),\nor follow a\n[lecture from the PLUMED masterclass](https://www.plumed-tutorials.org/lessons/21/004/data/NAVIGATION.html).\nIn short, during a metadynamics simulation an adaptive biasing potential is\nbuilt as a superimposition of Gaussians centered over configurations that have\nbeen previously visited by the trajectory. This discourages the system from remaining\nin high-probability configurations and accelerates sampling of free-energy barriers.\n\n.. figure:: metad-scheme.png\n :align: center\n :width: 600px\n\n A schematic representation of how metadynamics work by adaptively building\n a repulsive bias based on the trajectory of a molecule, compensating for\n low-energy regions in the free energy surface.\n\nCrucially, the bias is *not* built relative to the Cartesian coordinates of the atoms,\nbut relative to a lower-dimensional description of the system (so-called collective\nvariables) that are suited to describe the processes being studied.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Zundel cation $\\mathrm{H_5O_2^+}$ is one of the limiting\nstructures of the solvated proton, and in the gas phase leads to a\nstable structure, with the additional proton shared between two water\nmolecules (see the structure below).\nWe will use a potential fitted on high-end quantum-chemistry calculations\n[Huang et al. (2005)](http://doi.org/10.1063/1.1834500) to compute energy\nand forces acting on the atoms.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "zundel = ase.io.read(\"data/h5o2+.xyz\", \":\")\nchemiscope.show(frames=zundel, mode=\"structure\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As the two water molecules are separated, the proton remains attached\nto one of the two, effectively leading to a dissociated\n$\\mathrm{H_2O+H_3O^+}$ configuration. Thus, two natural\ncoordinates to describe the physics of this system are the distance\nbetween the O atoms, and the difference in coordination number of\nthe two O atoms, which is 0 for a shared proton and \u00b11 for the\ndissociated system.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running metadynamics calculations with ``i-PI`` and ``PLUMED``\n\nThe client-server architecture [i-PI](http://ipi-code.org) is based on makes it easy\nto combine multiple programs to realize complicated simulation workflows.\nIn this case we will use an implementation of the Zundel potential in a simple\ndriver code that is available in the i-PI repository, and use\n[PLUMED](http://plumed.org/) to compute collective variables and build\nthe adaptive bias. We will then perform some post-processing to\nestimate the free energy.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Installing the Python driver\n\ni-PI comes with a FORTRAN driver, which however has to be installed\nfrom source. We use a utility function to compile it. Note that this requires\na functioning build system with `gfortran` and `make`.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi.install_driver()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Defining the molecular dynamics setup\nThe `input-md.xml` file defines the way the MD simulation is performed.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xmlroot = ET.parse(\"data/input-md.xml\").getroot()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `` block describe the way communication will occur with the\ndriver code\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\" \" + ET.tostring(xmlroot.find(\"ffsocket\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and the `` section describes the MD setup.\nThis is a relatively standard NVT setup, with an efficient\ngeneralized Langevin equation thermostat (important to\ncompensate for the non-equilibrium nature of metadynamics).\nNote that the time step is rather long (the recommended value for\naqueous systems is around 0.5 fs). This is done to improve\nefficiency for this example, but you should check if it\naffects results in a realistic scenario.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\" \" + ET.tostring(xmlroot.find(\".//motion\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The metadynamics setup requires three ingredients:\na `` forcefield that defines what input to use\n(more on that later) and the file from which to initialize\nthe structural information (number of atoms, ...);\n`` is an advanced feature, available from\nPLUMED 2.10, that allows extracting internal variables\nfrom plumed and integrate them into the outputs of\ni-PI.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\" \" + ET.tostring(xmlroot.find(\"ffplumed\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `` section contains a `` key that\nspecifies that energy and forces from PLUMED should be\ntreated as a bias (so that e.g. are not included in the\npotential, even though they're used to propagate the\ntrajectory).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\" \" + ET.tostring(xmlroot.find(\".//ensemble\"), encoding=\"unicode\"))\n\n# The `` section contains a `` class that\n# instructs i-PI to call the PLUMED action that adds hills\n# along the trajectory.\n\nprint(\" \" + ET.tostring(xmlroot.find(\"smotion\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### CVs and metadynamics\n\nThe calculation of the collective variables and the\nmetadynamics bias is delegated to PLUMED, and controlled by\na separate `plumed-md.dat` input file.\nWithout going in detail into the syntax, one can recognize the\ncalculation of the distance between the O atoms `doo`,\nthe coordination of the two oxygens `co1` and `co2`,\nand the difference between the two, `dc`.\nThe `METAD` action specifies the CVs to be used, the pace of\nhill depositon (which is way too frequent here, but suitable for\nthis example), the width along the two CVs and the initial\nheight of the repulsive Gaussians (which are both too large to\nguarantee high resolution in CV and energy). The `BIASFACTOR` keyword specifies\nthat the height of the hills will be progressively reduced\naccording to the \"well-tempered metadynamics\" protocol, see\n[Barducci et al., Phys. Rev. Lett. (2008)](http://doi.org/10.1103/PhysRevLett.100.020603).\nA repulsive static bias (`UPPER_WALLS`) prevents complete dissociation of the\ncation by limiting the range of the O-O distance.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "with open(\"data/plumed-md.dat\", \"r\") as file:\n plumed_dat = file.read()\nprint(plumed_dat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running the simulations\n\nNow we can launch the actual calculations. On the the command line,\nthis requires launching i-PI first, and then the built-in driver,\nspecifying the appropriate communication mode, and the `zundel` potential.\nPLUMED is called from within i-PI as a library, so there is no need to\nlaunch a separate process. Note that the Zundel potential requires some data\nfiles, with a hard-coded location in the current working directory,\nwhich is why the driver should be run from within the ``data/`` folder.\n\n```bash\ni-pi data/input-md.xml > log &\nsleep 2\ncd data; i-pi-driver -u -a zundel -m zundel\n```\nThe same can be achieved from Python using ``subprocess.Popen``\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi_process = None\nif not os.path.exists(\"meta-md.out\"):\n # don't rerun if the outputs already exist\n ipi_process = subprocess.Popen([\"i-pi\", \"data/input-md.xml\"])\n time.sleep(2) # wait for i-PI to start\n driver_process = [\n subprocess.Popen(\n [\"i-pi-driver\", \"-u\", \"-a\", \"zundel\", \"-m\", \"zundel\"], cwd=\"data/\"\n )\n for i in range(1)\n ]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you run this in a notebook, you can go ahead and start loading\noutput files *before* i-PI has finished running by skipping this cell\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# wait for simulations to finish\nif ipi_process is not None:\n ipi_process.wait()\n for process in driver_process:\n process.wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Trajectory post-processing\n\nWe can now post-process the simulation to see metadynamics in action.\n\nFirst, we read the trajectory outputs. Note that these have all been\nprinted with the same stride\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "output_data, output_desc = ipi.read_output(\"meta-md.out\")\ncolvar_data = ipi.read_trajectory(\"meta-md.colvar_0\", format=\"extras\")[\n \"doo,dc,mtd.bias\"\n]\ntraj_data = ipi.read_trajectory(\"meta-md.pos_0.xyz\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "then, assemble a visualization\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "chemiscope.show(\n frames=traj_data,\n properties=dict(\n d_OO=10 * colvar_data[:, 0], # nm to \u00c5\n delta_coord=colvar_data[:, 1],\n bias=27.211386 * output_data[\"ensemble_bias\"], # Ha to eV\n time=2.4188843e-05 * output_data[\"time\"], # atomictime to ps\n ), # attime to ps\n settings=chemiscope.quick_settings(\n x=\"d_OO\", y=\"delta_coord\", z=\"bias\", color=\"time\", trajectory=True\n ),\n mode=\"default\",\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The visualization above shows how the growing metadynamics bias pushes\nprogressively the atoms towards geometries with larger O-O separations,\nand that for these distorted configurations the proton is not shared\nsymmetrically between the O atoms, but is preferentially attached to\none of the two water molecules.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Trajectory diagnostics\n\nThe time history of the bias is instructive, as it shows how the\nbias grows until the trajectory gets pushed in a new region (where the\nbias is zero) and then grows again. The envelope of the bias increase\nslows down over time, because the \"well-tempered\" deposition strategy\nreduces the height of the hills deposited in high-bias regions.\n\nNote that the potential energy has fluctuations that are larger than\nthe magnitude of the bias, although it shows a tendency to reach higher\nvalues as the simulation progresses. This is because only two degrees\nof freedom are affected by the bias, while all degrees of freedom\nundergo thermal fluctuations, which are dominant even for this\nsmall system.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\n\nax.plot(\n 2.4188843e-05 * output_data[\"time\"],\n 27.211386 * output_data[\"potential\"],\n \"r\",\n label=\"potential\",\n)\nax.plot(\n 2.4188843e-05 * output_data[\"time\"],\n 27.211386 * output_data[\"ensemble_bias\"],\n \"b\",\n label=\"bias\",\n)\n\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"energy / eV\")\nax.legend(loc=\"upper left\", ncols=1)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It's important to keep in mind that the growing metadynamics bias can\nlead to deviations from the quasi-equilibrium sampling that is necessary\nto recover the correct properties of the rare event. It is not easy\nto verify this condition, but one simple diagnostics that can highlight\nthe most evident problems is looking at the kinetic temperature of different\nportions of the system, computing a moving average to have a clearer signal.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def moving_average(arr, window_size):\n # Create a window of the specified size with equal weights\n window = np.ones(window_size) / window_size\n # Use the 'valid' mode to only return elements where the window fully\n # overlaps with the data\n return np.convolve(arr, window, mode=\"valid\")\n\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\n\nax.plot(\n 2.4188843e-05 * output_data[\"time\"][50:-49],\n moving_average(output_data[\"temperature(O)\"], 100),\n \"r\",\n label=r\"$T_\\mathrm{O}$\",\n)\nax.plot(\n 2.4188843e-05 * output_data[\"time\"][50:-49],\n moving_average(output_data[\"temperature(H)\"], 100),\n \"gray\",\n label=r\"$T_\\mathrm{H}$\",\n)\nax.plot(\n 2.4188843e-05 * output_data[\"time\"][50:-49],\n moving_average(output_data[\"temperature\"], 100),\n \"b\",\n label=\"T\",\n)\n\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"temperature / K\")\nax.legend(loc=\"upper left\", ncols=2)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is clear that the very high rate of biasing used in this demonstrative\nexample leads to a temperature that is consistently higher than the target,\nwith spikes up to 380 K and O and H atoms reaching different temperatures\n(i.e. equipartition is broken). While this does not affect the qualitative\nnature of the results, these parameters are unsuitable for a production run.\nNB: especially for small systems, the instantaneous kinetic temperature\ncan deviate by a large amount from the target temperature: only the mean\nvalue has actual meaning. However, a kinetic temperature that is consistently\nabove the target value indicates that the thermostat cannot dissipate\nefficiently the energy due to the growing bias.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Free energy profiles\n\nOne of the advantages of metadynamics is that it allows one to easily\nestimate the free-energy associated with the collective variables\nthat are used to accelerate sampling by summing the repulsive hills\nthat have been deposited during the run and taking the negative of\nthe total bias at the end of the trajectory.\n\nEven though more sophisticated strategies exist that provide explicit\nweighting factors to estimate the unbiased Boltzmann distribution\n(see e.g.\n[Giberti et al., JCTC 2020](http://doi.org/10.1021/acs.jctc.9b00907)),\nthis simple approach is good enough for this example, and can be\nrealized as a post-processing step using the ``plumed sum_hills`` module,\nthat also applies a (simple) correction to the negative bias that\nis needed when using the well-tempered bias scaling protocol.\nOn the command line,\n\n```bash\nplumed sum_hills --hills HILLS-md --min 0.21,-1 --max 0.31,1 --bin 100,100 \\\n --outfile FES-md --stride 100 --mintozero < data/plumed-md.dat\n```\nThe ``--stride`` option generates a series of files showing the estimates\nof $F$ at different times along the trajectory.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "with open(\"data/plumed-md.dat\", \"r\") as file:\n subprocess.run(\n [\n \"plumed\",\n \"sum_hills\",\n \"--hills\",\n \"HILLS-md\",\n \"--min\",\n \"0.21,-1\",\n \"--max\",\n \"0.31,1\",\n \"--bin\",\n \"100,100\",\n \"--outfile\",\n \"FES-md\",\n \"--stride\",\n \"100\",\n \"--mintozero\",\n ],\n stdin=file,\n text=True,\n )\n\n# rearrange data and converts to \u00c5 and eV\ndata = np.loadtxt(\"FES-md0.dat\", comments=\"#\")[:, :3]\nxyz_0 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape(\n 3, 101, 101\n)\ndata = np.loadtxt(\"FES-md2.dat\", comments=\"#\")[:, :3]\nxyz_2 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape(\n 3, 101, 101\n)\ndata = np.loadtxt(\"FES-md5.dat\", comments=\"#\")[:, :3]\nxyz_5 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape(\n 3, 101, 101\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plots show, left-to-right, the accumulation of the\nmetadynamics bias as simulation progresses.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(\n 1, 3, figsize=(8, 3), sharex=True, sharey=True, constrained_layout=True\n)\n\ncf_0 = ax[0].contourf(*xyz_0)\ncf_1 = ax[1].contourf(*xyz_2)\ncf_2 = ax[2].contourf(*xyz_5)\nfig.colorbar(cf_2, ax=ax, orientation=\"vertical\", label=r\"$F$ / eV\")\nax[0].set_ylabel(r\"$\\Delta C_\\mathrm{H}$\")\nax[0].set_xlabel(r\"$d_\\mathrm{OO}$ / \u00c5\")\nax[1].set_xlabel(r\"$d_\\mathrm{OO}$ / \u00c5\")\nax[2].set_xlabel(r\"$d_\\mathrm{OO}$ / \u00c5\")\nax[0].set_title(r\"$t=0.8$ ps\")\nax[1].set_title(r\"$t=2.5$ ps\")\nax[2].set_title(r\"$t=5.0$ ps\")\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Biasing a path integral calculation\n\nYou can see [this recipe](http://lab-cosmo.github.io/atomistic-cookbook/examples/latest/path-integrals)\nfor a brief introduction to path integral simulations with `i-PI`.\nFrom a practical perspective, very little needs to change with respect\nto the classical case.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xmlroot = ET.parse(\"data/input-pimd.xml\").getroot()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `nbeads` option determines the number of path integral\nreplicas. The value of 8 used here is not sufficient to converge\nquantum statistics at 300 K (a more typical value would be\naround 32). There are methods to reduce the number of replicas\nneeded for convergence, see e.g.\n[Ceriotti and Markland, Nat. Rev. Chem. (2018)](http://doi.org/10.1038/s41570-017-0109)\nbut we keep it simple here.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\" \" + ET.tostring(xmlroot.find(\".//initialize\"), encoding=\"unicode\")[:23])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Centroid bias\n\nAnother detail worth discussing is that the metadynamics bias\nis computed exclusively on the *centroid*, the mean position of\nthe ring-polymer beads. This is an extreme form of\nring polymer contraction\n[(Markland and Manolopoulos, J. Chem. Phys. (2008)](http://doi.org/10.1063/1.2953308)\nthat avoids computing for each replica the slowly-varying\nparts of the potential, but is not applied for computational\nsavings. When performing a quantum free-energy calculation it\nis important to distinguish between the free-energy computed\nas the logarithm of the probability of observing a given\nconfiguration (that depends on the distribution of the\nreplicas) and the free-energy taken as a tool to estimate\nreaction rates $k$ in a transition-state theory\nfashion $k\\propto e^{-\\Delta E^\\ddagger/kT}$,\nwhere the energy barrier $\\Delta E^\\ddagger$\nis better estimated from the distribution of the centroid.\nSee e.g.\n[Habershon et al., Annu. Rev. Phys. Chem. (2013)](http://doi.org/10.1146/annurev-physchem-040412-110122)\nfor a discussion of the subtleties involved in estimating\ntransition rates.\nIn practice, performing this contraction step is very easy\nin `i-PI`, because for each `` section - including\nthat corresponding to the bias - it is possible to specify\na different number of replicas. The configurations will\nbe automatically computed by Fourier interpolation.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\" \" + ET.tostring(xmlroot.find(\".//bias\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running the calculation\n\nThe other changes are purely cosmetic, and the calculation\ncan be launched very easily, using several drivers to parallelize\nthe energy evaluation over the beads (although this kind of calculations\nis not limited by the evaluation of the forces).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# don't rerun if the outputs already exist\nipi_process = None\nif not os.path.exists(\"meta-pimd.out\"):\n ipi_process = subprocess.Popen([\"i-pi\", \"data/input-pimd.xml\"])\n time.sleep(2) # wait for i-PI to start\n driver_process = [\n subprocess.Popen(\n [\"i-pi-driver\", \"-u\", \"-a\", \"zundel\", \"-m\", \"zundel\"], cwd=\"data/\"\n )\n for i in range(4)\n ]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you run this in a notebook, you can go ahead and start loading\noutput files _before_ i-PI has finished running by skipping this cell\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# wait for simulations to finish\nif ipi_process is not None:\n ipi_process.wait()\n for process in driver_process:\n process.wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analysis of the simulation\n\nA path integral simulation evolves multiple configurations at the same\ntime, forming a `ring polymer`. Each replica provides a sample of the\nquantum mechanical configuration distribution of the atoms. To provide\nan overall visualization of the path integral dynamics, we load all the\nreplicas and combine them using a utility function from the\n`chemiscope` library.`\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "output_data, output_desc = ipi.read_output(\"meta-pimd.out\")\ncolvar_data = ipi.read_trajectory(\"meta-pimd.colvar_0\", format=\"extras\")[\n \"doo,dc,mtd.bias\"\n]\npimd_traj_data = [ipi.read_trajectory(f\"meta-pimd.pos_{i}.xyz\") for i in range(8)]\n\n# combines the PI beads and sets up the visualization options\ntraj_pimd = chemiscope.ase_merge_pi_frames(pimd_traj_data)\ntraj_pimd[\"shapes\"][\"paths\"][\"parameters\"][\"global\"][\"radius\"] = 0.05\ntraj_pimd[\"properties\"] = dict(\n d_OO=10 * colvar_data[:, 0], # nm to \u00c5\n delta_coord=colvar_data[:, 1],\n bias=27.211386 * output_data[\"ensemble_bias\"], # Ha to eV\n time=2.4188843e-05 * output_data[\"time\"],\n)\ntraj_pimd[\"settings\"] = chemiscope.quick_settings(\n x=\"d_OO\",\n y=\"delta_coord\",\n z=\"bias\",\n color=\"time\",\n trajectory=True,\n structure_settings=dict(\n bonds=False,\n atoms=False,\n keepOrientation=True,\n unitCell=False,\n shape=[\n \"paths\",\n ],\n ),\n)\ntraj_pimd[\"settings\"][\"target\"] = \"structure\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualize the trajectory. Note the similar behavior as for the classical\ntrajectory, and the delocalization of the protons\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "chemiscope.show(**traj_pimd)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Free energy plots\n\nThe free energy profiles relative to $\\Delta C_\\mathrm{H}$\nand $d_\\mathrm{OO}$ can be computed exactly as for the\nclassical trajectory, using the `sum_hills` module.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "with open(\"data/plumed-pimd.dat\", \"r\") as file:\n subprocess.run(\n [\n \"plumed\",\n \"sum_hills\",\n \"--hills\",\n \"HILLS-pimd\",\n \"--min\",\n \"0.21,-1\",\n \"--max\",\n \"0.31,1\",\n \"--bin\",\n \"100,100\",\n \"--outfile\",\n \"FES-pimd\",\n \"--stride\",\n \"100\",\n \"--mintozero\",\n ],\n stdin=file,\n text=True,\n )\n\n# rearrange data and converts to \u00c5 and eV\ndata = np.loadtxt(\"FES-pimd0.dat\", comments=\"#\")[:, :3]\nxyz_pi_0 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape(\n 3, 101, 101\n)\ndata = np.loadtxt(\"FES-pimd2.dat\", comments=\"#\")[:, :3]\nxyz_pi_2 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape(\n 3, 101, 101\n)\ndata = np.loadtxt(\"FES-pimd5.dat\", comments=\"#\")[:, :3]\nxyz_pi_5 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape(\n 3, 101, 101\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as for a classical run, the metadynamics bias progressively\npushes the centroid (and the beads that are distributed around it)\nto sample a wider portion of the collective-variable space.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(\n 1, 3, figsize=(8, 3), sharex=True, sharey=True, constrained_layout=True\n)\n\ncf_0 = ax[0].contourf(*xyz_pi_0)\ncf_1 = ax[1].contourf(*xyz_pi_2)\ncf_2 = ax[2].contourf(*xyz_pi_5)\nfig.colorbar(cf_2, ax=ax, orientation=\"vertical\", label=r\"$F$ / eV\")\nax[0].set_ylabel(r\"$\\Delta C_\\mathrm{H}$\")\nax[0].set_xlabel(r\"$d_\\mathrm{OO}$ / \u00c5\")\nax[1].set_xlabel(r\"$d_\\mathrm{OO}$ / \u00c5\")\nax[2].set_xlabel(r\"$d_\\mathrm{OO}$ / \u00c5\")\nax[0].set_title(r\"$t=0.8$ ps\")\nax[1].set_title(r\"$t=2.5$ ps\")\nax[2].set_title(r\"$t=5.0$ ps\")\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Assessing quantum nuclear effects\n\nThe effect of nuclear quantization on the centroid free-energy\nis relatively small, despite the large delocalization of the\nprotons in the PIMD calculation. Looking more\ncarefully at the two distributions, one can notice that\nin the high-$d_\\mathrm{OO}$ region there is higher\ndelocalisation of the proton.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(\n 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True\n)\n\nlevels = np.linspace(0, 0.5, 6)\ncp1 = ax.contour(*xyz_5, colors=\"b\", levels=levels)\ncp2 = ax.contour(*xyz_pi_5, colors=\"r\", levels=levels)\nax.set_ylabel(r\"$\\Delta C_\\mathrm{H}$\")\nax.set_xlabel(r\"$d_\\mathrm{OO}$ / \u00c5\")\nax.legend(\n handles=[\n plt.Line2D([0], [0], color=\"b\", label=\"MD\"),\n plt.Line2D([0], [0], color=\"r\", label=\"PIMD\"),\n ]\n)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get a clear signal, we need better-converged calculations;\nthe `data/` folder contains inputs for these \"high quality\" runs,\nand free-energies obtained from them.\nThe results confirm the lowering of the free-energy barrier for\nthe $\\mathrm{H_3O^+ + H_2O} \\rightarrow \\mathrm{H_2O + H_3O^+}$\ntransition.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "with bz2.open(\"data/FES-md_hiq.bz2\", \"rt\") as f:\n data = np.loadtxt(f, comments=\"#\")[:, :3]\nxyz_md_hiq = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape(\n 3, 101, 101\n)\nwith bz2.open(\"data/FES-pimd_hiq.bz2\", \"rt\") as f:\n data = np.loadtxt(f, comments=\"#\")[:, :3]\nxyz_pi_hiq = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape(\n 3, 101, 101\n)\n\nfig, ax = plt.subplots(\n 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True\n)\n\nlevels = np.linspace(0, 0.5, 6)\ncp1 = ax.contour(*xyz_md_hiq, colors=\"b\", levels=levels)\ncp2 = ax.contour(*xyz_pi_hiq, colors=\"r\", levels=levels)\nax.set_ylabel(r\"$\\Delta C_\\mathrm{H}$\")\nax.set_xlabel(r\"$d_\\mathrm{OO}$ / \u00c5\")\nax.legend(\n handles=[\n plt.Line2D([0], [0], color=\"b\", label=\"MD\"),\n plt.Line2D([0], [0], color=\"r\", label=\"PIMD\"),\n ]\n)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The lowering of the barrier for proton hopping is clearly\nseen by taking 1D slices of the free energy at different O-O separations.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(\n 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True\n)\n\nax.plot(\n xyz_md_hiq[1, :, 50], xyz_md_hiq[2, :, 50], \"b\", label=r\"MD, $d_\\mathrm{OO}=2.6 $\u00c5\"\n)\nax.plot(\n xyz_pi_hiq[1, :, 50],\n xyz_pi_hiq[2, :, 50],\n \"r\",\n label=r\"PIMD, $d_\\mathrm{OO}=2.6 $\u00c5\",\n)\nax.plot(\n xyz_md_hiq[1, :, 60],\n xyz_md_hiq[2, :, 60],\n \"b--\",\n label=r\"MD, $d_\\mathrm{OO}=2.7 $\u00c5\",\n)\nax.plot(\n xyz_pi_hiq[1, :, 60],\n xyz_pi_hiq[2, :, 60],\n \"r--\",\n label=r\"PIMD, $d_\\mathrm{OO}=2.7 $\u00c5\",\n)\nax.set_ylim(0.08, 0.6)\nax.legend(ncols=2, loc=\"upper right\", fontsize=9)\nax.set_ylabel(r\"$F$ / eV\")\nax.set_xlabel(r\"$\\Delta C_\\mathrm{H}$\")\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This model system is representative of the behavior of protons\nalong a hydrogen bond in different conditions, where the environment\ndetermines the typical O-O separation, and whether the proton is shared\n(as in high pressure ice X) or preferentially attached to one of the two\nmolecules. Zero-point energy (and to a lesser extent tunneling)\nincreases the delocalization, and reduces the barrier for an excess\nproton to hop between water molecues.\n\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/372c6744f93b866ccf802a12006619bb/roy-gch.py b/_downloads/372c6744f93b866ccf802a12006619bb/roy-gch.py new file mode 100644 index 00000000..46ee05e5 --- /dev/null +++ b/_downloads/372c6744f93b866ccf802a12006619bb/roy-gch.py @@ -0,0 +1,304 @@ +""" +Generalized Convex Hull construction for the polymorphs of ROY +============================================================== + +:Authors: Michele Ceriotti `@ceriottm `_ + +This notebook analyzes the structures of 264 polymorphs of ROY, from +`Beran et Al, Chemical Science (2022) `__, +comparing the conventional density-energy convex hull with a Generalized Convex Hull +(GCH) analysis (see `Anelli et al., Phys. Rev. Materials +(2018) `__). +It uses features computed with `rascaline `__ +and uses the directional convex hull function from +`scikit-matter `__ +to make the figure. + +The GCH construction aims at determining structures, among a collection of +candidate configurations, that are stable or have the potential of being stabilized +by appropriate thermodynamic boundary conditions (pressure, doping, external fields, +...). It does so by using microscopic descriptors to determine the diversity of +structures, and assumes that configurations that are stable relative to other +configurations with similar descriptors are those that could be made +"locally" stable by suitable synthesis conditions. +""" + +# sphinx_gallery_thumbnail_number = 3 +import chemiscope +import matplotlib.tri +import numpy as np +from matplotlib import pyplot as plt +from metatensor import mean_over_samples +from rascaline import SoapPowerSpectrum +from sklearn.decomposition import PCA +from skmatter.datasets import load_roy_dataset +from skmatter.sample_selection import DirectionalConvexHull + + +# %% +# Loads the structures (that also contain properties in the ``info`` field) + +roy_data = load_roy_dataset() + +structures = roy_data["structures"] + +density = np.array([s.info["density"] for s in structures]) +energy = np.array([s.info["energy"] for s in structures]) +structype = np.array([s.info["type"] for s in structures]) +iknown = np.where(structype == "known")[0] +iothers = np.where(structype != "known")[0] + + +# %% +# Energy-density hull +# ------------------- +# +# The Directional Convex Hull routines can be used to compute a +# conventional density-energy hull (see +# `Hautier (2014) +# `_ for a pedagogic +# introduction to the convex hull construction in the context +# of atomistic simulations). + +dch_builder = DirectionalConvexHull(low_dim_idx=[0]) +dch_builder.fit(density.reshape(-1, 1), energy) + +# %% +# We can get the indices of the selection, and compute the distance from +# the hull + +sel = dch_builder.selected_idx_ +dch_dist = dch_builder.score_samples(density.reshape(-1, 1), energy) + + +# %% +# +# Hull energies +# ^^^^^^^^^^^^^ +# +# Structures on the hull are stable with respect to synthesis at constant +# molar volume. Any other structure would lower the energy by decomposing +# into a mixture of the two nearest structures along the hull. Given that +# the lattice energy is an imperfect proxy for the free energy, and that +# synthesis can be performed in other ways than by fixing the density, +# structures that are not exactly on the hull might also be stable. One +# can compute a “hull energy” as an indication of how close these +# structures are to being stable. + +fig, ax = plt.subplots(1, 1, figsize=(6, 4)) +ax.scatter(density, energy, c=dch_dist, marker=".") +ssel = sel[np.argsort(density[sel])] +ax.plot(density[ssel], energy[ssel], "k--") +ax.set_xlabel("density / g/cm$^3$") +ax.set_ylabel("energy / kJ/mol") +plt.show() + +print( + f"Mean hull energy for 'known' stable structures {dch_dist[iknown].mean()} kJ/mol" +) +print(f"Mean hull energy for 'other' structures {dch_dist[iothers].mean()} kJ/mol") + + +# %% +# Interactive visualization +# ^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# You can also visualize the hull with ``chemiscope`` in a juptyer notebook. +# + +cs = chemiscope.show( + structures, + dict( + energy=energy, + density=density, + hull_energy=dch_dist, + structure_type=structype, + ), + settings={ + "map": { + "x": {"property": "density"}, + "y": {"property": "energy"}, + "color": {"property": "hull_energy"}, + "symbol": "structure_type", + "size": {"factor": 35}, + }, + "structure": [{"unitCell": True, "supercell": {"0": 2, "1": 2, "2": 2}}], + }, +) +cs + +# %% +# +# Save chemiscope file in a format that can be shared and viewed on `chemiscope.org` +cs.save("roy_ch.json.gz") + +# %% +# Generalized Convex Hull +# ----------------------- +# +# A GCH is a similar construction, in which generic structural descriptors +# are used in lieu of composition, density or other thermodynamic +# constraints. The idea is that configurations that are found close to the +# GCH are locally stable with respect to structurally-similar +# configurations. In other terms, one can hope to find a thermodynamic +# constraint (i.e. synthesis conditions) that act differently on these +# structures in comparison with the others, and may potentially stabilize +# them. +# + + +# %% +# Compute structural descriptors +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# A first step is to computes suitable ML descriptors. Here we have used +# ``rascaline`` to evaluate average SOAP features for the structures. +# If you don't want to install these dependencies for this example you +# can also use the pre-computed features, but you can use this as a stub +# to apply this analysis to other chemical systems + +hypers = { + "cutoff": 4, + "max_radial": 6, + "max_angular": 4, + "atomic_gaussian_width": 0.7, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + "radial_basis": {"Gto": {"accuracy": 1e-6}}, + "center_atom_weight": 1.0, +} +calculator = SoapPowerSpectrum(**hypers) +rho2i = calculator.compute(structures) +rho2i = rho2i.keys_to_samples(["species_center"]).keys_to_properties( + ["species_neighbor_1", "species_neighbor_2"] +) +rho2i_structure = mean_over_samples(rho2i, sample_names=["center", "species_center"]) +np.savez("roy_features.npz", feats=rho2i_structure.block(0).values) + + +# features = roy_data["features"] +features = rho2i_structure.block(0).values + + +# %% +# PCA projection +# ^^^^^^^^^^^^^^ +# +# Computes PCA projection to generate low-dimensional descriptors that +# reflect structural diversity. Any other dimensionality reduction scheme +# could be used in a similar fashion. + +pca = PCA(n_components=4) +pca_features = pca.fit_transform(features) + +fig, ax = plt.subplots(1, 1, figsize=(6, 4)) +scatter = ax.scatter(pca_features[:, 0], pca_features[:, 1], c=energy) +ax.set_xlabel("PCA[1]") +ax.set_ylabel("PCA[2]") +cbar = fig.colorbar(scatter, ax=ax) +cbar.set_label("energy / kJ/mol") +plt.show() + + +# %% +# Builds the Generalized Convex Hull +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# Builds a convex hull on the first two PCA features + +dch_builder = DirectionalConvexHull(low_dim_idx=[0, 1]) +dch_builder.fit(pca_features, energy) +sel = dch_builder.selected_idx_ +dch_dist = dch_builder.score_samples(pca_features, energy) + + +# %% +# Generates a 3D Plot +# + +triang = matplotlib.tri.Triangulation(pca_features[sel, 0], pca_features[sel, 1]) +fig = plt.figure(figsize=(7, 5), tight_layout=True) +ax = fig.add_subplot(projection="3d") +ax.plot_trisurf(triang, energy[sel], color="gray") +ax.scatter(pca_features[:, 0], pca_features[:, 1], energy, c=dch_dist) +ax.set_xlabel("PCA[1]") +ax.set_ylabel("PCA[2]") +ax.set_zlabel("energy / kJ/mol\n \n", labelpad=11) +ax.view_init(25, 110) +plt.show() + + +# %% +# The GCH construction improves the separation between the hull energies +# of “known” and hypothetical polymorphs (compare with the density-energy +# values above) + +print( + f"Mean hull energy for 'known' stable structures {dch_dist[iknown].mean()} kJ/mol" +) +print(f"Mean hull energy for 'other' structures {dch_dist[iothers].mean()} kJ/mol") + + +# %% +# Visualize in a ``chemiscope`` widget + +for i, f in enumerate(structures): + for j in range(len(pca_features[i])): + f.info["pca_" + str(j + 1)] = pca_features[i, j] +structure_properties = chemiscope.extract_properties(structures) +structure_properties.update({"per_atom_energy": energy, "hull_energy": dch_dist}) + +# You can save a chemiscope file to disk (for viewing on chemiscope.org) + +chemiscope.write_input( + "roy_gch.json.gz", + frames=structures, + properties=structure_properties, + meta={ + "name": "GCH for ROY polymorphs", + "description": """ +Demonstration of the Generalized Convex Hull construction for +polymorphs of the ROY molecule. Molecules that are closest to +the hull built on PCA-based structural descriptors and having the +internal energy predicted by electronic-structure calculations as +the z axis are the most thermodynamically stable. Indeed most of the +known polymorphs of ROY are on (or very close) to this hull. +""", + "authors": ["Michele Ceriotti "], + "references": [ + 'A. Anelli, E. A. Engel, C. J. Pickard, and M. Ceriotti, \ + "Generalized convex hull construction for materials discovery," \ + Physical Review Materials 2(10), 103804 (2018).', + 'G. J. O. Beran, I. J. Sugden, C. Greenwell, D. H. Bowskill, \ + C. C. Pantelides, and C. S. Adjiman, "How many more polymorphs of \ + ROY remain undiscovered," Chem. Sci. 13(5), 1288–1297 (2022).', + ], + }, + settings={ + "map": { + "x": {"property": "pca_1"}, + "y": {"property": "pca_2"}, + "z": {"property": "energy"}, + "symbol": "type", + "color": {"property": "hull_energy"}, + "size": { + "factor": 35, + "mode": "linear", + "property": "", + "reverse": True, + }, + }, + "structure": [ + { + "bonds": True, + "unitCell": True, + "keepOrientation": True, + } + ], + }, +) + +# %% +# +# ... and also load one as an interactive viewer + +chemiscope.show_input("roy_gch.json.gz") diff --git a/_downloads/4a472fb66c1181d9511af7fde6c7f57c/gaas-map.zip b/_downloads/4a472fb66c1181d9511af7fde6c7f57c/gaas-map.zip new file mode 100644 index 00000000..d83fbc98 Binary files /dev/null and b/_downloads/4a472fb66c1181d9511af7fde6c7f57c/gaas-map.zip differ diff --git a/_downloads/4cc6d7251cc20e13dd91e533c7271a6a/charge-charge.xyz b/_downloads/4cc6d7251cc20e13dd91e533c7271a6a/charge-charge.xyz new file mode 100644 index 00000000..a988fbef --- /dev/null +++ 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energyA=-2617.69985845671 chargeB=-1 energyB=-6220.46984312555 distance=3.9205187003526993 pbc="T T T" +C 9.12400000 -6.69000000 22.74000000 0.54812534 0.27540558 0.51544675 +N 7.96000000 -6.55600000 21.83900000 -0.06067138 -0.54472055 1.47589351 +H 8.24600000 -6.67200000 20.86300000 0.71357011 0.67446814 -2.48421272 +H 7.55700000 -5.63000000 21.88900000 -0.13732947 0.67735084 -0.16143501 +H 7.23800000 -7.23200000 22.05200000 -0.46440763 -0.32070373 0.24175500 +H 9.98100000 -6.18400000 22.28300000 -0.11658090 0.09966175 -0.16086919 +H 9.39500000 -7.74000000 22.88700000 -0.20533470 -0.03823069 -0.07816330 +H 8.91513100 -6.21360700 23.70924000 -0.03626796 -0.17498244 -0.11527447 +C 7.96475462 -5.18650437 17.33327806 -0.26812990 -0.69031791 -0.59508119 +C 8.52475462 -4.97950437 18.72727806 0.59762984 1.95215844 0.93232784 +O 8.72575462 -6.00950437 19.42127806 -0.39722459 -3.60342175 0.69265250 +O 8.81775462 -3.88250437 19.23327806 -0.40216503 1.62861663 -0.82973478 +H 7.03575462 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energy=-8841.41457610454 label=CC chargeA=1 energyA=-2617.69985845671 chargeB=-1 energyB=-6220.46984312555 distance=5.412652146732347 pbc="T T T" +C 9.12400000 -6.69000000 22.74000000 0.92201804 0.21935019 0.62739256 +N 7.96000000 -6.55600000 21.83900000 0.68941340 -0.06309745 -0.22989421 +H 8.24600000 -6.67200000 20.86300000 0.09139508 -0.04888169 -0.87626260 +H 7.55700000 -5.63000000 21.88900000 -0.40332886 0.92228456 0.01436725 +H 7.23800000 -7.23200000 22.05200000 -0.76923102 -0.62306613 0.14501826 +H 9.98100000 -6.18400000 22.28300000 -0.07663673 0.08857951 -0.06528276 +H 9.39500000 -7.74000000 22.88700000 -0.23009505 -0.05074169 -0.09301661 +H 8.91513100 -6.21360700 23.70924000 -0.12277075 -0.15677957 -0.16712058 +C 7.85222690 -4.70947815 15.91560972 -0.31510743 -0.63508705 -0.64976259 +C 8.41222690 -4.50247815 17.30960972 0.62143319 0.64943159 1.18822378 +O 8.61322690 -5.53247815 18.00360972 -0.40221967 -2.53377437 0.26705063 +O 8.70522690 -3.40547815 17.81560972 -0.22385026 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8.91513100 -6.21360700 23.70924000 -0.13114381 -0.15368544 -0.16822250 +C 7.83347228 -4.62997378 15.67933167 -0.31813130 -0.62876149 -0.63338286 +C 8.39347228 -4.42297378 17.07333167 0.58105721 0.53509716 1.05383528 +O 8.59447228 -5.45297378 17.76733167 -0.36604656 -2.33300249 0.18893382 +O 8.68647228 -3.32597378 17.57933167 -0.19134877 2.07724439 -0.60846830 +H 6.90447228 -5.19297378 15.80233167 -0.21511829 -0.22335202 0.00291625 +H 8.51747228 -5.31197378 15.16833167 0.14492105 -0.24997186 -0.10968661 +H 7.60324328 -3.84516678 14.94375167 0.28958106 0.59035103 0.62833941 +15 +Lattice="30.0 0.0 0.0 0.0 30.0 0.0 0.0 0.0 30.0" Properties=species:S:1:pos:R:3:forces:R:3 energy=-8841.12862125546 label=CC chargeA=1 energyA=-2617.69985845671 chargeB=-1 energyB=-6220.46984312555 distance=5.910914934526397 pbc="T T T" +C 9.12400000 -6.69000000 22.74000000 0.98039135 0.20784383 0.65378493 +N 7.96000000 -6.55600000 21.83900000 0.79252864 -0.03760861 -0.28410172 +H 8.24600000 -6.67200000 20.86300000 0.07220453 -0.15129169 -0.73974234 +H 7.55700000 -5.63000000 21.88900000 -0.47041804 1.01227401 0.07797136 +H 7.23800000 -7.23200000 22.05200000 -0.87357192 -0.72203922 0.18096794 +H 9.98100000 -6.18400000 22.28300000 -0.07134261 0.08815780 -0.05214669 +H 9.39500000 -7.74000000 22.88700000 -0.23679433 -0.05608811 -0.09474408 +H 8.91513100 -6.21360700 23.70924000 -0.13655288 -0.15170370 -0.16939514 +C 7.81471766 -4.55046941 15.44305361 -0.31991754 -0.62066830 -0.62068308 +C 8.37471766 -4.34346941 16.83705361 0.54176178 0.43202167 0.94036629 +O 8.57571766 -5.37346941 17.53105361 -0.33544519 -2.16463188 0.13284808 +O 8.66771766 -3.24646941 17.34305361 -0.16267374 2.04497903 -0.54668903 +H 6.88571766 -5.11346941 15.56605361 -0.21561421 -0.22163280 0.00434242 +H 8.49871766 -5.23246941 14.93205361 0.14765766 -0.24852546 -0.10857215 +H 7.58448866 -3.76566241 14.70747361 0.28778648 0.58891342 0.62579320 +15 +Lattice="30.0 0.0 0.0 0.0 30.0 0.0 0.0 0.0 30.0" 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distance=6.792421743531683 pbc="T T T" +C 34.44500000 12.62500000 24.95900000 0.27713178 0.25678691 0.02626196 +C 33.70500000 11.92700000 26.09800000 0.57557534 0.20903733 0.77834247 +O 32.60000000 11.42900000 25.81100000 -1.75109155 -0.71910547 -0.76127557 +O 34.21200000 11.87200000 27.24800000 0.62750776 0.22868713 0.31888917 +H 33.75000000 13.28700000 24.44000000 -0.16648832 0.13824975 -0.17771510 +H 34.76300000 11.86300000 24.24500000 0.12650847 -0.14408928 -0.22194567 +H 35.32079000 13.21299000 25.27085000 -0.03039716 -0.13769190 0.12419576 +C 28.24010704 10.18662363 29.29509195 0.23101225 -0.11340096 -0.12530067 +C 27.89210704 8.56562363 27.44409195 0.03198110 0.35639080 0.53232861 +N 28.51410704 9.59262363 27.98309195 0.66726098 1.31191194 0.71157774 +N 26.88210704 7.97262363 28.05409195 -0.94133069 -0.75409548 0.29899221 +N 28.26510704 8.14362363 26.25909195 0.16127474 -0.86764955 -1.40612998 +H 29.31610704 9.95862363 27.46609195 -0.04748983 0.13444625 0.14725618 +H 29.16410704 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energy=-12894.7856852073 label=CC chargeA=1 energyA=-6669.20645149176 chargeB=-1 energyB=-6220.48400518575 distance=4.09611684385743 pbc="T T T" +C 0.01900000 -12.24500000 2.37200000 0.25491825 0.72592295 -0.04404492 +C 0.22300000 -9.83900000 1.84900000 0.79406799 -1.43290988 -0.35208236 +N 0.66900000 -11.08600000 1.75700000 -1.38027710 0.10461000 0.45682441 +N -0.87800000 -9.57200000 2.52900000 -1.29412298 0.45795589 0.78255904 +N 0.87600000 -8.85300000 1.26400000 0.15869282 0.70185850 -0.24460526 +H 1.57500000 -11.24100000 1.31700000 1.83358777 -0.62122385 -0.51212069 +H 0.56800000 -13.14900000 2.09900000 0.18440642 0.09199461 -0.05556416 +H -1.00300000 -12.34300000 1.99900000 -0.30295145 -0.11780312 -0.01989939 +H -1.44200000 -10.32000000 2.89200000 -0.18552092 -0.10248745 0.16372461 +H -1.21900000 -8.62500000 2.58900000 -0.18062966 0.01566042 0.06742378 +H 1.72400000 -9.06300000 0.75200000 1.06995869 -0.27772880 -0.42048099 +H 0.52800000 -7.90900000 1.29900000 0.03556961 0.13987524 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Properties=species:S:1:pos:R:3:forces:R:3 energy=-12893.5976487247 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=5.233746639606387 pbc="T T T" +C 25.65400000 -5.20500000 -2.23100000 -0.02457583 -0.14287467 -0.12667042 +C 25.43700000 -3.85300000 -1.56500000 -1.15024785 0.48192575 0.27112924 +O 26.43300000 -3.22700000 -1.14000000 2.29370442 0.94059550 0.60532708 +O 24.27400000 -3.40300000 -1.47500000 -1.24157638 -0.06804811 -0.28187319 +H 26.34900000 -5.06000000 -3.05900000 0.33543428 -0.12157948 -0.16227024 +H 24.71500000 -5.57700000 -2.64500000 -0.15462966 -0.12830728 0.04690626 +H 26.07672000 -5.94638300 -1.53698600 0.04738910 0.08948846 -0.02548417 +C 24.97931001 1.85371018 2.07255398 -0.33498138 -0.19215461 -0.40221457 +C 25.40831001 0.71371018 -0.07444602 0.31332548 -0.65862905 0.58879798 +N 25.94731001 -0.31928982 0.54955398 0.20462919 -0.02606294 -0.11121301 +N 24.94531001 1.75071018 0.61155398 -0.22652446 1.06428609 0.79205350 +N 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pbc="T T T" +C 25.65400000 -5.20500000 -2.23100000 -0.05580857 -0.17108762 -0.15378602 +C 25.43700000 -3.85300000 -1.56500000 -0.58131702 0.51109991 0.33964965 +O 26.43300000 -3.22700000 -1.14000000 1.90181014 0.47931435 0.39802489 +O 24.27400000 -3.40300000 -1.47500000 -1.40785744 -0.04363963 -0.23943019 +H 26.34900000 -5.06000000 -3.05900000 0.32846862 -0.11484266 -0.16463427 +H 24.71500000 -5.57700000 -2.64500000 -0.17072528 -0.15318664 0.02760716 +H 26.07672000 -5.94638300 -1.53698600 0.04051124 0.08872440 -0.01949925 +C 24.93993003 2.76713055 2.47766193 -0.31509757 -0.19157025 -0.38930336 +C 25.36893003 1.62713055 0.33066193 0.02798797 -0.24639176 0.46036261 +N 25.90793003 0.59413055 0.95466193 0.40814117 -0.70515029 -0.12851091 +N 24.90593003 2.66413055 1.01666193 -0.18011326 0.98079719 0.83549321 +N 25.28593003 1.61413055 -0.98433807 -0.08651364 0.14011066 -1.11429129 +H 26.06893003 0.62213055 1.94466193 0.00721208 -0.22943826 0.30588142 +H 26.17993003 -0.23586945 0.41966193 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energyA=-6669.20645149176 chargeB=-1 energyB=-6220.48400518575 distance=6.141506759716005 pbc="T T T" +C 32.59000000 -10.26800000 58.76100000 -0.68333797 0.46999934 0.68424615 +C 31.01900000 -11.54600000 60.23100000 0.34783159 0.32738940 -0.52287693 +N 29.86200000 -11.49700000 60.84900000 -1.31927437 0.07591202 0.80205960 +N 31.29100000 -10.55900000 59.39400000 0.59953176 -0.02397709 -0.56611966 +N 31.82000000 -12.58200000 60.45800000 0.34214774 -0.20160055 0.06018444 +H 29.30600000 -10.65300000 60.75300000 -0.38408029 0.02588988 0.16497004 +H 29.60200000 -12.19700000 61.53200000 -0.18312841 0.05320462 0.02581607 +H 30.57700000 -9.82700000 59.36500000 0.04937226 0.28998742 -0.30992996 +H 32.67200000 -12.69900000 59.93600000 0.24322269 -0.21010667 -0.04926215 +H 31.49700000 -13.30000000 61.09500000 0.21951807 -0.25518371 0.00455295 +H 32.42700000 -9.97000000 57.72400000 0.00318239 0.00761205 -0.11719264 +H 33.27200000 -11.11900000 58.79900000 -0.00979166 -0.07382722 0.01106741 +H 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Properties=species:S:1:pos:R:3:forces:R:3 energy=-12894.280031935 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=4.503553881387339 pbc="T T T" +C 12.98100000 17.69200000 25.94800000 -0.35575176 -0.31589437 0.76694120 +C 12.12100000 17.80500000 24.71700000 0.95525929 1.35221535 -1.03847820 +O 11.25200000 16.92500000 24.47100000 -2.29128963 -1.76045920 0.18225512 +O 12.41100000 18.73500000 23.94100000 -0.00507030 0.59766514 -0.31911878 +H 13.24200000 18.68100000 26.32900000 0.06184794 0.13602021 0.00537219 +H 13.90100000 17.18800000 25.64900000 0.23907087 -0.19129135 0.09412720 +H 12.47004000 17.11600000 26.73359000 0.21582576 -0.10429758 0.07343542 +C 8.62441722 16.90762320 21.42903241 0.43728495 -0.16337958 0.69830249 +C 7.88141722 16.81162320 23.81103241 0.48126016 -0.05831989 -1.04739221 +N 8.81841722 16.85862320 22.88503241 -0.75736343 0.12568904 -1.51508035 +N 6.57841722 16.84262320 23.51803241 -0.67959141 0.02106224 -0.27391103 +N 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16.61624640 25.07306483 0.78528118 0.12602404 0.51473331 +H 7.41283443 16.56624640 25.70306483 0.33636392 0.02683060 0.04507434 +H 7.36383443 17.03124640 21.04306483 -0.13226724 0.23318188 -0.02908268 +H 8.70483443 15.89924640 20.90506483 0.05871704 -0.17654692 -0.21013258 +H 9.05112543 17.64185640 20.89021483 -0.18697717 0.00696028 0.08257973 +20 +Lattice="30.0 0.0 0.0 0.0 30.0 0.0 0.0 0.0 30.0" Properties=species:S:1:pos:R:3:forces:R:3 energy=-12893.6417526352 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=4.999645142729246 pbc="T T T" +C 12.98100000 17.69200000 25.94800000 -0.28811898 -0.30568602 0.79825392 +C 12.12100000 17.80500000 24.71700000 0.51062320 0.94459191 -1.13281032 +O 11.25200000 16.92500000 24.47100000 -2.08743016 -1.60679740 0.25293453 +O 12.41100000 18.73500000 23.94100000 0.13685490 0.84193762 -0.38925819 +H 13.24200000 18.68100000 26.32900000 0.07265372 0.14721934 0.02075202 +H 13.90100000 17.18800000 25.64900000 0.24961557 -0.18922421 0.09726704 +H 12.47004000 17.11600000 26.73359000 0.20655691 -0.10197987 0.06754006 +C 8.18325165 16.81886961 21.21109724 0.51198318 -0.17337082 0.58036133 +C 7.44025165 16.72286961 23.59309724 0.27233828 -0.06193547 -0.88954246 +N 8.37725165 16.76986961 22.66709724 -0.24015890 0.16707170 -1.30390492 +N 6.13725165 16.75386961 23.30009724 -0.50409794 0.01481735 -0.27340795 +N 7.85325165 16.62786961 24.83309724 -0.16654766 -0.12103506 1.32695728 +H 9.33625165 16.75086961 23.01109724 0.88659457 0.19894469 0.18147458 +H 5.82725165 16.77086961 22.33709724 -0.08964785 0.02370175 0.16945893 +H 5.45625165 16.72286961 24.04209724 -0.19305701 0.00855014 -0.02985300 +H 8.86025165 16.57186961 24.96409724 0.62652264 0.11967150 0.59125694 +H 7.19225165 16.52186961 25.59409724 0.35482764 0.02711708 0.07030344 +H 7.14325165 16.98686961 20.93409724 -0.12485611 0.23377607 -0.01275032 +H 8.48425165 15.85486961 20.79609724 0.05730635 -0.17382975 -0.20622745 +H 8.83054265 17.59747961 20.78124724 -0.19196235 0.00645945 0.08119454 +20 +Lattice="30.0 0.0 0.0 0.0 30.0 0.0 0.0 0.0 30.0" Properties=species:S:1:pos:R:3:forces:R:3 energy=-12893.3487761903 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=5.247968996564185 pbc="T T T" +C 12.98100000 17.69200000 25.94800000 -0.26214910 -0.29555882 0.81086678 +C 12.12100000 17.80500000 24.71700000 0.34186037 0.75825628 -1.15724763 +O 11.25200000 16.92500000 24.47100000 -1.88051904 -1.51331328 0.31440509 +O 12.41100000 18.73500000 23.94100000 0.19510784 0.94356250 -0.42263603 +H 13.24200000 18.68100000 26.32900000 0.07766337 0.15218788 0.02817619 +H 13.90100000 17.18800000 25.64900000 0.25343543 -0.18864217 0.09766410 +H 12.47004000 17.11600000 26.73359000 0.20204296 -0.10081794 0.06426360 +C 7.96266886 16.77449281 21.10212966 0.53134956 -0.17766572 0.53829803 +C 7.21966886 16.67849281 23.48412966 0.18455214 -0.06057164 -0.85264148 +N 8.15666886 16.72549281 22.55812966 -0.11680591 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12.98100000 17.69200000 25.94800000 -0.23863500 -0.28001340 0.81897402 +C 12.12100000 17.80500000 24.71700000 0.19187624 0.55994359 -1.14972697 +O 11.25200000 16.92500000 24.47100000 -1.66813568 -1.40103290 0.36259613 +O 12.41100000 18.73500000 23.94100000 0.24473620 1.03550299 -0.46193218 +H 13.24200000 18.68100000 26.32900000 0.08308216 0.15686928 0.03592068 +H 13.90100000 17.18800000 25.64900000 0.25641209 -0.18791731 0.09729401 +H 12.47004000 17.11600000 26.73359000 0.19654636 -0.09850820 0.05818435 +C 7.74208608 16.73011601 20.99316207 0.54694955 -0.18261069 0.50494457 +C 6.99908608 16.63411601 23.37516207 0.09704433 -0.04896869 -0.82700123 +N 7.93608608 16.68111601 22.44916207 -0.02368459 0.19196933 -1.25552057 +N 5.69608608 16.66511601 23.08216207 -0.37051152 0.00996477 -0.26284114 +N 7.41208608 16.53911601 24.61516207 -0.02700958 -0.10945606 1.28969508 +H 8.89508608 16.66211601 22.79316207 0.55455688 0.14546255 -0.02003825 +H 5.38608608 16.68211601 22.11916207 -0.10180087 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0.01432358 +H 7.82250329 15.72173921 20.46919448 0.04917858 -0.16859704 -0.20403341 +H 8.16879429 17.46434921 20.45434448 -0.20228754 0.00931389 0.07126991 +20 +Lattice="30.0 0.0 0.0 0.0 30.0 0.0 0.0 0.0 30.0" Properties=species:S:1:pos:R:3:forces:R:3 energy=-12892.6773656391 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=5.9937767370030866 pbc="T T T" +C 12.98100000 17.69200000 25.94800000 -0.17755875 -0.18954708 0.72681690 +C 12.12100000 17.80500000 24.71700000 0.12093818 -0.05925948 -0.47097423 +O 11.25200000 16.92500000 24.47100000 -1.26513527 -1.01531755 0.20007969 +O 12.41100000 18.73500000 23.94100000 0.23840123 1.22876233 -0.77880250 +H 13.24200000 18.68100000 26.32900000 0.09707844 0.19379480 0.05660562 +H 13.90100000 17.18800000 25.64900000 0.26455416 -0.19502315 0.08302623 +H 12.47004000 17.11600000 26.73359000 0.14235947 -0.09265902 0.03773811 +C 7.30092051 16.64136241 20.77522690 0.62197895 -0.22450392 0.49211641 +C 6.55792051 16.54536241 23.15722690 -0.16883942 0.24378298 -0.77252562 +N 7.49492051 16.59236241 22.23122690 0.32085341 0.10585654 -1.41364654 +N 5.25492051 16.57636241 22.86422690 -0.34687004 -0.00326828 -0.27834801 +N 6.97092051 16.45036241 24.39722690 0.21696832 -0.14119585 1.45930807 +H 8.45392051 16.57336241 22.57522690 0.22136113 0.09804013 -0.15989885 +H 4.94492051 16.59336241 21.90122690 -0.13229592 -0.02571329 0.07775715 +H 4.57392051 16.54536241 23.60622690 -0.23688651 -0.04037733 0.06031952 +H 7.97792051 16.39436241 24.52822690 0.09671188 0.00322368 0.68294141 +H 6.30992051 16.34436241 25.15822690 0.31762238 0.00394836 0.10795693 +H 6.26092051 16.80936241 20.49822690 -0.13305450 0.23694503 0.03834569 +H 7.60192051 15.67736241 20.36022690 0.01212386 -0.13895713 -0.21175425 +H 7.94821151 17.41997241 20.34537690 -0.21031101 0.01146825 0.06293827 +20 +Lattice="30.0 0.0 0.0 0.0 30.0 0.0 0.0 0.0 30.0" Properties=species:S:1:pos:R:3:forces:R:3 energy=-12892.5157633701 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=6.242602554777832 pbc="T T T" +C 12.98100000 17.69200000 25.94800000 -0.19902086 -0.21962487 0.79759456 +C 12.12100000 17.80500000 24.71700000 -0.07212314 -0.04678756 -0.86501817 +O 11.25200000 16.92500000 24.47100000 -1.10840021 -0.97359089 0.36308635 +O 12.41100000 18.73500000 23.94100000 0.28353617 1.21417220 -0.64199958 +H 13.24200000 18.68100000 26.32900000 0.09755719 0.16998956 0.05852058 +H 13.90100000 17.18800000 25.64900000 0.26133120 -0.18608930 0.09462405 +H 12.47004000 17.11600000 26.73359000 0.17708639 -0.08818795 0.03422642 +C 7.08033772 16.59698561 20.66625931 0.60250224 -0.21079416 0.46195515 +C 6.33733772 16.50098561 23.04825931 -0.19954284 0.10334833 -0.78388242 +N 7.27433772 16.54798561 22.12225931 0.28330326 0.18351434 -1.34550810 +N 5.03433772 16.53198561 22.75525931 -0.28067357 0.01214492 -0.25972692 +N 6.75033772 16.40598561 24.28825931 0.17517426 -0.10358347 1.40189714 +H 8.23333772 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a/_downloads/4dd8b470da0d1f3672e0a6f90c77c550/sample-selection.py b/_downloads/4dd8b470da0d1f3672e0a6f90c77c550/sample-selection.py new file mode 100644 index 00000000..01aa8dc0 --- /dev/null +++ b/_downloads/4dd8b470da0d1f3672e0a6f90c77c550/sample-selection.py @@ -0,0 +1,360 @@ +""" +Sample and Feature Selection with FPS and CUR +============================================= + +:Authors: Davide Tisi `@DavideTisi `_ + +In this tutorial we generate descriptors using rascaline, then select a subset +of structures using both the farthest-point sampling (FPS) and CUR algorithms +implemented in scikit-matter. Finally, we also generate a selection of +the most important features using the same techniques. + +First, import all the necessary packages +""" + +# %% + +import ase.io +import chemiscope +import metatensor +import numpy as np +from equisolve.numpy import feature_selection, sample_selection +from matplotlib import pyplot as plt +from rascaline import SoapPowerSpectrum +from sklearn.decomposition import PCA +from skmatter import feature_selection as skfeat_selection + + +# %% +# Load molecular data +# ------------------- +# +# Load 500 example BTO structures from file, reading them using +# `ASE `_. + +# Load a subset of :download:`structures ` of the example dataset +n_frames = 500 +frames = ase.io.read("input-fps.xyz", f":{n_frames}", format="extxyz") + +# %% +# Compute SOAP descriptors using rascaline +# ---------------------------------------- +# +# First, define the rascaline hyperparameters used to compute SOAP. + + +# rascaline hyperparameters +hypers = { + "cutoff": 6.0, + "max_radial": 8, + "max_angular": 6, + "atomic_gaussian_width": 0.3, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + "radial_basis": {"Gto": {"accuracy": 1e-6}}, + "radial_scaling": {"Willatt2018": {"exponent": 4, "rate": 1, "scale": 3.5}}, + "center_atom_weight": 1.0, +} + +# Generate a SOAP power spectrum +calculator = SoapPowerSpectrum(**hypers) +rho2i = calculator.compute(frames) + + +# Makes a dense block +atom_soap = rho2i.keys_to_properties(["species_neighbor_1", "species_neighbor_2"]) + +atom_soap_single_block = atom_soap.keys_to_samples(keys_to_move=["species_center"]) + +# Sum over atomic centers to compute structure features +struct_soap = metatensor.sum_over_samples( + atom_soap_single_block, sample_names=["center", "species_center"] +) + + +print("atom feature descriptor shape:", atom_soap.block(0).values.shape) +print( + "atom feature descriptor (all in one block) shape:", + atom_soap_single_block.block(0).values.shape, +) +print("structure feature descriptor shape:", struct_soap.block(0).values.shape) + + +# %% +# Perform atomic environment (i.e. sample) selection +# --------------------------------------------------- +# +# Using FPS and CUR algorithms, we can perform selection of atomic environments. +# These are implemented in equisolve, which provides a wrapper around +# scikit-matter to allow for interfacing with data stored in the metatensor +# format. +# +# Suppose we want to select the 10 most diverse environments for each chemical +# species. +# +# First, we can use the `keys_to_properties` operation in metatensor to move the +# neighbour species indices to the properties of the TensorBlocks. The resulting +# descriptor will be a TensorMap comprised of three blocks, one for each +# chemical species, where the chemical species indices are solely present in the +# keys. + + +print("----Atomic environment selection-----") +# Define the number of structures to select using FPS/CUR +n_envs = 25 + +print(atom_soap) +print(atom_soap.block(0)) + +# %% Now let's perform sample selection on the atomic environments. We want to +# select 10 atomic environments for each chemical species. + +# Define the number of structures *per block* to select using FPS +n_envs = 10 + +# FPS sample selection +selector_atomic_fps = sample_selection.FPS(n_to_select=n_envs, initialize="random").fit( + atom_soap +) + +# Print the selected envs for each block +print("atomic envs selected with FPS:\n") +for key, block in selector_atomic_fps.support.items(): + print("species_center:", key, "\n(struct_idx, atom_idx)\n", block.samples.values) + +selector_atomic_cur = sample_selection.CUR(n_to_select=n_envs).fit(atom_soap) +# Print the selected envs for each block +print("atomic envs selected with CUR:\n") +for key, block in selector_atomic_cur.support.items(): + print("species_center:", key, "\n(struct_idx, atom_idx)\n", block.samples.values) + + +# %% +# Selecting from a combined pool of atomic environments +# ----------------------------------------------------- +# +# One can also select from a combined pool of atomic environments and +# structures, instead of selecting an equal number of atomic environments for +# each chemical species. In this case, we can move the 'species_center' key to samples +# such that our descriptor is a TensorMap consisting of a single block. Upon +# sample selection, the most diverse atomic environments will be selected, +# regardless of their chemical species. +print("----All atomic environment selection-----") + +print("keys", atom_soap.keys) +print("blocks", atom_soap[0]) +print("samples in first block", atom_soap[0].samples) + +# Using the original SOAP descriptor, move all keys to properties. + + +# Define the number of structures to select using FPS +n_envs = 10 + +# FPS sample selection +selector_atomic_fps = sample_selection.FPS(n_to_select=n_envs, initialize="random").fit( + atom_soap_single_block +) +print( + "atomic envs selected with FPS: \n (struct_idx, atom_idx, species_center) \n", + selector_atomic_fps.support.block(0).samples.values, +) + + +# %% +# Perform structure (i.e. sample) selection with FPS/CUR +# --------------------------------------------------------- +# +# Instead of atomic environments, one can also select diverse structures. We can +# use the `sum_over_samples` operation in metatensor to define features in the +# structural basis instead of the atomic basis. This is done by summing over the +# atomic environments, labeled by the 'center' index in the samples of the +# TensorMap. +# +# Alternatively, one could use the `mean_over_samples` operation, depending on +# the specific inhomogeneity of the size of the structures in the training set. + +print("----Structure selection-----") + +# Define the number of structures to select *per block* using FPS +n_structures = 10 + +# FPS structure selection +selector_struct_fps = sample_selection.FPS( + n_to_select=n_structures, initialize="random" +).fit(struct_soap) +struct_fps_idxs = selector_struct_fps.support.block(0).samples.values.flatten() + +print("structures selected with FPS:\n", struct_fps_idxs) + +# CUR structure selection +selector_struct_cur = sample_selection.CUR(n_to_select=n_structures).fit(struct_soap) +struct_cur_idxs = selector_struct_cur.support.block(0).samples.values.flatten() +print("structures selected with CUR:\n", struct_cur_idxs) + + +# Slice structure descriptor along axis 0 to contain only the selected structures +struct_soap_fps = struct_soap.block(0).values[struct_fps_idxs, :] +struct_soap_cur = struct_soap.block(0).values[struct_cur_idxs, :] +assert struct_soap_fps.shape == struct_soap_cur.shape + +print("Structure descriptor shape before selection ", struct_soap.block(0).values.shape) +print("Structure descriptor shape after selection (FPS)", struct_soap_fps.shape) +print("Structure descriptor shape after selection (CUR)", struct_soap_cur.shape) + + +# %% +# Visualize selected structures +# ----------------------------- +# +# sklearn can be used to perform PCA dimensionality reduction on the SOAP +# descriptors. The resulting PC coordinates can be used to visualize the the +# data alongside their structures in a chemiscope widget. +# + +# Generate a structure PCA +struct_soap_pca = PCA(n_components=2).fit_transform(struct_soap.block(0).values) +assert struct_soap_pca.shape == (n_frames, 2) + + +# %% +# Plot the PCA map +# ~~~~~~~~~~~~~~~~ +# +# Notice how the selected points avoid the densely-sampled area, and cover +# the periphery of the dataset + +# Matplotlib plot +fig, ax = plt.subplots(1, 1, figsize=(6, 4)) +scatter = ax.scatter(struct_soap_pca[:, 0], struct_soap_pca[:, 1], c="red") +ax.plot( + struct_soap_pca[struct_cur_idxs, 0], + struct_soap_pca[struct_cur_idxs, 1], + "ko", + fillstyle="none", + label="FPS selection", +) +ax.set_xlabel("PCA[1]") +ax.set_ylabel("PCA[2]") +ax.legend() +fig.show() + + +# %% +# Creates a chemiscope viewer +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# + +# Selected level +selection_levels = [] +for i in range(len(frames)): + level = 0 + if i in struct_cur_idxs: + level += 1 + if i in struct_fps_idxs: + level += 2 + if level == 0: + level = "Not selected" + elif level == 1: + level = "CUR" + elif level == 2: + level = "FPS" + else: + level = "FPS+CUR" + selection_levels.append(level) + +properties = chemiscope.extract_properties(frames) + +properties.update( + { + "PC1": struct_soap_pca[:, 0], + "PC2": struct_soap_pca[:, 1], + "selection": np.array(selection_levels), + } +) + +widget = chemiscope.show( + frames, + properties=properties, + settings={ + "map": { + "x": {"property": "PC1"}, + "y": {"property": "PC2"}, + "color": {"property": "energy"}, + "symbol": "selection", + "size": {"factor": 50}, + }, + "structure": [{"unitCell": True}], + }, +) +widget.save("sample-selection.json.gz") + +# display, if in notebook or sphinx +widget + +# %% +# Perform feature selection +# ------------------------- +# +# Now perform feature selection. In this example we will go back to using the +# descriptor decomposed into atomic environments, as opposed to the one +# decomposed into structure environments, but only use FPS for brevity. +print("----Feature selection-----") + +# Define the number of features to select +n_features = 200 + +# FPS feature selection +feat_fps = feature_selection.FPS(n_to_select=n_features, initialize="random").fit( + atom_soap_single_block +) + +# Slice atomic descriptor along axis 1 to contain only the selected features +# atom_soap_single_block_fps = atom_soap_single_block.block(0).values[:, feat_fps_idxs] +atom_soap_single_block_fps = metatensor.slice( + atom_soap_single_block, + axis="properties", + labels=feat_fps.support.block(0).properties, +) + +print( + "atomic descriptor shape before selection ", + atom_soap_single_block.block(0).values.shape, +) +print( + "atomic descriptor shape after selection ", + atom_soap_single_block_fps.block(0).values.shape, +) + +# %% + +# %% +# Perform feature selection (skmatter) +# ------------------------------------ +# +# Now perform feature selection. In this example we will go back to using the +# descriptor decomposed into atomic environments, as opposed to the one +# decomposed into structure environments, but only use FPS for brevity. + +print("----Feature selection (skmatter)-----") + +# Define the number of features to select +n_features = 200 + +# FPS feature selection +feat_fps = skfeat_selection.FPS(n_to_select=n_features, initialize="random").fit( + atom_soap_single_block.block(0).values +) +feat_fps_idxs = feat_fps.selected_idx_ + +print("Feature indices obtained with FPS ", feat_fps_idxs) + +# Slice atomic descriptor along axis 1 to contain only the selected features +atom_dscrptr_fps = atom_soap_single_block.block(0).values[:, feat_fps_idxs] + +print( + "atomic descriptor shape before selection ", + atom_soap_single_block.block(0).values.shape, +) +print("atomic descriptor shape after selection ", atom_dscrptr_fps.shape) + +# %% diff --git a/_downloads/5277b730cb28e8c8301658e8d74988d3/thermostats.py b/_downloads/5277b730cb28e8c8301658e8d74988d3/thermostats.py new file mode 100644 index 00000000..606c5a22 --- /dev/null +++ b/_downloads/5277b730cb28e8c8301658e8d74988d3/thermostats.py @@ -0,0 +1,903 @@ +""" +Constant-temperature MD and thermostats +======================================= + +:Authors: Michele Ceriotti `@ceriottm `_ + +This recipe gives a practical introduction to finite-temperature +molecular dynamics simulations, and provides a guide to choose the +most appropriate thermostat for the simulation at hand. + +As for other examples in the cookbook, a small simulation of liquid +water is used as an archetypal example. Molecular dynamics, sampling, +and constant-temperature simulations are discussed in much detail in +the book "Understanding Molecular Simulations" by Daan Frenkel and Berend Smit. +This +`seminal paper by H.C.Andersen `_ +provides a good historical introduction to the problem of +thermostatting, and this +`PhD thesis +`_ +provides a more detailed background to several of the techniques +discussed in this recipe. +""" + +import os + +# %% +import subprocess +import time +import xml.etree.ElementTree as ET + +import chemiscope +import ipi +import matplotlib as mpl +import matplotlib.pyplot as plt +import numpy as np +from ipi.utils.tools.acf_xyz import compute_acf_xyz +from ipi.utils.tools.gle import get_gle_matrices, gle_frequency_kernel, isra_deconvolute + + +# %% +# Constant-temperature sampling of (thermo)dynamics +# ------------------------------------------------- +# +# Even though Hamilton's equations in classical mechanics conserve the total +# energy of the group of atoms in a simulation, experimental boundary conditions +# usually involve exchange of heat with the surroundings, especially when considering +# the relatively small supercells that are often used in simulations. +# +# The goal of a constant-temperature MD simulation is to compute efficiently thermal +# averages of the form :math:`\langle A(q,p)\rangle_\beta`, where the average +# of the observable :math:`A(q,p)` is +# evaluated over the Boltzmann distribution at inverse temperature +# :math:`\beta=1/k_\mathrm{B}T`, +# :math:`P(q,p)=Q^{-1} \exp(-\beta(p^2/2m + V(q)))` +# In all these scenarios, optimizing the simulation involves reducing as much as +# possible the *autocorrelation time* of the observable. +# +# Constant-temperature sampling is also important when one wants to compute +# *dynamical* properties. In principle these would require +# constant-energy trajectories, as any thermostatting procedure modifies +# the dynamics of the system. However, the initial conditions +# should usually be determined from constant-temperature conditions, +# averaging over multiple constant-energy trajectories. +# As we shall see, this protocol can often be simplified greatly, by choosing +# thermostats that don't interfere with the natural microscopic dynamics. + +# %% +# Running simulations +# ~~~~~~~~~~~~~~~~~~~ +# +# We use `i-PI `_ together with a ``LAMMPS`` driver to run +# all the simulations in this recipe. The two codes need to be run separately, +# and communicate atomic positions, energy and forces through a socket interface. +# +# The LAMMPS input defines the parameters of the +# `q-TIP4P/f water model `_, +# while the XML-formatted input of i-PI describes the setup of the +# MD simulation. +# +# We begin running a constant-energy calculation, that +# we will use to illustrate the metrics that can be applied to +# assess the performance of a thermostatting scheme. If it is the +# first time you see an ``i-PI`` input, you may want to look at +# the input file side-by-sidewith the +# `input reference `_. + +# Open and read the XML file +with open("data/input_nve.xml", "r") as file: + xml_content = file.read() +print(xml_content) + +# %% +# The part of the input that describes the molecular dynamics integrator +# is the ``motion`` class. For this run, it specifies an *NVE* ensemble, and +# a ``timestep`` of 1 fs for the integrator. + +xmlroot = ET.parse("data/input_nve.xml").getroot() +print(" " + ET.tostring(xmlroot.find(".//motion"), encoding="unicode")) + +# %% +# Note that this -- and other runs in this example -- are too short to +# provide quantitative results, and you may want to increase the +# ```` parameter so that the simulation runs for at least +# a few tens of ps. The time step of 1 fs is also at the limit of what +# is acceptable for running simulations of water. 0.5 fs would be a +# safer, stabler value. + + +# %% +# To launch i-PI and LAMMPS from the command line you can just +# execute the following commands +# +# .. code-block:: bash +# +# i-pi data/input_nve.xml > log & +# sleep 2 +# lmp -in data/in.lmp & +# +# To launch the external processes from a Python script +# proceed as follows: + +ipi_process = None +if not os.path.exists("simulation_nve.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input_nve.xml"]) + time.sleep(4) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(1)] + +# %% +# If you run this in a notebook, you can go ahead and start loading +# output files *before* i-PI and LAMMPS have finished running, by +# skipping this cell + +if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + + +# %% +# Analyzing the simulation +# ~~~~~~~~~~~~~~~~~~~~~~~~ +# +# After the simulation is finished, we can look at the outputs. +# The outputs include the trajectory of positions, the velocities +# and a number of energetic observables + +output_data, output_desc = ipi.read_output("simulation_nve.out") +traj_data = ipi.read_trajectory("simulation_nve.pos_0.xyz") + +# %% +# The trajectory shows mostly local vibrations on this short time scale, +# but if you re-run with a longer ```` settings you should be +# able to observe diffusing molecules in the liquid. + +chemiscope.show( + traj_data, + mode="structure", + settings=chemiscope.quick_settings( + trajectory=True, structure_settings={"unitCell": True} + ), +) + +# %% +# Potential and kinetic energy fluctuate, but the total energy is +# (almost) constant, the small fluctuations being due to integration +# errors, that are quite large with the long time step used for this +# example. If you run with smaller ```` values, you should +# see that the energy conservation condition is fulfilled with higher +# accuracy. + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["potential"] - output_data["potential"][0], + "b-", + label="Potential, $V$", +) +ax.plot( + output_data["time"], + output_data["kinetic_md"], + "r-", + label="Kinetic, $K$", +) +ax.plot( + output_data["time"], + output_data["conserved"] - output_data["conserved"][0], + "k-", + label="Conserved, $H$", +) +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"energy / eV") +ax.legend() +plt.show() + +# %% +# In a classical MD simulation, based on the momentum :math:`\mathbf{p}` +# of each atom, it is possible to evaluate its *kinetic temperature +# estimator* :math:`T=\langle \mathbf{p}^2/m \rangle /3k_B` the average is to +# be intended over a converged trajectory. Keep in mind that +# +# 1. The *instantaneous* value of this estimator is meaningless +# 2. It is only well-defined in a constant-temperature simulation, so here +# it only gives a sense of whether atomic momenta are close to what one +# would expect at 300 K. +# +# With these caveats in mind, we can observe that the simulation has higher +# velocities than expected at 300 K, and that there is no equipartition, the +# O atoms having on average a higher energy than the H atoms. + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["temperature(O)"], + "r-", + label="O atoms", +) +ax.plot( + output_data["time"], + output_data["temperature(H)"], + "c-", + label="H atoms", +) +ax.plot(output_data["time"], output_data["temperature"], "k-", label="All atoms") +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"$\tilde{T}$ / K") +ax.legend() +plt.show() + +# %% +# In order to investigate the dynamics more carefully, we +# compute the velocity-velocity autocorrelation function +# :math:`c_{vv}(t)=\sum_i \langle \mathbf{v}_i(t) \cdot \mathbf{v}_i(0) \rangle`. +# We use a utility function that reads the outputs of ``i-PI`` +# and computes both the autocorrelation function and its Fourier +# transform. +# :math:`c_{vv}(t)` contains information on the time scale and amplitude +# of molecular motion, and is closely related to the vibrational density +# of states and to spectroscopic observables such as IR and Raman spectra. + +acf_nve = compute_acf_xyz( + "simulation_nve.vel_0.xyz", + maximum_lag=600, + length_zeropadding=2000, + spectral_windowing="cosine-blackman", + timestep=1, + time_units="femtosecond", + skip=100, +) + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + acf_nve[0][:1200] * 2.4188843e-05, # atomic time to ps + acf_nve[1][:1200] * 1e5, + "r-", +) +ax.set_xlabel(r"$t$ / ps$") +ax.set_ylabel(r"$c_{vv}$ / arb. units") +plt.show() + +# %% +# The power spectrum (that can be computed as the Fourier transform of +# :math:`c_{vv}`) reveals the frequencies of stretching, bending and libration +# modes of water; the :math:`\omega\rightarrow 0` limit is proportional +# to the diffusion coefficient. +# We also load the results from a reference calculation (average of 8 +# trajectories initiated from NVT-equilibrated samples, shown as the +# confidence interval). You can see how to run these reference calculations +# from the script ``data/run_traj.sh``. +# The differences are due to the short trajectory, and to the fact that the +# NVE trajectory is not equilibrated at 300 K. + +ha2cm1 = 219474.63 + +# Loads reference trajectory +acf_ref = np.loadtxt("data/traj-all_facf.data") + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + +ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", +) + +ax.loglog(acf_nve[3][:1200] * ha2cm1, acf_nve[4][:1200] * 1e5, "r-", label="NVE") +ax.set_xlabel(r"$\omega$ / cm$^{-1}$") +ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") +ax.legend() +plt.show() + +# %% +# Langevin thermostatting +# ----------------------- +# +# In order to perform a simulations that samples configurations +# consistent with a Boltzmann distribution :math:`e^{-V(x)/k_B T}` +# one needs to modify the equations of motion. There are many +# different approaches to do this, some of which lead to deterministic +# dynamics; the two more widely used deterministic thermostats +# are the +# `Berendsen thermostat `_ +# which does not sample the Boltzmann distribution exactly and +# should never be used given the many more rigorous alternatives, +# and the Nosé-Hoover thermostat, that requires a +# `"chain" implementation `_ +# to be ergodic, which amounts essentially to a complicated way +# to generate poor-quality pseudo-random numbers. +# +# Given the limitations of deterministic thermostats, in this +# recipe we focus on stochastic thermostats, that model the +# coupling to the chaotic dynamics of an external bath through +# explicit random numbers. Langevin dynamics amounts to adding +# to Hamilton's equations of motion, for each degree of freedom, +# a term of the form +# +# .. math:: +# +# \dot{p} = -\gamma p + \sqrt{2\gamma m k_B T} \, \xi(t) +# +# where :math:` +# \gamma` is a friction coefficient, and :math:`\xi` +# uncorrelated random numbers that mimic collisions with the bath +# particles. The friction can be seen as the inverse of a +# characteristic *coupling time scale* +# :math:`\tau=1/\gamma` that describes how strongly the bath +# interacts with the system. + +# %% +# Setting up a thermostat in ``i-PI`` +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# In order to set up a thermostat in ``i-PI``, one simply needs +# to adjust the ```` block, to perform ``nvt`` dynamics +# and include an appropriate ```` section. +# Here we use a very-strongly coupled Langevin thermostat, +# with :math:`\tau=10~fs`. + +xmlroot = ET.parse("data/input_higamma.xml").getroot() +print(" " + ET.tostring(xmlroot.find(".//dynamics"), encoding="unicode")) + +# %% +# ``i-PI`` and ``LAMMPS`` are launched as above ... + +ipi_process = None +if not os.path.exists("simulation_higamma.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input_higamma.xml"]) + time.sleep(4) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(1)] + +# %% +# ... and you should probably wait until they're done, +# it'll take less than a minute. + +if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + +# %% +# Analysis of the trajectory +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# The temperature converges very quickly to the target value +# (fluctuations are to be expected, given that as discussed above +# the temperature estimator is just the instantaneous kinetic energy, +# that is not constant). There is also equipartition between O and H. + +output_data, output_desc = ipi.read_output("simulation_higamma.out") +traj_data = ipi.read_trajectory("simulation_higamma.pos_0.xyz") + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["temperature(O)"], + "r-", + label="O atoms", +) +ax.plot( + output_data["time"], + output_data["temperature(H)"], + "c-", + label="H atoms", +) +ax.plot(output_data["time"], output_data["temperature"], "k-", label="All atoms") +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"$\tilde{T}$ / K") +ax.legend() +plt.show() + + +# %% +# The velocity-velocity correlation function shows how much +# this thermostat affects the system dynamics. The high-frequency peaks, +# corresponding to stretches and bending, are +# greatly broadened, and the :math:`\omega\rightarrow 0` +# limit of :math:`\hat{c}_{vv}`, corresponding to the +# diffusion coefficient, is reduced by almost a factor of 5. +# This last observation highlights that a too-aggressive +# thermostat is not only disrupting the dynamics: +# it also slows down diffusion through phase space, +# making the dynamics less efficient at sampling slow, +# collective motions. We shall see further down various +# methods to counteract this effect, but in general one should +# use a weaker coupling, that improves the sampling of configuration +# space even though it slows down the convergence of the +# kinetic energy. If you want a thermostat that equilibrates +# aggressively the temperature while disturbing less the diffusive +# modes, you may try the *fast-forward Langevin* thermostat +# `(Hijazi et al., JCP (2018)) `_ +# that can be activated with the option ``mode="ffl"``. + +# compute the v-v acf +acf_higamma = compute_acf_xyz( + "simulation_higamma.vel_0.xyz", + maximum_lag=600, + length_zeropadding=2000, + spectral_windowing="cosine-blackman", + timestep=1, + time_units="femtosecond", + skip=100, +) + +# and plot +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", +) +ax.loglog( + acf_higamma[3][:1200] * ha2cm1, + acf_higamma[4][:1200] * 1e5, + "b-", + label=r"Langevin, $\tau=10$fs", +) +ax.set_xlabel(r"$\omega$ / cm$^{-1}$") +ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") +ax.legend() +plt.show() + +# %% +# Global thermostats: stochastic velocity rescaling +# ------------------------------------------------- +# +# An alternative approach to sample the canonical Boltzmann +# distribution while introducing fewer disturbances to the system +# dynamics is to use a *global* thermostat, i.e. a scheme that +# targets the *total* kinetic energy of the system, rather than that +# of individual degrees of freedom. +# We recommend the "stochastic velocity rescaling" thermostat +# `(Bussi, Donadio, Parrinello, JCP (2007)) `_ +# that acts by rescaling the total momentum vector, adding a +# suitably distributed random noise term. + + +# %% +# Setting up a thermostat in ``i-PI`` +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# Stochastic velocity rescaling is implemented in ``i-PI`` +# can be selected by setting ``mode="svr"``, and has a +# ``tau`` parameter that corresponds to the time scale of the +# coupling. + +xmlroot = ET.parse("data/input_svr.xml").getroot() +print(" " + ET.tostring(xmlroot.find(".//thermostat"), encoding="unicode")) + +# %% +# We run a simulation with the usual set up ... + +ipi_process = None +if not os.path.exists("simulation_svr.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input_svr.xml"]) + time.sleep(4) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(1)] + +# %% +# ... and wait for it to finish. + +if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + +# %% +# Analysis of the trajectory +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# The kinetic temperature of the trajectory equilibrates very +# rapidly to the target value. However, it takes a bit longer +# (approximately 0.5 ps) to reach equipartition between O and H +# atoms. This is an important shortcoming of global thermostats: +# since they only target the total kinetic energy, they must rely +# on internal energy redistribution to reach equilibrium between +# different degrees of freedom. +# Liquid water is a very ergodic system, in which all degrees of +# freedom are strongly coupled, so this is not a major issue. However +# care must be taken when modeling a quasi-harmonic crystal (e.g. +# diamond, a metal, or an inorganic crystal), or a molecular system +# in which the coupling between molecules is weaker (e.g. methane, +# or another apolar compound). + +output_data, output_desc = ipi.read_output("simulation_svr.out") +traj_data = ipi.read_trajectory("simulation_svr.pos_0.xyz") + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["temperature(O)"], + "r-", + label="O atoms", +) +ax.plot( + output_data["time"], + output_data["temperature(H)"], + "c-", + label="H atoms", +) +ax.plot(output_data["time"], output_data["temperature"], "k-", label="All atoms") +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"$\tilde{T}$ / K") +ax.legend() +plt.show() + + +# %% +# The velocity-velocity autocorrelation function is +# essentially indistinguishable from the reference, computed +# with an ensemble of NVE trajectories starting from canonical +# samples. In fact, the small discrepancies are mostly due to +# incomplete convergence of the averages in the short trajectory. +# +# This highlights the advantages of a global thermostat, that +# does not disrupt the natural diffusion in configuration space, +# and can often be used to compute dynamical, time-dependent +# observables out of a single trajectory -- which is far more +# practical than performing a collection of NVE trajectories. + +acf_svr = compute_acf_xyz( + "simulation_svr.vel_0.xyz", + maximum_lag=600, + length_zeropadding=2000, + spectral_windowing="cosine-blackman", + timestep=1, + time_units="femtosecond", + skip=100, +) + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", +) +ax.loglog( + acf_svr[3][:1200] * ha2cm1, + acf_svr[4][:1200] * 1e5, + "b-", + label=r"SVR, $\tau=10$fs", +) +ax.set_xlabel(r"$\omega$ / cm$^{-1}$") +ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") +ax.legend() +plt.show() + +# %% +# Generalized Langevin Equation thermostat +# ---------------------------------------- +# +# The issue with a Langevin thermostat is that, for a given coupling +# time :math:`\tau`, only molecular motions with a comparable time scale +# are sampled efficiently: faster modes are *underdamped*, and slower modes +# are *overdamped*, cf. the slowing down of diffusive behavior. +# +# A possible solution to this problem is using a +# *Generalized Langevin Equation (GLE)* thermostat. A GLE +# thermostat uses a matrix generalization of the Langevin term, +# in which the physical momentum is supplemented by a few fictitious +# momenta :math:`\mathbf{s}`, i.e. +# +# .. math:: +# +# (\dot{p},\dot{\mathbf{s}}) = -\mathbf{A}_p (p,\mathbf{s})\ +# +\mathbf{B}_p (\xi,\boldsymbol{\xi}) +# +# +# Here :math:`\mathbf{A}_p` is the *drift matrix* and :math:`\mathbf{B}_p` +# is a diffusion matrix which, for canonical sampling, is determined by the target +# temperature and the drift matrix through a fluctuation-dissipation relation. +# The key idea is that :math:`\mathbf{A}_p` provides a lot of flexibility in defining +# the behavior of the GLE, that can be tuned to achieve near-optimal sampling +# for every degree of freedom (effectively acting as if the coupling constant was +# tuned separately for slow and fast molecular motions). +# The general idea and the practical implementation are discussed in +# `(Ceriotti et al. JCTC (2010)) `_ +# which also discusses other applications of the same principle, including +# performing simulations with a non-equilibrium *quantum thermostat* that +# mimics the quantum the quantum mechanical behavior of light nuclei. + +# %% +# Setting up a thermostat in ``i-PI`` +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# A GLE thermostat can be activated using ``mode="gle"``. +# The drift matrix used here has been generated from the +# `GLE4MD website `_, using parameters that +# aim for the most efficient sampling possible with the short +# simulation time (2 ps). The `online generator +# `_ +# can be tuned to provide the best possible sampling for the system +# of interest, the most important parameter being the slowest time scale +# that one is interested in sampling (typically a fraction of the total +# simulation time). The range of frequencies that is optimized can then +# be tuned so as to reach, roughly, the maximum frequency present in the +# system. + +xmlroot = ET.parse("data/input_gle.xml").getroot() +print(" " + ET.tostring(xmlroot.find(".//thermostat"), encoding="unicode")) + +# %% +# We launch ``i-PI`` as usual ... + +ipi_process = None +if not os.path.exists("simulation_gle.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input_gle.xml"]) + time.sleep(4) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(1)] + +# %% +# ... and wait for simulations to finish. + +if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + +# %% +# Analysis of the trajectory +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# The kinetic temperature equilibrates quickly to the target value. +# Since the GLE is a local thermostat, targeting each degree of freedom +# separately, equipartition is also reached quickly. Sampling is less +# fast than with an aggressive Langevin thermostat, because the GLE targets +# each vibrational frequency separately, to minimize the impact on diffusion. +output_data, output_desc = ipi.read_output("simulation_gle.out") +traj_data = ipi.read_trajectory("simulation_gle.pos_0.xyz") + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["temperature(O)"], + "r-", + label="O atoms", +) +ax.plot( + output_data["time"], + output_data["temperature(H)"], + "c-", + label="H atoms", +) +ax.plot(output_data["time"], output_data["temperature"], "k-", label="All atoms") +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"$\tilde{T}$ / K") +ax.legend() +plt.show() + + +# %% +# :math:`\hat{c}_{vv}` reflects the adaptive behavior of the GLE. +# The fast modes are damped aggressively, leading to a large +# broadening of the high frequency peaks, but librations and diffusive +# modes are much less dampened than in the high-coupling Langevin case. +# An optimal-coupling GLE is a safe choice to sample any system, from +# molecular liquids to harmonic crystals, although a stochastic velocity +# rescaling is preferable if one is interested in preserving the natural +# dynamics. + +acf_gle = compute_acf_xyz( + "simulation_gle.vel_0.xyz", + maximum_lag=600, + length_zeropadding=2000, + spectral_windowing="cosine-blackman", + timestep=1, + time_units="femtosecond", + skip=100, +) + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", +) +ax.loglog( + acf_gle[3][:1200] * ha2cm1, + acf_gle[4][:1200] * 1e5, + "b-", + label=r"GLE", +) +ax.set_xlabel(r"$\omega$ / cm$^{-1}$") +ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") +ax.legend() +plt.show() + +# %% +# R-L purification +# ~~~~~~~~~~~~~~~~ +# +# What if you also want to extract dynamical information from a GLE +# (or Langevin) trajectory? It is actually possible to post-process the +# power spectrum, performing a deconvolution based on the amount of +# disturbance introduced by the GLE, that can be predicted analytically +# in the harmonic limit. +# The idea, discussed in `(Rossi et al., JCP (2018)) +# `_ +# is that if :math:`\hat{y}(\omega)` is the "natural" NVE power +# spectrum, and :math:`k_{\mathrm{GLE}}(\omega_0, \omega)` is the power +# spectrum predicted for a harmonic oscillator of frequency :math:`\omega_0`, +# then the spectrum from the GLE dynamics will be approximately +# +# .. math:: +# +# \hat{y}_{\mathrm{GLE}}(\omega) = \int \mathrm{d}\omega' +# k_{\mathrm{GLE}}(\omega', \omega) \hat{y}(\omega') +# +# The kernel can be computed analytically for all frequencies that +# are relevant for the power spectrum, based on the GLE parameters +# extracted from the input of ``i-PI``. + +n_omega = 1200 +Ap, Cp, Dp = get_gle_matrices("data/input_gle.xml") +gle_kernel = gle_frequency_kernel(acf_gle[3][:n_omega], Ap, Dp) + + +lomega = acf_gle[3][:n_omega] * ha2cm1 +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +levels = np.logspace(np.log10(gle_kernel.min()), np.log10(gle_kernel.max()), num=50) +contour = ax.contourf(lomega, lomega, gle_kernel, norm=mpl.colors.LogNorm()) +ax.set_xscale("log") +ax.set_yscale("log") +ax.set_xlabel(r"$\omega_0$ / cm$^{-1}$") +ax.set_ylabel(r"$\omega$ / cm$^{-1}$") +ax.set_xlim(10, 5000) +ax.set_ylim(10, 5000) +cbar = fig.colorbar(contour, ticks=[1e1, 1e3, 1e5, 1e7]) + +# %% +# The deconvolution is based on the Iterative Image Space +# Reconstruction Algorithm, which preserves the positive-definiteness +# of the spectrum + +isra_acf, history, errors, laplace = isra_deconvolute( + acf_gle[3][:n_omega], acf_gle[4][:n_omega], gle_kernel, 64, 4 +) + +# %% +# Even though the ISRA algorithm is less prone to enhancing noise than +# other deconvolution algorithms, successive iterations sharpen the spectrum +# but introduce higher and higher levles of noise, particularly on the +# low-frequency end of the spectrum so one has to choose when to stop. + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.loglog( + acf_gle[3][:1200] * ha2cm1, + acf_gle[4][:1200] * 1e5, + "b-", + label=r"GLE", +) +ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[0] * 1e5, + ":", + color="#4000D0", + label=r"iter[1]", +) +ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[2] * 1e5, + ":", + color="#A000A0", + label=r"iter[9]", +) +ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[4] * 1e5, + ":", + color="#D00040", + label=r"iter[17]", +) +ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[12] * 1e5, + ":", + color="#FF0000", + label=r"iter[49]", +) + +ax.set_xlabel(r"$\omega$ / cm$^{-1}$") +ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") +ax.legend() +plt.show() + +# %% +# Especially in the high-frequency region, the deconvolution +# algorithm succees in recovering the underlying NVE dynamics, +# which can be useful whenever one wants to optimize statistical +# efficiency while still being able to estimate dynamical +# properties. + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", +) +ax.loglog( + acf_gle[3][:1200] * ha2cm1, + acf_gle[4][:1200] * 1e5, + "b-", + label=r"GLE", +) +ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[2] * 1e5, + "r-", + label=r"GLE$\rightarrow$ NVE (iter[5])", +) +ax.set_xlabel(r"$\omega$ / cm$^{-1}$") +ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") +ax.legend() +plt.show() + + +# %% +# Running with LAMMPS +# ~~~~~~~~~~~~~~~~~~~ +# +# GLE thermostats (as well as conventional Langevin, and +# stochastic velocity rescaling) are also implemented natively +# in ``LAMMPS``. +# +# An example of ``LAMMPS`` input containing a GLE thermostat can +# be found in ``data/gle.lmp``. See also the +# `documentation of the fix gle command +# `_ +# +# .. code-block:: text +# +# fix 1 all gle 6 300 300 31415 data/smart.A +# +# The drift matrix can be obtained from the same website, simply +# asking to output the matrix in raw format, choosing units consistent +# with the ``LAMMPS`` settings, e.g. for this `optimal sampling setup +# `_ +# + +# %% +# We can run ``LAMMPS`` from the command line +# +# .. code-block:: bash +# +# lmp -in data/gle.lmp & +# +# or from Python + +lmp_process = None +if not os.path.exists("lammps_out.dat"): + lmp_process = subprocess.Popen(["lmp", "-in", "data/gle.lmp"]) + +# %% +# ... and wait +# + +if lmp_process is not None: + lmp_process.wait() + +# %% +# The simulation is much faster (for such a small system and +# cheap potential the overhead of ``i-PI``'s client-server mechanism +# is substantial) and leads to similar results for the kinetic temperature +# + +traj_data = np.loadtxt("lammps_out.dat") + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + traj_data[:, 0] * 1e-3, + traj_data[:, 1], + "k-", + label="All atoms", +) +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"$\tilde{T}$ / K") +ax.legend() +plt.show() diff --git a/_downloads/54cb049367bea2b1604e2df18dc055b4/sample-selection.ipynb b/_downloads/54cb049367bea2b1604e2df18dc055b4/sample-selection.ipynb new file mode 100644 index 00000000..f406c136 --- /dev/null +++ b/_downloads/54cb049367bea2b1604e2df18dc055b4/sample-selection.ipynb @@ -0,0 +1,241 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Sample and Feature Selection with FPS and CUR\n\n:Authors: Davide Tisi [@DavideTisi](https://github.com/DavideTisi)\n\nIn this tutorial we generate descriptors using rascaline, then select a subset\nof structures using both the farthest-point sampling (FPS) and CUR algorithms\nimplemented in scikit-matter. Finally, we also generate a selection of\nthe most important features using the same techniques.\n\nFirst, import all the necessary packages\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import ase.io\nimport chemiscope\nimport metatensor\nimport numpy as np\nfrom equisolve.numpy import feature_selection, sample_selection\nfrom matplotlib import pyplot as plt\nfrom rascaline import SoapPowerSpectrum\nfrom sklearn.decomposition import PCA\nfrom skmatter import feature_selection as skfeat_selection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Load molecular data\n\nLoad 500 example BTO structures from file, reading them using\n[ASE](https://wiki.fysik.dtu.dk/ase/).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Load a subset of :download:`structures ` of the example dataset\nn_frames = 500\nframes = ase.io.read(\"input-fps.xyz\", f\":{n_frames}\", format=\"extxyz\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute SOAP descriptors using rascaline\n\nFirst, define the rascaline hyperparameters used to compute SOAP.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# rascaline hyperparameters\nhypers = {\n \"cutoff\": 6.0,\n \"max_radial\": 8,\n \"max_angular\": 6,\n \"atomic_gaussian_width\": 0.3,\n \"cutoff_function\": {\"ShiftedCosine\": {\"width\": 0.5}},\n \"radial_basis\": {\"Gto\": {\"accuracy\": 1e-6}},\n \"radial_scaling\": {\"Willatt2018\": {\"exponent\": 4, \"rate\": 1, \"scale\": 3.5}},\n \"center_atom_weight\": 1.0,\n}\n\n# Generate a SOAP power spectrum\ncalculator = SoapPowerSpectrum(**hypers)\nrho2i = calculator.compute(frames)\n\n\n# Makes a dense block\natom_soap = rho2i.keys_to_properties([\"species_neighbor_1\", \"species_neighbor_2\"])\n\natom_soap_single_block = atom_soap.keys_to_samples(keys_to_move=[\"species_center\"])\n\n# Sum over atomic centers to compute structure features\nstruct_soap = metatensor.sum_over_samples(\n atom_soap_single_block, sample_names=[\"center\", \"species_center\"]\n)\n\n\nprint(\"atom feature descriptor shape:\", atom_soap.block(0).values.shape)\nprint(\n \"atom feature descriptor (all in one block) shape:\",\n atom_soap_single_block.block(0).values.shape,\n)\nprint(\"structure feature descriptor shape:\", struct_soap.block(0).values.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Perform atomic environment (i.e. sample) selection\n\nUsing FPS and CUR algorithms, we can perform selection of atomic environments.\nThese are implemented in equisolve, which provides a wrapper around\nscikit-matter to allow for interfacing with data stored in the metatensor\nformat.\n\nSuppose we want to select the 10 most diverse environments for each chemical\nspecies.\n\nFirst, we can use the `keys_to_properties` operation in metatensor to move the\nneighbour species indices to the properties of the TensorBlocks. The resulting\ndescriptor will be a TensorMap comprised of three blocks, one for each\nchemical species, where the chemical species indices are solely present in the\nkeys.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"----Atomic environment selection-----\")\n# Define the number of structures to select using FPS/CUR\nn_envs = 25\n\nprint(atom_soap)\nprint(atom_soap.block(0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "select 10 atomic environments for each chemical species.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Define the number of structures *per block* to select using FPS\nn_envs = 10\n\n# FPS sample selection\nselector_atomic_fps = sample_selection.FPS(n_to_select=n_envs, initialize=\"random\").fit(\n atom_soap\n)\n\n# Print the selected envs for each block\nprint(\"atomic envs selected with FPS:\\n\")\nfor key, block in selector_atomic_fps.support.items():\n print(\"species_center:\", key, \"\\n(struct_idx, atom_idx)\\n\", block.samples.values)\n\nselector_atomic_cur = sample_selection.CUR(n_to_select=n_envs).fit(atom_soap)\n# Print the selected envs for each block\nprint(\"atomic envs selected with CUR:\\n\")\nfor key, block in selector_atomic_cur.support.items():\n print(\"species_center:\", key, \"\\n(struct_idx, atom_idx)\\n\", block.samples.values)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Selecting from a combined pool of atomic environments\n\nOne can also select from a combined pool of atomic environments and\nstructures, instead of selecting an equal number of atomic environments for\neach chemical species. In this case, we can move the 'species_center' key to samples\nsuch that our descriptor is a TensorMap consisting of a single block. Upon\nsample selection, the most diverse atomic environments will be selected,\nregardless of their chemical species.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"----All atomic environment selection-----\")\n\nprint(\"keys\", atom_soap.keys)\nprint(\"blocks\", atom_soap[0])\nprint(\"samples in first block\", atom_soap[0].samples)\n\n# Using the original SOAP descriptor, move all keys to properties.\n\n\n# Define the number of structures to select using FPS\nn_envs = 10\n\n# FPS sample selection\nselector_atomic_fps = sample_selection.FPS(n_to_select=n_envs, initialize=\"random\").fit(\n atom_soap_single_block\n)\nprint(\n \"atomic envs selected with FPS: \\n (struct_idx, atom_idx, species_center) \\n\",\n selector_atomic_fps.support.block(0).samples.values,\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Perform structure (i.e. sample) selection with FPS/CUR\n\nInstead of atomic environments, one can also select diverse structures. We can\nuse the `sum_over_samples` operation in metatensor to define features in the\nstructural basis instead of the atomic basis. This is done by summing over the\natomic environments, labeled by the 'center' index in the samples of the\nTensorMap.\n\nAlternatively, one could use the `mean_over_samples` operation, depending on\nthe specific inhomogeneity of the size of the structures in the training set.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"----Structure selection-----\")\n\n# Define the number of structures to select *per block* using FPS\nn_structures = 10\n\n# FPS structure selection\nselector_struct_fps = sample_selection.FPS(\n n_to_select=n_structures, initialize=\"random\"\n).fit(struct_soap)\nstruct_fps_idxs = selector_struct_fps.support.block(0).samples.values.flatten()\n\nprint(\"structures selected with FPS:\\n\", struct_fps_idxs)\n\n# CUR structure selection\nselector_struct_cur = sample_selection.CUR(n_to_select=n_structures).fit(struct_soap)\nstruct_cur_idxs = selector_struct_cur.support.block(0).samples.values.flatten()\nprint(\"structures selected with CUR:\\n\", struct_cur_idxs)\n\n\n# Slice structure descriptor along axis 0 to contain only the selected structures\nstruct_soap_fps = struct_soap.block(0).values[struct_fps_idxs, :]\nstruct_soap_cur = struct_soap.block(0).values[struct_cur_idxs, :]\nassert struct_soap_fps.shape == struct_soap_cur.shape\n\nprint(\"Structure descriptor shape before selection \", struct_soap.block(0).values.shape)\nprint(\"Structure descriptor shape after selection (FPS)\", struct_soap_fps.shape)\nprint(\"Structure descriptor shape after selection (CUR)\", struct_soap_cur.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Visualize selected structures\n\nsklearn can be used to perform PCA dimensionality reduction on the SOAP\ndescriptors. The resulting PC coordinates can be used to visualize the the\ndata alongside their structures in a chemiscope widget.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Generate a structure PCA\nstruct_soap_pca = PCA(n_components=2).fit_transform(struct_soap.block(0).values)\nassert struct_soap_pca.shape == (n_frames, 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plot the PCA map\n\nNotice how the selected points avoid the densely-sampled area, and cover\nthe periphery of the dataset\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Matplotlib plot\nfig, ax = plt.subplots(1, 1, figsize=(6, 4))\nscatter = ax.scatter(struct_soap_pca[:, 0], struct_soap_pca[:, 1], c=\"red\")\nax.plot(\n struct_soap_pca[struct_cur_idxs, 0],\n struct_soap_pca[struct_cur_idxs, 1],\n \"ko\",\n fillstyle=\"none\",\n label=\"FPS selection\",\n)\nax.set_xlabel(\"PCA[1]\")\nax.set_ylabel(\"PCA[2]\")\nax.legend()\nfig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Creates a chemiscope viewer\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Selected level\nselection_levels = []\nfor i in range(len(frames)):\n level = 0\n if i in struct_cur_idxs:\n level += 1\n if i in struct_fps_idxs:\n level += 2\n if level == 0:\n level = \"Not selected\"\n elif level == 1:\n level = \"CUR\"\n elif level == 2:\n level = \"FPS\"\n else:\n level = \"FPS+CUR\"\n selection_levels.append(level)\n\nproperties = chemiscope.extract_properties(frames)\n\nproperties.update(\n {\n \"PC1\": struct_soap_pca[:, 0],\n \"PC2\": struct_soap_pca[:, 1],\n \"selection\": np.array(selection_levels),\n }\n)\n\nwidget = chemiscope.show(\n frames,\n properties=properties,\n settings={\n \"map\": {\n \"x\": {\"property\": \"PC1\"},\n \"y\": {\"property\": \"PC2\"},\n \"color\": {\"property\": \"energy\"},\n \"symbol\": \"selection\",\n \"size\": {\"factor\": 50},\n },\n \"structure\": [{\"unitCell\": True}],\n },\n)\nwidget.save(\"sample-selection.json.gz\")\n\n# display, if in notebook or sphinx\nwidget" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Perform feature selection\n\nNow perform feature selection. In this example we will go back to using the\ndescriptor decomposed into atomic environments, as opposed to the one\ndecomposed into structure environments, but only use FPS for brevity.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"----Feature selection-----\")\n\n# Define the number of features to select\nn_features = 200\n\n# FPS feature selection\nfeat_fps = feature_selection.FPS(n_to_select=n_features, initialize=\"random\").fit(\n atom_soap_single_block\n)\n\n# Slice atomic descriptor along axis 1 to contain only the selected features\n# atom_soap_single_block_fps = atom_soap_single_block.block(0).values[:, feat_fps_idxs]\natom_soap_single_block_fps = metatensor.slice(\n atom_soap_single_block,\n axis=\"properties\",\n labels=feat_fps.support.block(0).properties,\n)\n\nprint(\n \"atomic descriptor shape before selection \",\n atom_soap_single_block.block(0).values.shape,\n)\nprint(\n \"atomic descriptor shape after selection \",\n atom_soap_single_block_fps.block(0).values.shape,\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Perform feature selection (skmatter)\n\nNow perform feature selection. In this example we will go back to using the\ndescriptor decomposed into atomic environments, as opposed to the one\ndecomposed into structure environments, but only use FPS for brevity.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"----Feature selection (skmatter)-----\")\n\n# Define the number of features to select\nn_features = 200\n\n# FPS feature selection\nfeat_fps = skfeat_selection.FPS(n_to_select=n_features, initialize=\"random\").fit(\n atom_soap_single_block.block(0).values\n)\nfeat_fps_idxs = feat_fps.selected_idx_\n\nprint(\"Feature indices obtained with FPS \", feat_fps_idxs)\n\n# Slice atomic descriptor along axis 1 to contain only the selected features\natom_dscrptr_fps = atom_soap_single_block.block(0).values[:, feat_fps_idxs]\n\nprint(\n \"atomic descriptor shape before selection \",\n atom_soap_single_block.block(0).values.shape,\n)\nprint(\"atomic descriptor shape after selection \", atom_dscrptr_fps.shape)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/579a8571a79bc457a528f6ee99701555/data.zip b/_downloads/579a8571a79bc457a528f6ee99701555/data.zip new file mode 100644 index 00000000..0f7f0f4a Binary files /dev/null and b/_downloads/579a8571a79bc457a528f6ee99701555/data.zip differ diff --git a/_downloads/58547081d5f0a1a26f167e9bb3a01b2c/thermostats.ipynb b/_downloads/58547081d5f0a1a26f167e9bb3a01b2c/thermostats.ipynb new file mode 100644 index 00000000..dcca2ef3 --- /dev/null +++ b/_downloads/58547081d5f0a1a26f167e9bb3a01b2c/thermostats.ipynb @@ -0,0 +1,672 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Constant-temperature MD and thermostats\n\n:Authors: Michele Ceriotti [@ceriottm](https://github.com/ceriottm/)\n\nThis recipe gives a practical introduction to finite-temperature\nmolecular dynamics simulations, and provides a guide to choose the\nmost appropriate thermostat for the simulation at hand.\n\nAs for other examples in the cookbook, a small simulation of liquid\nwater is used as an archetypal example. Molecular dynamics, sampling,\nand constant-temperature simulations are discussed in much detail in\nthe book \"Understanding Molecular Simulations\" by Daan Frenkel and Berend Smit.\nThis\n[seminal paper by H.C.Andersen](https://doi.org/10.1063/1.439486)\nprovides a good historical introduction to the problem of\nthermostatting, and this\n[PhD thesis](https://www.research-collection.ethz.ch/handle/20.500.11850/152344)\nprovides a more detailed background to several of the techniques\ndiscussed in this recipe.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import subprocess\nimport time\nimport xml.etree.ElementTree as ET\n\nimport chemiscope\nimport ipi\nimport matplotlib as mpl\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom ipi.utils.tools.acf_xyz import compute_acf_xyz\nfrom ipi.utils.tools.gle import get_gle_matrices, gle_frequency_kernel, isra_deconvolute" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constant-temperature sampling of (thermo)dynamics\n\nEven though Hamilton's equations in classical mechanics conserve the total\nenergy of the group of atoms in a simulation, experimental boundary conditions\nusually involve exchange of heat with the surroundings, especially when considering\nthe relatively small supercells that are often used in simulations.\n\nThe goal of a constant-temperature MD simulation is to compute efficiently thermal\naverages of the form $\\langle A(q,p)\\rangle_\\beta$, where the average\nof the observable $A(q,p)$ is\nevaluated over the Boltzmann distribution at inverse temperature\n$\\beta=1/k_\\mathrm{B}T$,\n$P(q,p)=Q^{-1} \\exp(-\\beta(p^2/2m + V(q)))$\nIn all these scenarios, optimizing the simulation involves reducing as much as\npossible the *autocorrelation time* of the observable.\n\nConstant-temperature sampling is also important when one wants to compute\n*dynamical* properties. In principle these would require\nconstant-energy trajectories, as any thermostatting procedure modifies\nthe dynamics of the system. However, the initial conditions\nshould usually be determined from constant-temperature conditions,\naveraging over multiple constant-energy trajectories.\nAs we shall see, this protocol can often be simplified greatly, by choosing\nthermostats that don't interfere with the natural microscopic dynamics.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running simulations\n\nWe use [i-PI](http://ipi-code.org) together with a ``LAMMPS`` driver to run\nall the simulations in this recipe. The two codes need to be run separately,\nand communicate atomic positions, energy and forces through a socket interface.\n\nThe LAMMPS input defines the parameters of the\n[q-TIP4P/f water model](http://doi.org/10.1063/1.3167790),\nwhile the XML-formatted input of i-PI describes the setup of the\nMD simulation.\n\nWe begin running a constant-energy calculation, that\nwe will use to illustrate the metrics that can be applied to\nassess the performance of a thermostatting scheme. If it is the\nfirst time you see an ``i-PI`` input, you may want to look at\nthe input file side-by-sidewith the\n[input reference](https://docs.ipi-code.org/input-tags.html).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Open and read the XML file\nwith open(\"data/input_nve.xml\", \"r\") as file:\n xml_content = file.read()\nprint(xml_content)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The part of the input that describes the molecular dynamics integrator\nis the ``motion`` class. For this run, it specifies an *NVE* ensemble, and\na ``timestep`` of 1 fs for the integrator.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xmlroot = ET.parse(\"data/input_nve.xml\").getroot()\nprint(\" \" + ET.tostring(xmlroot.find(\".//motion\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that this -- and other runs in this example -- are too short to\nprovide quantitative results, and you may want to increase the\n```` parameter so that the simulation runs for at least\na few tens of ps. The time step of 1 fs is also at the limit of what\nis acceptable for running simulations of water. 0.5 fs would be a\nsafer, stabler value.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To launch i-PI and LAMMPS from the command line you can just\nexecute the following commands\n\n```bash\ni-pi data/input_nve.xml > log &\nsleep 2\nlmp -in data/in.lmp &\n```\nTo launch the external processes from a Python script\nproceed as follows:\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi_process = None\nif not os.path.exists(\"simulation_nve.out\"):\n ipi_process = subprocess.Popen([\"i-pi\", \"data/input_nve.xml\"])\n time.sleep(4) # wait for i-PI to start\n lmp_process = [subprocess.Popen([\"lmp\", \"-in\", \"data/in.lmp\"]) for i in range(1)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you run this in a notebook, you can go ahead and start loading\noutput files *before* i-PI and LAMMPS have finished running, by\nskipping this cell\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "if ipi_process is not None:\n ipi_process.wait()\n lmp_process[0].wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analyzing the simulation\n\nAfter the simulation is finished, we can look at the outputs.\nThe outputs include the trajectory of positions, the velocities\nand a number of energetic observables\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "output_data, output_desc = ipi.read_output(\"simulation_nve.out\")\ntraj_data = ipi.read_trajectory(\"simulation_nve.pos_0.xyz\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The trajectory shows mostly local vibrations on this short time scale,\nbut if you re-run with a longer ```` settings you should be\nable to observe diffusing molecules in the liquid.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "chemiscope.show(\n traj_data,\n mode=\"structure\",\n settings=chemiscope.quick_settings(\n trajectory=True, structure_settings={\"unitCell\": True}\n ),\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Potential and kinetic energy fluctuate, but the total energy is\n(almost) constant, the small fluctuations being due to integration\nerrors, that are quite large with the long time step used for this\nexample. If you run with smaller ```` values, you should\nsee that the energy conservation condition is fulfilled with higher\naccuracy.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"potential\"] - output_data[\"potential\"][0],\n \"b-\",\n label=\"Potential, $V$\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"kinetic_md\"],\n \"r-\",\n label=\"Kinetic, $K$\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"conserved\"] - output_data[\"conserved\"][0],\n \"k-\",\n label=\"Conserved, $H$\",\n)\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"energy / eV\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In a classical MD simulation, based on the momentum $\\mathbf{p}$\nof each atom, it is possible to evaluate its *kinetic temperature\nestimator* $T=\\langle \\mathbf{p}^2/m \\rangle /3k_B$ the average is to\nbe intended over a converged trajectory. Keep in mind that\n\n1. The *instantaneous* value of this estimator is meaningless\n2. It is only well-defined in a constant-temperature simulation, so here\n it only gives a sense of whether atomic momenta are close to what one\n would expect at 300 K.\n\nWith these caveats in mind, we can observe that the simulation has higher\nvelocities than expected at 300 K, and that there is no equipartition, the\nO atoms having on average a higher energy than the H atoms.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"temperature(O)\"],\n \"r-\",\n label=\"O atoms\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"temperature(H)\"],\n \"c-\",\n label=\"H atoms\",\n)\nax.plot(output_data[\"time\"], output_data[\"temperature\"], \"k-\", label=\"All atoms\")\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"$\\tilde{T}$ / K\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to investigate the dynamics more carefully, we\ncompute the velocity-velocity autocorrelation function\n$c_{vv}(t)=\\sum_i \\langle \\mathbf{v}_i(t) \\cdot \\mathbf{v}_i(0) \\rangle$.\nWe use a utility function that reads the outputs of ``i-PI``\nand computes both the autocorrelation function and its Fourier\ntransform.\n$c_{vv}(t)$ contains information on the time scale and amplitude\nof molecular motion, and is closely related to the vibrational density\nof states and to spectroscopic observables such as IR and Raman spectra.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "acf_nve = compute_acf_xyz(\n \"simulation_nve.vel_0.xyz\",\n maximum_lag=600,\n length_zeropadding=2000,\n spectral_windowing=\"cosine-blackman\",\n timestep=1,\n time_units=\"femtosecond\",\n skip=100,\n)\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n acf_nve[0][:1200] * 2.4188843e-05, # atomic time to ps\n acf_nve[1][:1200] * 1e5,\n \"r-\",\n)\nax.set_xlabel(r\"$t$ / ps$\")\nax.set_ylabel(r\"$c_{vv}$ / arb. units\")\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The power spectrum (that can be computed as the Fourier transform of\n$c_{vv}$) reveals the frequencies of stretching, bending and libration\nmodes of water; the $\\omega\\rightarrow 0$ limit is proportional\nto the diffusion coefficient.\nWe also load the results from a reference calculation (average of 8\ntrajectories initiated from NVT-equilibrated samples, shown as the\nconfidence interval). You can see how to run these reference calculations\nfrom the script ``data/run_traj.sh``.\nThe differences are due to the short trajectory, and to the fact that the\nNVE trajectory is not equilibrated at 300 K.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ha2cm1 = 219474.63\n\n# Loads reference trajectory\nacf_ref = np.loadtxt(\"data/traj-all_facf.data\")\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\n\nax.fill_between(\n acf_ref[:1200, 0] * ha2cm1,\n (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5,\n (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5,\n color=\"gray\",\n label=\"reference\",\n)\n\nax.loglog(acf_nve[3][:1200] * ha2cm1, acf_nve[4][:1200] * 1e5, \"r-\", label=\"NVE\")\nax.set_xlabel(r\"$\\omega$ / cm$^{-1}$\")\nax.set_ylabel(r\"$\\hat{c}_{vv}$ / arb. units\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Langevin thermostatting\n\nIn order to perform a simulations that samples configurations\nconsistent with a Boltzmann distribution $e^{-V(x)/k_B T}$\none needs to modify the equations of motion. There are many\ndifferent approaches to do this, some of which lead to deterministic\ndynamics; the two more widely used deterministic thermostats\nare the\n[Berendsen thermostat](https://doi.org/10.1063/1.448118)\nwhich does not sample the Boltzmann distribution exactly and\nshould never be used given the many more rigorous alternatives,\nand the Nos\u00e9-Hoover thermostat, that requires a\n[\"chain\" implementation](https://doi.org/10.1063/1.463940)\nto be ergodic, which amounts essentially to a complicated way\nto generate poor-quality pseudo-random numbers.\n\nGiven the limitations of deterministic thermostats, in this\nrecipe we focus on stochastic thermostats, that model the\ncoupling to the chaotic dynamics of an external bath through\nexplicit random numbers. Langevin dynamics amounts to adding\nto Hamilton's equations of motion, for each degree of freedom,\na term of the form\n\n\\begin{align}\\dot{p} = -\\gamma p + \\sqrt{2\\gamma m k_B T} \\, \\xi(t)\\end{align}\n\nwhere $\n\\gamma$ is a friction coefficient, and $\\xi$\nuncorrelated random numbers that mimic collisions with the bath\nparticles. The friction can be seen as the inverse of a\ncharacteristic *coupling time scale*\n$\\tau=1/\\gamma$ that describes how strongly the bath\ninteracts with the system.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setting up a thermostat in ``i-PI``\n\nIn order to set up a thermostat in ``i-PI``, one simply needs\nto adjust the ```` block, to perform ``nvt`` dynamics\nand include an appropriate ```` section.\nHere we use a very-strongly coupled Langevin thermostat,\nwith $\\tau=10~fs$.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xmlroot = ET.parse(\"data/input_higamma.xml\").getroot()\nprint(\" \" + ET.tostring(xmlroot.find(\".//dynamics\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``i-PI`` and ``LAMMPS`` are launched as above ...\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi_process = None\nif not os.path.exists(\"simulation_higamma.out\"):\n ipi_process = subprocess.Popen([\"i-pi\", \"data/input_higamma.xml\"])\n time.sleep(4) # wait for i-PI to start\n lmp_process = [subprocess.Popen([\"lmp\", \"-in\", \"data/in.lmp\"]) for i in range(1)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and you should probably wait until they're done,\nit'll take less than a minute.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "if ipi_process is not None:\n ipi_process.wait()\n lmp_process[0].wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analysis of the trajectory\n\nThe temperature converges very quickly to the target value\n(fluctuations are to be expected, given that as discussed above\nthe temperature estimator is just the instantaneous kinetic energy,\nthat is not constant). There is also equipartition between O and H.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "output_data, output_desc = ipi.read_output(\"simulation_higamma.out\")\ntraj_data = ipi.read_trajectory(\"simulation_higamma.pos_0.xyz\")\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"temperature(O)\"],\n \"r-\",\n label=\"O atoms\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"temperature(H)\"],\n \"c-\",\n label=\"H atoms\",\n)\nax.plot(output_data[\"time\"], output_data[\"temperature\"], \"k-\", label=\"All atoms\")\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"$\\tilde{T}$ / K\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The velocity-velocity correlation function shows how much\nthis thermostat affects the system dynamics. The high-frequency peaks,\ncorresponding to stretches and bending, are\ngreatly broadened, and the $\\omega\\rightarrow 0$\nlimit of $\\hat{c}_{vv}$, corresponding to the\ndiffusion coefficient, is reduced by almost a factor of 5.\nThis last observation highlights that a too-aggressive\nthermostat is not only disrupting the dynamics:\nit also slows down diffusion through phase space,\nmaking the dynamics less efficient at sampling slow,\ncollective motions. We shall see further down various\nmethods to counteract this effect, but in general one should\nuse a weaker coupling, that improves the sampling of configuration\nspace even though it slows down the convergence of the\nkinetic energy. If you want a thermostat that equilibrates\naggressively the temperature while disturbing less the diffusive\nmodes, you may try the *fast-forward Langevin* thermostat\n[(Hijazi et al., JCP (2018))](https://doi.org/10.1063/1.5029833)\nthat can be activated with the option ``mode=\"ffl\"``.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# compute the v-v acf\nacf_higamma = compute_acf_xyz(\n \"simulation_higamma.vel_0.xyz\",\n maximum_lag=600,\n length_zeropadding=2000,\n spectral_windowing=\"cosine-blackman\",\n timestep=1,\n time_units=\"femtosecond\",\n skip=100,\n)\n\n# and plot\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.fill_between(\n acf_ref[:1200, 0] * ha2cm1,\n (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5,\n (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5,\n color=\"gray\",\n label=\"reference\",\n)\nax.loglog(\n acf_higamma[3][:1200] * ha2cm1,\n acf_higamma[4][:1200] * 1e5,\n \"b-\",\n label=r\"Langevin, $\\tau=10$fs\",\n)\nax.set_xlabel(r\"$\\omega$ / cm$^{-1}$\")\nax.set_ylabel(r\"$\\hat{c}_{vv}$ / arb. units\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Global thermostats: stochastic velocity rescaling\n\nAn alternative approach to sample the canonical Boltzmann\ndistribution while introducing fewer disturbances to the system\ndynamics is to use a *global* thermostat, i.e. a scheme that\ntargets the *total* kinetic energy of the system, rather than that\nof individual degrees of freedom.\nWe recommend the \"stochastic velocity rescaling\" thermostat\n[(Bussi, Donadio, Parrinello, JCP (2007))](https://doi.org/10.1063/1.2408420)\nthat acts by rescaling the total momentum vector, adding a\nsuitably distributed random noise term.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setting up a thermostat in ``i-PI``\n\nStochastic velocity rescaling is implemented in ``i-PI``\ncan be selected by setting ``mode=\"svr\"``, and has a\n``tau`` parameter that corresponds to the time scale of the\ncoupling.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xmlroot = ET.parse(\"data/input_svr.xml\").getroot()\nprint(\" \" + ET.tostring(xmlroot.find(\".//thermostat\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We run a simulation with the usual set up ...\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi_process = None\nif not os.path.exists(\"simulation_svr.out\"):\n ipi_process = subprocess.Popen([\"i-pi\", \"data/input_svr.xml\"])\n time.sleep(4) # wait for i-PI to start\n lmp_process = [subprocess.Popen([\"lmp\", \"-in\", \"data/in.lmp\"]) for i in range(1)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and wait for it to finish.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "if ipi_process is not None:\n ipi_process.wait()\n lmp_process[0].wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analysis of the trajectory\n\nThe kinetic temperature of the trajectory equilibrates very\nrapidly to the target value. However, it takes a bit longer\n(approximately 0.5 ps) to reach equipartition between O and H\natoms. This is an important shortcoming of global thermostats:\nsince they only target the total kinetic energy, they must rely\non internal energy redistribution to reach equilibrium between\ndifferent degrees of freedom.\nLiquid water is a very ergodic system, in which all degrees of\nfreedom are strongly coupled, so this is not a major issue. However\ncare must be taken when modeling a quasi-harmonic crystal (e.g.\ndiamond, a metal, or an inorganic crystal), or a molecular system\nin which the coupling between molecules is weaker (e.g. methane,\nor another apolar compound).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "output_data, output_desc = ipi.read_output(\"simulation_svr.out\")\ntraj_data = ipi.read_trajectory(\"simulation_svr.pos_0.xyz\")\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"temperature(O)\"],\n \"r-\",\n label=\"O atoms\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"temperature(H)\"],\n \"c-\",\n label=\"H atoms\",\n)\nax.plot(output_data[\"time\"], output_data[\"temperature\"], \"k-\", label=\"All atoms\")\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"$\\tilde{T}$ / K\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The velocity-velocity autocorrelation function is\nessentially indistinguishable from the reference, computed\nwith an ensemble of NVE trajectories starting from canonical\nsamples. In fact, the small discrepancies are mostly due to\nincomplete convergence of the averages in the short trajectory.\n\nThis highlights the advantages of a global thermostat, that\ndoes not disrupt the natural diffusion in configuration space,\nand can often be used to compute dynamical, time-dependent\nobservables out of a single trajectory -- which is far more\npractical than performing a collection of NVE trajectories.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "acf_svr = compute_acf_xyz(\n \"simulation_svr.vel_0.xyz\",\n maximum_lag=600,\n length_zeropadding=2000,\n spectral_windowing=\"cosine-blackman\",\n timestep=1,\n time_units=\"femtosecond\",\n skip=100,\n)\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.fill_between(\n acf_ref[:1200, 0] * ha2cm1,\n (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5,\n (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5,\n color=\"gray\",\n label=\"reference\",\n)\nax.loglog(\n acf_svr[3][:1200] * ha2cm1,\n acf_svr[4][:1200] * 1e5,\n \"b-\",\n label=r\"SVR, $\\tau=10$fs\",\n)\nax.set_xlabel(r\"$\\omega$ / cm$^{-1}$\")\nax.set_ylabel(r\"$\\hat{c}_{vv}$ / arb. units\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generalized Langevin Equation thermostat\n\nThe issue with a Langevin thermostat is that, for a given coupling\ntime $\\tau$, only molecular motions with a comparable time scale\nare sampled efficiently: faster modes are *underdamped*, and slower modes\nare *overdamped*, cf. the slowing down of diffusive behavior.\n\nA possible solution to this problem is using a\n*Generalized Langevin Equation (GLE)* thermostat. A GLE\nthermostat uses a matrix generalization of the Langevin term,\nin which the physical momentum is supplemented by a few fictitious\nmomenta $\\mathbf{s}$, i.e.\n\n\\begin{align}(\\dot{p},\\dot{\\mathbf{s}}) = -\\mathbf{A}_p (p,\\mathbf{s})\\\n +\\mathbf{B}_p (\\xi,\\boldsymbol{\\xi})\\end{align}\n\n\nHere $\\mathbf{A}_p$ is the *drift matrix* and $\\mathbf{B}_p$\nis a diffusion matrix which, for canonical sampling, is determined by the target\ntemperature and the drift matrix through a fluctuation-dissipation relation.\nThe key idea is that $\\mathbf{A}_p$ provides a lot of flexibility in defining\nthe behavior of the GLE, that can be tuned to achieve near-optimal sampling\nfor every degree of freedom (effectively acting as if the coupling constant was\ntuned separately for slow and fast molecular motions).\nThe general idea and the practical implementation are discussed in\n[(Ceriotti et al. JCTC (2010))](http://doi.org/10.1021/ct900563s)\nwhich also discusses other applications of the same principle, including\nperforming simulations with a non-equilibrium *quantum thermostat* that\nmimics the quantum the quantum mechanical behavior of light nuclei.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setting up a thermostat in ``i-PI``\n\nA GLE thermostat can be activated using ``mode=\"gle\"``.\nThe drift matrix used here has been generated from the\n[GLE4MD website](http://gle4md.org), using parameters that\naim for the most efficient sampling possible with the short\nsimulation time (2 ps). The [online generator](https://gle4md.org/index.html?page=matrix&kind=smart&tslow=1&utslow=ps&smrange=6-2&outmode=ipi&aunits=ps)\ncan be tuned to provide the best possible sampling for the system\nof interest, the most important parameter being the slowest time scale\nthat one is interested in sampling (typically a fraction of the total\nsimulation time). The range of frequencies that is optimized can then\nbe tuned so as to reach, roughly, the maximum frequency present in the\nsystem.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xmlroot = ET.parse(\"data/input_gle.xml\").getroot()\nprint(\" \" + ET.tostring(xmlroot.find(\".//thermostat\"), encoding=\"unicode\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We launch ``i-PI`` as usual ...\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi_process = None\nif not os.path.exists(\"simulation_gle.out\"):\n ipi_process = subprocess.Popen([\"i-pi\", \"data/input_gle.xml\"])\n time.sleep(4) # wait for i-PI to start\n lmp_process = [subprocess.Popen([\"lmp\", \"-in\", \"data/in.lmp\"]) for i in range(1)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and wait for simulations to finish.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "if ipi_process is not None:\n ipi_process.wait()\n lmp_process[0].wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analysis of the trajectory\n\nThe kinetic temperature equilibrates quickly to the target value.\nSince the GLE is a local thermostat, targeting each degree of freedom\nseparately, equipartition is also reached quickly. Sampling is less\nfast than with an aggressive Langevin thermostat, because the GLE targets\neach vibrational frequency separately, to minimize the impact on diffusion.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "output_data, output_desc = ipi.read_output(\"simulation_gle.out\")\ntraj_data = ipi.read_trajectory(\"simulation_gle.pos_0.xyz\")\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"temperature(O)\"],\n \"r-\",\n label=\"O atoms\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"temperature(H)\"],\n \"c-\",\n label=\"H atoms\",\n)\nax.plot(output_data[\"time\"], output_data[\"temperature\"], \"k-\", label=\"All atoms\")\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"$\\tilde{T}$ / K\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\hat{c}_{vv}$ reflects the adaptive behavior of the GLE.\nThe fast modes are damped aggressively, leading to a large\nbroadening of the high frequency peaks, but librations and diffusive\nmodes are much less dampened than in the high-coupling Langevin case.\nAn optimal-coupling GLE is a safe choice to sample any system, from\nmolecular liquids to harmonic crystals, although a stochastic velocity\nrescaling is preferable if one is interested in preserving the natural\ndynamics.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "acf_gle = compute_acf_xyz(\n \"simulation_gle.vel_0.xyz\",\n maximum_lag=600,\n length_zeropadding=2000,\n spectral_windowing=\"cosine-blackman\",\n timestep=1,\n time_units=\"femtosecond\",\n skip=100,\n)\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.fill_between(\n acf_ref[:1200, 0] * ha2cm1,\n (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5,\n (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5,\n color=\"gray\",\n label=\"reference\",\n)\nax.loglog(\n acf_gle[3][:1200] * ha2cm1,\n acf_gle[4][:1200] * 1e5,\n \"b-\",\n label=r\"GLE\",\n)\nax.set_xlabel(r\"$\\omega$ / cm$^{-1}$\")\nax.set_ylabel(r\"$\\hat{c}_{vv}$ / arb. units\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### R-L purification\n\nWhat if you also want to extract dynamical information from a GLE\n(or Langevin) trajectory? It is actually possible to post-process the\npower spectrum, performing a deconvolution based on the amount of\ndisturbance introduced by the GLE, that can be predicted analytically\nin the harmonic limit.\nThe idea, discussed in [(Rossi et al., JCP (2018))](http://doi.org/10.1063/1.499053610.1063/1.4990536)\nis that if $\\hat{y}(\\omega)$ is the \"natural\" NVE power\nspectrum, and $k_{\\mathrm{GLE}}(\\omega_0, \\omega)$ is the power\nspectrum predicted for a harmonic oscillator of frequency $\\omega_0$,\nthen the spectrum from the GLE dynamics will be approximately\n\n\\begin{align}\\hat{y}_{\\mathrm{GLE}}(\\omega) = \\int \\mathrm{d}\\omega'\n k_{\\mathrm{GLE}}(\\omega', \\omega) \\hat{y}(\\omega')\\end{align}\n\nThe kernel can be computed analytically for all frequencies that\nare relevant for the power spectrum, based on the GLE parameters\nextracted from the input of ``i-PI``.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_omega = 1200\nAp, Cp, Dp = get_gle_matrices(\"data/input_gle.xml\")\ngle_kernel = gle_frequency_kernel(acf_gle[3][:n_omega], Ap, Dp)\n\n\nlomega = acf_gle[3][:n_omega] * ha2cm1\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nlevels = np.logspace(np.log10(gle_kernel.min()), np.log10(gle_kernel.max()), num=50)\ncontour = ax.contourf(lomega, lomega, gle_kernel, norm=mpl.colors.LogNorm())\nax.set_xscale(\"log\")\nax.set_yscale(\"log\")\nax.set_xlabel(r\"$\\omega_0$ / cm$^{-1}$\")\nax.set_ylabel(r\"$\\omega$ / cm$^{-1}$\")\nax.set_xlim(10, 5000)\nax.set_ylim(10, 5000)\ncbar = fig.colorbar(contour, ticks=[1e1, 1e3, 1e5, 1e7])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The deconvolution is based on the Iterative Image Space\nReconstruction Algorithm, which preserves the positive-definiteness\nof the spectrum\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "isra_acf, history, errors, laplace = isra_deconvolute(\n acf_gle[3][:n_omega], acf_gle[4][:n_omega], gle_kernel, 64, 4\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even though the ISRA algorithm is less prone to enhancing noise than\nother deconvolution algorithms, successive iterations sharpen the spectrum\nbut introduce higher and higher levles of noise, particularly on the\nlow-frequency end of the spectrum so one has to choose when to stop.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.loglog(\n acf_gle[3][:1200] * ha2cm1,\n acf_gle[4][:1200] * 1e5,\n \"b-\",\n label=r\"GLE\",\n)\nax.loglog(\n acf_gle[3][:1200] * ha2cm1,\n history[0] * 1e5,\n \":\",\n color=\"#4000D0\",\n label=r\"iter[1]\",\n)\nax.loglog(\n acf_gle[3][:1200] * ha2cm1,\n history[2] * 1e5,\n \":\",\n color=\"#A000A0\",\n label=r\"iter[9]\",\n)\nax.loglog(\n acf_gle[3][:1200] * ha2cm1,\n history[4] * 1e5,\n \":\",\n color=\"#D00040\",\n label=r\"iter[17]\",\n)\nax.loglog(\n acf_gle[3][:1200] * ha2cm1,\n history[12] * 1e5,\n \":\",\n color=\"#FF0000\",\n label=r\"iter[49]\",\n)\n\nax.set_xlabel(r\"$\\omega$ / cm$^{-1}$\")\nax.set_ylabel(r\"$\\hat{c}_{vv}$ / arb. units\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Especially in the high-frequency region, the deconvolution\nalgorithm succees in recovering the underlying NVE dynamics,\nwhich can be useful whenever one wants to optimize statistical\nefficiency while still being able to estimate dynamical\nproperties.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.fill_between(\n acf_ref[:1200, 0] * ha2cm1,\n (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5,\n (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5,\n color=\"gray\",\n label=\"reference\",\n)\nax.loglog(\n acf_gle[3][:1200] * ha2cm1,\n acf_gle[4][:1200] * 1e5,\n \"b-\",\n label=r\"GLE\",\n)\nax.loglog(\n acf_gle[3][:1200] * ha2cm1,\n history[2] * 1e5,\n \"r-\",\n label=r\"GLE$\\rightarrow$ NVE (iter[5])\",\n)\nax.set_xlabel(r\"$\\omega$ / cm$^{-1}$\")\nax.set_ylabel(r\"$\\hat{c}_{vv}$ / arb. units\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running with LAMMPS\n\nGLE thermostats (as well as conventional Langevin, and\nstochastic velocity rescaling) are also implemented natively\nin ``LAMMPS``.\n\nAn example of ``LAMMPS`` input containing a GLE thermostat can\nbe found in ``data/gle.lmp``. See also the\n[documentation of the fix gle command](https://docs.lammps.org/fix_gle.html)\n\n```text\nfix 1 all gle 6 300 300 31415 data/smart.A\n```\nThe drift matrix can be obtained from the same website, simply\nasking to output the matrix in raw format, choosing units consistent\nwith the ``LAMMPS`` settings, e.g. for this [optimal sampling setup](https://gle4md.org/index.html?page=matrix&kind=smart&tslow=1&utslow=ps&smrange=6-2&outmode=raw&aunits=fs)\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can run ``LAMMPS`` from the command line\n\n```bash\nlmp -in data/gle.lmp &\n```\nor from Python\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "lmp_process = None\nif not os.path.exists(\"lammps_out.dat\"):\n lmp_process = subprocess.Popen([\"lmp\", \"-in\", \"data/gle.lmp\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and wait\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "if lmp_process is not None:\n lmp_process.wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The simulation is much faster (for such a small system and\ncheap potential the overhead of ``i-PI``'s client-server mechanism\nis substantial) and leads to similar results for the kinetic temperature\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "traj_data = np.loadtxt(\"lammps_out.dat\")\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n traj_data[:, 0] * 1e-3,\n traj_data[:, 1],\n \"k-\",\n label=\"All atoms\",\n)\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"$\\tilde{T}$ / K\")\nax.legend()\nplt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/58f311a250ec4f9cd7abf17b492ae2f6/pi-metad.py b/_downloads/58f311a250ec4f9cd7abf17b492ae2f6/pi-metad.py new file mode 100644 index 00000000..52a17382 --- /dev/null +++ b/_downloads/58f311a250ec4f9cd7abf17b492ae2f6/pi-metad.py @@ -0,0 +1,783 @@ +r""" +Path integral metadynamics +========================== + +:Authors: Michele Ceriotti `@ceriottm `_ + +This example shows how to run a free-energy sampling calculation that +combines path integral molecular dynamics to model nuclear quantum effects +and metadynamics to accelerate sampling of the high-free-energy regions. + +The rather complicated setup combines `i-PI `_ +to perform path integral +MD, its built-in driver to compute energy and forces for the Zundel +:math:`\mathrm{H_5O_2^+}` cation, and `PLUMED `_ +to perform metadynamics. +If you want to see an example in a more realistic scenario, you can look at +`this paper (Rossi et al., JCTC (2020)) +`_, +in which this +methodology is used to simulate the decomposition of methanesulphonic +acid in a solution of phenol and hydrogen peroxide. + +Note also that, in order to keep the execution time of this example as +low as possible, several parameters are set to values that would not be +suitable for an accurate, converged simulation. +They will be highlighted and more reasonable values will be provided. +"High-quality" runs can also be realized substituting the input files +used in this example with those labeled with the ``_hiq`` suffix, that +are also provided in the ``data/`` folder. +""" + +# %% + +import bz2 +import os +import subprocess +import time +import xml.etree.ElementTree as ET + +import ase +import ase.io +import chemiscope +import ipi +import matplotlib.pyplot as plt +import numpy as np + + +# %% +# Metadynamics for the Zundel cation +# ---------------------------------- +# +# Metadynamics is a method to accelerate sampling of rare events - microscopic processes +# that are too infrequent to be observed over the time scale (ns-µs) accessible to +# molecular dynamics simulations. You can read one of the many excellent reviews +# on metadynamics (see e.g. +# `Bussi and Branduardi (2015) `_), +# or follow a +# `lecture from the PLUMED masterclass +# `_. +# In short, during a metadynamics simulation an adaptive biasing potential is +# built as a superimposition of Gaussians centered over configurations that have +# been previously visited by the trajectory. This discourages the system from remaining +# in high-probability configurations and accelerates sampling of free-energy barriers. +# +# .. figure:: metad-scheme.png +# :align: center +# :width: 600px +# +# A schematic representation of how metadynamics work by adaptively building +# a repulsive bias based on the trajectory of a molecule, compensating for +# low-energy regions in the free energy surface. +# +# Crucially, the bias is *not* built relative to the Cartesian coordinates of the atoms, +# but relative to a lower-dimensional description of the system (so-called collective +# variables) that are suited to describe the processes being studied. + +# %% +# +# The Zundel cation :math:`\mathrm{H_5O_2^+}` is one of the limiting +# structures of the solvated proton, and in the gas phase leads to a +# stable structure, with the additional proton shared between two water +# molecules (see the structure below). +# We will use a potential fitted on high-end quantum-chemistry calculations +# `Huang et al. (2005) `_ to compute energy +# and forces acting on the atoms. + +zundel = ase.io.read("data/h5o2+.xyz", ":") +chemiscope.show(frames=zundel, mode="structure") + +# %% +# +# As the two water molecules are separated, the proton remains attached +# to one of the two, effectively leading to a dissociated +# :math:`\mathrm{H_2O+H_3O^+}` configuration. Thus, two natural +# coordinates to describe the physics of this system are the distance +# between the O atoms, and the difference in coordination number of +# the two O atoms, which is 0 for a shared proton and ±1 for the +# dissociated system. + +# %% +# Running metadynamics calculations with ``i-PI`` and ``PLUMED`` +# -------------------------------------------------------------- +# +# The client-server architecture `i-PI `_ is based on makes it easy +# to combine multiple programs to realize complicated simulation workflows. +# In this case we will use an implementation of the Zundel potential in a simple +# driver code that is available in the i-PI repository, and use +# `PLUMED `_ to compute collective variables and build +# the adaptive bias. We will then perform some post-processing to +# estimate the free energy. + + +# %% +# Installing the Python driver +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# i-PI comes with a FORTRAN driver, which however has to be installed +# from source. We use a utility function to compile it. Note that this requires +# a functioning build system with `gfortran` and `make`. + +ipi.install_driver() + +# %% +# Defining the molecular dynamics setup +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# The `input-md.xml` file defines the way the MD simulation is performed. + +xmlroot = ET.parse("data/input-md.xml").getroot() + +# %% +# The `` block describe the way communication will occur with the +# driver code + +print(" " + ET.tostring(xmlroot.find("ffsocket"), encoding="unicode")) + +# %% +# ... and the `` section describes the MD setup. +# This is a relatively standard NVT setup, with an efficient +# generalized Langevin equation thermostat (important to +# compensate for the non-equilibrium nature of metadynamics). +# Note that the time step is rather long (the recommended value for +# aqueous systems is around 0.5 fs). This is done to improve +# efficiency for this example, but you should check if it +# affects results in a realistic scenario. + +print(" " + ET.tostring(xmlroot.find(".//motion"), encoding="unicode")) + +# %% +# The metadynamics setup requires three ingredients: +# a `` forcefield that defines what input to use +# (more on that later) and the file from which to initialize +# the structural information (number of atoms, ...); +# `` is an advanced feature, available from +# PLUMED 2.10, that allows extracting internal variables +# from plumed and integrate them into the outputs of +# i-PI. + +print(" " + ET.tostring(xmlroot.find("ffplumed"), encoding="unicode")) + +# %% +# The `` section contains a `` key that +# specifies that energy and forces from PLUMED should be +# treated as a bias (so that e.g. are not included in the +# potential, even though they're used to propagate the +# trajectory). + +print(" " + ET.tostring(xmlroot.find(".//ensemble"), encoding="unicode")) + +# The `` section contains a `` class that +# instructs i-PI to call the PLUMED action that adds hills +# along the trajectory. + +print(" " + ET.tostring(xmlroot.find("smotion"), encoding="unicode")) + + +# %% +# CVs and metadynamics +# ~~~~~~~~~~~~~~~~~~~~ +# +# The calculation of the collective variables and the +# metadynamics bias is delegated to PLUMED, and controlled by +# a separate `plumed-md.dat` input file. +# Without going in detail into the syntax, one can recognize the +# calculation of the distance between the O atoms `doo`, +# the coordination of the two oxygens `co1` and `co2`, +# and the difference between the two, `dc`. +# The `METAD` action specifies the CVs to be used, the pace of +# hill depositon (which is way too frequent here, but suitable for +# this example), the width along the two CVs and the initial +# height of the repulsive Gaussians (which are both too large to +# guarantee high resolution in CV and energy). The `BIASFACTOR` keyword specifies +# that the height of the hills will be progressively reduced +# according to the "well-tempered metadynamics" protocol, see +# `Barducci et al., Phys. Rev. Lett. (2008) +# `_. +# A repulsive static bias (`UPPER_WALLS`) prevents complete dissociation of the +# cation by limiting the range of the O-O distance. + +with open("data/plumed-md.dat", "r") as file: + plumed_dat = file.read() +print(plumed_dat) + +# %% +# Running the simulations +# ~~~~~~~~~~~~~~~~~~~~~~~ +# +# Now we can launch the actual calculations. On the the command line, +# this requires launching i-PI first, and then the built-in driver, +# specifying the appropriate communication mode, and the `zundel` potential. +# PLUMED is called from within i-PI as a library, so there is no need to +# launch a separate process. Note that the Zundel potential requires some data +# files, with a hard-coded location in the current working directory, +# which is why the driver should be run from within the ``data/`` folder. +# +# .. code-block:: bash +# +# i-pi data/input-md.xml > log & +# sleep 2 +# cd data; i-pi-driver -u -a zundel -m zundel +# +# The same can be achieved from Python using ``subprocess.Popen`` + +ipi_process = None +if not os.path.exists("meta-md.out"): + # don't rerun if the outputs already exist + ipi_process = subprocess.Popen(["i-pi", "data/input-md.xml"]) + time.sleep(2) # wait for i-PI to start + driver_process = [ + subprocess.Popen( + ["i-pi-driver", "-u", "-a", "zundel", "-m", "zundel"], cwd="data/" + ) + for i in range(1) + ] + +# %% +# If you run this in a notebook, you can go ahead and start loading +# output files *before* i-PI has finished running by skipping this cell + +# wait for simulations to finish +if ipi_process is not None: + ipi_process.wait() + for process in driver_process: + process.wait() + +# %% +# Trajectory post-processing +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# We can now post-process the simulation to see metadynamics in action. +# +# First, we read the trajectory outputs. Note that these have all been +# printed with the same stride + +output_data, output_desc = ipi.read_output("meta-md.out") +colvar_data = ipi.read_trajectory("meta-md.colvar_0", format="extras")[ + "doo,dc,mtd.bias" +] +traj_data = ipi.read_trajectory("meta-md.pos_0.xyz") + +# %% +# then, assemble a visualization +chemiscope.show( + frames=traj_data, + properties=dict( + d_OO=10 * colvar_data[:, 0], # nm to Å + delta_coord=colvar_data[:, 1], + bias=27.211386 * output_data["ensemble_bias"], # Ha to eV + time=2.4188843e-05 * output_data["time"], # atomictime to ps + ), # attime to ps + settings=chemiscope.quick_settings( + x="d_OO", y="delta_coord", z="bias", color="time", trajectory=True + ), + mode="default", +) + + +# %% +# The visualization above shows how the growing metadynamics bias pushes +# progressively the atoms towards geometries with larger O-O separations, +# and that for these distorted configurations the proton is not shared +# symmetrically between the O atoms, but is preferentially attached to +# one of the two water molecules. + +# %% +# Trajectory diagnostics +# ...................... +# +# The time history of the bias is instructive, as it shows how the +# bias grows until the trajectory gets pushed in a new region (where the +# bias is zero) and then grows again. The envelope of the bias increase +# slows down over time, because the "well-tempered" deposition strategy +# reduces the height of the hills deposited in high-bias regions. +# +# Note that the potential energy has fluctuations that are larger than +# the magnitude of the bias, although it shows a tendency to reach higher +# values as the simulation progresses. This is because only two degrees +# of freedom are affected by the bias, while all degrees of freedom +# undergo thermal fluctuations, which are dominant even for this +# small system. + + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + +ax.plot( + 2.4188843e-05 * output_data["time"], + 27.211386 * output_data["potential"], + "r", + label="potential", +) +ax.plot( + 2.4188843e-05 * output_data["time"], + 27.211386 * output_data["ensemble_bias"], + "b", + label="bias", +) + +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"energy / eV") +ax.legend(loc="upper left", ncols=1) +plt.show() + +# %% +# +# It's important to keep in mind that the growing metadynamics bias can +# lead to deviations from the quasi-equilibrium sampling that is necessary +# to recover the correct properties of the rare event. It is not easy +# to verify this condition, but one simple diagnostics that can highlight +# the most evident problems is looking at the kinetic temperature of different +# portions of the system, computing a moving average to have a clearer signal. + + +def moving_average(arr, window_size): + # Create a window of the specified size with equal weights + window = np.ones(window_size) / window_size + # Use the 'valid' mode to only return elements where the window fully + # overlaps with the data + return np.convolve(arr, window, mode="valid") + + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + +ax.plot( + 2.4188843e-05 * output_data["time"][50:-49], + moving_average(output_data["temperature(O)"], 100), + "r", + label=r"$T_\mathrm{O}$", +) +ax.plot( + 2.4188843e-05 * output_data["time"][50:-49], + moving_average(output_data["temperature(H)"], 100), + "gray", + label=r"$T_\mathrm{H}$", +) +ax.plot( + 2.4188843e-05 * output_data["time"][50:-49], + moving_average(output_data["temperature"], 100), + "b", + label="T", +) + +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"temperature / K") +ax.legend(loc="upper left", ncols=2) +plt.show() + +# %% +# It is clear that the very high rate of biasing used in this demonstrative +# example leads to a temperature that is consistently higher than the target, +# with spikes up to 380 K and O and H atoms reaching different temperatures +# (i.e. equipartition is broken). While this does not affect the qualitative +# nature of the results, these parameters are unsuitable for a production run. +# NB: especially for small systems, the instantaneous kinetic temperature +# can deviate by a large amount from the target temperature: only the mean +# value has actual meaning. However, a kinetic temperature that is consistently +# above the target value indicates that the thermostat cannot dissipate +# efficiently the energy due to the growing bias. + +# %% +# Free energy profiles +# .................... +# +# One of the advantages of metadynamics is that it allows one to easily +# estimate the free-energy associated with the collective variables +# that are used to accelerate sampling by summing the repulsive hills +# that have been deposited during the run and taking the negative of +# the total bias at the end of the trajectory. +# +# Even though more sophisticated strategies exist that provide explicit +# weighting factors to estimate the unbiased Boltzmann distribution +# (see e.g. +# `Giberti et al., JCTC 2020 +# `_), +# this simple approach is good enough for this example, and can be +# realized as a post-processing step using the ``plumed sum_hills`` module, +# that also applies a (simple) correction to the negative bias that +# is needed when using the well-tempered bias scaling protocol. +# On the command line, +# +# .. code-block:: bash +# +# plumed sum_hills --hills HILLS-md --min 0.21,-1 --max 0.31,1 --bin 100,100 \ +# --outfile FES-md --stride 100 --mintozero < data/plumed-md.dat +# +# The ``--stride`` option generates a series of files showing the estimates +# of :math:`F` at different times along the trajectory. + +with open("data/plumed-md.dat", "r") as file: + subprocess.run( + [ + "plumed", + "sum_hills", + "--hills", + "HILLS-md", + "--min", + "0.21,-1", + "--max", + "0.31,1", + "--bin", + "100,100", + "--outfile", + "FES-md", + "--stride", + "100", + "--mintozero", + ], + stdin=file, + text=True, + ) + +# rearrange data and converts to Å and eV +data = np.loadtxt("FES-md0.dat", comments="#")[:, :3] +xyz_0 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 +) +data = np.loadtxt("FES-md2.dat", comments="#")[:, :3] +xyz_2 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 +) +data = np.loadtxt("FES-md5.dat", comments="#")[:, :3] +xyz_5 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 +) + +# %% +# The plots show, left-to-right, the accumulation of the +# metadynamics bias as simulation progresses. + +fig, ax = plt.subplots( + 1, 3, figsize=(8, 3), sharex=True, sharey=True, constrained_layout=True +) + +cf_0 = ax[0].contourf(*xyz_0) +cf_1 = ax[1].contourf(*xyz_2) +cf_2 = ax[2].contourf(*xyz_5) +fig.colorbar(cf_2, ax=ax, orientation="vertical", label=r"$F$ / eV") +ax[0].set_ylabel(r"$\Delta C_\mathrm{H}$") +ax[0].set_xlabel(r"$d_\mathrm{OO}$ / Å") +ax[1].set_xlabel(r"$d_\mathrm{OO}$ / Å") +ax[2].set_xlabel(r"$d_\mathrm{OO}$ / Å") +ax[0].set_title(r"$t=0.8$ ps") +ax[1].set_title(r"$t=2.5$ ps") +ax[2].set_title(r"$t=5.0$ ps") +plt.show() + +# %% +# Biasing a path integral calculation +# ----------------------------------- +# +# You can see `this recipe +# `_ +# for a brief introduction to path integral simulations with `i-PI`. +# From a practical perspective, very little needs to change with respect +# to the classical case. + +xmlroot = ET.parse("data/input-pimd.xml").getroot() + +# %% +# The `nbeads` option determines the number of path integral +# replicas. The value of 8 used here is not sufficient to converge +# quantum statistics at 300 K (a more typical value would be +# around 32). There are methods to reduce the number of replicas +# needed for convergence, see e.g. +# `Ceriotti and Markland, Nat. Rev. Chem. (2018) +# `_ +# but we keep it simple here. + +print(" " + ET.tostring(xmlroot.find(".//initialize"), encoding="unicode")[:23]) + +# %% +# Centroid bias +# ~~~~~~~~~~~~~ +# +# Another detail worth discussing is that the metadynamics bias +# is computed exclusively on the *centroid*, the mean position of +# the ring-polymer beads. This is an extreme form of +# ring polymer contraction +# `(Markland and Manolopoulos, J. Chem. Phys. (2008) +# `_ +# that avoids computing for each replica the slowly-varying +# parts of the potential, but is not applied for computational +# savings. When performing a quantum free-energy calculation it +# is important to distinguish between the free-energy computed +# as the logarithm of the probability of observing a given +# configuration (that depends on the distribution of the +# replicas) and the free-energy taken as a tool to estimate +# reaction rates :math:`k` in a transition-state theory +# fashion :math:`k\propto e^{-\Delta E^\ddagger/kT}`, +# where the energy barrier :math:`\Delta E^\ddagger` +# is better estimated from the distribution of the centroid. +# See e.g. +# `Habershon et al., Annu. Rev. Phys. Chem. (2013) +# `_ +# for a discussion of the subtleties involved in estimating +# transition rates. +# In practice, performing this contraction step is very easy +# in `i-PI`, because for each `` section - including +# that corresponding to the bias - it is possible to specify +# a different number of replicas. The configurations will +# be automatically computed by Fourier interpolation. + +print(" " + ET.tostring(xmlroot.find(".//bias"), encoding="unicode")) + +# %% +# Running the calculation +# ~~~~~~~~~~~~~~~~~~~~~~~ +# +# The other changes are purely cosmetic, and the calculation +# can be launched very easily, using several drivers to parallelize +# the energy evaluation over the beads (although this kind of calculations +# is not limited by the evaluation of the forces). + +# don't rerun if the outputs already exist +ipi_process = None +if not os.path.exists("meta-pimd.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input-pimd.xml"]) + time.sleep(2) # wait for i-PI to start + driver_process = [ + subprocess.Popen( + ["i-pi-driver", "-u", "-a", "zundel", "-m", "zundel"], cwd="data/" + ) + for i in range(4) + ] + +# %% +# +# If you run this in a notebook, you can go ahead and start loading +# output files _before_ i-PI has finished running by skipping this cell + +# wait for simulations to finish +if ipi_process is not None: + ipi_process.wait() + for process in driver_process: + process.wait() + +# %% +# Analysis of the simulation +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# A path integral simulation evolves multiple configurations at the same +# time, forming a `ring polymer`. Each replica provides a sample of the +# quantum mechanical configuration distribution of the atoms. To provide +# an overall visualization of the path integral dynamics, we load all the +# replicas and combine them using a utility function from the +# `chemiscope` library.` + + +output_data, output_desc = ipi.read_output("meta-pimd.out") +colvar_data = ipi.read_trajectory("meta-pimd.colvar_0", format="extras")[ + "doo,dc,mtd.bias" +] +pimd_traj_data = [ipi.read_trajectory(f"meta-pimd.pos_{i}.xyz") for i in range(8)] + +# combines the PI beads and sets up the visualization options +traj_pimd = chemiscope.ase_merge_pi_frames(pimd_traj_data) +traj_pimd["shapes"]["paths"]["parameters"]["global"]["radius"] = 0.05 +traj_pimd["properties"] = dict( + d_OO=10 * colvar_data[:, 0], # nm to Å + delta_coord=colvar_data[:, 1], + bias=27.211386 * output_data["ensemble_bias"], # Ha to eV + time=2.4188843e-05 * output_data["time"], +) +traj_pimd["settings"] = chemiscope.quick_settings( + x="d_OO", + y="delta_coord", + z="bias", + color="time", + trajectory=True, + structure_settings=dict( + bonds=False, + atoms=False, + keepOrientation=True, + unitCell=False, + shape=[ + "paths", + ], + ), +) +traj_pimd["settings"]["target"] = "structure" + +# %% +# +# Visualize the trajectory. Note the similar behavior as for the classical +# trajectory, and the delocalization of the protons + +chemiscope.show(**traj_pimd) + + +# %% +# Free energy plots +# ~~~~~~~~~~~~~~~~~ +# +# The free energy profiles relative to :math:`\Delta C_\mathrm{H}` +# and :math:`d_\mathrm{OO}` can be computed exactly as for the +# classical trajectory, using the `sum_hills` module. + +with open("data/plumed-pimd.dat", "r") as file: + subprocess.run( + [ + "plumed", + "sum_hills", + "--hills", + "HILLS-pimd", + "--min", + "0.21,-1", + "--max", + "0.31,1", + "--bin", + "100,100", + "--outfile", + "FES-pimd", + "--stride", + "100", + "--mintozero", + ], + stdin=file, + text=True, + ) + +# rearrange data and converts to Å and eV +data = np.loadtxt("FES-pimd0.dat", comments="#")[:, :3] +xyz_pi_0 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 +) +data = np.loadtxt("FES-pimd2.dat", comments="#")[:, :3] +xyz_pi_2 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 +) +data = np.loadtxt("FES-pimd5.dat", comments="#")[:, :3] +xyz_pi_5 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 +) + +# %% +# Just as for a classical run, the metadynamics bias progressively +# pushes the centroid (and the beads that are distributed around it) +# to sample a wider portion of the collective-variable space. + +fig, ax = plt.subplots( + 1, 3, figsize=(8, 3), sharex=True, sharey=True, constrained_layout=True +) + +cf_0 = ax[0].contourf(*xyz_pi_0) +cf_1 = ax[1].contourf(*xyz_pi_2) +cf_2 = ax[2].contourf(*xyz_pi_5) +fig.colorbar(cf_2, ax=ax, orientation="vertical", label=r"$F$ / eV") +ax[0].set_ylabel(r"$\Delta C_\mathrm{H}$") +ax[0].set_xlabel(r"$d_\mathrm{OO}$ / Å") +ax[1].set_xlabel(r"$d_\mathrm{OO}$ / Å") +ax[2].set_xlabel(r"$d_\mathrm{OO}$ / Å") +ax[0].set_title(r"$t=0.8$ ps") +ax[1].set_title(r"$t=2.5$ ps") +ax[2].set_title(r"$t=5.0$ ps") +plt.show() + +# %% +# Assessing quantum nuclear effects +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# The effect of nuclear quantization on the centroid free-energy +# is relatively small, despite the large delocalization of the +# protons in the PIMD calculation. Looking more +# carefully at the two distributions, one can notice that +# in the high-:math:`d_\mathrm{OO}` region there is higher +# delocalisation of the proton. + +fig, ax = plt.subplots( + 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True +) + +levels = np.linspace(0, 0.5, 6) +cp1 = ax.contour(*xyz_5, colors="b", levels=levels) +cp2 = ax.contour(*xyz_pi_5, colors="r", levels=levels) +ax.set_ylabel(r"$\Delta C_\mathrm{H}$") +ax.set_xlabel(r"$d_\mathrm{OO}$ / Å") +ax.legend( + handles=[ + plt.Line2D([0], [0], color="b", label="MD"), + plt.Line2D([0], [0], color="r", label="PIMD"), + ] +) +plt.show() + +# %% +# +# To get a clear signal, we need better-converged calculations; +# the `data/` folder contains inputs for these "high quality" runs, +# and free-energies obtained from them. +# The results confirm the lowering of the free-energy barrier for +# the :math:`\mathrm{H_3O^+ + H_2O} \rightarrow \mathrm{H_2O + H_3O^+}` +# transition. + +with bz2.open("data/FES-md_hiq.bz2", "rt") as f: + data = np.loadtxt(f, comments="#")[:, :3] +xyz_md_hiq = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 +) +with bz2.open("data/FES-pimd_hiq.bz2", "rt") as f: + data = np.loadtxt(f, comments="#")[:, :3] +xyz_pi_hiq = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 +) + +fig, ax = plt.subplots( + 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True +) + +levels = np.linspace(0, 0.5, 6) +cp1 = ax.contour(*xyz_md_hiq, colors="b", levels=levels) +cp2 = ax.contour(*xyz_pi_hiq, colors="r", levels=levels) +ax.set_ylabel(r"$\Delta C_\mathrm{H}$") +ax.set_xlabel(r"$d_\mathrm{OO}$ / Å") +ax.legend( + handles=[ + plt.Line2D([0], [0], color="b", label="MD"), + plt.Line2D([0], [0], color="r", label="PIMD"), + ] +) +plt.show() + +# %% +# +# The lowering of the barrier for proton hopping is clearly +# seen by taking 1D slices of the free energy at different O-O separations. + +fig, ax = plt.subplots( + 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True +) + +ax.plot( + xyz_md_hiq[1, :, 50], xyz_md_hiq[2, :, 50], "b", label=r"MD, $d_\mathrm{OO}=2.6 $Å" +) +ax.plot( + xyz_pi_hiq[1, :, 50], + xyz_pi_hiq[2, :, 50], + "r", + label=r"PIMD, $d_\mathrm{OO}=2.6 $Å", +) +ax.plot( + xyz_md_hiq[1, :, 60], + xyz_md_hiq[2, :, 60], + "b--", + label=r"MD, $d_\mathrm{OO}=2.7 $Å", +) +ax.plot( + xyz_pi_hiq[1, :, 60], + xyz_pi_hiq[2, :, 60], + "r--", + label=r"PIMD, $d_\mathrm{OO}=2.7 $Å", +) +ax.set_ylim(0.08, 0.6) +ax.legend(ncols=2, loc="upper right", fontsize=9) +ax.set_ylabel(r"$F$ / eV") +ax.set_xlabel(r"$\Delta C_\mathrm{H}$") +plt.show() + +# %% +# This model system is representative of the behavior of protons +# along a hydrogen bond in different conditions, where the environment +# determines the typical O-O separation, and whether the proton is shared +# (as in high pressure ice X) or preferentially attached to one of the two +# molecules. Zero-point energy (and to a lesser extent tunneling) +# increases the delocalization, and reduces the barrier for an excess +# proton to hop between water molecues. diff --git a/_downloads/597d3fbd5c13b3195d61c3c1381648e5/lode-linear.zip b/_downloads/597d3fbd5c13b3195d61c3c1381648e5/lode-linear.zip new file mode 100644 index 00000000..3a078ee0 Binary files /dev/null and b/_downloads/597d3fbd5c13b3195d61c3c1381648e5/lode-linear.zip differ diff --git a/_downloads/59a2e54bf0c573fdc3c0b810a05c930c/data.zip b/_downloads/59a2e54bf0c573fdc3c0b810a05c930c/data.zip new file mode 100644 index 00000000..4fa50ae7 Binary files /dev/null and b/_downloads/59a2e54bf0c573fdc3c0b810a05c930c/data.zip differ diff --git a/_downloads/5b1c4e22a9037fdd90b3ffe8aaf577e9/environment.yml b/_downloads/5b1c4e22a9037fdd90b3ffe8aaf577e9/environment.yml new file mode 100644 index 00000000..58e31a11 --- /dev/null +++ b/_downloads/5b1c4e22a9037fdd90b3ffe8aaf577e9/environment.yml @@ -0,0 +1,13 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - rust > 1.65 + - pip: + - ase==3.22.1 + - matplotlib + - rascaline @ git+https://github.com/Luthaf/rascaline@ca957642f512e141c7570e987aadc05c7ac71983 + - torch + - scipy + - numpy diff --git a/_downloads/5ca4686e07e3a8416afa68821d23425c/environment.yml b/_downloads/5ca4686e07e3a8416afa68821d23425c/environment.yml new file mode 100644 index 00000000..b8d7a9a8 --- /dev/null +++ b/_downloads/5ca4686e07e3a8416afa68821d23425c/environment.yml @@ -0,0 +1,20 @@ +channels: + - plumed/label/nightly + - conda-forge +dependencies: + - python=3.11 + - pip + - gfortran + - make + - git + - plumed + - py-plumed + - pip: + - ase==3.22.1 + - chemiscope + - git+https://github.com/i-pi/i-pi.git@main#egg=ipi + - matplotlib + - skmatter +variables: + PYTHONPATH: + PLUMED_KERNEL: diff --git a/_downloads/61cac41226274764c3aff5e112f310da/roy-gch.ipynb b/_downloads/61cac41226274764c3aff5e112f310da/roy-gch.ipynb new file mode 100644 index 00000000..ecf30235 --- /dev/null +++ b/_downloads/61cac41226274764c3aff5e112f310da/roy-gch.ipynb @@ -0,0 +1,284 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Generalized Convex Hull construction for the polymorphs of ROY\n\n:Authors: Michele Ceriotti [@ceriottm](https://github.com/ceriottm/)\n\nThis notebook analyzes the structures of 264 polymorphs of ROY, from\n[Beran et Al, Chemical Science (2022)](https://doi.org/10.1039/D1SC06074K)_,\ncomparing the conventional density-energy convex hull with a Generalized Convex Hull\n(GCH) analysis (see [Anelli et al., Phys. Rev. Materials\n(2018)](https://doi.org/10.1103/PhysRevMaterials.2.103804)_).\nIt uses features computed with [rascaline](https://github.com/lab-cosmo/rascaline)_\nand uses the directional convex hull function from\n[scikit-matter](https://github.com/lab-cosmo/scikit-matter)_\nto make the figure.\n\nThe GCH construction aims at determining structures, among a collection of\ncandidate configurations, that are stable or have the potential of being stabilized\nby appropriate thermodynamic boundary conditions (pressure, doping, external fields,\n...). It does so by using microscopic descriptors to determine the diversity of\nstructures, and assumes that configurations that are stable relative to other\nconfigurations with similar descriptors are those that could be made\n\"locally\" stable by suitable synthesis conditions.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# sphinx_gallery_thumbnail_number = 3\nimport chemiscope\nimport matplotlib.tri\nimport numpy as np\nfrom matplotlib import pyplot as plt\nfrom metatensor import mean_over_samples\nfrom rascaline import SoapPowerSpectrum\nfrom sklearn.decomposition import PCA\nfrom skmatter.datasets import load_roy_dataset\nfrom skmatter.sample_selection import DirectionalConvexHull" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Loads the structures (that also contain properties in the ``info`` field)\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "roy_data = load_roy_dataset()\n\nstructures = roy_data[\"structures\"]\n\ndensity = np.array([s.info[\"density\"] for s in structures])\nenergy = np.array([s.info[\"energy\"] for s in structures])\nstructype = np.array([s.info[\"type\"] for s in structures])\niknown = np.where(structype == \"known\")[0]\niothers = np.where(structype != \"known\")[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Energy-density hull\n\nThe Directional Convex Hull routines can be used to compute a\nconventional density-energy hull (see\n[Hautier (2014)](http://doi.org/10.1007/128_2013_486) for a pedagogic\nintroduction to the convex hull construction in the context\nof atomistic simulations).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "dch_builder = DirectionalConvexHull(low_dim_idx=[0])\ndch_builder.fit(density.reshape(-1, 1), energy)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can get the indices of the selection, and compute the distance from\nthe hull\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sel = dch_builder.selected_idx_\ndch_dist = dch_builder.score_samples(density.reshape(-1, 1), energy)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Hull energies\n\nStructures on the hull are stable with respect to synthesis at constant\nmolar volume. Any other structure would lower the energy by decomposing\ninto a mixture of the two nearest structures along the hull. Given that\nthe lattice energy is an imperfect proxy for the free energy, and that\nsynthesis can be performed in other ways than by fixing the density,\nstructures that are not exactly on the hull might also be stable. One\ncan compute a \u201chull energy\u201d as an indication of how close these\nstructures are to being stable.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(6, 4))\nax.scatter(density, energy, c=dch_dist, marker=\".\")\nssel = sel[np.argsort(density[sel])]\nax.plot(density[ssel], energy[ssel], \"k--\")\nax.set_xlabel(\"density / g/cm$^3$\")\nax.set_ylabel(\"energy / kJ/mol\")\nplt.show()\n\nprint(\n f\"Mean hull energy for 'known' stable structures {dch_dist[iknown].mean()} kJ/mol\"\n)\nprint(f\"Mean hull energy for 'other' structures {dch_dist[iothers].mean()} kJ/mol\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interactive visualization\n\nYou can also visualize the hull with ``chemiscope`` in a juptyer notebook.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "cs = chemiscope.show(\n structures,\n dict(\n energy=energy,\n density=density,\n hull_energy=dch_dist,\n structure_type=structype,\n ),\n settings={\n \"map\": {\n \"x\": {\"property\": \"density\"},\n \"y\": {\"property\": \"energy\"},\n \"color\": {\"property\": \"hull_energy\"},\n \"symbol\": \"structure_type\",\n \"size\": {\"factor\": 35},\n },\n \"structure\": [{\"unitCell\": True, \"supercell\": {\"0\": 2, \"1\": 2, \"2\": 2}}],\n },\n)\ncs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Save chemiscope file in a format that can be shared and viewed on `chemiscope.org`\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "cs.save(\"roy_ch.json.gz\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generalized Convex Hull\n\nA GCH is a similar construction, in which generic structural descriptors\nare used in lieu of composition, density or other thermodynamic\nconstraints. The idea is that configurations that are found close to the\nGCH are locally stable with respect to structurally-similar\nconfigurations. In other terms, one can hope to find a thermodynamic\nconstraint (i.e.\u00a0synthesis conditions) that act differently on these\nstructures in comparison with the others, and may potentially stabilize\nthem.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Compute structural descriptors\n\nA first step is to computes suitable ML descriptors. Here we have used\n``rascaline`` to evaluate average SOAP features for the structures.\nIf you don't want to install these dependencies for this example you\ncan also use the pre-computed features, but you can use this as a stub\nto apply this analysis to other chemical systems\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "hypers = {\n \"cutoff\": 4,\n \"max_radial\": 6,\n \"max_angular\": 4,\n \"atomic_gaussian_width\": 0.7,\n \"cutoff_function\": {\"ShiftedCosine\": {\"width\": 0.5}},\n \"radial_basis\": {\"Gto\": {\"accuracy\": 1e-6}},\n \"center_atom_weight\": 1.0,\n}\ncalculator = SoapPowerSpectrum(**hypers)\nrho2i = calculator.compute(structures)\nrho2i = rho2i.keys_to_samples([\"species_center\"]).keys_to_properties(\n [\"species_neighbor_1\", \"species_neighbor_2\"]\n)\nrho2i_structure = mean_over_samples(rho2i, sample_names=[\"center\", \"species_center\"])\nnp.savez(\"roy_features.npz\", feats=rho2i_structure.block(0).values)\n\n\n# features = roy_data[\"features\"]\nfeatures = rho2i_structure.block(0).values" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### PCA projection\n\nComputes PCA projection to generate low-dimensional descriptors that\nreflect structural diversity. Any other dimensionality reduction scheme\ncould be used in a similar fashion.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pca = PCA(n_components=4)\npca_features = pca.fit_transform(features)\n\nfig, ax = plt.subplots(1, 1, figsize=(6, 4))\nscatter = ax.scatter(pca_features[:, 0], pca_features[:, 1], c=energy)\nax.set_xlabel(\"PCA[1]\")\nax.set_ylabel(\"PCA[2]\")\ncbar = fig.colorbar(scatter, ax=ax)\ncbar.set_label(\"energy / kJ/mol\")\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Builds the Generalized Convex Hull\n\nBuilds a convex hull on the first two PCA features\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "dch_builder = DirectionalConvexHull(low_dim_idx=[0, 1])\ndch_builder.fit(pca_features, energy)\nsel = dch_builder.selected_idx_\ndch_dist = dch_builder.score_samples(pca_features, energy)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generates a 3D Plot\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "triang = matplotlib.tri.Triangulation(pca_features[sel, 0], pca_features[sel, 1])\nfig = plt.figure(figsize=(7, 5), tight_layout=True)\nax = fig.add_subplot(projection=\"3d\")\nax.plot_trisurf(triang, energy[sel], color=\"gray\")\nax.scatter(pca_features[:, 0], pca_features[:, 1], energy, c=dch_dist)\nax.set_xlabel(\"PCA[1]\")\nax.set_ylabel(\"PCA[2]\")\nax.set_zlabel(\"energy / kJ/mol\\n \\n\", labelpad=11)\nax.view_init(25, 110)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The GCH construction improves the separation between the hull energies\nof \u201cknown\u201d and hypothetical polymorphs (compare with the density-energy\nvalues above)\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\n f\"Mean hull energy for 'known' stable structures {dch_dist[iknown].mean()} kJ/mol\"\n)\nprint(f\"Mean hull energy for 'other' structures {dch_dist[iothers].mean()} kJ/mol\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualize in a ``chemiscope`` widget\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for i, f in enumerate(structures):\n for j in range(len(pca_features[i])):\n f.info[\"pca_\" + str(j + 1)] = pca_features[i, j]\nstructure_properties = chemiscope.extract_properties(structures)\nstructure_properties.update({\"per_atom_energy\": energy, \"hull_energy\": dch_dist})\n\n# You can save a chemiscope file to disk (for viewing on chemiscope.org)\n\nchemiscope.write_input(\n \"roy_gch.json.gz\",\n frames=structures,\n properties=structure_properties,\n meta={\n \"name\": \"GCH for ROY polymorphs\",\n \"description\": \"\"\"\nDemonstration of the Generalized Convex Hull construction for\npolymorphs of the ROY molecule. Molecules that are closest to\nthe hull built on PCA-based structural descriptors and having the\ninternal energy predicted by electronic-structure calculations as\nthe z axis are the most thermodynamically stable. Indeed most of the\nknown polymorphs of ROY are on (or very close) to this hull.\n\"\"\",\n \"authors\": [\"Michele Ceriotti \"],\n \"references\": [\n 'A. Anelli, E. A. Engel, C. J. Pickard, and M. Ceriotti, \\\n \"Generalized convex hull construction for materials discovery,\" \\\n Physical Review Materials 2(10), 103804 (2018).',\n 'G. J. O. Beran, I. J. Sugden, C. Greenwell, D. H. Bowskill, \\\n C. C. Pantelides, and C. S. Adjiman, \"How many more polymorphs of \\\n ROY remain undiscovered,\" Chem. Sci. 13(5), 1288\u20131297 (2022).',\n ],\n },\n settings={\n \"map\": {\n \"x\": {\"property\": \"pca_1\"},\n \"y\": {\"property\": \"pca_2\"},\n \"z\": {\"property\": \"energy\"},\n \"symbol\": \"type\",\n \"color\": {\"property\": \"hull_energy\"},\n \"size\": {\n \"factor\": 35,\n \"mode\": \"linear\",\n \"property\": \"\",\n \"reverse\": True,\n },\n },\n \"structure\": [\n {\n \"bonds\": True,\n \"unitCell\": True,\n \"keepOrientation\": True,\n }\n ],\n },\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and also load one as an interactive viewer\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "chemiscope.show_input(\"roy_gch.json.gz\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/62b1217b7f64a94ea92cd43a62433b84/dos-align.ipynb b/_downloads/62b1217b7f64a94ea92cd43a62433b84/dos-align.ipynb new file mode 100644 index 00000000..d7a4892f --- /dev/null +++ b/_downloads/62b1217b7f64a94ea92cd43a62433b84/dos-align.ipynb @@ -0,0 +1,543 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# A ML model for the electron density of states\n:Authors: How Wei Bin [@HowWeiBin](https://github.com/HowWeiBin/)\n\nThis tutorial would go through the entire machine learning framework for the electronic\ndensity of states (DOS). It will cover the construction of the DOS and SOAP\ndescriptors from ase Atoms and eigenenergy results. A simple neural network will\nthen be constructed and the model parameters, along with the energy reference will be\noptimized during training. A total of three energy reference will be used, the average\nHartree potential, the Fermi level, and an optimized energy reference starting from\nthe Fermi level energy reference. The performance of each model is then compared.\n\nFirst, lets begin by importing the necessary packages and helper functions\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import os\nimport zipfile\n\nimport ase\nimport ase.io\nimport matplotlib.pyplot as plt\nimport numpy as np\nimport requests\nimport torch\nfrom rascaline import SoapPowerSpectrum\nfrom scipy.interpolate import CubicHermiteSpline, interp1d\nfrom scipy.optimize import brentq\nfrom torch.utils.data import BatchSampler, DataLoader, Dataset, RandomSampler" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 0: Load Structures and Eigenenergies\n1) Downloading and Extracting Data\n2) Loading Data\n3) Find range of eigenenergies\n\nWe take a small subset of 104 structures in the Si dataset from `Bartok et al.,\n2018 `.\nEach structure in the dataset contains two atoms.\n\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1) Downloading and Extracting Data\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "filename = \"dataset.zip\"\nif not os.path.exists(filename):\n url = \"https://github.com/HowWeiBin/datasets/archive/refs/tags/Silicon-Diamonds.zip\"\n response = requests.get(url)\n response.raise_for_status()\n with open(filename, \"wb\") as f:\n f.write(response.content)\n\nwith zipfile.ZipFile(\"./dataset.zip\", \"r\") as zip_ref:\n zip_ref.extractall(\"./\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2) Loading Data\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "structures = ase.io.read(\"./datasets-Silicon-Diamonds/diamonds.xyz\", \":\")\nn_structures = len(structures)\nn_atoms = torch.tensor([len(i) for i in structures])\neigenenergies = torch.load(\"./datasets-Silicon-Diamonds/diamond_energies.pt\")\nk_normalization = torch.tensor(\n [len(i) for i in eigenenergies]\n) # Calculates number of kpoints sampled per structure\nprint(f\"Total number of structures: {len(structures)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3) Find range of eigenenergies\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Process eigenenergies to flattened torch tensors\n\ntotal_eigenenergies = [torch.flatten(torch.tensor(i)) for i in eigenenergies]\n\n# Get lowest and highest value of eigenenergies to know the range of eigenenergies\n\nall_eigenenergies = torch.hstack(total_eigenenergies)\nminE = torch.min(all_eigenenergies)\nmaxE = torch.max(all_eigenenergies)\nprint(f\"The lowest eigenenergy in the dataset is {minE:.3}\")\nprint(f\"The highest eigenenergy in the dataset is {maxE:.3}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Constructing the DOS with different energy references\n1) Construct the DOS using the original reference\n2) Calculate the Fermi level from the DOS\n3) Build a set of eigenenergies, with the energy reference set to the fermi level\n4) Truncate the DOS energy window so that the DOS is well-defined at each point\n5) Construct the DOS in the truncated energy window under both references\n6) Construct Splines for the DOS to facilitate interpolation during model training\n\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1) Construct the DOS using the original reference\nThe DOS will first be constructed from the full set of eigenenergies to\ndetermine the Fermi level of each structure. The original reference is the\nAverage Hartree Potential in this example.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# To ensure that all the eigenenergies are fully represented after\n# gaussian broadening, the energy axis of the DOS extends\n# 3eV wider than the range of values for the eigenenergies\nenergy_lower_bound = minE - 1.5\nenergy_upper_bound = maxE + 1.5\n\n# Gaussian Smearing for the eDOS, 0.3eV is the appropriate value for this dataset\n\nsigma = torch.tensor(0.3)\nenergy_interval = 0.05\n# energy axis, with a grid interval of 0.05 eV\n\nx_dos = torch.arange(energy_lower_bound, energy_upper_bound, energy_interval)\nprint(\n f\"The energy axis ranges from {energy_lower_bound:.3} to \\\n{energy_upper_bound:.3}, consisting of {len(x_dos)} grid points\"\n)\n\n# normalization factor for each DOS, factor of 2 is included\n# because each eigenenergy can be occupied by 2 electrons\n\nnormalization = 2 * (\n 1 / torch.sqrt(2 * torch.tensor(np.pi) * sigma**2) / n_atoms / k_normalization\n)\n\ntotal_edos = []\n\nfor structure_eigenenergies in total_eigenenergies:\n e_dos = torch.sum(\n # Builds a gaussian on each eigenenergy\n # and calculates the value on each grid point\n torch.exp(-0.5 * ((x_dos - structure_eigenenergies.view(-1, 1)) / sigma) ** 2),\n dim=0,\n )\n total_edos.append(e_dos)\n\ntotal_edos = torch.vstack(total_edos)\ntotal_edos = (total_edos.T * normalization).T\n\nprint(f\"The final shape of all the DOS in the dataset is: {list(total_edos.shape)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2) Calculate the Fermi level from the DOS\nNow we integration the DOS, and then use cubic interpolation and brentq\nto calculate the fermi level. Since only the 4 valence electrons in Silicon\nare represented in this energy range, we take the point where the DOS integrates\nto 4 as the fermi level.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fermi_levels = []\ntotal_i_edos = torch.cumulative_trapezoid(\n total_edos, x_dos, axis=1\n) # Integrate the DOS along the energy axis\nfor i in total_i_edos:\n interpolated = interp1d(\n x_dos[:-1], i - 4, kind=\"cubic\", copy=True, assume_sorted=True\n ) # We use i-4 because Silicon has 4 electrons in this energy range\n Ef = brentq(\n interpolated, x_dos[0] + 0.1, x_dos[-1] - 0.1\n ) # Fermi Level is the point where the (integrated DOS - 4) = 0\n # 0.1 is added and subtracted to prevent brentq from going out of range\n fermi_levels.append(Ef)\nfermi_levels = torch.tensor(fermi_levels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3) Build a set of eigenenergies, with the energy reference set to the fermi level\nUsing the fermi levels, we are now able to change the energy reference\nof the eigenenergies to the fermi level\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "total_eigenenergies_Ef = []\nfor index, energies in enumerate(total_eigenenergies):\n total_eigenenergies_Ef.append(energies - fermi_levels[index])\n\nall_eigenenergies_Ef = torch.hstack(total_eigenenergies_Ef)\n\nminE_Ef = torch.min(all_eigenenergies_Ef)\nmaxE_Ef = torch.max(all_eigenenergies_Ef)\nprint(f\"The lowest eigenenergy using the fermi level energy reference is {minE_Ef:.3}\")\nprint(f\"The highest eigenenergy using the fermi level energy reference is {maxE_Ef:.3}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4) Truncate the DOS energy window so that the DOS is well-defined at each point\nWith the fermi levels, we can also truncate the energy window for DOS prediction.\nIn this example, we truncate the energy window such that it is 3eV above\nthe highest Fermi level in the dataset.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# For the Average Hartree Potential energy reference\nx_dos_H = torch.arange(minE - 1.5, max(fermi_levels) + 3, energy_interval)\n\n# For the Fermi Level Energy Reference, all the Fermi levels in the dataset is 0eV\nx_dos_Ef = torch.arange(minE_Ef - 1.5, 3, energy_interval)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 5) Construct the DOS in the truncated energy window under both references\nHere we construct 2 different targets where they differ in the energy reference\nchosen. These targets will then be treated as different datasets for the model\nto learn on.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# For the Average Hartree Potential energy reference\n\ntotal_edos_H = []\n\nfor structure_eigenenergies_H in total_eigenenergies:\n e_dos = torch.sum(\n torch.exp(\n -0.5 * ((x_dos_H - structure_eigenenergies_H.view(-1, 1)) / sigma) ** 2\n ),\n dim=0,\n )\n total_edos_H.append(e_dos)\n\ntotal_edos_H = torch.vstack(total_edos_H)\ntotal_edos_H = (total_edos_H.T * normalization).T\n\n\n# For the Fermi Level Energy Reference\n\ntotal_edos_Ef = []\n\nfor structure_eigenenergies_Ef in total_eigenenergies_Ef:\n e_dos = torch.sum(\n torch.exp(\n -0.5 * ((x_dos_Ef - structure_eigenenergies_Ef.view(-1, 1)) / sigma) ** 2\n ),\n dim=0,\n )\n total_edos_Ef.append(e_dos)\n\ntotal_edos_Ef = torch.vstack(total_edos_Ef)\ntotal_edos_Ef = (total_edos_Ef.T * normalization).T" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 6) Construct Splines for the DOS to facilitate interpolation during model training\nBuilding Cubic Hermite Splines on the DOS on the truncated energy window\nto facilitate interpolation during training. Cubic Hermite Splines takes\nin information on the value and derivative of a function at a point to build splines.\nThus, we will have to compute both the value and derivative at each spline position\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Functions to compute the value and derivative of the DOS at each energy value, x\ndef edos_value(x, eigenenergies, normalization):\n e_dos_E = (\n torch.sum(\n torch.exp(-0.5 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2), dim=0\n )\n * normalization\n )\n\n return e_dos_E\n\n\ndef edos_derivative(x, eigenenergies, normalization):\n dfn_dos_E = (\n torch.sum(\n torch.exp(-0.5 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2)\n * (-1 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2),\n dim=0,\n )\n * normalization\n )\n\n return dfn_dos_E\n\n\ntotal_splines_H = []\n# the splines have a higher energy range in case the shift is high\nspline_positions_H = torch.arange(minE - 2, max(fermi_levels) + 6, energy_interval)\n\nfor index, structure_eigenenergies_H in enumerate(total_eigenenergies):\n e_dos_H = edos_value(\n spline_positions_H, structure_eigenenergies_H, normalization[index]\n )\n e_dos_H_grad = edos_derivative(\n spline_positions_H, structure_eigenenergies_H, normalization[index]\n )\n spliner = CubicHermiteSpline(spline_positions_H, e_dos_H, e_dos_H_grad)\n total_splines_H.append(torch.tensor(spliner.c))\n\ntotal_splines_H = torch.stack(total_splines_H)\n\ntotal_splines_Ef = []\nspline_positions_Ef = torch.arange(minE_Ef - 2, 6, energy_interval)\n\nfor index, structure_eigenenergies_Ef in enumerate(total_eigenenergies_Ef):\n e_dos_Ef = edos_value(\n spline_positions_Ef, structure_eigenenergies_Ef, normalization[index]\n )\n e_dos_Ef_grad = edos_derivative(\n spline_positions_Ef, structure_eigenenergies_Ef, normalization[index]\n )\n spliner = CubicHermiteSpline(spline_positions_Ef, e_dos_Ef, e_dos_Ef_grad)\n total_splines_Ef.append(torch.tensor(spliner.c))\n\ntotal_splines_Ef = torch.stack(total_splines_Ef)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have stored the splines coefficients (spliner.c) as torch tensors,\nas such as we will need to write a function to evaluate the DOS from\nthe splines positions and coefficients.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def evaluate_spline(spline_coefs, spline_positions, x):\n \"\"\"\n spline_coefs: shape of (n x 4 x spline_positions)\n\n return value: shape of (n x x)\n\n x : shape of (n x n_points)\n \"\"\"\n interval = torch.round(\n spline_positions[1] - spline_positions[0], decimals=4\n ) # get spline grid intervals\n x = torch.clamp(\n x, min=spline_positions[0], max=spline_positions[-1] - 0.0005\n ) # restrict x to fall within the spline interval\n # 0.0005 is substracted to combat errors arising from precision\n indexes = torch.floor(\n (x - spline_positions[0]) / interval\n ).long() # Obtain the index for the appropriate spline coefficients\n expanded_index = indexes.unsqueeze(dim=1).expand(-1, 4, -1)\n x_1 = x - spline_positions[indexes]\n x_2 = x_1 * x_1\n x_3 = x_2 * x_1\n x_0 = torch.ones_like(x_1)\n x_powers = torch.stack([x_3, x_2, x_1, x_0]).permute(1, 0, 2)\n value = torch.sum(\n torch.mul(x_powers, torch.gather(spline_coefs, 2, expanded_index)), axis=1\n )\n\n return value # returns the value of the DOS at the energy positions, x." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets look at the accuracy of the splines.\nTest 1: Ability to reproduce the correct values at the default x_dos positions\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "shifts = torch.zeros(n_structures)\nx_dos_splines = x_dos_H + shifts.view(-1, 1)\nspline_dos_H = evaluate_spline(total_splines_H, spline_positions_H, x_dos_splines)\n\nplt.plot(x_dos_H, total_edos_H[0], color=\"red\", label=\"True DOS\")\nplt.plot(x_dos_H, spline_dos_H[0], color=\"blue\", linestyle=\"--\", label=\"Spline DOS\")\nplt.legend()\nplt.xlabel(\"Energy [eV]\")\nplt.ylabel(\"DOS\")\nprint(\"Both lines lie on each other\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test 2: Ability to reproduce the correct values at the shifted x_dos positions\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "shifts = torch.zeros(n_structures) + 0.3\nx_dos_splines = x_dos_Ef + shifts.view(-1, 1)\nspline_dos_Ef = evaluate_spline(total_splines_Ef, spline_positions_Ef, x_dos_splines)\n\nplt.plot(x_dos_Ef, total_edos_Ef[0], color=\"red\", label=\"True DOS\")\nplt.plot(x_dos_Ef, spline_dos_Ef[0], color=\"blue\", linestyle=\"--\", label=\"Spline DOS\")\nplt.legend()\nplt.xlabel(\"Energy [eV]\")\nplt.ylabel(\"DOS\")\nprint(\"Both spectras look very similar\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Compute SOAP power spectrum for the dataset\n\nWe first define the hyperparameters to compute the\nSOAP power spectrum using rascaline.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "HYPER_PARAMETERS = {\n \"cutoff\": 4.0,\n \"max_radial\": 8,\n \"max_angular\": 6,\n \"atomic_gaussian_width\": 0.45,\n \"center_atom_weight\": 1.0,\n \"radial_basis\": {\"Gto\": {}},\n \"cutoff_function\": {\n \"Step\": {},\n },\n \"radial_scaling\": {\n \"Willatt2018\": {\n \"exponent\": 5,\n \"rate\": 1,\n \"scale\": 3.0,\n },\n },\n}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We feed the Hyperparameters into rascaline to compute the SOAP Power spectrum\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "calculator = SoapPowerSpectrum(**HYPER_PARAMETERS)\nR_total_soap = calculator.compute(structures)\n# Transform the tensormap to a single block containing a dense representation\nR_total_soap.keys_to_samples(\"species_center\")\nR_total_soap.keys_to_properties([\"species_neighbor_1\", \"species_neighbor_2\"])\n\n# Now we extract the data tensor from the single block\ntotal_atom_soap = []\nfor structure_i in range(n_structures):\n a_i = R_total_soap.block(0).samples[\"structure\"] == structure_i\n total_atom_soap.append(torch.tensor(R_total_soap.block(0).values[a_i, :]))\n\ntotal_soap = torch.stack(total_atom_soap)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 3: Building a Simple MLP Model\n\n1) Split the data into Training, Validation and Test\n2) Define the dataloader and the Model Architecture\n3) Define relevant loss functions for training and inference\n4) Define the training loop\n5) Evaluate the model\n\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1) Split the data into Training, Validation and Test\nWe will first split the data in a 7:1:2 manner, corresponding to train, val and test.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "np.random.seed(0)\ntrain_index = np.arange(n_structures)\nnp.random.shuffle(train_index)\ntest_mark = int(0.8 * n_structures)\nval_mark = int(0.7 * n_structures)\ntest_index = train_index[test_mark:]\nval_index = train_index[val_mark:test_mark]\ntrain_index = train_index[:val_mark]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2) Define the dataloader and the Model Architecture\nWe will now build a dataloader and dataset to facillitate training the model batchwise\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def generate_atomstructure_index(n_atoms_per_structure):\n \"\"\"Generate a sequence of indices for each atom in the structure.\n The indices correspond to index of the structure that the atom belongs to\n\n Args:\n n_atoms_per_structure ([array]):\n [Array containing the number of atoms each structure contains]\n\n Return s:\n [tensor]: [Total index, matching atoms to structure]\n \"\"\"\n # n_structures = len(n_atoms_per_structure)\n total_index = []\n for i, atoms in enumerate(n_atoms_per_structure):\n indiv_index = torch.zeros(atoms) + i\n total_index.append(indiv_index)\n total_index = torch.hstack(total_index)\n return total_index.long()\n\n\nclass AtomicDataset(Dataset):\n def __init__(self, features, n_atoms_per_structure):\n self.features = features\n self.n_structures = len(n_atoms_per_structure)\n self.n_atoms_per_structure = n_atoms_per_structure\n self.index = generate_atomstructure_index(self.n_atoms_per_structure)\n assert torch.sum(n_atoms_per_structure) == len(features)\n\n def __len__(self):\n return self.n_structures\n\n def __getitem__(self, idx):\n if isinstance(idx, list): # If a list of indexes is given\n feature_indexes = []\n\n for i in idx:\n feature_indexes.append((self.index == i).nonzero(as_tuple=True)[0])\n\n feature_indexes = torch.hstack(feature_indexes)\n\n return (\n self.features[feature_indexes],\n idx,\n generate_atomstructure_index(self.n_atoms_per_structure[idx]),\n )\n\n else:\n feature_indexes = (self.index == idx).nonzero(as_tuple=True)[0]\n return (\n self.features[feature_indexes],\n idx,\n self.n_atoms_per_structure[idx],\n )\n\n\ndef collate(\n batch,\n): # Defines how to collate the outputs of the __getitem__ function at each batch\n for x, idx, index in batch:\n return (x, idx, index)\n\n\nx_train = torch.flatten(total_soap[train_index], 0, 1).float()\ntotal_atomic_soaps = torch.vstack(total_atom_soap).float()\ntrain_features = AtomicDataset(x_train, n_atoms[train_index])\nfull_atomstructure_index = generate_atomstructure_index(n_atoms)\n# Will be required later to collate atomic predictions into structural predictions\n\n# Build a Dataloader that samples from the AtomicDataset in random batches\nSampler = RandomSampler(train_features)\nBSampler = BatchSampler(Sampler, batch_size=32, drop_last=False)\ntraindata_loader = DataLoader(train_features, sampler=BSampler, collate_fn=collate)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will now define a simple three layer MLP model, consisting of three layers.\nThe align keyword is used to indicate that the energy reference will be optimized\nduring training. The alignment parameter refers to the adjustments made to the\ninitial energy referenced and will be initialized as zeros.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class SOAP_NN(torch.nn.Module):\n def __init__(self, input_dims, L1, n_train, target_dims, align):\n super(SOAP_NN, self).__init__()\n self.target_dims = target_dims\n self.fc1 = torch.nn.Linear(input_dims, L1)\n self.fc2 = torch.nn.Linear(L1, target_dims)\n self.silu = torch.nn.SiLU()\n self.align = align\n if align:\n initial_alignment = torch.zeros(n_train)\n self.alignment = torch.nn.parameter.Parameter(initial_alignment)\n\n def forward(self, x):\n result = self.fc1(x)\n result = self.silu(result)\n result = self.fc2(result)\n return result" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will use a small network architecture, whereby the input layer corresponds\nto the size of the SOAP features, 448, the intermediate layer corresponds to\na tenth size of the input layer and the final layer corresponds\nto the number of outputs.\n\nAs a shorthand, the model that optimizes the energy reference during\ntraining will be called the alignment model\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_outputs_H = len(x_dos_H)\nn_outputs_Ef = len(x_dos_Ef)\n\n\nModel_H = SOAP_NN(\n x_train.shape[1],\n x_train.shape[1] // 10,\n len(train_index),\n n_outputs_H,\n align=False,\n)\nModel_Ef = SOAP_NN(\n x_train.shape[1],\n x_train.shape[1] // 10,\n len(train_index),\n n_outputs_Ef,\n align=False,\n)\nModel_Align = SOAP_NN(\n x_train.shape[1],\n x_train.shape[1] // 10,\n len(train_index),\n n_outputs_Ef,\n align=True,\n)\n# The alignment model takes the fermi level energy reference as the starting point" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3) Define relevant loss functions for training and inference\nWe will now define some loss functions that will be useful when we implement\nthe model training loop later and during model evaluation on the test set.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def t_get_mse(a, b, xdos):\n \"\"\"Compute mean error between two Density of States.\n The mean error is integrated across the entire energy grid\n to provide a single value to characterize the error\n\n Args:\n a ([tensor]): [Predicted DOS]\n b ([tensor]): [True DOS]\n xdos ([tensor], optional): [Energy axis of DOS]\n\n Returns:\n [float]: [MSE]\n \"\"\"\n if len(a.size()) > 1:\n mse = (torch.trapezoid((a - b) ** 2, xdos, axis=1)).mean()\n else:\n mse = (torch.trapezoid((a - b) ** 2, xdos, axis=0)).mean()\n return mse\n\n\ndef t_get_rmse(a, b, xdos):\n \"\"\"Compute root mean squared error between two Density of States .\n\n Args:\n a ([tensor]): [Predicted DOS]\n b ([tensor]): [True DOS]\n xdos ([tensor], optional): [Energy axis of DOS]\n\n Raises:\n ValueError: [Occurs if tensor shapes are mismatched]\n\n Returns:\n [float]: [RMSE or %RMSE]\n \"\"\"\n\n if len(a.size()) > 1:\n rmse = torch.sqrt((torch.trapezoid((a - b) ** 2, xdos, axis=1)).mean())\n else:\n rmse = torch.sqrt((torch.trapezoid((a - b) ** 2, xdos, axis=0)).mean())\n return rmse\n\n\ndef Opt_RMSE_spline(y_pred, xdos, target_splines, spline_positions, n_epochs):\n \"\"\"Evaluates RMSE on the optimal shift of energy axis.\n The optimal shift is found via gradient descent after a gridsearch is performed.\n\n Args:\n y_pred ([tensor]): [Prediction/s of DOS]\n xdos ([tensor]): [Energy axis]\n target_splines ([tensor]): [Contains spline coefficients]\n spline_positions ([tensor]): [Contains spline positions]\n n_epochs ([int]): [Number of epochs to run for Gradient Descent]\n\n Returns:\n [rmse([float]), optimal_shift[tensor]]:\n [RMSE on optimal shift, the optimal shift itself]\n\n \"\"\"\n optim_search_mse = []\n offsets = torch.arange(-2, 2, 0.1)\n # Grid-search is first done to reduce number of epochs needed for\n # gradient descent, typically 50 epochs will be sufficient\n # if searching within 0.1\n with torch.no_grad():\n for offset in offsets:\n shifts = torch.zeros(y_pred.shape[0]) + offset\n shifted_target = evaluate_spline(\n target_splines, spline_positions, xdos + shifts.view(-1, 1)\n )\n loss_i = ((y_pred - shifted_target) ** 2).mean(dim=1)\n optim_search_mse.append(loss_i)\n optim_search_mse = torch.vstack(optim_search_mse)\n min_index = torch.argmin(optim_search_mse, dim=0)\n optimal_offset = offsets[min_index]\n\n offset = optimal_offset\n\n shifts = torch.nn.parameter.Parameter(offset.float())\n opt_adam = torch.optim.Adam([shifts], lr=1e-2)\n best_error = torch.zeros(len(shifts)) + 100\n best_shifts = shifts.clone()\n for _ in range(n_epochs):\n shifted_target = evaluate_spline(\n target_splines, spline_positions, xdos + shifts.view(-1, 1)\n ).detach()\n\n def closure():\n opt_adam.zero_grad()\n shifted_target = evaluate_spline(\n target_splines, spline_positions, xdos + shifts.view(-1, 1)\n )\n loss_i = ((y_pred - shifted_target) ** 2).mean()\n loss_i.backward(gradient=torch.tensor(1), inputs=shifts)\n return loss_i\n\n opt_adam.step(closure)\n\n with torch.no_grad():\n each_loss = ((y_pred - shifted_target) ** 2).mean(dim=1).float()\n index = each_loss < best_error\n best_error[index] = each_loss[index].clone()\n best_shifts[index] = shifts[index].clone()\n\n # Evaluate\n\n optimal_shift = best_shifts\n shifted_target = evaluate_spline(\n target_splines, spline_positions, xdos + optimal_shift.view(-1, 1)\n )\n rmse = t_get_rmse(y_pred, shifted_target, xdos)\n return rmse, optimal_shift" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4) Define the training loop\n\nWe will now define the model training loop, for simplicity we will only\ntrain each model for a fixed number of epochs, learning rate, and batch_size.\nThe training and validation error at each epoch will be saved.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def train_model(model_to_train, fixed_DOS, structure_splines, spline_positions, x_dos):\n \"\"\"Trains a model for 500 epochs\n\n Args:\n model_to_train ([torch.nn.Module]): [ML Model]\n fixed_DOS ([tensor]): [Contains the DOS at a fixed energy reference,\n useful for models that don't optimize the energy reference]\n structure_splines ([tensor]): [Contains spline coefficients]\n spline_positions ([tensor]): [Contains spline positions]\n x_dos ([tensor]): [Energy axis for the prediction]\n\n Returns:\n [train_loss_history([tensor]),\n val_loss_history[tensor],\n structure_results[tensor]]:\n\n [Respective loss histories and final structure predictions]\n \"\"\"\n lr = 1e-2\n n_epochs = 500\n\n opt = torch.optim.Adam(model_to_train.parameters(), lr=lr)\n\n train_loss_history = []\n val_loss_history = []\n\n for _epoch in range(n_epochs):\n for x_data, idx, index in traindata_loader:\n opt.zero_grad()\n predictions = model_to_train.forward(x_data)\n structure_results = torch.zeros([len(idx), model_to_train.target_dims])\n # Sum atomic predictions in each structure\n structure_results = structure_results.index_add_(\n 0, index, predictions\n ) / n_atoms[train_index[idx]].view(-1, 1)\n if model_to_train.align:\n alignment = model_to_train.alignment\n alignment = alignment - torch.mean(alignment)\n # Enforce that the alignments have a mean of zero since a constant\n # value across the dataset is meaningless when optimizing the\n # relative energy reference\n target = evaluate_spline(\n structure_splines[train_index[idx]],\n spline_positions,\n x_dos + alignment[idx].view(-1, 1),\n ) # Shifts the target based on the alignment value\n pred_loss = t_get_mse(structure_results, target, x_dos)\n pred_loss.backward()\n else:\n pred_loss = t_get_mse(\n structure_results, fixed_DOS[train_index[idx]], x_dos\n )\n pred_loss.backward()\n\n opt.step()\n with torch.no_grad():\n all_pred = model_to_train.forward(total_atomic_soaps.float())\n structure_results = torch.zeros([n_structures, model_to_train.target_dims])\n structure_results = structure_results.index_add_(\n 0, full_atomstructure_index, all_pred\n ) / (n_atoms).view(-1, 1)\n if model_to_train.align:\n # Evaluate model on optimal shift as there is no information\n # regarding the shift from the fermi level energy reference\n # during inference\n\n alignment = model_to_train.alignment\n alignment = alignment - torch.mean(alignment)\n target = evaluate_spline(\n structure_splines[train_index],\n spline_positions,\n x_dos + alignment.view(-1, 1),\n )\n\n train_loss = t_get_rmse(structure_results[train_index], target, x_dos)\n val_loss, val_shifts = Opt_RMSE_spline(\n structure_results[val_index],\n x_dos,\n structure_splines[val_index],\n spline_positions,\n 50,\n )\n\n else:\n train_loss = t_get_rmse(\n structure_results[train_index], fixed_DOS[train_index], x_dos\n )\n val_loss = t_get_rmse(\n structure_results[val_index], fixed_DOS[val_index], x_dos\n )\n\n train_loss_history.append(train_loss)\n val_loss_history.append(val_loss)\n train_loss_history = torch.tensor(train_loss_history)\n val_loss_history = torch.tensor(val_loss_history)\n return (\n train_loss_history,\n val_loss_history,\n structure_results,\n )\n # returns the loss history and the final set of predictions" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "H_trainloss, H_valloss, H_predictions = train_model(\n Model_H, total_edos_H, total_splines_H, spline_positions_H, x_dos_H\n)\n\nEf_trainloss, Ef_valloss, Ef_predictions = train_model(\n Model_Ef, total_edos_Ef, total_splines_Ef, spline_positions_Ef, x_dos_Ef\n)\n\nAlign_trainloss, Align_valloss, Align_predictions = train_model(\n Model_Align, total_edos_Ef, total_splines_Ef, spline_positions_Ef, x_dos_Ef\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets plot the train loss histories to compare their learning behaviour\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "epochs = np.arange(500)\n\n\nplt.plot(epochs, H_trainloss, color=\"red\", label=\"Avg Hartree Potential\")\nplt.plot(epochs, Ef_trainloss, color=\"blue\", label=\"Fermi Level\")\nplt.plot(epochs, Align_trainloss, color=\"green\", label=\"Optimized Reference\")\nplt.legend()\nplt.yscale(value=\"log\")\nplt.xlabel(\"Epochs\")\nplt.ylabel(\"RMSE\")\nplt.title(\"Train Loss vs Epoch\")\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets plot the val loss histories to compare their learning behaviour\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "plt.plot(epochs, H_valloss, color=\"red\", label=\"Avg Hartree Potential\")\nplt.plot(epochs, Ef_valloss, color=\"blue\", label=\"Fermi Level\")\nplt.plot(epochs, Align_valloss, color=\"green\", label=\"Optimized Reference\")\nplt.legend()\nplt.yscale(value=\"log\")\nplt.xlabel(\"Epochs\")\nplt.ylabel(\"RMSE\")\nplt.title(\"Validation Loss vs Epoch\")\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 5) Evaluate the model\nWe will now evaluate the model performance on the test set\nbased on the model predictions we obtained previously\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "H_testloss = Opt_RMSE_spline(\n H_predictions[test_index],\n x_dos_H,\n total_splines_H[test_index],\n spline_positions_H,\n 200,\n) # We use 200 epochs just so it the error a little bit more converged\nEf_testloss = Opt_RMSE_spline(\n Ef_predictions[test_index],\n x_dos_Ef,\n total_splines_Ef[test_index],\n spline_positions_Ef,\n 200,\n) # We use 200 epochs just so it the error a little bit more converged\nAlign_testloss = Opt_RMSE_spline(\n Align_predictions[test_index],\n x_dos_Ef,\n total_splines_Ef[test_index],\n spline_positions_Ef,\n 200,\n) # We use 200 epochs just so it the error a little bit more converged\n\nprint(f\"Test RMSE for average Hartree Potential: {H_testloss[0].item():.3}\")\nprint(f\"Test RMSE for Fermi Level: {Ef_testloss[0].item():.3}\")\nprint(f\"Test RMSE for Optimized Reference: {Align_testloss[0].item():.3}\")\n\nprint(\n \"The difference in effectiveness between the Optimized Reference \\\nand the Fermi Level will increase with more epochs\"\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot Training DOSes at different energy reference to visualize\nthe impact of the energy reference. From the plots we can see\nthat the optimized energy reference has better alignment of\ncommon spectral patterns across the dataset\n\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n\nAverage Hartree Energy Reference\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for i in total_edos_H[train_index]:\n plt.plot(x_dos_H, i, color=\"C0\", alpha=0.6)\nplt.title(\"Energy Reference - Average Hartree Potential\")\nplt.xlabel(\"Energy [eV]\")\nplt.ylabel(\"DOS\")\nplt.show()\nprint(\"The DOSes, despite looking similar, are offset along the energy axis\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Fermi Level Energy Reference\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for i in total_edos_Ef[train_index]:\n plt.plot(x_dos_Ef, i, color=\"C0\", alpha=0.6)\nplt.title(\"Energy Reference - Fermi Level\")\nplt.xlabel(\"Energy [eV]\")\nplt.ylabel(\"DOS\")\nplt.show()\n\nprint(\"It is better aligned but still quite some offset\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Optimized Energy Reference\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "shifts = Model_Align.alignment.detach()\nshifts = shifts - torch.mean(shifts)\nx_dos_splines = x_dos_Ef + shifts.view(-1, 1)\ntotal_edos_align = evaluate_spline(\n total_splines_Ef[train_index], spline_positions_Ef, x_dos_splines\n)\n\nfor i in total_edos_align:\n plt.plot(x_dos_Ef, i, color=\"C0\", alpha=0.6)\nplt.title(\"Energy Reference - Optimized\")\nplt.xlabel(\"Energy [eV]\")\nplt.ylabel(\"DOS\")\nplt.show()\nprint(\"The DOS alignment is better under the optimized energy reference\")\nprint(\"The difference will increase with more training epochs\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/64137e0eebfcb548a6786ce728aa41b4/environment.yml b/_downloads/64137e0eebfcb548a6786ce728aa41b4/environment.yml new file mode 100644 index 00000000..6d18827e --- /dev/null +++ b/_downloads/64137e0eebfcb548a6786ce728aa41b4/environment.yml @@ -0,0 +1,12 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - lammps + - pip: + - ase==3.22.1 + - chemiscope>=0.7 + - git+https://github.com/i-pi/i-pi.git@main + - matplotlib + - skmatter diff --git a/_downloads/6cadff1f3492fc92f1615765051399cd/environment.yml b/_downloads/6cadff1f3492fc92f1615765051399cd/environment.yml new file mode 100644 index 00000000..27cf94ce --- /dev/null +++ b/_downloads/6cadff1f3492fc92f1615765051399cd/environment.yml @@ -0,0 +1,12 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - rust >=1.65 + - pip: + - ase==3.22.1 + - equisolve @ git+https://github.com/lab-cosmo/equisolve.git@c858bedef4b2799eb445e4c92535ee387224089a + - matplotlib + - metatensor + - rascaline @ git+https://github.com/Luthaf/rascaline@ca957642f512e141c7570e987aadc05c7ac71983 diff --git a/_downloads/6e397e9158b2a5505af1904db0846a5c/run_calcs.sh b/_downloads/6e397e9158b2a5505af1904db0846a5c/run_calcs.sh new file mode 100644 index 00000000..59a8ff53 --- /dev/null +++ b/_downloads/6e397e9158b2a5505af1904db0846a5c/run_calcs.sh @@ -0,0 +1,7 @@ +#! /bin/bash + +for i in $(find ./production/ -mindepth 1 -type d); do + cd $i + cp2k.ssmp -i in.cp2k + cd - +done diff --git a/_downloads/71c5cdd3040f0ebf209e70539664ca89/environment.yml b/_downloads/71c5cdd3040f0ebf209e70539664ca89/environment.yml new file mode 100644 index 00000000..6d18827e --- /dev/null +++ b/_downloads/71c5cdd3040f0ebf209e70539664ca89/environment.yml @@ -0,0 +1,12 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - lammps + - pip: + - ase==3.22.1 + - chemiscope>=0.7 + - git+https://github.com/i-pi/i-pi.git@main + - matplotlib + - skmatter diff --git a/_downloads/8052f55b323764c2ee21cbfef5187bf4/lpr.ipynb b/_downloads/8052f55b323764c2ee21cbfef5187bf4/lpr.ipynb new file mode 100644 index 00000000..d3792473 --- /dev/null +++ b/_downloads/8052f55b323764c2ee21cbfef5187bf4/lpr.ipynb @@ -0,0 +1,201 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Local Prediction Rigidity analysis\n\n:Authors: Sanggyu \"Raymond\" Chong [@SanggyuChong](https://github.com/sanggyuChong/);\n Federico Grasselli [@fgrassel](https://github.com/fgrassel/)\n\nIn this tutorial, we calculate the SOAP descriptors of an amorphous\nsilicon dataset using rascaline, then compute the local prediction\nrigidity (LPR) for the atoms of a \"test\" set before and after\nmodifications to the \"training\" dataset has been made.\n\nFirst, we import all the necessary packages:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import os\nimport tarfile\n\nimport numpy as np\nimport requests\nfrom ase.io import read\nfrom matplotlib import pyplot as plt\nfrom matplotlib.colors import LogNorm\nfrom rascaline import SoapPowerSpectrum\nfrom sklearn.decomposition import PCA\nfrom skmatter.metrics import local_prediction_rigidity as lpr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Load and prepare amorphous silicon data\n\n\nWe first download the dataset associated with LPR\nanalysis from Materials Cloud and load the the amorphous\nsilicon structures using [ASE](https://wiki.fysik.dtu.dk/ase/).\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "filename = \"LPR_supp_notebook_dataset.tar.gz\"\nif not os.path.exists(filename):\n url = \"https://rb.gy/wxsrug\" # shortened URL\n response = requests.get(url)\n response.raise_for_status()\n with open(filename, \"wb\") as f:\n f.write(response.content)\n\nwith tarfile.open(filename) as tar:\n tar.extractall(path=\".\")\n\nframes_pristine = read(\"datasets/Si_amo_defect_free.xyz\", \":\")\nframes_defect = read(\"datasets/Si_amo_defect_containing.xyz\", \":\")\n\n# Randomly shuffle the structures\n\nnp.random.seed(20230215)\n\nids = list(range(len(frames_pristine)))\nnp.random.shuffle(ids)\nframes_pristine = [frames_pristine[ii] for ii in ids]\n\nids = list(range(len(frames_defect)))\nnp.random.shuffle(ids)\nframes_defect = [frames_defect[ii] for ii in ids]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now further refine the loaded datasets according the the\nnumber of coordinated atoms that each atomic environment exhibits.\n\"Pristine\" refers to structures where all of the atoms have strictly\n4 coordinating atoms. \"Defect\" refers to structures that contain\natoms with coordination numbers other than 4.\n\nWe use :code:`get_all_distances` funciton of :code:`ase.Atoms` to detect the\nnumber of coordinated atoms.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "cur_cutoff = 2.7\nrefined_pristine_frames = []\nfor frame in frames_pristine:\n neighs = (frame.get_all_distances(mic=True) < cur_cutoff).sum(axis=0) - 1\n if neighs.max() > 4 or neighs.min() < 4:\n continue\n else:\n refined_pristine_frames.append(frame)\n\nrefined_defect_frames = []\nfor frame in frames_defect:\n neighs = (frame.get_all_distances(mic=True) < cur_cutoff).sum(axis=0) - 1\n num_defects = (neighs > 4).sum() + (neighs < 4).sum()\n if num_defects > 4:\n refined_defect_frames.append(frame)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute SOAP descriptors using rascaline\n\nNow, we move on and compute the SOAP descriptors for the refined\nstructures. First, define the rascaline hyperparameters used to\ncompute SOAP. Among the hypers, notice that the cutoff is chosen\nto be 2.85 \u00c5, and the radial scaling is turned off. These were\nheuristic choices made to accentuate the difference in the LPR\nbased on the nearest-neighbor coordination. (Do not blindly\nuse this set of hypers for production-quality model training!)\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Hypers dictionary\nhypers = {\n \"cutoff\": 2.85,\n \"max_radial\": 10,\n \"max_angular\": 12,\n \"atomic_gaussian_width\": 0.5,\n \"center_atom_weight\": 1.0,\n \"radial_basis\": {\"Gto\": {\"spline_accuracy\": 1e-8}},\n \"cutoff_function\": {\"ShiftedCosine\": {\"width\": 0.1}},\n \"radial_scaling\": None,\n}\n# Define rascaline calculator\ncalculator = SoapPowerSpectrum(**hypers)\n\n# Calculate the SOAP power spectrum\nXlist_pristine = []\nfor frame in refined_pristine_frames:\n descriptor = calculator.compute(frame)\n Xlist_pristine.append(np.array(descriptor.block().values))\n\nXlist_defect = []\nfor frame in refined_defect_frames:\n descriptor = calculator.compute(frame)\n Xlist_defect.append(np.array(descriptor.block().values))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Organize structures into \"training\" and \"test\" sets\n\nNow we move on and compute the SOAP descriptors for the refined\nstructures. First, define the rascaline hyperparameters used to\ncompute SOAP.\n\nNotice that the format in which we handle the descriptors is as a\nlist of :code:`np.array` descriptor blocks. This is to ensure\ncompatibility with how things have been implemented in the LPR\nmodule of :code:`scikit-matter`.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "n_train = 400\nn_add = 50\nn_test = 50\n\nX_pristine = [Xlist for Xlist in Xlist_pristine[: n_train + n_add]]\nX_defect = [Xlist for Xlist in Xlist_defect[:n_add]]\nX_test = [Xlist for Xlist in Xlist_defect[n_add : n_add + n_test]]\n\n# Save coordination values for visualization\ntest_coord = []\nfor frame in refined_defect_frames[n_add : n_add + n_test]:\n coord = (frame.get_all_distances(mic=True) < cur_cutoff - 0.05).sum(axis=0) - 1\n test_coord += coord.tolist()\ntest_coord = np.array(test_coord)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the LPR for the test set\n\nNext, we will use the :code:`local_prediction_rigidity` module of\n[scikit-matter](https://scikit-matter.readthedocs.io/en/latest/)\nto compute the LPRs for the test set that we have set apart.\n\nLPR reflects how the ML model perceives a local environment,\ngiven a collection of other structures, similar or different.\nIt should then carry over some of the details involved in training\nthe model, in this case the regularization strength.\n\nFor this example, we have foregone on the actual model training,\nand so we define an arbitrary value for the alpha.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "alpha = 1e-4\nLPR_test, rank = lpr(X_pristine, X_test, alpha)\nLPR_test = np.hstack(LPR_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Visualizing the LPR on a PCA map\n\nWe now visualize the LPRs of the test set on a PCA map,\nwhere the PCA is performed on the SOAP descriptors of\ndefect-containing dataset.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pca = PCA(n_components=5)\ndescriptors_all = calculator.compute(refined_defect_frames)\npca.fit_transform(descriptors_all.block().values)\nPCA_test = pca.transform(np.vstack(X_test))\n\nrmin = np.log10(LPR_test.min()) + 0.5\nrmax = np.log10(LPR_test.max()) - 0.5\n\nfig = plt.figure(figsize=(5, 4), dpi=200)\nax = fig.add_subplot()\nim = ax.scatter(\n PCA_test[:, 0],\n PCA_test[:, 1],\n c=LPR_test,\n s=20,\n linewidths=0,\n norm=LogNorm(vmin=10**rmin, vmax=10**rmax),\n cmap=\"viridis\",\n)\n\nax.set_xlabel(\"PC1\")\nax.set_ylabel(\"PC2\")\nfig.colorbar(im, ax=ax, label=\"LPR\")\nax.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the PCA map, where each point corresponds to an\natomic environment of the test set structures, one\ncan observe 4 different clusters of points, arranged\nalong PC1. This corresponds to the coordination numbers\nranging from 3 to 6. Since the training set contains\nstructures exclusively composed of 4-coordinated atoms,\nLPR is distinctly high for the second, main cluster of\npoints, and quite low for the three other clusters.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Studying the LPR after dataset modification\n\nWe now want to see what would happen when defect structures\nare included into the training set of the model. For this,\nwe first create a modified dataset that incorporates in the\ndefect structures, and recompute the LPR.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "X_new = X_pristine[:n_train] + X_defect[:n_add]\nLPR_test_new, rank = lpr(X_new, X_test, alpha)\nLPR_test_new = np.hstack(LPR_test_new)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then visualize the change in the LPR with the\nmodification of the dataset by plotting the same PCA\nmap, but now colored by the ratio of new set of LPR\nvalues (after dataset modification) over the original\none.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig = plt.figure(figsize=(5, 4), dpi=200)\nax = fig.add_subplot()\nim = ax.scatter(\n PCA_test[:, 0],\n PCA_test[:, 1],\n c=LPR_test_new / LPR_test,\n s=20,\n linewidths=0,\n # norm=LogNorm(vmin=10**rmin, vmax=10**rmax),\n cmap=\"OrRd\",\n)\nax.set_xlabel(\"PC1\")\nax.set_ylabel(\"PC2\")\nfig.colorbar(im, ax=ax, label=r\"LPR$_{\\mathrm{new}}$ / LPR$_{\\mathrm{old}}$\")\nax.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is apparent that while the LPR stays more or less consistent for the\n4-coordinated atoms, it is significantly enhanced for the defective environments\nas a result of the inclusion of defective structures in the training set.\n\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/87860011d67b243cba3a72df0fa64d08/lode-linear.ipynb b/_downloads/87860011d67b243cba3a72df0fa64d08/lode-linear.ipynb new file mode 100644 index 00000000..d31e6771 --- /dev/null +++ b/_downloads/87860011d67b243cba3a72df0fa64d08/lode-linear.ipynb @@ -0,0 +1,446 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Long-distance Equivariants: a tutorial\n\n:Authors: Philip Loche [@PicoCentauri](https://github.com/PicoCentauri/),\n Kevin Huguenin-Dumittan [@kvhuguenin](https://github.com/kvhuguenin)\n\nThis tutorial explains how Long range equivariant descriptors can be constructed using\nrascaline and the resulting descriptors be used to construct a linear model with\nequisolve\n\nFirst, import all the necessary packages\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import ase.io\nimport matplotlib.pyplot as plt\nimport metatensor\nimport numpy as np\nfrom equisolve.numpy.models.linear_model import Ridge\nfrom equisolve.utils.convert import ase_to_tensormap\nfrom rascaline import AtomicComposition, LodeSphericalExpansion, SphericalExpansion\nfrom rascaline.utils import PowerSpectrum" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 0: Prepare Data Set\n\n### Get structures\n\nWe take a small subset of the dimer dataset from [A. Grisafi et al.,\n2021](https://pubs.rsc.org/en/content/articlelanding/2021/sc/d0sc04934d)\nfor which we additionally calculated the forces. Each structure in the\ndataset contains two small organic molecules which are extended along a\ncertain direction in the subsequent structures.\n\nFor speeding up the calculations we already selected the first 130\n:download:`structures ` of the charge-charge molecule\npairs.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "frames = ase.io.read(\"charge-charge.xyz\", \":\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Convert target properties to metatensor format\n\nIf we want to train models using the\n[equisolve](https://github.com/lab-cosmo/equisolve) package, we need to\nconvert the target properties (in this case, the energies and forces)\ninto the appropriate format #justequistorethings\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "y = ase_to_tensormap(frames, energy=\"energy\", forces=\"forces\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Compute short-range and LODE features\n\nDefine hypers and get the expansion coefficients $\\langle anlm | \\rho_i \\rangle$\nand $\\langle anlm | V_i \\rangle$\n\nThe short-range and long-range descriptors have very similar hyperparameters. We\nhighlight the differences below.\n\nWe first define the hyperparameters for the short-range (SR) part. These will be used\nto create SOAP features.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "SR_HYPERS = {\n \"cutoff\": 3.0,\n \"max_radial\": 6,\n \"max_angular\": 2,\n \"atomic_gaussian_width\": 0.3,\n \"center_atom_weight\": 1.0,\n \"radial_basis\": {\"Gto\": {}},\n \"cutoff_function\": {\"ShiftedCosine\": {\"width\": 0.5}},\n}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And next the hyperparaters for the LODE / long-range (LR) part\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "LR_HYPERS = {\n # Cutoff on which to project potential density\n \"cutoff\": 3.0,\n # keep max_radial slightly smaller than for SR part\n \"max_radial\": 3,\n # max_angular should be <= 4, more precisely, max_angular + potential_exponent < 10\n \"max_angular\": 2,\n # keep at >=1, WARNING: CUBIC SCALING, do not use values <0.5\n \"atomic_gaussian_width\": 3.0,\n \"center_atom_weight\": 1.0,\n \"radial_basis\": {\"Gto\": {}},\n # the exponent p that determines the 1/r^p potential\n \"potential_exponent\": 1,\n}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then use the above defined hyperparaters to define the per atom short range (sr)\nand long range (sr) descriptors.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "calculator_sr = SphericalExpansion(**SR_HYPERS)\ncalculator_lr = LodeSphericalExpansion(**LR_HYPERS)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that LODE requires periodic systems. Therefore, if the data set does not come\nwith periodic boundary conditions by default you can not use the data set and you will\nface an error if you try to compute the features.\n\nAs you notices the calculation of the long range features takes significant more time\ncompared to the sr features.\n\nTaking a look at the output we find that the resulting\n:py:class:`metatensor.TensorMap` are quite similar in their structure. The short range\n:py:class:`metatensor.TensorMap` contains more blocks due to the higher\n``max_angular`` paramater we choosed above.\n\n### Generate the rotational invariants (power spectra)\n\nRotationally invariant features can be obtained by taking two of the calculators that\nwere defines above.\n\nFor the short-range part, we use the SOAP vector which is obtained by computing the\ninvariant combinations of the form $\\rho \\otimes \\rho$.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ps_calculator_sr = PowerSpectrum(calculator_sr, calculator_sr)\nps_sr = ps_calculator_sr.compute(frames, gradients=[\"positions\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We calculate gradients with respect to pistions by providing the\n``gradients=[\"positions\"]`` option to the\n:py:meth:`rascaline.calculators.CalculatorBase.compute()` method.\n\nFor the long-range part, we combine the long-range descriptor $V$ with one a\nshort-range density $\\rho$ to get $\\rho \\otimes V$ features.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ps_calculator_lr = PowerSpectrum(calculator_sr, calculator_lr)\nps_lr = ps_calculator_lr.compute(systems=frames, gradients=[\"positions\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Building a Simple Linear SR + LR Model with energy baselining\n\n### Preprocessing (model dependent)\n\nFor our current model, we do not wish to treat the individual center and\nneighbor species separately. Thus, we move the ``\"species_center\"`` key\ninto the ``sample`` direction, over which we will later sum over.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ps_sr = ps_sr.keys_to_samples(\"species_center\")\nps_lr = ps_lr.keys_to_samples(\"species_center\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For linear models only: Sum features up over atoms (``samples``) in the same\nstructure.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sample_names_to_sum = [\"center\", \"species_center\"]\n\nps_sr = metatensor.sum_over_samples(ps_sr, sample_names=sample_names_to_sum)\nps_lr = metatensor.sum_over_samples(ps_lr, sample_names=sample_names_to_sum)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Initialize tensormaps for energy baselining\n\nWe add a simple extra descriptor :py:class:`rascaline.AtomicComposition` that stores\nhow many atoms of each chemical species are contained in the structures. This is used\nfor energy baselining.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "calculator_co = AtomicComposition(per_structure=False)\ndescriptor_co = calculator_co.compute(frames, gradients=[\"positions\"])\n\nco = descriptor_co.keys_to_properties([\"species_center\"])\nco = metatensor.sum_over_samples(co, sample_names=[\"center\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The :py:class:`rascaline.AtomicComposition` calculator also allows to directly perform\nthe the sum over center atoms by using the following lines.\n\n.. code:: python\n\n descriptor_co = AtomicComposition(per_structure=True).compute(**compute_args)\n co = descriptor_co.keys_to_properties([\"species_center\"])\n\n### Stack all the features together for linear model\n\nA linear model on SR + LR features can be thought of as a linear model\nbuilt on a feature vector that is simply the concatenation of the SR and\nLR features.\n\nFurthermore, energy baselining can be performed by concatenating the information about\nchemical species as well. There is an metatensor function called\n:py:func:`metatensor.join()` for this purpose. Formally, we can write for the SR\nmodel.\n\nX_sr: $1 \\oplus \\left(\\rho \\otimes \\rho\\right)$\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "X_sr = metatensor.join([co, ps_sr], axis=\"properties\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We used the ``axis=\"properties\"`` parameter since we want to concatenate along the\nfeatures/properties dimensions.\n\nFor the long range model we can formerly write\n\nX_lr: $1 \\oplus \\left(\\rho \\otimes \\rho\\right) \\oplus \\left(\\rho \\otimes\nV\\right)$\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "X_lr = metatensor.join([co, ps_sr, ps_lr], axis=\"properties\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The features are now ready! Let us now perform some actual learning. Below we\ninitialize two instances of the :py:class:`equisolve.numpy.models.linear_model.Ridge`\nclass. :py:class:`equisolve.numpy.models.linear_model.Ridge` will perform a regression\nwith respect to ``\"values\"`` (energies) and ``\"positions\"`` gradients (forces).\n\nIf you only want a fit with respect to energies you can remove the gradients with\n``metatensor.remove_gradients()``\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "clf_sr = Ridge()\nclf_lr = Ridge()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Split training and target data into train and test dat\n\nSplit the training and the test data by the distance $r_{\\rm\ntrain}=6\\,\\mathrm{\u00c5}$ between the center of mass of the two molecules. A structure\nwith a $r_{\\rm train}<6 {\\rm \u00c5}$ is used for training.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "r_cut = 6.0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We calculate the indices from the dataset by list comprehension. The center of mass\ndistance is stored in the ``\"distance\"\"`` attribute.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "idx_train = [i for i, f in enumerate(frames) if f.info[\"distance\"] < r_cut]\nidx_test = [i for i, f in enumerate(frames) if f.info[\"distance\"] >= r_cut]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For doing the split we define two ``Labels`` instances and combine them in a\n:py:class:`List`.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "samples_train = metatensor.Labels([\"structure\"], np.reshape(idx_train, (-1, 1)))\nsamples_test = metatensor.Labels([\"structure\"], np.reshape(idx_test, (-1, 1)))\ngrouped_labels = [samples_train, samples_test]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That we use as input to the :py:func:`metatensor.split()` function\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "X_sr_train, X_sr_test = metatensor.split(\n X_sr, axis=\"samples\", grouped_labels=grouped_labels\n)\n\nX_lr_train, X_lr_test = metatensor.split(\n X_lr, axis=\"samples\", grouped_labels=grouped_labels\n)\n\ny_train, y_test = metatensor.split(y, axis=\"samples\", grouped_labels=grouped_labels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fit the model\n\nFor this model, we use a very simple regularization scheme where all features are\nregularized in the same way (the amount being controlled by the parameter ``alpha``).\nFor more advanced regularization schemes (regularizing energies and forces differently\nand/or the SR and LR parts differently), see further down.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "clf_sr.fit(X_sr_train, y_train, alpha=1e-6)\nclf_lr.fit(X_lr_train, y_train, alpha=1e-6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Evaluation\n\nFor evaluating the model we calculate the RMSEs using the ``score()`` method. With the\n``parameter_key`` parameter we select which RMSE should be calculated.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\n \"SR: RMSE energies = \"\n f\"{clf_sr.score(X_sr_test, y_test, parameter_key='values')[0]:.3f} eV\"\n)\nprint(\n \"SR: RMSE forces = \"\n f\"{clf_sr.score(X_sr_test, y_test, parameter_key='positions')[0]:.3f} eV/\u00c5\"\n)\n\nprint(\n \"LR: RMSE energies = \"\n f\"{clf_lr.score(X_lr_test, y_test, parameter_key='values')[0]:.3f} eV\"\n)\nprint(\n \"LR: RMSE forces = \"\n f\"{clf_lr.score(X_lr_test, y_test, parameter_key='positions')[0]:.3f} eV/\u00c5\"\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find that the RMSE of the energy and the force of the LR model is smaller compared\nto the SR model. From this we conclude that the LR model performs better for the\nselection of the dataset.\n\nWe additionally, can plot of the binding energy as a function of the distance. For the\nplot we select some properties from the dataset\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "dist = np.array([f.info[\"distance\"] for f in frames])\nenergies = np.array([f.info[\"energy\"] for f in frames])\nmonomer_energies = np.array([f.info[\"energyA\"] + f.info[\"energyB\"] for f in frames])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and select only the indices corresponding to our test set.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we calculate the predicted SR and LR ``TensorMaps``.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "y_sr_pred = clf_sr.predict(X_sr)\ny_lr_pred = clf_lr.predict(X_lr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And, finally perform the plot.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "plt.scatter(\n dist, y.block().values[:, 0] - monomer_energies, label=\"target data\", color=\"black\"\n)\n\nplt.scatter(\n dist,\n y_sr_pred.block().values[:, 0] - monomer_energies,\n label=\"short range model\",\n marker=\"x\",\n)\n\nplt.scatter(\n dist,\n y_lr_pred.block().values[:, 0] - monomer_energies,\n label=\"long range model\",\n marker=\"s\",\n facecolor=\"None\",\n edgecolor=\"orange\",\n)\n\nplt.xlabel(\"center of mass distance in \u00c5\")\nplt.ylabel(r\"$E - E_\\mathrm{monomer}$ in eV\")\nplt.axvline(r_cut, c=\"red\", label=r\"$r_\\mathrm{train}$\")\n\nplt.legend()\nplt.tight_layout()\nplt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/89f739150c737d83b9f5bb306c62ba22/lode-linear.py b/_downloads/89f739150c737d83b9f5bb306c62ba22/lode-linear.py new file mode 100644 index 00000000..6ac4c0b8 --- /dev/null +++ b/_downloads/89f739150c737d83b9f5bb306c62ba22/lode-linear.py @@ -0,0 +1,395 @@ +""" +Long-distance Equivariants: a tutorial +====================================== + +:Authors: Philip Loche `@PicoCentauri `_, + Kevin Huguenin-Dumittan `@kvhuguenin `_ + +This tutorial explains how Long range equivariant descriptors can be constructed using +rascaline and the resulting descriptors be used to construct a linear model with +equisolve + +First, import all the necessary packages +""" + +# %% + +import ase.io +import matplotlib.pyplot as plt +import metatensor +import numpy as np +from equisolve.numpy.models.linear_model import Ridge +from equisolve.utils.convert import ase_to_tensormap +from rascaline import AtomicComposition, LodeSphericalExpansion, SphericalExpansion +from rascaline.utils import PowerSpectrum + + +# %% +# +# Step 0: Prepare Data Set +# ------------------------ +# +# Get structures +# ~~~~~~~~~~~~~~ +# +# We take a small subset of the dimer dataset from `A. Grisafi et al., +# 2021 `_ +# for which we additionally calculated the forces. Each structure in the +# dataset contains two small organic molecules which are extended along a +# certain direction in the subsequent structures. +# +# For speeding up the calculations we already selected the first 130 +# :download:`structures ` of the charge-charge molecule +# pairs. + +frames = ase.io.read("charge-charge.xyz", ":") + + +# %% +# +# Convert target properties to metatensor format +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# If we want to train models using the +# `equisolve `_ package, we need to +# convert the target properties (in this case, the energies and forces) +# into the appropriate format #justequistorethings + +y = ase_to_tensormap(frames, energy="energy", forces="forces") + + +# %% +# +# Step 1: Compute short-range and LODE features +# --------------------------------------------- +# +# Define hypers and get the expansion coefficients :math:`\langle anlm | \rho_i \rangle` +# and :math:`\langle anlm | V_i \rangle` +# +# The short-range and long-range descriptors have very similar hyperparameters. We +# highlight the differences below. +# +# We first define the hyperparameters for the short-range (SR) part. These will be used +# to create SOAP features. + +SR_HYPERS = { + "cutoff": 3.0, + "max_radial": 6, + "max_angular": 2, + "atomic_gaussian_width": 0.3, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {}}, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, +} + + +# %% +# +# And next the hyperparaters for the LODE / long-range (LR) part + + +LR_HYPERS = { + # Cutoff on which to project potential density + "cutoff": 3.0, + # keep max_radial slightly smaller than for SR part + "max_radial": 3, + # max_angular should be <= 4, more precisely, max_angular + potential_exponent < 10 + "max_angular": 2, + # keep at >=1, WARNING: CUBIC SCALING, do not use values <0.5 + "atomic_gaussian_width": 3.0, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {}}, + # the exponent p that determines the 1/r^p potential + "potential_exponent": 1, +} + + +# %% +# We then use the above defined hyperparaters to define the per atom short range (sr) +# and long range (sr) descriptors. + +calculator_sr = SphericalExpansion(**SR_HYPERS) +calculator_lr = LodeSphericalExpansion(**LR_HYPERS) + + +# %% +# +# Note that LODE requires periodic systems. Therefore, if the data set does not come +# with periodic boundary conditions by default you can not use the data set and you will +# face an error if you try to compute the features. +# +# As you notices the calculation of the long range features takes significant more time +# compared to the sr features. +# +# Taking a look at the output we find that the resulting +# :py:class:`metatensor.TensorMap` are quite similar in their structure. The short range +# :py:class:`metatensor.TensorMap` contains more blocks due to the higher +# ``max_angular`` paramater we choosed above. +# +# Generate the rotational invariants (power spectra) +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# Rotationally invariant features can be obtained by taking two of the calculators that +# were defines above. +# +# For the short-range part, we use the SOAP vector which is obtained by computing the +# invariant combinations of the form :math:`\rho \otimes \rho`. + +ps_calculator_sr = PowerSpectrum(calculator_sr, calculator_sr) +ps_sr = ps_calculator_sr.compute(frames, gradients=["positions"]) + + +# %% +# +# We calculate gradients with respect to pistions by providing the +# ``gradients=["positions"]`` option to the +# :py:meth:`rascaline.calculators.CalculatorBase.compute()` method. +# +# For the long-range part, we combine the long-range descriptor :math:`V` with one a +# short-range density :math:`\rho` to get :math:`\rho \otimes V` features. + +ps_calculator_lr = PowerSpectrum(calculator_sr, calculator_lr) +ps_lr = ps_calculator_lr.compute(systems=frames, gradients=["positions"]) + + +# %% +# +# Step 2: Building a Simple Linear SR + LR Model with energy baselining +# --------------------------------------------------------------------- +# +# Preprocessing (model dependent) +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# For our current model, we do not wish to treat the individual center and +# neighbor species separately. Thus, we move the ``"species_center"`` key +# into the ``sample`` direction, over which we will later sum over. + +ps_sr = ps_sr.keys_to_samples("species_center") +ps_lr = ps_lr.keys_to_samples("species_center") + + +# %% +# +# For linear models only: Sum features up over atoms (``samples``) in the same +# structure. + +sample_names_to_sum = ["center", "species_center"] + +ps_sr = metatensor.sum_over_samples(ps_sr, sample_names=sample_names_to_sum) +ps_lr = metatensor.sum_over_samples(ps_lr, sample_names=sample_names_to_sum) + + +# %% +# +# Initialize tensormaps for energy baselining +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# We add a simple extra descriptor :py:class:`rascaline.AtomicComposition` that stores +# how many atoms of each chemical species are contained in the structures. This is used +# for energy baselining. + +calculator_co = AtomicComposition(per_structure=False) +descriptor_co = calculator_co.compute(frames, gradients=["positions"]) + +co = descriptor_co.keys_to_properties(["species_center"]) +co = metatensor.sum_over_samples(co, sample_names=["center"]) + +# %% +# +# The :py:class:`rascaline.AtomicComposition` calculator also allows to directly perform +# the the sum over center atoms by using the following lines. +# +# .. code:: python +# +# descriptor_co = AtomicComposition(per_structure=True).compute(**compute_args) +# co = descriptor_co.keys_to_properties(["species_center"]) +# +# Stack all the features together for linear model +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# A linear model on SR + LR features can be thought of as a linear model +# built on a feature vector that is simply the concatenation of the SR and +# LR features. +# +# Furthermore, energy baselining can be performed by concatenating the information about +# chemical species as well. There is an metatensor function called +# :py:func:`metatensor.join()` for this purpose. Formally, we can write for the SR +# model. +# +# X_sr: :math:`1 \oplus \left(\rho \otimes \rho\right)` + +X_sr = metatensor.join([co, ps_sr], axis="properties") + + +# %% +# +# We used the ``axis="properties"`` parameter since we want to concatenate along the +# features/properties dimensions. +# +# For the long range model we can formerly write +# +# X_lr: :math:`1 \oplus \left(\rho \otimes \rho\right) \oplus \left(\rho \otimes +# V\right)` + +X_lr = metatensor.join([co, ps_sr, ps_lr], axis="properties") + + +# %% +# +# The features are now ready! Let us now perform some actual learning. Below we +# initialize two instances of the :py:class:`equisolve.numpy.models.linear_model.Ridge` +# class. :py:class:`equisolve.numpy.models.linear_model.Ridge` will perform a regression +# with respect to ``"values"`` (energies) and ``"positions"`` gradients (forces). +# +# If you only want a fit with respect to energies you can remove the gradients with +# ``metatensor.remove_gradients()`` + +clf_sr = Ridge() +clf_lr = Ridge() + + +# %% +# +# Split training and target data into train and test dat +# ------------------------------------------------------ +# +# Split the training and the test data by the distance :math:`r_{\rm +# train}=6\,\mathrm{Å}` between the center of mass of the two molecules. A structure +# with a :math:`r_{\rm train}<6 {\rm Å}` is used for training. + +r_cut = 6.0 + + +# %% +# +# We calculate the indices from the dataset by list comprehension. The center of mass +# distance is stored in the ``"distance""`` attribute. + +idx_train = [i for i, f in enumerate(frames) if f.info["distance"] < r_cut] +idx_test = [i for i, f in enumerate(frames) if f.info["distance"] >= r_cut] + + +# %% +# +# For doing the split we define two ``Labels`` instances and combine them in a +# :py:class:`List`. + +samples_train = metatensor.Labels(["structure"], np.reshape(idx_train, (-1, 1))) +samples_test = metatensor.Labels(["structure"], np.reshape(idx_test, (-1, 1))) +grouped_labels = [samples_train, samples_test] + + +# %% +# +# That we use as input to the :py:func:`metatensor.split()` function + +X_sr_train, X_sr_test = metatensor.split( + X_sr, axis="samples", grouped_labels=grouped_labels +) + +X_lr_train, X_lr_test = metatensor.split( + X_lr, axis="samples", grouped_labels=grouped_labels +) + +y_train, y_test = metatensor.split(y, axis="samples", grouped_labels=grouped_labels) + + +# %% +# +# Fit the model +# ------------- +# +# For this model, we use a very simple regularization scheme where all features are +# regularized in the same way (the amount being controlled by the parameter ``alpha``). +# For more advanced regularization schemes (regularizing energies and forces differently +# and/or the SR and LR parts differently), see further down. + +clf_sr.fit(X_sr_train, y_train, alpha=1e-6) +clf_lr.fit(X_lr_train, y_train, alpha=1e-6) + + +# %% +# +# Evaluation +# ---------- +# +# For evaluating the model we calculate the RMSEs using the ``score()`` method. With the +# ``parameter_key`` parameter we select which RMSE should be calculated. + +print( + "SR: RMSE energies = " + f"{clf_sr.score(X_sr_test, y_test, parameter_key='values')[0]:.3f} eV" +) +print( + "SR: RMSE forces = " + f"{clf_sr.score(X_sr_test, y_test, parameter_key='positions')[0]:.3f} eV/Å" +) + +print( + "LR: RMSE energies = " + f"{clf_lr.score(X_lr_test, y_test, parameter_key='values')[0]:.3f} eV" +) +print( + "LR: RMSE forces = " + f"{clf_lr.score(X_lr_test, y_test, parameter_key='positions')[0]:.3f} eV/Å" +) + + +# %% +# +# We find that the RMSE of the energy and the force of the LR model is smaller compared +# to the SR model. From this we conclude that the LR model performs better for the +# selection of the dataset. +# +# We additionally, can plot of the binding energy as a function of the distance. For the +# plot we select some properties from the dataset + +dist = np.array([f.info["distance"] for f in frames]) +energies = np.array([f.info["energy"] for f in frames]) +monomer_energies = np.array([f.info["energyA"] + f.info["energyB"] for f in frames]) + + +# %% +# +# and select only the indices corresponding to our test set. + + +# %% +# +# Next we calculate the predicted SR and LR ``TensorMaps``. + +y_sr_pred = clf_sr.predict(X_sr) +y_lr_pred = clf_lr.predict(X_lr) + + +# %% +# +# And, finally perform the plot. + +plt.scatter( + dist, y.block().values[:, 0] - monomer_energies, label="target data", color="black" +) + +plt.scatter( + dist, + y_sr_pred.block().values[:, 0] - monomer_energies, + label="short range model", + marker="x", +) + +plt.scatter( + dist, + y_lr_pred.block().values[:, 0] - monomer_energies, + label="long range model", + marker="s", + facecolor="None", + edgecolor="orange", +) + +plt.xlabel("center of mass distance in Å") +plt.ylabel(r"$E - E_\mathrm{monomer}$ in eV") +plt.axvline(r_cut, c="red", label=r"$r_\mathrm{train}$") + +plt.legend() +plt.tight_layout() +plt.show() diff --git a/_downloads/94018b4b1798aa421f0916f03cd04ae9/data.zip b/_downloads/94018b4b1798aa421f0916f03cd04ae9/data.zip new file mode 100644 index 00000000..08f83947 Binary files /dev/null and b/_downloads/94018b4b1798aa421f0916f03cd04ae9/data.zip differ diff --git a/_downloads/9686437d3cc3327b109d561fa42242c0/pi-metad.zip b/_downloads/9686437d3cc3327b109d561fa42242c0/pi-metad.zip new file mode 100644 index 00000000..42752323 Binary files /dev/null and b/_downloads/9686437d3cc3327b109d561fa42242c0/pi-metad.zip differ diff --git a/_downloads/9ae4cdde3e7099e2bf76d10302eae3e8/environment.yml b/_downloads/9ae4cdde3e7099e2bf76d10302eae3e8/environment.yml new file mode 100644 index 00000000..c2d0ea1e --- /dev/null +++ b/_downloads/9ae4cdde3e7099e2bf76d10302eae3e8/environment.yml @@ -0,0 +1,12 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - lammps + - pip: + - ase==3.22.1 + - chemiscope>=0.7 + - ipi + - matplotlib + - skmatter diff --git a/_downloads/a00b581f2f0e1dd89a20b5a5d0f66025/environment.yml b/_downloads/a00b581f2f0e1dd89a20b5a5d0f66025/environment.yml new file mode 100644 index 00000000..ac282979 --- /dev/null +++ b/_downloads/a00b581f2f0e1dd89a20b5a5d0f66025/environment.yml @@ -0,0 +1,26 @@ +channels: + - conda-forge +dependencies: + - python>=3.11 + - pip + - graphviz + - pyscf=2.3.0 + - rust>=1.65 + - pip: + - pyscfad @ git+https://github.com/fishjojo/pyscfad.git@ml#egg=pyscfad + - ase==3.22.1 + - seekpath + - requests + - metatensor + - metatensor-core + - metatensor-learn + - metatensor-operations + - metatensor-torch + - --extra-index-url https://download.pytorch.org/whl/cpu + - rascaline-torch @ git+https://github.com/luthaf/rascaline#subdirectory=python/rascaline-torch + - lightning + - xitorch + - keras_core + - tensorboard + - torchviz + - mlelec @ git+https://github.com/curiosity54/mlelec.git@tutorial_periodic#egg=mlelec diff --git a/_downloads/a17a480a207dc60b848e8b91a240947d/periodic-hamiltonian.ipynb b/_downloads/a17a480a207dc60b848e8b91a240947d/periodic-hamiltonian.ipynb new file mode 100644 index 00000000..1567410b --- /dev/null +++ b/_downloads/a17a480a207dc60b848e8b91a240947d/periodic-hamiltonian.ipynb @@ -0,0 +1,677 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Periodic Hamiltonian learning\n\n:Authors: Paolo Pegolo [@ppegolo](https://github.com/ppegolo)_,\n Jigyasa Nigam [@curiosity54](https://github.com/curiosity54)_\n\nThis tutorial explains how to train a machine learning model for the\nelectronic Hamiltonian of a periodic system. Even though we focus on\nperiodic systems, the code and techniques presented here can be directly\ntransferred to molecules.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, import the necessary packages\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import os\nimport warnings\nimport zipfile\n\nimport matplotlib.image as mpimg\nimport matplotlib.pyplot as plt\nimport numpy as np\nimport requests\nimport torch\nfrom matplotlib.animation import FuncAnimation\nfrom mlelec.data.derived_properties import compute_eigenvalues\nfrom mlelec.data.mldataset import MLDataset\nfrom mlelec.data.qmdataset import QMDataset\nfrom mlelec.models.equivariant_lightning import LitEquivariantModel, MSELoss\nfrom mlelec.utils.pbc_utils import blocks_to_matrix\nfrom mlelec.utils.plot_utils import plot_bands_frame\n\n\nwarnings.filterwarnings(\"ignore\")\ntorch.set_default_dtype(torch.float64)\n\n# sphinx_gallery_thumbnail_number = 3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Get Data and Prepare Data Set\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The data set contains 35 distorted graphene unit cells containing 2\natoms. The reference density functional theory (DFT) calculations are\nperformed with [CP2K](https://www.cp2k.org/)_ using a minimal\n[STO-3G](https://en.wikipedia.org/wiki/STO-nG_basis_sets)_ basis and\nthe [PBE](https://doi.org/10.1103/PhysRevLett.77.3865)_ functional.\nThe Kohn-Sham equations are solved on a Monkhorst-Pack grid of\n$15\\times 15\\times 1$ points in the Brillouin zone of the crystal.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Obtain structures and DFT data\n\nGenerating training structures requires running a suitable DFT code,\nand converting the output data in a format that can be processed by\nthe ML library ``mlelec``. Given that it takes some time to run even\nthese small calculations, we provide pre-computed data, but you can\nalso find instructions on how to generate data from scratch.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Run your own cp2k calculations\n\nIf you have computational resources, you can run the DFT calculations\nneeded to produce the data set. [This other\ntutorial](https://tinyurl.com/cp2krun)_ in the atomistic cookbook can\nhelp you set up the CP2K calculations for this data set, using the\n``reftraj_hamiltonian.cp2k`` file provided in ``data/``. To do the same\nfor another data set, adapt the reftraj file.\nWe will provide here some of the functions in the [batch-cp2k\ntutorial](https://tinyurl.com/cp2krun)_ that need to be adapted to the\ncurrent data set. Note however you will have to modify these and combine\nthem with other tutorials to actually generate the data.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Start by importing all the modules from the [batch-cp2k\ntutorial](https://tinyurl.com/cp2krun)_ and run the cell to install\nCP2K. Run also the cells up to the one defining ``write_cp2k_in``.\nThe following code snippet defines a slighly modified version of that function,\nallowing for non-orthorombic supercell, and accounting for the reftraj file\nname change.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n def write_cp2k_in(\n fname: str,\n project_name: str,\n last_snapshot: int,\n cell_a: List[float],\n cell_b: List[float],\n cell_c: List[float],\n ) -> None:\n \"\"\"Writes a cp2k input file from a template.\n\n Importantly, it writes the location of the basis set definitions,\n determined from the path of the system CP2K install to the input file.\n \"\"\"\n\n cp2k_in = open(\"reftraj_hamiltonian.cp2k\", \"r\").read()\n\n cp2k_in = cp2k_in.replace(\"//PROJECT//\", project_name)\n cp2k_in = cp2k_in.replace(\"//LAST_SNAPSHOT//\", str(last_snapshot))\n cp2k_in = cp2k_in.replace(\"//CELL_A//\", \" \".join([f\"{c:.6f}\" for c in cell_a]))\n cp2k_in = cp2k_in.replace(\"//CELL_B//\", \" \".join([f\"{c:.6f}\" for c in cell_b]))\n cp2k_in = cp2k_in.replace(\"//CELL_C//\", \" \".join([f\"{c:.6f}\" for c in cell_c]))\n\n with open(fname, \"w\") as f:\n f.write(cp2k_in)\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Unlike the [batch-cp2k tutorial](https://tinyurl.com/cp2krun)_, the\ncurrent data set includes a single stoichiometry, $\\mathrm{C_2}$.\nTherefore, you can run this cell to set the calculation scripts up.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n project_name = 'graphene'\n frames = ase_read('C2.xyz', index=':')\n os.makedirs(project_name, exist_ok=True)\n os.makedirs(f\"{project_name}/FOCK\", exist_ok=True)\n os.makedirs(f\"{project_name}/OVER\", exist_ok=True)\n\n write_cp2k_in(\n f\"{project_name}/in.cp2k\",\n project_name=project_name,\n last_snapshot=len(frames),\n cell_a=frames[0].cell.array[0],\n cell_b=frames[0].cell.array[1],\n cell_c=frames[0].cell.array[2],\n )\n\n ase_write(f\"{project_name}/init.xyz\", frames[0])\n write_reftraj(f\"{project_name}/reftraj.xyz\", frames)\n write_cellfile(f\"{project_name}/reftraj.cell\", frames)\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The CP2K calculations can be simply run using:\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n subprocess.run((\n f\"cp2k.ssmp -i {project_name}/in.cp2k \"\n \"> {project_name}/out.cp2k\"\n ),\n shell=True)\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the calculations are done, we can parse the results with:\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n from scipy.sparse import csr_matrix\n\n nao = 10\n ifr = 1\n fock = []\n over = []\n with open(f\"{project_name}/out.cp2k\", \"r\") as outfile:\n T_lists = [] # List to hold all T_list instances\n while True:\n line = outfile.readline()\n if not line:\n break\n if line.strip().split()[:3] != [\"KS\", \"CSR\", \"write|\"]:\n continue\n else:\n nT = int(line.strip().split()[3])\n outfile.readline() # Skip the next line if necessary\n T_list = [] # Initialize a new T_list for this block\n for _ in range(nT):\n line = outfile.readline()\n if not line:\n break\n T_list.append([np.int32(j) for j in line.strip().split()[1:4]])\n T_list = np.array(T_list)\n T_lists.append(T_list) # Append the T_list to T_lists\n fock_ = {}\n over_ = {}\n for iT, T in enumerate(\n T_list\n ): # Loop through the translations and load matrices\n T = T.tolist()\n r, c, data = np.loadtxt(\n (\n f\"{project_name}/FOCK/{project_name}\"\n f\"-KS_SPIN_1_R_{iT+1}-1_{ifr}.csr\"\n ),\n unpack=True,\n )\n r = np.int32(r - 1)\n c = np.int32(c - 1)\n fock_[tuple(T)] = csr_matrix(\n (data, (r, c)), shape=(nao, nao)\n ).toarray()\n\n r, c, data = np.loadtxt(\n (\n f\"{project_name}/OVER/{project_name}\"\n f\"-S_SPIN_1_R_{iT+1}-1_{ifr}.csr\"\n ),\n unpack=True,\n )\n r = np.int32(r - 1)\n c = np.int32(c - 1)\n over_[tuple(T)] = csr_matrix(\n (data, (r, c)), shape=(nao, nao)\n ).toarray()\n fock.append(fock_)\n over.append(over_)\n ifr += 1\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can now save the matrices to ``.npy`` files, and a file with the\nk-grids used in the calculations.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n os.makedirs(\"data\", exist_ok=True)\n # Save the Hamiltonians\n np.save(\"data/graphene_fock.npy\", fock)\n # Save the overlaps\n np.save(\"data/graphene_ovlp.npy\", over)\n # Write a file with the k-grids, one line per structure\n np.savetxt('data/kmesh.dat', [[15,15,1]]*len(frames), fmt='%d')\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Download precomputed data\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the sake of simplicity, you can also download precomputed data and\nrun just the machine learning part of the notebook using these data.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "filename = \"precomputed.zip\"\nif not os.path.exists(filename):\n url = (\n \"https://github.com/curiosity54/mlelec/raw/\"\n \"tutorial_periodic/examples/periodic_tutorial/precomputed.zip\"\n )\n response = requests.get(url)\n response.raise_for_status()\n with open(filename, \"wb\") as f:\n f.write(response.content)\n\nwith zipfile.ZipFile(filename, \"r\") as zip_ref:\n zip_ref.extractall(\"./\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Periodic Hamiltonians in real and reciprocal space\n\nThe DFT calculations for the dataset above were performed using a\n*minimal* STO-3G basis. The basis set is specified for each species\nusing three quantum numbers, $n$, $l$, $m$. $n$\nis usually a natural number relating to the *radial* extent or\nresolution whereas $l$ and $m$ specify the *angular\ncomponents* determining the shape of the orbital and its orientation in\nspace. For example, $1s$ orbitals correspond to $n=1$,\n$l=0$ and $m=0$, while a $2p_z$ orbital corresponds to\n$n=2$, $l=1$ and $m=0$. For the STO-3G basis-set,\nthese quantum numbers for Carbon (identified by its atomic number) are\ngiven as follows.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "basis = \"sto-3g\"\norbitals = {\n \"sto-3g\": {6: [[1, 0, 0], [2, 0, 0], [2, 1, -1], [2, 1, 0], [2, 1, 1]]},\n}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For each *frame* which of either train and test structures, the QM data\ncomprises the configuration, along with the corresponding *overlap* and\n*Hamiltonian* (used interchangeably with *Fock*) matrices in the basis\nspecified above, as well as the $k$-point grid that was used for the\ncalculation.\n\nNote that we are currently specifying these matrices in *real-space*,\n$\\mathbf{H}(\\mathbf{t})$ , such that the element\n$\\langle \\mathbf{0} i nlm| \\hat{H}| \\mathbf{t} i' n'l'm'\\rangle$\nindicates the interaction between orbital $nlm$ on atom $i$\nin the undisplaced cell (denoted by the null lattice translation,\n$\\mathbf{t}=\\mathbf{0}$) and orbital $n'l'm'$ on atom\n$i'$ in a periodic copy of the unit cell translated by\n$\\mathbf{t}$. A short-hand notation for\n$\\langle \\mathbf{0} i nlm| \\hat{H}| \\mathbf{t} i' n'l'm'\\rangle$\nis $H_{\\small\\substack{i,nlm\\\\i',n'l'm'}}(\\mathbf{t})$\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. figure:: graphene_lattice.png\n :alt: Representation of a graphene unit cell and some replicas.\n :width: 600px\n\n Representation of a graphene unit cell and its\n $3 \\times 3 \\times 1$ replicas in real space. The central cell\n is denoted by $\\mathbf{t}=(0,0,0)$, while the cells translated\n by a single lattice vector along directions 1 and 2 are denoted by\n $\\mathbf{t}=(1,0,0)$ and $\\mathbf{t}=(0,1,0)$,\n respectively. The Hamiltonian matrix element between the $1s$\n orbital on atom $i$ in the central unit cell and the\n $2p_z$ orbital on atom $i'$ in the\n $\\mathbf{t}=(1,0,0)$ cell is schematically represented.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, we can provide the matrices in *reciprocal* (or\nFourier, $k$) space. These are related to the real-space matrices\nby a *Bloch sum*,\n\n\\begin{align}\\mathbf{H}(\\mathbf{k})=\\sum_{\\mathbf{t}}\\\n e^{i\\mathbf{k}\\cdot\\mathbf{t}} \\mathbf{H}(\\mathbf{t}).\\end{align}\n\n\nIn the case the input matrices are in reciprocal space, there should be\none matrix per $k$-point in the grid.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### A ``QMDataset`` to store the DFT data\nThe ``QMDataset`` class holds all the relevant data\nobtained from a quantum-mechanical (in this case, DFT) calculation,\ncombining information from the files containing structures,\nHamiltonians and overlap matrices, and $k$-point mesh.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "qmdata = QMDataset.from_file(\n # File containing the atomistic structures\n frames_path=\"data/C2.xyz\",\n # File containing the Hamiltonian (of Fock) matrices\n fock_realspace_path=\"graphene_fock.npy\",\n # File containing the overlap matrices\n overlap_realspace_path=\"graphene_ovlp.npy\",\n # File containing the k-point grids used for the DFT calculations\n kmesh_path=\"kmesh.dat\",\n # Physical dimensionality of the system. Graphene is a 2D material\n dimension=2,\n # Device where to run the calculations\n # (can be 'cpu' or 'cuda', if GPUs are available)\n device=\"cpu\",\n # Name of the basis set used for the calculations\n orbs_name=basis,\n # List of quantum numbers associated with the basis set orbitals\n orbs=orbitals[basis],\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Quantities stored in ``QMDataset`` can be accessed as attributes,\ne.g.\u00a0``qmdata.fock_realspace`` is a list (one element per structure) of\ndictionaries labeled by the indices of the unit cell real-space\ntranslations containing ``torch.Tensor``.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "structure_idx = 0\nrealspace_translation = 0, 0, 0\nprint(f\"The real-space Hamiltonian matrix for structure {structure_idx} labeled by\")\nprint(f\"translation T={realspace_translation} is:\")\nprint(f\"{qmdata.fock_realspace[structure_idx][realspace_translation]}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Machine learning data set\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Symmetries of the Hamiltonian matrix\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The data stored in ``QMDataset`` can be transformed into a format that\nis optimal for machine learning modeling by leveraging the underlying\n*physical symmetries* that characterize the atomistic structure, the\nbasis set, and their associated matrices.\n\nThe Hamiltonian matrix is a complex learning target, indexed by two\natoms and the orbitals centered on them. Each\n$\\mathbf{H}(\\mathbf{k})$ is a *Hermitian* matrix, while in real\nspace, periodicity introduces a *symmetry over translation pairs* such\nthat $\\mathbf{H}(-\\mathbf{t}) = \\mathbf{H}(\\mathbf{t})^\\dagger$,\nwhere the dagger, $\\dagger$, denotes Hermitian conjugation.\n\nTo address the symmetries associated with swapping atomic indices or\norbital labels, we divide the matrix into *blocks labeled by pairs of\natom types*.\n\n- ``block_type = 0``, or *on-site* blocks, consist of elements\n corresponding to the interaction of orbitals on the same atom,\n $i = i'$.\n\n- ``block_type = 2``, or *cross-species* blocks, consist of elements\n corresponding to orbitals centered on atoms of distinct species.\n Since the two atoms can be distinguished, they can be consistently\n arranged in a predetermined order.\n\n- ``block_type = 1, -1``, or *same-species* blocks, consist of\n elements corresponding to orbitals centered on distinct atoms of the\n same species. As these atoms are indistinguishable and cannot be\n ordered definitively, the pair must be symmetrized for permutations.\n We construct symmetric and antisymmetric combinations\n $(\\mathbf{H}_{\\small\\substack{i,nlm\\\\i',n'l'm'}}(\\mathbf{t})\\pm\\\n \\mathbf{H}_{\\small\\substack{i',nlm\\\\i,n'l'm'}}(\\mathbf{-t}))$\n that correspond to ``block_type`` $+1$ and $-1$,\n respectively.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Equivariant structure of the Hamiltonians\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even though the Hamiltonian operator under consideration is invariant,\n*its representation transforms under the action of structural rotations\nand inversions* due to the choice of the basis functions. Each of the\nblocks has elements of the form\n$\\langle\\mathbf{0}inlm|\\hat{H}|\\mathbf{t}i'n'l'm'\\rangle$, which\nare in an *uncoupled* representation and transform as a product of\n(real) spherical harmonics, $Y_l^m \\otimes Y_{l'}^{m'}$.\n\nThis product can be decomposed into a direct sum of irreducible\nrepresentations (irreps) of $\\mathrm{SO(3)}$,\n\n\\begin{align}\\lambda \\mu:\\lambda \\in [|l_1-l_2|,l_1+l_2],\\mu \\in [-\\lambda,\\lambda],\\end{align}\n\nwhich express the Hamiltonian blocks in terms of contributions that\nrotate independently and can be modeled using a feature that\ngeometrically describes the pair of atoms under consideration and shares\nthe same symmetry. We use the notation\n$H_{ii';nn'll'}^{\\lambda\\mu}$ to indicate the elements of the\nHamiltonian in this coupled basis.\n\nThe resulting irreps form a *coupled* representation, each of which\ntransforms as a spherical harmonic $Y^\\mu_\\lambda$ under\n$\\mathrm{SO(3)}$ rotations, but may exhibit more complex behavior\nunder inversions. For example, spherical harmonics transform under\ninversion, $\\hat{i}$, as polar tensors:\n\n\\begin{align}\\hat{i}Y^\\mu_\\lambda = (-1)^\\lambda Y^\\mu_\\lambda.\\end{align}\n\nSome of the coupled basis terms transform like $Y^\\mu_\\lambda$,\nwhile others instead transform as pseudotensors,\n\n\\begin{align}\\hat{i}H^{\\lambda\\mu}=(-1)^{\\lambda+1}H^{\\lambda\\mu}\\end{align}\n\nwhere we omit for simplicity the indices that are not directly associated\nwith inversion and rotation symmetry. For more details about the block\ndecomposition, please refer to [Nigam et al., J. Chem. Phys. 156, 014115\n(2022)](https://pubs.aip.org/aip/jcp/article/156/1/014115/2839817)_.\n\nThe following is an animation of a trajectory along a [Lissajous\ncurve](https://en.wikipedia.org/wiki/Lissajous_curve)_ in 3D space,\nalongside a colormap representing the values of the real-space\nHamiltonian matrix elements of the graphene unit cell in a minimal\nSTO-3G basis. From the animation, it is evident how invariant elements,\nsuch as those associated with interactions between $s$ orbitals,\ndo not change under structural rotations. On the other hand,\ninteractions allowing for equivariant components, such as the\n$s$-$p$ block, change under rotations.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "image_files = sorted(\n [\n f\"frames/{f}\"\n for f in os.listdir(\"./frames\")\n if f.startswith(\"rot_\") and f.endswith(\".png\")\n ]\n)\nimages = [mpimg.imread(img) for img in image_files]\nfig, ax = plt.subplots()\nimg_display = ax.imshow(images[0])\nax.axis(\"off\")\n\n\ndef update(frame):\n img_display.set_data(images[frame])\n return [img_display]\n\n\nani = FuncAnimation(fig, update, frames=len(images), interval=20, blit=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n from IPython.display import HTML\n HTML(ani.to_jshtml())\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Mapping geometric features to Hamiltonian targets\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each Hamiltonian block obtained from the procedure [described\nabove](#symmetries-of-the-hamiltonian-matrix)_ can be modeled using\nsymmetrized features.\n\nElements of ``block_type=0`` are indexed by a single atom and are best\ndescribed by a symmetrized atom-centered density correlation\n([ACDC](https://doi.org/10.1063/1.5090481)_), denoted by\n$|\\overline{\\rho_{i}^{\\otimes \\nu}; \\sigma; \\lambda\\mu }\\rangle$,\nwhere $\\nu$ refers to the correlation (body)-order, and\u2014just as\nfor the blocks\u2014$\\lambda \\mu$ indicate the $\\mathrm{SO(3)}$\nirrep to which the feature is symmetrized. The symbol $\\sigma$\ndenotes the inversion parity.\n\nFor other blocks, such as ``block_type=2``, which explicitly reference\ntwo atoms, we use [two-center](https://doi.org/10.1063/5.0072784)_\nACDCs, $|\\overline{\\rho_{ii'}^{\\otimes \\nu}; \\lambda\\mu }\\rangle$.\n\nFor ``block_type=1, -1``, we ensure equivariance with respect to atom\nindex permutation by constructing symmetric and antisymmetric pair\nfeatures:\n$(|\\overline{\\rho_{ii'}^{\\otimes \\nu};\\lambda\\mu }\\rangle\\pm\\\n|\\overline{\\rho_{i'i}^{\\otimes \\nu};\\lambda\\mu }\\rangle)$.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The features are discretized on a basis of radial functions and\nspherical harmonics, and their performance may depend on the\n*resolution* of the functions included in the model. There are\nadditional hyperparameters, such as the *cutoff* radius, which\ncontrols the extent of the atomic environment, and Gaussian widths. In\nthe following, we allow for flexibility in discretizing the\natom-centered and two-centered ACDCs by defining the hyperparameters for\nthe single-center (SC) $\\lambda$-SOAP and two-center (TC) ACDC\ndescriptors.\n\nThe single and two-center descriptors have very similar hyperparameters,\nexcept for the cutoff radius, which is larger for the two-center\ndescriptors to explicitly include distant pairs of atoms.\n\nNote that the descriptors of pairs of atoms separated by distances\ngreater than the cutoff radius are identically zero. Thus, any model\nbased on these descriptors would predict an identically zero value for\nthese pairs.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "SC_HYPERS = {\n \"cutoff\": 3.0,\n \"max_radial\": 6,\n \"max_angular\": 6,\n \"atomic_gaussian_width\": 0.5,\n \"center_atom_weight\": 1,\n \"radial_basis\": {\"Gto\": {}},\n \"cutoff_function\": {\"ShiftedCosine\": {\"width\": 0.5}},\n}\n\nTC_HYPERS = {\n \"cutoff\": 6.0,\n \"max_radial\": 6,\n \"max_angular\": 6,\n \"atomic_gaussian_width\": 0.3,\n \"center_atom_weight\": 1.0,\n \"radial_basis\": {\"Gto\": {}},\n \"cutoff_function\": {\"ShiftedCosine\": {\"width\": 0.5}},\n}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then use the above defined hyperparameters to compute the descriptor\nand initialize a ``MLDataset`` instance, which contains, among other\nthings, the Hamiltonian block decomposition and the geometric features\ndescribed above.\n\nIn addition to computing the descriptors, ``MLDataset`` takes the data\nstored in the ``QMDataset`` instance and puts it in a form required to\ntrain a ML model.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``item_names`` argument is a list of names of the quantities we want\nto compute and target in the ML model training, or that we want to be\nable to access later.\n\nFor example, ``fock_blocks`` is a\n[metatensor.Tensormap](https://tinyurl.com/tenmap)_ containing the\nHamiltonian coupled blocks. We also want to access the overlap matrices\nin $k$-space (``overlap_kspace``) to be able to compute the\nHamiltonian eigenvalues in the $k$-grid.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mldata = MLDataset(\n # A QMDataset instance\n qmdata,\n # The names of the quantities to compute/initialize for the training\n item_names=[\"fock_blocks\", \"overlap_kspace\"],\n # Hypers for the SC descriptors\n hypers_atom=SC_HYPERS,\n # Hypers for the TC descriptors\n hypers_pair=TC_HYPERS,\n # Cutoff for the angular quantum number to use in the Clebsh-Gordan iterations\n lcut=4,\n # Fraction of structures in the training set\n train_frac=0.7,\n # Fraction of structures in the validation set\n val_frac=0.2,\n # Fraction of structures in the test set\n test_frac=0.1,\n # Whether to shuffle or not the structure indices before splitting the data set\n shuffle=True,\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The matrix decomposition into blocks and the calculations of geometric\nfeatures is performed by the ``MLDataset`` class.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``mldata.features`` is ``metatensor.TensorMap`` containing the\nstuctures\u2019 descriptors\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "mldata.features" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``mldata.items`` is a ``namedtuple`` containing the quantities defined\nin ``item_names``. e.g.\u00a0the coupled Hamiltonian blocks:\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print(\"The TensorMap containing the Hamiltonian coupled blocks is\")\nmldata.items.fock_blocks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or the overlap matrices:\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "structure_idx = 0\nk_idx = 0\nprint(f\"The overlap matrix for structure {structure_idx} at the {k_idx}-th k-point is\")\nmldata.items.overlap_kspace[structure_idx][k_idx]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A machine learning model for the electronic Hamiltonian of graphene\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Linear model\n\nIn simple cases, such as the present one, it is convenient to start with\na linear model that directly maps the geometric descriptors to the\ntarget coupled blocks. This can be achieved using [Ridge regression](https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.Ridge.html)_\nas implemented in [scikit-learn](https://scikit-learn.org/stable/)_.\n\nThe linear regression model is expressed as\n\n\\begin{align}H_{ii',\\mathbf{Q}}^{\\lambda\\mu}(\\mathbf{t}) = \\\n \\sum_\\mathbf{q} w_{\\mathbf{q}}^{\\mathbf{Q},\\lambda} \\\n (\\rho_{ii'}^{\\otimes \\nu}(\\mathbf{t}))_{\\mathbf{q}}^{\\lambda\\mu},\\end{align}\n\nwhere a shorthand notation for the features has been introduced. Here,\n$\\mathbf{Q}$ includes all labels indicating the involved orbitals,\natomic species, and permutation symmetry, while $\\mathbf{q}$\nrepresents the feature dimension. The quantities\n$w_{\\mathbf{q}}^{\\mathbf{Q},\\lambda}$ are the model\u2019s weights.\nNote that different weights are associated with different values of\n$\\mathbf{Q}$ and $\\lambda$, but not with specific atom pairs\nor the translation vector, whose dependence arises only through the\ndescriptors.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In ``mlelec``, a linear model can be trained through the\n``LitEquivariantModel`` class, which accepts an ``init_from_ridge``\nkeyword. When set to ``True``, this initializes the weights of a more\ngeneral ``torch.nn.Module`` with the weights provided by Ridge\nregression.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will pass other keyword arguments to ``LitEquivariantModel``, to be\nable to further train the weights on top to the initial Ridge\nregression.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "model = LitEquivariantModel(\n mldata=mldata, # a MLDataset instance\n nlayers=0, # The number of hidden layers\n nhidden=1, # The number of neurons in each hidden layer\n init_from_ridge=True, # If True, initialize the weights and biases of the\n # purely linear model from Ridge regression\n optimizer=\"LBFGS\", # Type of optimizer. Adam is likely better for\n # a more general neural network\n activation=\"SiLU\", # The nonlinear activation function\n learning_rate=1e-3, # Initial learning rate (LR)\n lr_scheduler_patience=10,\n lr_scheduler_factor=0.7,\n lr_scheduler_min_lr=1e-6,\n loss_fn=MSELoss(), # Use the mean square error as loss function\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Model\u2019s accuracy in reproducing derived properties\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Hamiltonian coupled blocks predicted by the ML model can be accessed\nfrom ``model.forward()``\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "predicted_blocks = model.forward(mldata.features)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The real-space blocks can be transformed to Hamiltonian matrices via the\n``mlelec.utils.pbc_utils.blocks_to_matrix`` function. The resulting\nreal-space Hamiltonians can be Fourier transformed to give the\n$k$-space ones.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "HT = blocks_to_matrix(\n predicted_blocks,\n orbitals[\"sto-3g\"],\n {A: qmdata.structures[A] for A in range(len(qmdata))},\n detach=True,\n)\nHk = qmdata.bloch_sum(HT, is_tensor=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Kohn-Sham eigenvalues\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then compute the eigenvalues on the $k$-grid used for the\ncalculation to assess the model accuracy in predicting band energies.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "target_eigenvalues = compute_eigenvalues(qmdata.fock_kspace, qmdata.overlap_kspace)\npredicted_eigenvalues = compute_eigenvalues(Hk, qmdata.overlap_kspace)\n\nHartree = 27.211386024367243 # eV\n\nplt.rcParams[\"font.size\"] = 14\nfig, ax = plt.subplots()\nax.set_aspect(\"equal\")\n\nx_text = 0.38\ny_text = 0.2\nd = 0.06\n\nfor i, (idx, label) in enumerate(\n zip(\n [mldata.train_idx, mldata.val_idx, mldata.test_idx],\n [\"train\", \"validation\", \"test\"],\n )\n):\n\n target = (\n torch.stack([target_eigenvalues[i] for i in idx]).flatten().detach() * Hartree\n )\n prediction = (\n torch.stack([predicted_eigenvalues[i] for i in idx]).flatten().detach()\n * Hartree\n )\n\n non_core_states = target > -100\n rmse = np.sqrt(\n np.mean(\n (target.numpy()[non_core_states] - prediction.numpy()[non_core_states]) ** 2\n )\n )\n ax.scatter(target, prediction, marker=\".\", label=label, alpha=0.5)\n ax.text(\n x=x_text,\n y=y_text - d * i,\n s=rf\"$\\mathrm{{RMSE_{{{label}}}={rmse:.2f}\\,eV}}$\",\n transform=ax.transAxes,\n )\n\nxmin, xmax = ax.get_xlim()\nax.plot([xmin, xmax], [xmin, xmax], \"--k\")\nax.set_xlim(xmin, xmax)\nax.set_ylim(xmin, xmax)\nax.legend()\nax.set_xlabel(\"Target eigenvalues (eV)\")\nax.set_ylabel(\"Predicted eigenvalues (eV)\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Graphene band structure\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Apart from the eigenvalues on a mesh in the Brillouin zone, we can use\nthe real-space Hamiltonians predicted by the model to compute the band\nstructure along high-symmetry paths.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(figsize=(8, 4.8))\n\nidx = 0\n\nhandles = []\n\nwith warnings.catch_warnings():\n warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n\n # Plot reference\n ax, h_ref = plot_bands_frame(\n qmdata.fock_realspace[idx], idx, qmdata, ax=ax, color=\"blue\", lw=2\n )\n\n # Plot prediction\n ax, h_pred = plot_bands_frame(\n HT[idx], idx, qmdata, ax=ax, color=\"lime\", ls=\"--\", lw=2\n )\n\nax.set_ylim(-30, 30)\nax.legend(\n [h_ref, h_pred],\n [\"Reference\", \"Prediction\"],\n loc=\"center left\",\n bbox_to_anchor=(1, 0.5),\n)\nfig.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adding nonlinearities\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The model used above consists of several submodels, one for each Hamiltonian\ncoupled block. Each submodel can be extended to a [multilayer\nperceptron](https://en.wikipedia.org/wiki/Multilayer_perceptron)_\n(MLP) that maps the corresponding set of geometric features to the\nHamiltonian coupled block. Nonlinearities are applied to the invariants\nconstructed from each equivariant feature block using the\n``EquivariantNonlinearity`` module. This section outlines the process to\nmodify the model to introduce non-linear terms. Given that the time\nto train and evaluate the model would then increase, this section\nincludes snippets of code, but is not a complete implementation and\nis not executed when running this example.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The architecture of ``EquivariantNonlinearity`` can be visualized with\n``torchviz`` with the following snippet:\n\n.. code:: python\n\n import torch\n from mlelec.models.equivariant_model import EquivariantNonLinearity\n from torchviz import make_dot\n m = EquivariantNonLinearity(torch.nn.SiLU(), layersize = 10)\n y = m.forward(torch.randn(3,3,10))\n dot = make_dot(y, dict(m.named_parameters()))\n dot.graph_attr.update(size='150,150')\n dot.render(\"equivariantnonlinear\", format=\"png\")\n dot\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. figure:: equivariantnonlinear.png\n :alt: Graph representing the architecture of EquivariantNonLinearity\n :width: 300px\n\n Graph representing the architecture of EquivariantNonLinearity\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The global architecture of the MLP, implemented in ``simpleMLP``, can be\nvisualized with\n\n.. code:: python\n\n import torch\n from mlelec.models.equivariant_model import simpleMLP\n from torchviz import make_dot\n mlp = simpleMLP(\n nin=10,\n nout=1,\n nhidden=1,\n nlayers=1,\n bias=True,\n activation='SiLU',\n apply_layer_norm=True\n )\n y = mlp.forward(torch.randn(1,1,10))\n dot = make_dot(y, dict(mlp.named_parameters()))\n dot.graph_attr.update(size='150,150')\n dot.render(\"simpleMLP\", format=\"png\")\n dot\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. figure:: simpleMLP.png\n :alt: Graph representing the architecture of simpleMLP\n :width: 600px\n\n Graph representing the architecture of simpleMLP\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Set up the training loop for stochastic gradient descent\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Import additional modules needed to monitor the training.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n import lightning.pytorch as pl\n from lightning.pytorch.callbacks import EarlyStopping\n from mlelec.callbacks.logging import LoggingCallback\n from mlelec.models.equivariant_lightning import MLDatasetDataModule\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We set up a callback for logging training information such as the\ntraining and validation losses.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n logger_callback = LoggingCallback(log_every_n_epochs=5)\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We set up an early stopping criterion to stop the training when the\nvalidation loss function stops decreasing.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n early_stopping = EarlyStopping(\n monitor=\"val_loss\", min_delta=1e-3, patience=10, verbose=False, mode=\"min\"\n )\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We define a ``lighting.pytorch.Trainer`` instance to handle the training\nloop. For example, we can further optimize the weights for 50 epochs using\nthe [LBFGS](https://en.wikipedia.org/wiki/Limited-memory_BFGS)_\noptimizer.\n\nNote that PyTorch Lightning requires the definition of a data module to\ninstantiate DataLoaders to be used during the training.\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n data_module = MLDatasetDataModule(mldata, batch_size=16, num_workers=0)\n\n trainer = pl.Trainer(\n max_epochs=50,\n accelerator=\"cpu\",\n check_val_every_n_epoch=10,\n callbacks=[early_stopping, logger_callback],\n logger=False,\n enable_checkpointing=False,\n )\n\n trainer.fit(model, data_module)\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We compute the test set loss to assess the model accuracy on an unseen\nset of structures\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".. code:: python\n\n trainer.test(model, data_module)\n\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this case, Ridge regression already provides good accuracy, so\nfurther optimizing the weights offers limited improvement. However, for\nmore complex datasets, the benefits of additional optimization can be\nsignificant.\n\n\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/a58e2543da5a6b5daa9cea5c8b3c3a21/lpr.py b/_downloads/a58e2543da5a6b5daa9cea5c8b3c3a21/lpr.py new file mode 100644 index 00000000..b0887e17 --- /dev/null +++ b/_downloads/a58e2543da5a6b5daa9cea5c8b3c3a21/lpr.py @@ -0,0 +1,265 @@ +""" +Local Prediction Rigidity analysis +================================== + +:Authors: Sanggyu "Raymond" Chong `@SanggyuChong `_; + Federico Grasselli `@fgrassel `_ + +In this tutorial, we calculate the SOAP descriptors of an amorphous +silicon dataset using rascaline, then compute the local prediction +rigidity (LPR) for the atoms of a "test" set before and after +modifications to the "training" dataset has been made. + +First, we import all the necessary packages: +""" + +# %% +import os +import tarfile + +import numpy as np +import requests +from ase.io import read +from matplotlib import pyplot as plt +from matplotlib.colors import LogNorm +from rascaline import SoapPowerSpectrum +from sklearn.decomposition import PCA +from skmatter.metrics import local_prediction_rigidity as lpr + + +# %% +# Load and prepare amorphous silicon data +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# +# We first download the dataset associated with LPR +# analysis from Materials Cloud and load the the amorphous +# silicon structures using `ASE `_. + +filename = "LPR_supp_notebook_dataset.tar.gz" +if not os.path.exists(filename): + url = "https://rb.gy/wxsrug" # shortened URL + response = requests.get(url) + response.raise_for_status() + with open(filename, "wb") as f: + f.write(response.content) + +with tarfile.open(filename) as tar: + tar.extractall(path=".") + +frames_pristine = read("datasets/Si_amo_defect_free.xyz", ":") +frames_defect = read("datasets/Si_amo_defect_containing.xyz", ":") + +# Randomly shuffle the structures + +np.random.seed(20230215) + +ids = list(range(len(frames_pristine))) +np.random.shuffle(ids) +frames_pristine = [frames_pristine[ii] for ii in ids] + +ids = list(range(len(frames_defect))) +np.random.shuffle(ids) +frames_defect = [frames_defect[ii] for ii in ids] + +# %% +# We now further refine the loaded datasets according the the +# number of coordinated atoms that each atomic environment exhibits. +# "Pristine" refers to structures where all of the atoms have strictly +# 4 coordinating atoms. "Defect" refers to structures that contain +# atoms with coordination numbers other than 4. +# +# We use :code:`get_all_distances` funciton of :code:`ase.Atoms` to detect the +# number of coordinated atoms. + +cur_cutoff = 2.7 +refined_pristine_frames = [] +for frame in frames_pristine: + neighs = (frame.get_all_distances(mic=True) < cur_cutoff).sum(axis=0) - 1 + if neighs.max() > 4 or neighs.min() < 4: + continue + else: + refined_pristine_frames.append(frame) + +refined_defect_frames = [] +for frame in frames_defect: + neighs = (frame.get_all_distances(mic=True) < cur_cutoff).sum(axis=0) - 1 + num_defects = (neighs > 4).sum() + (neighs < 4).sum() + if num_defects > 4: + refined_defect_frames.append(frame) + + +# %% +# Compute SOAP descriptors using rascaline +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# Now, we move on and compute the SOAP descriptors for the refined +# structures. First, define the rascaline hyperparameters used to +# compute SOAP. Among the hypers, notice that the cutoff is chosen +# to be 2.85 Å, and the radial scaling is turned off. These were +# heuristic choices made to accentuate the difference in the LPR +# based on the nearest-neighbor coordination. (Do not blindly +# use this set of hypers for production-quality model training!) + +# Hypers dictionary +hypers = { + "cutoff": 2.85, + "max_radial": 10, + "max_angular": 12, + "atomic_gaussian_width": 0.5, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {"spline_accuracy": 1e-8}}, + "cutoff_function": {"ShiftedCosine": {"width": 0.1}}, + "radial_scaling": None, +} +# Define rascaline calculator +calculator = SoapPowerSpectrum(**hypers) + +# Calculate the SOAP power spectrum +Xlist_pristine = [] +for frame in refined_pristine_frames: + descriptor = calculator.compute(frame) + Xlist_pristine.append(np.array(descriptor.block().values)) + +Xlist_defect = [] +for frame in refined_defect_frames: + descriptor = calculator.compute(frame) + Xlist_defect.append(np.array(descriptor.block().values)) + +# %% +# Organize structures into "training" and "test" sets +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# Now we move on and compute the SOAP descriptors for the refined +# structures. First, define the rascaline hyperparameters used to +# compute SOAP. +# +# Notice that the format in which we handle the descriptors is as a +# list of :code:`np.array` descriptor blocks. This is to ensure +# compatibility with how things have been implemented in the LPR +# module of :code:`scikit-matter`. + +n_train = 400 +n_add = 50 +n_test = 50 + +X_pristine = [Xlist for Xlist in Xlist_pristine[: n_train + n_add]] +X_defect = [Xlist for Xlist in Xlist_defect[:n_add]] +X_test = [Xlist for Xlist in Xlist_defect[n_add : n_add + n_test]] + +# Save coordination values for visualization +test_coord = [] +for frame in refined_defect_frames[n_add : n_add + n_test]: + coord = (frame.get_all_distances(mic=True) < cur_cutoff - 0.05).sum(axis=0) - 1 + test_coord += coord.tolist() +test_coord = np.array(test_coord) + +# %% +# Compute the LPR for the test set +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# Next, we will use the :code:`local_prediction_rigidity` module of +# `scikit-matter `_ +# to compute the LPRs for the test set that we have set apart. +# +# LPR reflects how the ML model perceives a local environment, +# given a collection of other structures, similar or different. +# It should then carry over some of the details involved in training +# the model, in this case the regularization strength. +# +# For this example, we have foregone on the actual model training, +# and so we define an arbitrary value for the alpha. + +alpha = 1e-4 +LPR_test, rank = lpr(X_pristine, X_test, alpha) +LPR_test = np.hstack(LPR_test) + +# %% +# Visualizing the LPR on a PCA map +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# We now visualize the LPRs of the test set on a PCA map, +# where the PCA is performed on the SOAP descriptors of +# defect-containing dataset. + +pca = PCA(n_components=5) +descriptors_all = calculator.compute(refined_defect_frames) +pca.fit_transform(descriptors_all.block().values) +PCA_test = pca.transform(np.vstack(X_test)) + +rmin = np.log10(LPR_test.min()) + 0.5 +rmax = np.log10(LPR_test.max()) - 0.5 + +fig = plt.figure(figsize=(5, 4), dpi=200) +ax = fig.add_subplot() +im = ax.scatter( + PCA_test[:, 0], + PCA_test[:, 1], + c=LPR_test, + s=20, + linewidths=0, + norm=LogNorm(vmin=10**rmin, vmax=10**rmax), + cmap="viridis", +) + +ax.set_xlabel("PC1") +ax.set_ylabel("PC2") +fig.colorbar(im, ax=ax, label="LPR") +ax.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False) +plt.show() + +# %% +# In the PCA map, where each point corresponds to an +# atomic environment of the test set structures, one +# can observe 4 different clusters of points, arranged +# along PC1. This corresponds to the coordination numbers +# ranging from 3 to 6. Since the training set contains +# structures exclusively composed of 4-coordinated atoms, +# LPR is distinctly high for the second, main cluster of +# points, and quite low for the three other clusters. + + +# %% +# Studying the LPR after dataset modification +# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +# +# We now want to see what would happen when defect structures +# are included into the training set of the model. For this, +# we first create a modified dataset that incorporates in the +# defect structures, and recompute the LPR. + +X_new = X_pristine[:n_train] + X_defect[:n_add] +LPR_test_new, rank = lpr(X_new, X_test, alpha) +LPR_test_new = np.hstack(LPR_test_new) + +# %% +# We then visualize the change in the LPR with the +# modification of the dataset by plotting the same PCA +# map, but now colored by the ratio of new set of LPR +# values (after dataset modification) over the original +# one. + +fig = plt.figure(figsize=(5, 4), dpi=200) +ax = fig.add_subplot() +im = ax.scatter( + PCA_test[:, 0], + PCA_test[:, 1], + c=LPR_test_new / LPR_test, + s=20, + linewidths=0, + # norm=LogNorm(vmin=10**rmin, vmax=10**rmax), + cmap="OrRd", +) +ax.set_xlabel("PC1") +ax.set_ylabel("PC2") +fig.colorbar(im, ax=ax, label=r"LPR$_{\mathrm{new}}$ / LPR$_{\mathrm{old}}$") +ax.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False) +plt.show() + +# %% +# It is apparent that while the LPR stays more or less consistent for the +# 4-coordinated atoms, it is significantly enhanced for the defective environments +# as a result of the inclusion of defective structures in the training set. + + +# %% diff --git a/_downloads/ab58b2811af545cfb312fbb1499797cd/roy-gch.zip b/_downloads/ab58b2811af545cfb312fbb1499797cd/roy-gch.zip new file mode 100644 index 00000000..d554f985 Binary files /dev/null and b/_downloads/ab58b2811af545cfb312fbb1499797cd/roy-gch.zip differ diff --git a/_downloads/acef7f4b78ef4bb781ee98c79cb1dfe9/gaas-map.ipynb b/_downloads/acef7f4b78ef4bb781ee98c79cb1dfe9/gaas-map.ipynb new file mode 100644 index 00000000..647f8790 --- /dev/null +++ b/_downloads/acef7f4b78ef4bb781ee98c79cb1dfe9/gaas-map.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# PCA/PCovR Visualization of a training dataset for a potential\n\n:Authors: Michele Ceriotti [@ceriottm](https://github.com/ceriottm/),\n Giulio Imbalzano\n\nThis example uses ``rascaline`` and ``metatensor`` to compute\nstructural properties for the structures in a training dataset\nfor a ML potential.\nThese are then used with simple dimensionality reduction algorithms\n(implemented in ``sklearn`` and ``skmatter``) to obtain a simplified\ndescription of the dataset, that is then visualized using\n``chemiscope``.\n\nThis example uses the dataset from\n[Imbalzano (2021)](http://doi.org/10.1103/PhysRevMaterials.5.063804)\nand the principal covariate regression scheme as implemented in\n[Helfrecht (2020)](http://doi.org/10.1088/2632-2153/aba9ef).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import os\n\nimport ase\nimport ase.io\nimport chemiscope\nimport numpy as np\nimport requests\nfrom matplotlib import pyplot as plt\nfrom metatensor import mean_over_samples\nfrom rascaline import AtomicComposition, SoapPowerSpectrum\nfrom sklearn.decomposition import PCA\nfrom sklearn.linear_model import RidgeCV\nfrom skmatter.decomposition import PCovR\nfrom skmatter.preprocessing import StandardFlexibleScaler\n\n\n# sphinx_gallery_thumbnail_number = 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we load the structures, extracting some of the properties for\nmore convenient manipulation. These are\n$\\mathrm{Ga}_x\\mathrm{As}_{1-x}$ structures used in [Imbalzano &\nCeriotti (2021)](http://doi.org/10.1103/PhysRevMaterials.5.063804)_ to\ntrain a ML potential to describe the full composition range.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "filename = \"gaas_training.xyz\"\nif not os.path.exists(filename):\n url = f\"https://zenodo.org/records/10566825/files/{filename}\"\n response = requests.get(url)\n response.raise_for_status()\n with open(filename, \"wb\") as f:\n f.write(response.content)\n\nstructures = ase.io.read(filename, \":\")\nenergy = np.array([f.info[\"energy\"] for f in structures])\nnatoms = np.array([len(f) for f in structures])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Remove atomic energy baseline\n\nEnergies from an electronic structure calculation contain a very large\n\u201cself\u201d contributions from the atoms, which can obscure the important\ndifferences in cohesive energies between structures. We can build an\napproximate model based on the chemical nature of the atoms, $a_i$\n\n\\begin{align}E(A) = \\sum_{i\\in A} e_{a_i}\\end{align}\n\nwhere $e_a$ are atomic energies that can be determined by linear\nregression.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# rascaline has an `AtomicComposition` calculator that streamlines\n# this (simple) calculation\ncalculator = AtomicComposition(**{\"per_structure\": True})\nrho0 = calculator.compute(structures)\n\n# the descriptors are returned as a `TensorMap` object, that contains\n# the composition data in a sparse storage format\nrho0\n\n# for easier manipulation, we extract the features as a dense vector\n# of composition weights\ncomp_feats = rho0.keys_to_properties([\"species_center\"]).block(0).values\n\n# a one-liner to fit a linear model and compute \"dressed energies\"\natom_energy = (\n RidgeCV(alphas=np.geomspace(1e-8, 1e2, 20))\n .fit(comp_feats, energy)\n .predict(comp_feats)\n)\ncohesive_peratom = (energy - atom_energy) / natoms" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The baseline makes up a large fraction of the total energy, but actually\nthe residual (which is the part that matters) is still large.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(6, 4))\nax.plot(energy / natoms, atom_energy / natoms, \"b.\")\nax.set_xlabel(\"Energy / (eV/atom)\")\nax.set_ylabel(\"Atomic e. / (eV/atom)\")\nplt.show()\nprint(f\"RMSE / (eV/atom): {np.sqrt(np.mean((cohesive_peratom)**2))}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute structural descriptors\n\nIn order to visualize the structures as a low-dimensional map, we start\nby computing suitable ML descriptors. Here we have used ``rascaline`` to\nevaluate average SOAP features for the structures.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# hypers for evaluating rascaline features\nhypers = {\n \"cutoff\": 4.5,\n \"max_radial\": 6,\n \"max_angular\": 4,\n \"atomic_gaussian_width\": 0.3,\n \"cutoff_function\": {\"ShiftedCosine\": {\"width\": 0.5}},\n \"radial_basis\": {\"Gto\": {\"accuracy\": 1e-6}},\n \"center_atom_weight\": 1.0,\n}\ncalculator = SoapPowerSpectrum(**hypers)\nrho2i = calculator.compute(structures)\n\n# neighbor types go to the keys for sparsity (this way one can\n# compute a heterogeneous dataset without having blocks of zeros)\nrho2i = rho2i.keys_to_samples([\"species_center\"]).keys_to_properties(\n [\"species_neighbor_1\", \"species_neighbor_2\"]\n)\n\n# computes structure-level descriptors and then extracts\n# the features as a dense array\nrho2i_structure = mean_over_samples(rho2i, sample_names=[\"center\", \"species_center\"])\nrho2i = None # releases memory\nfeatures = rho2i_structure.block(0).values" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We standardize (per atom) energy and features (computed as a *mean* over\natomic environments) so that they can be combined on the same footings.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sf_energy = StandardFlexibleScaler().fit_transform(cohesive_peratom.reshape(-1, 1))\nsf_feats = StandardFlexibleScaler().fit_transform(features)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## PCA and PCovR projection\n\nComputes PCA projection to generate low-dimensional descriptors that\nreflect structural diversity. Any other dimensionality reduction scheme\ncould be used in a similar fashion.\n\nWe also compute the principal covariate regression (PCovR) descriptors,\nthat reduce dimensionality while combining a variance preserving\ncriterion with the requirement that the low-dimensional features are\ncapable of estimating a target quantity (here, the energy).\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# PCA\npca = PCA(n_components=4)\npca_features = pca.fit_transform(sf_feats)\n\nfig, ax = plt.subplots(1, 1, figsize=(6, 4))\nscatter = ax.scatter(pca_features[:, 0], pca_features[:, 1], c=cohesive_peratom)\nax.set_xlabel(\"PCA[1]\")\nax.set_ylabel(\"PCA[2]\")\ncbar = fig.colorbar(scatter, ax=ax)\ncbar.set_label(\"energy / eV/at.\")\nplt.show()\n\n# computes PCovR map\npcovr = PCovR(n_components=4)\npcovr_features = pcovr.fit_transform(sf_feats, sf_energy)\n\nfig, ax = plt.subplots(1, 1, figsize=(6, 4))\nscatter = ax.scatter(pcovr_features[:, 0], pcovr_features[:, 1], c=cohesive_peratom)\nax.set_xlabel(\"PCovR[1]\")\nax.set_ylabel(\"PCovR[2]\")\ncbar = fig.colorbar(scatter, ax=ax)\ncbar.set_label(\"energy / (eV/at.)\")\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Chemiscope visualization\n\nVisualizes the structure-property map using a chemiscope widget (and\ngenerates a .json file that can be viewed on\n[chemiscope.org](https://chemiscope.org)_).\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# extracts force data (adding considerably to the dataset size...)\nforce_vectors = chemiscope.ase_vectors_to_arrows(structures, scale=1)\nforce_vectors[\"parameters\"][\"global\"][\"color\"] = 0x505050\n\n# adds properties to the ASE frames\nfor i, f in enumerate(structures):\n for j in range(len(pca_features[i])):\n f.info[\"pca_\" + str(j + 1)] = pca_features[i, j]\nfor i, f in enumerate(structures):\n for j in range(len(pcovr_features[i])):\n f.info[\"pcovr_\" + str(j + 1)] = pcovr_features[i, j]\nfor i, f in enumerate(structures):\n f.info[\"cohesive_energy\"] = cohesive_peratom[i]\n f.info[\"x_ga\"] = comp_feats[i, 0] / comp_feats[i].sum()\n\n# it would also be easy to add the properties manually, this is just a dictionary\nstructure_properties = chemiscope.extract_properties(structures)\n\ncs = chemiscope.show(\n frames=structures,\n properties=structure_properties,\n shapes={\"forces\": force_vectors},\n # the settings are a tad verbose, but give full control over the visualization\n settings={\n \"map\": {\n \"x\": {\"property\": \"pcovr_1\"},\n \"y\": {\"property\": \"pcovr_2\"},\n \"color\": {\"property\": \"x_ga\"},\n },\n \"structure\": [\n {\n \"bonds\": True,\n \"unitCell\": True,\n \"shape\": [\"forces\"],\n \"keepOrientation\": False,\n }\n ],\n },\n meta={\n \"name\": \"GaAs training data\",\n \"description\": \"\"\"\nA collection of Ga(x)As(1-x) structures to train a MLIP,\nincluding force and energy data.\n\"\"\",\n \"authors\": [\"Giulio Imbalzano\", \"Michele Ceriotti\"],\n \"references\": [\n \"\"\"\nG. Imbalzano and M. Ceriotti, 'Modeling the Ga/As binary system across\ntemperatures and compositions from first principles,'\nPhys. Rev. Materials 5(6), 063804 (2021).\n\"\"\",\n \"Original dataset: https://archive.materialscloud.org/record/2021.226\",\n ],\n },\n)\n\ncs.save(\"gaas_map.chemiscope.json.gz\")\n\ncs # display if in a notebook" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/ae0da8b1ee160a1314e0f4a70d65ba5f/reference-trajectory.py b/_downloads/ae0da8b1ee160a1314e0f4a70d65ba5f/reference-trajectory.py new file mode 100644 index 00000000..4fb6e77c --- /dev/null +++ b/_downloads/ae0da8b1ee160a1314e0f4a70d65ba5f/reference-trajectory.py @@ -0,0 +1,304 @@ +r""" +Batch run of CP2K calculations +============================== + +:Authors: Matthias Kellner `@bananenpampe `_, + Philip Loche `@PicoCentauri `_ + +This is an example how to perform single point calculations based on list of structures +using `CP2K `_ using its `reftraj functionality +`_. The inputs are a +set of structures in :download:`example.xyz` using the DFT parameters defined in +:download:`reftraj_template.cp2k`. The reference DFT parameters are taken from `Cheng et +al. Ab initio thermodynamics of liquid and solid water 2019 +`_. Due to the small size of the test +structure and convergence issues, we have decreased the size of the ``CUTOFF_RADIUS`` +from :math:`6.0\,\mathrm{Å}` to :math:`3.0\,\mathrm{Å}`. For actual production +calculations adapt the template! +""" + +# %% +# We start the example by importing the required packages. + +import os +import platform +import subprocess +from typing import List, Union + +import ase.io +import ase.visualize.plot +import matplotlib.pyplot as plt +import numpy as np +import requests + + +# %% +# +# Install CP2K +# ------------ +# +# We'll need a working installation of cp2k. The best way to do so depends on your +# platform, here are some possible solutions, but feel free to replace them with another +# installation method. + +if platform.system() == "Linux": + # use conda on Linux + subprocess.run(["conda", "install", "cp2k", "-c", "conda-forge", "-y"], check=True) +elif platform.system() == "Darwin": + # use homebrew on macOS + subprocess.run(["brew", "install", "cp2k"], check=True) +else: + print("no known way to install cp2k, skipping installation") + + +# %% +# Define necessary functions +# -------------------------- +# Next we below define necessary helper functions to run the example. + + +def write_reftraj(fname: str, frames: Union[ase.Atoms, List[ase.Atoms]]) -> None: + """Writes a list of ase atoms objects to a reference trajectory. + + A reference trajectory is the CP2K compatible format for the compuation of batches. + All frames must have the stoichiometry/composition. + """ + + if isinstance(frames, ase.Atoms): + frames = [frames] + + out = "" + for i, atoms in enumerate(frames): + if ( + len(atoms) != len(frames[0]) + or atoms.get_chemical_formula() != frames[0].get_chemical_formula() + ): + raise ValueError( + f"Atom symbols in frame {i},{atoms.get_chemical_formula()} are " + f"different compared to inital frame " + f"{frames[0].get_chemical_formula()}. " + "CP2K does not support changing atom types within a reftraj run!" + ) + + out += f"{len(atoms):>8}\n i = {i + 1:>8}, time = {0:>12.3f}\n" + for atom in atoms: + pos = atom.position + out += f"{atom.symbol}{pos[0]:24.15f}{pos[1]:24.15f}{pos[2]:24.15f}\n" + out += "\n" + with open(fname, "w") as f: + f.write(out) + + +# %% + + +def write_cellfile(fname: str, frames: Union[ase.Atoms, List[ase.Atoms]]) -> None: + """Writes a cellfile for a list of ``ase.Atoms``. + + A Cellfile accompanies a reftraj containing the cell parameters. + """ + if isinstance(frames, ase.Atoms): + frames = [frames] + + out = ( + "# " + "Step " + "Time [fs] " + "Ax [Angstrom] " + "Ay [Angstrom] " + "Az [Angstrom] " + "Bx [Angstrom] " + "By [Angstrom] " + "Bz [Angstrom] " + "Cx [Angstrom] " + "Cy [Angstrom] " + "Cz [Angstrom] " + "Volume [Angstrom^3]\n" + ) + + for i, atoms in enumerate(frames): + out += f"{i + 1:>8}{0:>12.3f}" + out += "".join([f"{c:>20.10f}" for c in atoms.cell.flatten()]) + out += f"{atoms.cell.volume:>25.10f}" + out += "\n" + + with open(fname, "w") as f: + f.write(out) + + +# %% + + +def write_cp2k_in( + fname: str, project_name: str, last_snapshot: int, cell: List[float] +) -> None: + """Writes a cp2k input file from a template. + + Importantly, it writes the location of the basis set definitions, + determined from the path of the system CP2K install to the input file. + """ + + cp2k_in = open("reftraj_template.cp2k", "r").read() + + cp2k_in = cp2k_in.replace("//PROJECT//", project_name) + cp2k_in = cp2k_in.replace("//LAST_SNAPSHOT//", str(last_snapshot)) + cp2k_in = cp2k_in.replace("//CELL//", " ".join([f"{c:.6f}" for c in cell])) + + with open(fname, "w") as f: + f.write(cp2k_in) + + +# %% +# +# We will now download basis set files from CP2K website. Depending on your CP2K +# installation, this might not be necessary! + + +def download_parameter(file): + path = os.path.join("parameters", file) + + if not os.path.exists(path): + url = f"https://raw.githubusercontent.com/cp2k/cp2k/support/v2024.1/data/{file}" + response = requests.get(url) + response.raise_for_status() + with open(path, "wb") as f: + f.write(response.content) + + +os.makedirs("parameters", exist_ok=True) +for file in ["GTH_BASIS_SETS", "BASIS_ADMM", "POTENTIAL", "dftd3.dat", "t_c_g.dat"]: + download_parameter(file) + + +# %% +# Prepare calculation inputs +# -------------------------- +# During this example we will create a directory named ``project_directory`` containing +# the subdirectories for each stoichiometry. This is necessary, because CP2K can only +# run calculations using a fixed stoichiometry at a time, using its ``reftraj`` +# functionality. +# +# Below we define the general information for the CP2K run. This includes the reference +# files for the structures, the ``project_name`` used to build the name of the +# trajectory during the CP2K run, the ``project_directory`` where we store all +# simulation output as well as the path ``write_to_file`` which is the name of the file +# containing the computed energies and forces of the simulation. + +frames_full = ase.io.read("example.xyz", ":") +project_name = "test_calcs" # name of the global PROJECT +project_directory = "production" +write_to_file = "out.xyz" + +# %% +# Below we show the initial configuration of two water molecules in a cubic box with a +# side length of :math:`\approx 4\,\mathrm{Å}`. + +ase.visualize.plot.plot_atoms(frames_full[0]) + +plt.xlabel("Å") +plt.ylabel("Å") + +plt.show() + +# %% +# We now extract the stoichiometry from the input dataset using ASE's +# :py:meth:`ase.symbols.Symbols.get_chemical_formula` method. + +frames_dict = {} + +for atoms in frames_full: + chemical_formula = atoms.get_chemical_formula() + try: + frames_dict[chemical_formula] + except KeyError: + frames_dict[chemical_formula] = [] + + frames_dict[chemical_formula].append(atoms) + +# %% +# Based on the stoichiometries we create one calculation subdirectories for the +# calculations. (reftraj, input and cellfile). For our example this is only is one +# directory named ``H4O2`` because our dataset consists only of a single structure with +# two water molecules. + +for stoichiometry, frames in frames_dict.items(): + current_directory = f"{project_directory}/{stoichiometry}" + os.makedirs(current_directory, exist_ok=True) + + write_cp2k_in( + f"{current_directory}/in.cp2k", + project_name=project_name, + last_snapshot=len(frames), + cell=frames[0].cell.diagonal(), + ) + + ase.io.write(f"{current_directory}/init.xyz", frames[0]) + write_reftraj(f"{current_directory}/reftraj.xyz", frames) + write_cellfile(f"{current_directory}/reftraj.cell", frames) + +# %% +# Run simulations +# --------------- +# Now we have all ingredients to run the simulations. Below we call the bash script +# :download:`run_calcs.sh`. +# +# .. literalinclude:: run_calcs.sh +# :language: bash +# +# This script will loop through all stoichiometry subdirectories and call the CP2K +# engine. + +# run the bash script directly from this script +subprocess.run("bash run_calcs.sh", shell=True) + +# %% +# .. note:: +# +# For a usage on an HPC environment you can parallelize the loop over the +# sub-directories and submit and single job per stoichiometry. +# +# Load results +# ------------ +# After the simulation we load the results and perform a unit version from the default +# CP2K output units (Bohr and Hartree) to Å and eV. + +cflength = 0.529177210903 # Bohr -> Å +cfenergy = 27.211386245988 # Hartree -> eV +cfforce = cfenergy / cflength # Hartree/Bohr -> eV/Å + +# %% +# Finally, we store the results as :class:`ase.Atoms` in the ``new_frames`` list and +# write them to the ``project_directory`` using the ``new_fname``. Here it will be +# written to ``production/out_dft.xyz``. + +new_frames = [] + +for stoichiometry, frames in frames_dict.items(): + current_directory = f"{project_directory}/{stoichiometry}" + + frames_dft = ase.io.read(f"{current_directory}/{project_name}-pos-1.xyz", ":") + forces_dft = ase.io.read(f"{current_directory}/{project_name}-frc-1.xyz", ":") + cell_dft = np.atleast_2d(np.loadtxt(f"{current_directory}/{project_name}-1.cell"))[ + :, 2:-1 + ] + + for i_atoms, atoms in enumerate(frames_dft): + frames_ref = frames[i_atoms] + + # Check consistent positions + if not np.allclose(atoms.positions, frames_ref.positions): + raise ValueError(f"Positions in frame {i_atoms} are not the same.") + + # Check consistent cell + if not np.allclose(frames_ref.cell.flatten(), cell_dft[i_atoms]): + raise ValueError(f"Cell dimensions in frame {i_atoms} are not the same.") + + atoms.info["E"] *= cfenergy + atoms.pbc = True + atoms.cell = frames_ref.cell + atoms.set_array("forces", cfforce * forces_dft[i_atoms].positions) + + new_frames += frames_dft + +new_fname = f"{os.path.splitext(os.path.basename(write_to_file))[0]}_dft.xyz" +ase.io.write(f"{project_directory}/{new_fname}", new_frames) diff --git a/_downloads/aff5eecc36386b5390fd6d11df5c3838/data.zip b/_downloads/aff5eecc36386b5390fd6d11df5c3838/data.zip new file mode 100644 index 00000000..c5b9a3e1 Binary files /dev/null and b/_downloads/aff5eecc36386b5390fd6d11df5c3838/data.zip differ diff --git a/_downloads/b130988d387c627a2afb4ff91c430422/environment.yml b/_downloads/b130988d387c627a2afb4ff91c430422/environment.yml new file mode 100644 index 00000000..4c2b74a6 --- /dev/null +++ b/_downloads/b130988d387c627a2afb4ff91c430422/environment.yml @@ -0,0 +1,11 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - rust >=1.65 + - pip: + - ase==3.22.1 + - matplotlib + - rascaline @ git+https://github.com/Luthaf/rascaline@5c2a79838bda0a52d0fde2fbe65941f4792c4cae + - skmatter diff --git a/_downloads/b59df37786d0d368d9bf73d930d78801/heat-capacity.zip b/_downloads/b59df37786d0d368d9bf73d930d78801/heat-capacity.zip new file mode 100644 index 00000000..b9805246 Binary files /dev/null and b/_downloads/b59df37786d0d368d9bf73d930d78801/heat-capacity.zip differ diff --git a/_downloads/b6b84bf8dd77ad82cc02fbec9e101f88/periodic-hamiltonian.zip b/_downloads/b6b84bf8dd77ad82cc02fbec9e101f88/periodic-hamiltonian.zip new file mode 100644 index 00000000..02ecb68c Binary files /dev/null and b/_downloads/b6b84bf8dd77ad82cc02fbec9e101f88/periodic-hamiltonian.zip differ diff --git a/_downloads/beac0e7cadaac3a5e3f35db1c93eb0d6/data.zip b/_downloads/beac0e7cadaac3a5e3f35db1c93eb0d6/data.zip new file mode 100644 index 00000000..75387698 Binary files /dev/null and b/_downloads/beac0e7cadaac3a5e3f35db1c93eb0d6/data.zip differ diff --git a/_downloads/c1382a1742282359674fed148953d82f/environment.yml b/_downloads/c1382a1742282359674fed148953d82f/environment.yml new file mode 100644 index 00000000..f720fd36 --- /dev/null +++ b/_downloads/c1382a1742282359674fed148953d82f/environment.yml @@ -0,0 +1,14 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - rust >=1.65 + - pip: + - ase==3.22.1 + - chemiscope>=0.7 + - matplotlib + - metatensor + - rascaline @ git+https://github.com/Luthaf/rascaline@ca957642f512e141c7570e987aadc05c7ac71983 + - scikit-learn + - skmatter diff --git a/_downloads/c30ae838fdaa9326592e1ef5414c0d62/gaas-map.py b/_downloads/c30ae838fdaa9326592e1ef5414c0d62/gaas-map.py new file mode 100644 index 00000000..99bdad6a --- /dev/null +++ b/_downloads/c30ae838fdaa9326592e1ef5414c0d62/gaas-map.py @@ -0,0 +1,261 @@ +r""" +PCA/PCovR Visualization of a training dataset for a potential +============================================================= + +:Authors: Michele Ceriotti `@ceriottm `_, + Giulio Imbalzano + +This example uses ``rascaline`` and ``metatensor`` to compute +structural properties for the structures in a training dataset +for a ML potential. +These are then used with simple dimensionality reduction algorithms +(implemented in ``sklearn`` and ``skmatter``) to obtain a simplified +description of the dataset, that is then visualized using +``chemiscope``. + +This example uses the dataset from +`Imbalzano (2021) `_ +and the principal covariate regression scheme as implemented in +`Helfrecht (2020) `_. +""" + +import os + +import ase +import ase.io +import chemiscope +import numpy as np +import requests +from matplotlib import pyplot as plt +from metatensor import mean_over_samples +from rascaline import AtomicComposition, SoapPowerSpectrum +from sklearn.decomposition import PCA +from sklearn.linear_model import RidgeCV +from skmatter.decomposition import PCovR +from skmatter.preprocessing import StandardFlexibleScaler + + +# sphinx_gallery_thumbnail_number = 2 + +###################################################################### +# First, we load the structures, extracting some of the properties for +# more convenient manipulation. These are +# :math:`\mathrm{Ga}_x\mathrm{As}_{1-x}` structures used in `Imbalzano & +# Ceriotti (2021) `__ to +# train a ML potential to describe the full composition range. +# + +filename = "gaas_training.xyz" +if not os.path.exists(filename): + url = f"https://zenodo.org/records/10566825/files/{filename}" + response = requests.get(url) + response.raise_for_status() + with open(filename, "wb") as f: + f.write(response.content) + +structures = ase.io.read(filename, ":") +energy = np.array([f.info["energy"] for f in structures]) +natoms = np.array([len(f) for f in structures]) + + +###################################################################### +# Remove atomic energy baseline +# ----------------------------- +# +# Energies from an electronic structure calculation contain a very large +# “self” contributions from the atoms, which can obscure the important +# differences in cohesive energies between structures. We can build an +# approximate model based on the chemical nature of the atoms, :math:`a_i` +# +# .. math:: E(A) = \sum_{i\in A} e_{a_i} +# +# where :math:`e_a` are atomic energies that can be determined by linear +# regression. +# + +# rascaline has an `AtomicComposition` calculator that streamlines +# this (simple) calculation +calculator = AtomicComposition(**{"per_structure": True}) +rho0 = calculator.compute(structures) + +# the descriptors are returned as a `TensorMap` object, that contains +# the composition data in a sparse storage format +rho0 + +# for easier manipulation, we extract the features as a dense vector +# of composition weights +comp_feats = rho0.keys_to_properties(["species_center"]).block(0).values + +# a one-liner to fit a linear model and compute "dressed energies" +atom_energy = ( + RidgeCV(alphas=np.geomspace(1e-8, 1e2, 20)) + .fit(comp_feats, energy) + .predict(comp_feats) +) +cohesive_peratom = (energy - atom_energy) / natoms + + +###################################################################### +# The baseline makes up a large fraction of the total energy, but actually +# the residual (which is the part that matters) is still large. +# + +fig, ax = plt.subplots(1, 1, figsize=(6, 4)) +ax.plot(energy / natoms, atom_energy / natoms, "b.") +ax.set_xlabel("Energy / (eV/atom)") +ax.set_ylabel("Atomic e. / (eV/atom)") +plt.show() +print(f"RMSE / (eV/atom): {np.sqrt(np.mean((cohesive_peratom)**2))}") + + +###################################################################### +# Compute structural descriptors +# ------------------------------ +# +# In order to visualize the structures as a low-dimensional map, we start +# by computing suitable ML descriptors. Here we have used ``rascaline`` to +# evaluate average SOAP features for the structures. +# + +# hypers for evaluating rascaline features +hypers = { + "cutoff": 4.5, + "max_radial": 6, + "max_angular": 4, + "atomic_gaussian_width": 0.3, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + "radial_basis": {"Gto": {"accuracy": 1e-6}}, + "center_atom_weight": 1.0, +} +calculator = SoapPowerSpectrum(**hypers) +rho2i = calculator.compute(structures) + +# neighbor types go to the keys for sparsity (this way one can +# compute a heterogeneous dataset without having blocks of zeros) +rho2i = rho2i.keys_to_samples(["species_center"]).keys_to_properties( + ["species_neighbor_1", "species_neighbor_2"] +) + +# computes structure-level descriptors and then extracts +# the features as a dense array +rho2i_structure = mean_over_samples(rho2i, sample_names=["center", "species_center"]) +rho2i = None # releases memory +features = rho2i_structure.block(0).values + + +###################################################################### +# We standardize (per atom) energy and features (computed as a *mean* over +# atomic environments) so that they can be combined on the same footings. +# + +sf_energy = StandardFlexibleScaler().fit_transform(cohesive_peratom.reshape(-1, 1)) +sf_feats = StandardFlexibleScaler().fit_transform(features) + + +###################################################################### +# PCA and PCovR projection +# ------------------------ +# +# Computes PCA projection to generate low-dimensional descriptors that +# reflect structural diversity. Any other dimensionality reduction scheme +# could be used in a similar fashion. +# +# We also compute the principal covariate regression (PCovR) descriptors, +# that reduce dimensionality while combining a variance preserving +# criterion with the requirement that the low-dimensional features are +# capable of estimating a target quantity (here, the energy). +# + +# PCA +pca = PCA(n_components=4) +pca_features = pca.fit_transform(sf_feats) + +fig, ax = plt.subplots(1, 1, figsize=(6, 4)) +scatter = ax.scatter(pca_features[:, 0], pca_features[:, 1], c=cohesive_peratom) +ax.set_xlabel("PCA[1]") +ax.set_ylabel("PCA[2]") +cbar = fig.colorbar(scatter, ax=ax) +cbar.set_label("energy / eV/at.") +plt.show() + +# computes PCovR map +pcovr = PCovR(n_components=4) +pcovr_features = pcovr.fit_transform(sf_feats, sf_energy) + +fig, ax = plt.subplots(1, 1, figsize=(6, 4)) +scatter = ax.scatter(pcovr_features[:, 0], pcovr_features[:, 1], c=cohesive_peratom) +ax.set_xlabel("PCovR[1]") +ax.set_ylabel("PCovR[2]") +cbar = fig.colorbar(scatter, ax=ax) +cbar.set_label("energy / (eV/at.)") +plt.show() + + +###################################################################### +# Chemiscope visualization +# ------------------------ +# +# Visualizes the structure-property map using a chemiscope widget (and +# generates a .json file that can be viewed on +# `chemiscope.org `__). +# + +# extracts force data (adding considerably to the dataset size...) +force_vectors = chemiscope.ase_vectors_to_arrows(structures, scale=1) +force_vectors["parameters"]["global"]["color"] = 0x505050 + +# adds properties to the ASE frames +for i, f in enumerate(structures): + for j in range(len(pca_features[i])): + f.info["pca_" + str(j + 1)] = pca_features[i, j] +for i, f in enumerate(structures): + for j in range(len(pcovr_features[i])): + f.info["pcovr_" + str(j + 1)] = pcovr_features[i, j] +for i, f in enumerate(structures): + f.info["cohesive_energy"] = cohesive_peratom[i] + f.info["x_ga"] = comp_feats[i, 0] / comp_feats[i].sum() + +# it would also be easy to add the properties manually, this is just a dictionary +structure_properties = chemiscope.extract_properties(structures) + +cs = chemiscope.show( + frames=structures, + properties=structure_properties, + shapes={"forces": force_vectors}, + # the settings are a tad verbose, but give full control over the visualization + settings={ + "map": { + "x": {"property": "pcovr_1"}, + "y": {"property": "pcovr_2"}, + "color": {"property": "x_ga"}, + }, + "structure": [ + { + "bonds": True, + "unitCell": True, + "shape": ["forces"], + "keepOrientation": False, + } + ], + }, + meta={ + "name": "GaAs training data", + "description": """ +A collection of Ga(x)As(1-x) structures to train a MLIP, +including force and energy data. +""", + "authors": ["Giulio Imbalzano", "Michele Ceriotti"], + "references": [ + """ +G. Imbalzano and M. Ceriotti, 'Modeling the Ga/As binary system across +temperatures and compositions from first principles,' +Phys. Rev. Materials 5(6), 063804 (2021). +""", + "Original dataset: https://archive.materialscloud.org/record/2021.226", + ], + }, +) + +cs.save("gaas_map.chemiscope.json.gz") + +cs # display if in a notebook diff --git a/_downloads/d26f5b90e59503961ba96aba6341b129/reference-trajectory.zip b/_downloads/d26f5b90e59503961ba96aba6341b129/reference-trajectory.zip new file mode 100644 index 00000000..db596d2e Binary files /dev/null and b/_downloads/d26f5b90e59503961ba96aba6341b129/reference-trajectory.zip differ diff --git a/_downloads/d997f92a427513b3b0c833f5b65889cf/reftraj_template.cp2k b/_downloads/d997f92a427513b3b0c833f5b65889cf/reftraj_template.cp2k new file mode 100644 index 00000000..fe83ba8d --- /dev/null +++ b/_downloads/d997f92a427513b3b0c833f5b65889cf/reftraj_template.cp2k @@ -0,0 +1,144 @@ +@SET PREP 0 + +@SET SCF_GUESS RESTART +@SET SCREEN_ON_INITIAL_P TRUE + +@IF ${PREP} + @SET SCF_GUESS ATOMIC + @SET SCREEN_ON_INITIAL_P FALSE +@ENDIF + +&GLOBAL + PROJECT //PROJECT// + PREFERRED_FFT_LIBRARY FFTW + FFTW_PLAN_TYPE MEASURE + RUN_TYPE MD + PRINT_LEVEL LOW +&END GLOBAL + +&MOTION + &PRINT + &CELL + &EACH + MD 1 + &END EACH + &END CELL + &FORCES + &EACH + MD 1 + &END EACH + &END FORCES + &END PRINT + &MD + ENSEMBLE REFTRAJ + &REFTRAJ ! Loads an external trajectory file and performs analysis on the loaded snapshots. + EVAL_ENERGY_FORCES TRUE + EVAL_FORCES TRUE + CELL_FILE_NAME reftraj.cell + TRAJ_FILE_NAME reftraj.xyz + FIRST_SNAPSHOT 1 + VARIABLE_VOLUME TRUE + LAST_SNAPSHOT //LAST_SNAPSHOT// + &END REFTRAJ + &END MD +&END MOTION + +&FORCE_EVAL + &PRINT + &FORCES + &EACH + MD 1 + &END EACH + &END FORCES + &END PRINT + &DFT + BASIS_SET_FILE_NAME ../../parameters/GTH_BASIS_SETS + BASIS_SET_FILE_NAME ../../parameters/BASIS_ADMM + POTENTIAL_FILE_NAME ../../parameters/POTENTIAL + &MGRID + CUTOFF 400 + &END MGRID + &SCF + SCF_GUESS ${SCF_GUESS} + MAX_SCF 20 + EPS_SCF 5.0E-7 + &OT + MINIMIZER DIIS + PRECONDITIONER FULL_ALL + &END OT + &OUTER_SCF + MAX_SCF 20 + EPS_SCF 5.0E-7 + &END OUTER_SCF + &END SCF + &QS + EPS_DEFAULT 1.0E-12 + EPS_PGF_ORB 1.0E-16 + EXTRAPOLATION_ORDER 5 + &END QS + &XC # revPBE0-TC-D3 + &XC_FUNCTIONAL + &PBE + PARAMETRIZATION REVPBE + SCALE_X 0.75 + SCALE_C 1.0 + &END + &END XC_FUNCTIONAL + &HF + FRACTION 0.25 + &SCREENING + EPS_SCHWARZ 1.0E-6 + SCREEN_ON_INITIAL_P ${SCREEN_ON_INITIAL_P} + &END + &MEMORY + MAX_MEMORY 37000 + EPS_STORAGE_SCALING 0.1 + &END + &INTERACTION_POTENTIAL + POTENTIAL_TYPE TRUNCATED + CUTOFF_RADIUS 3.0 + T_C_G_DATA ../../parameters/t_c_g.dat + &END + &HF_INFO + &END HF_INFO + &END + &VDW_POTENTIAL + POTENTIAL_TYPE PAIR_POTENTIAL + &PAIR_POTENTIAL + TYPE DFTD3 + R_CUTOFF 15 + LONG_RANGE_CORRECTION TRUE + REFERENCE_FUNCTIONAL revPBE0 + PARAMETER_FILE_NAME ../../parameters/dftd3.dat + &END + &END + &XC_GRID + XC_DERIV SPLINE2 + &END + &END XC + &AUXILIARY_DENSITY_MATRIX_METHOD + METHOD BASIS_PROJECTION + ADMM_PURIFICATION_METHOD MO_DIAG + &END AUXILIARY_DENSITY_MATRIX_METHOD + &END DFT + &SUBSYS + &TOPOLOGY + COORD_FILE_NAME init.xyz + COORD_FILE_FORMAT XYZ + CONN_FILE_FORMAT GENERATE + &END TOPOLOGY + &CELL + ABC [angstrom] //CELL// + &END CELL + &KIND H + BASIS_SET TZV2P-GTH + BASIS_SET AUX_FIT cpFIT3 + POTENTIAL GTH-PBE-q1 + &END KIND + &KIND O + BASIS_SET TZV2P-GTH + BASIS_SET AUX_FIT cpFIT3 + POTENTIAL GTH-PBE-q6 + &END KIND + &END SUBSYS +&END FORCE_EVAL diff --git a/_downloads/db9adeac0042e3126c9d37f1c33e3b6f/reference-trajectory.ipynb b/_downloads/db9adeac0042e3126c9d37f1c33e3b6f/reference-trajectory.ipynb new file mode 100644 index 00000000..72847e0f --- /dev/null +++ b/_downloads/db9adeac0042e3126c9d37f1c33e3b6f/reference-trajectory.ipynb @@ -0,0 +1,252 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Batch run of CP2K calculations\n\n:Authors: Matthias Kellner [@bananenpampe](https://github.com/bananenpampe/),\n Philip Loche [@PicoCentauri](https://github.com/PicoCentauri/)\n\nThis is an example how to perform single point calculations based on list of structures\nusing [CP2K](https://www.cp2k.org) using its [reftraj functionality](https://manual.cp2k.org/trunk/CP2K_INPUT/MOTION/MD/REFTRAJ.html). The inputs are a\nset of structures in :download:`example.xyz` using the DFT parameters defined in\n:download:`reftraj_template.cp2k`. The reference DFT parameters are taken from [Cheng et\nal. Ab initio thermodynamics of liquid and solid water 2019](https://www.pnas.org/doi/10.1073/pnas.1815117116). Due to the small size of the test\nstructure and convergence issues, we have decreased the size of the ``CUTOFF_RADIUS``\nfrom $6.0\\,\\mathrm{\u00c5}$ to $3.0\\,\\mathrm{\u00c5}$. For actual production\ncalculations adapt the template!\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We start the example by importing the required packages.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import os\nimport platform\nimport subprocess\nfrom typing import List, Union\n\nimport ase.io\nimport ase.visualize.plot\nimport matplotlib.pyplot as plt\nimport numpy as np\nimport requests" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Install CP2K\n\nWe'll need a working installation of cp2k. The best way to do so depends on your\nplatform, here are some possible solutions, but feel free to replace them with another\ninstallation method.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "if platform.system() == \"Linux\":\n # use conda on Linux\n subprocess.run([\"conda\", \"install\", \"cp2k\", \"-c\", \"conda-forge\", \"-y\"], check=True)\nelif platform.system() == \"Darwin\":\n # use homebrew on macOS\n subprocess.run([\"brew\", \"install\", \"cp2k\"], check=True)\nelse:\n print(\"no known way to install cp2k, skipping installation\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define necessary functions\nNext we below define necessary helper functions to run the example.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def write_reftraj(fname: str, frames: Union[ase.Atoms, List[ase.Atoms]]) -> None:\n \"\"\"Writes a list of ase atoms objects to a reference trajectory.\n\n A reference trajectory is the CP2K compatible format for the compuation of batches.\n All frames must have the stoichiometry/composition.\n \"\"\"\n\n if isinstance(frames, ase.Atoms):\n frames = [frames]\n\n out = \"\"\n for i, atoms in enumerate(frames):\n if (\n len(atoms) != len(frames[0])\n or atoms.get_chemical_formula() != frames[0].get_chemical_formula()\n ):\n raise ValueError(\n f\"Atom symbols in frame {i},{atoms.get_chemical_formula()} are \"\n f\"different compared to inital frame \"\n f\"{frames[0].get_chemical_formula()}. \"\n \"CP2K does not support changing atom types within a reftraj run!\"\n )\n\n out += f\"{len(atoms):>8}\\n i = {i + 1:>8}, time = {0:>12.3f}\\n\"\n for atom in atoms:\n pos = atom.position\n out += f\"{atom.symbol}{pos[0]:24.15f}{pos[1]:24.15f}{pos[2]:24.15f}\\n\"\n out += \"\\n\"\n with open(fname, \"w\") as f:\n f.write(out)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def write_cellfile(fname: str, frames: Union[ase.Atoms, List[ase.Atoms]]) -> None:\n \"\"\"Writes a cellfile for a list of ``ase.Atoms``.\n\n A Cellfile accompanies a reftraj containing the cell parameters.\n \"\"\"\n if isinstance(frames, ase.Atoms):\n frames = [frames]\n\n out = (\n \"# \"\n \"Step \"\n \"Time [fs] \"\n \"Ax [Angstrom] \"\n \"Ay [Angstrom] \"\n \"Az [Angstrom] \"\n \"Bx [Angstrom] \"\n \"By [Angstrom] \"\n \"Bz [Angstrom] \"\n \"Cx [Angstrom] \"\n \"Cy [Angstrom] \"\n \"Cz [Angstrom] \"\n \"Volume [Angstrom^3]\\n\"\n )\n\n for i, atoms in enumerate(frames):\n out += f\"{i + 1:>8}{0:>12.3f}\"\n out += \"\".join([f\"{c:>20.10f}\" for c in atoms.cell.flatten()])\n out += f\"{atoms.cell.volume:>25.10f}\"\n out += \"\\n\"\n\n with open(fname, \"w\") as f:\n f.write(out)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def write_cp2k_in(\n fname: str, project_name: str, last_snapshot: int, cell: List[float]\n) -> None:\n \"\"\"Writes a cp2k input file from a template.\n\n Importantly, it writes the location of the basis set definitions,\n determined from the path of the system CP2K install to the input file.\n \"\"\"\n\n cp2k_in = open(\"reftraj_template.cp2k\", \"r\").read()\n\n cp2k_in = cp2k_in.replace(\"//PROJECT//\", project_name)\n cp2k_in = cp2k_in.replace(\"//LAST_SNAPSHOT//\", str(last_snapshot))\n cp2k_in = cp2k_in.replace(\"//CELL//\", \" \".join([f\"{c:.6f}\" for c in cell]))\n\n with open(fname, \"w\") as f:\n f.write(cp2k_in)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will now download basis set files from CP2K website. Depending on your CP2K\ninstallation, this might not be necessary!\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def download_parameter(file):\n path = os.path.join(\"parameters\", file)\n\n if not os.path.exists(path):\n url = f\"https://raw.githubusercontent.com/cp2k/cp2k/support/v2024.1/data/{file}\"\n response = requests.get(url)\n response.raise_for_status()\n with open(path, \"wb\") as f:\n f.write(response.content)\n\n\nos.makedirs(\"parameters\", exist_ok=True)\nfor file in [\"GTH_BASIS_SETS\", \"BASIS_ADMM\", \"POTENTIAL\", \"dftd3.dat\", \"t_c_g.dat\"]:\n download_parameter(file)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Prepare calculation inputs\nDuring this example we will create a directory named ``project_directory`` containing\nthe subdirectories for each stoichiometry. This is necessary, because CP2K can only\nrun calculations using a fixed stoichiometry at a time, using its ``reftraj``\nfunctionality.\n\nBelow we define the general information for the CP2K run. This includes the reference\nfiles for the structures, the ``project_name`` used to build the name of the\ntrajectory during the CP2K run, the ``project_directory`` where we store all\nsimulation output as well as the path ``write_to_file`` which is the name of the file\ncontaining the computed energies and forces of the simulation.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "frames_full = ase.io.read(\"example.xyz\", \":\")\nproject_name = \"test_calcs\" # name of the global PROJECT\nproject_directory = \"production\"\nwrite_to_file = \"out.xyz\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we show the initial configuration of two water molecules in a cubic box with a\nside length of $\\approx 4\\,\\mathrm{\u00c5}$.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ase.visualize.plot.plot_atoms(frames_full[0])\n\nplt.xlabel(\"\u00c5\")\nplt.ylabel(\"\u00c5\")\n\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now extract the stoichiometry from the input dataset using ASE's\n:py:meth:`ase.symbols.Symbols.get_chemical_formula` method.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "frames_dict = {}\n\nfor atoms in frames_full:\n chemical_formula = atoms.get_chemical_formula()\n try:\n frames_dict[chemical_formula]\n except KeyError:\n frames_dict[chemical_formula] = []\n\n frames_dict[chemical_formula].append(atoms)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Based on the stoichiometries we create one calculation subdirectories for the\ncalculations. (reftraj, input and cellfile). For our example this is only is one\ndirectory named ``H4O2`` because our dataset consists only of a single structure with\ntwo water molecules.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for stoichiometry, frames in frames_dict.items():\n current_directory = f\"{project_directory}/{stoichiometry}\"\n os.makedirs(current_directory, exist_ok=True)\n\n write_cp2k_in(\n f\"{current_directory}/in.cp2k\",\n project_name=project_name,\n last_snapshot=len(frames),\n cell=frames[0].cell.diagonal(),\n )\n\n ase.io.write(f\"{current_directory}/init.xyz\", frames[0])\n write_reftraj(f\"{current_directory}/reftraj.xyz\", frames)\n write_cellfile(f\"{current_directory}/reftraj.cell\", frames)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run simulations\nNow we have all ingredients to run the simulations. Below we call the bash script\n:download:`run_calcs.sh`.\n\n.. literalinclude:: run_calcs.sh\n :language: bash\n\nThis script will loop through all stoichiometry subdirectories and call the CP2K\nengine.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# run the bash script directly from this script\nsubprocess.run(\"bash run_calcs.sh\", shell=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Note

For a usage on an HPC environment you can parallelize the loop over the\n sub-directories and submit and single job per stoichiometry.

\n\n## Load results\nAfter the simulation we load the results and perform a unit version from the default\nCP2K output units (Bohr and Hartree) to \u00c5 and eV.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "cflength = 0.529177210903 # Bohr -> \u00c5\ncfenergy = 27.211386245988 # Hartree -> eV\ncfforce = cfenergy / cflength # Hartree/Bohr -> eV/\u00c5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we store the results as :class:`ase.Atoms` in the ``new_frames`` list and\nwrite them to the ``project_directory`` using the ``new_fname``. Here it will be\nwritten to ``production/out_dft.xyz``.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "new_frames = []\n\nfor stoichiometry, frames in frames_dict.items():\n current_directory = f\"{project_directory}/{stoichiometry}\"\n\n frames_dft = ase.io.read(f\"{current_directory}/{project_name}-pos-1.xyz\", \":\")\n forces_dft = ase.io.read(f\"{current_directory}/{project_name}-frc-1.xyz\", \":\")\n cell_dft = np.atleast_2d(np.loadtxt(f\"{current_directory}/{project_name}-1.cell\"))[\n :, 2:-1\n ]\n\n for i_atoms, atoms in enumerate(frames_dft):\n frames_ref = frames[i_atoms]\n\n # Check consistent positions\n if not np.allclose(atoms.positions, frames_ref.positions):\n raise ValueError(f\"Positions in frame {i_atoms} are not the same.\")\n\n # Check consistent cell\n if not np.allclose(frames_ref.cell.flatten(), cell_dft[i_atoms]):\n raise ValueError(f\"Cell dimensions in frame {i_atoms} are not the same.\")\n\n atoms.info[\"E\"] *= cfenergy\n atoms.pbc = True\n atoms.cell = frames_ref.cell\n atoms.set_array(\"forces\", cfforce * forces_dft[i_atoms].positions)\n\n new_frames += frames_dft\n\nnew_fname = f\"{os.path.splitext(os.path.basename(write_to_file))[0]}_dft.xyz\"\nase.io.write(f\"{project_directory}/{new_fname}\", new_frames)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/_downloads/e389cfcd09e1fc1fab157bbb32fe0788/path-integrals.zip b/_downloads/e389cfcd09e1fc1fab157bbb32fe0788/path-integrals.zip new file mode 100644 index 00000000..fd22906c Binary files /dev/null and b/_downloads/e389cfcd09e1fc1fab157bbb32fe0788/path-integrals.zip differ diff --git a/_downloads/e7554e760ee8c061289c684f5c666feb/path-integrals.py b/_downloads/e7554e760ee8c061289c684f5c666feb/path-integrals.py new file mode 100644 index 00000000..1e182020 --- /dev/null +++ b/_downloads/e7554e760ee8c061289c684f5c666feb/path-integrals.py @@ -0,0 +1,332 @@ +""" +Path integral molecular dynamics +================================ + +:Authors: Michele Ceriotti `@ceriottm `_ + +This example shows how to run a path integral molecular dynamics +simulation using ``i-PI``, analyze the output and visualize the +trajectory in ``chemiscope``. It uses `LAMMPS `_ +as the driver to simulate the `q-TIP4P/f water +model `_. +""" + +import subprocess +import time + +import chemiscope +import ipi +import matplotlib.pyplot as plt +import numpy as np + + +# %% +# Quantum nuclear effects and path integral methods +# ------------------------------------------------- +# +# The Born-Oppenheimer approximation separates the joint quantum mechanical +# problem for electrons and nuclei into two independent problems. Even though +# often one makes the additional approximation of treating nuclei as classical +# particles, this is not necessary, and in some cases (typically when H atoms are +# present) can add considerable error. +# +# +# .. figure:: pimd-slices-round.png +# :align: center +# :width: 600px +# +# A representation of ther ring-polymer Hamiltonian for a water molecule. +# +# In order to describe the quantum mechanical nature of light nuclei +# (nuclear quantum effects) one of the most widely-applicable methods uses +# the *path integral formalism* to map the quantum partition function of a +# set of distinguishable particles onto the classical partition function of +# *ring polymers* composed by multiple beads (replicas) with +# corresponding atoms in adjacent replicas being connected by harmonic +# springs. +# `The textbook by Tuckerman `_ +# contains a pedagogic introduction to the topic, while +# `this paper `_ outlines the implementation +# used in ``i-PI``. +# +# The classical partition function of the path converges to quantum statistics +# in the limit of a large number of replicas. In this example, we will use a +# technique based on generalized Langevin dynamics, known as +# `PIGLET `_ to accelerate the +# convergence. + + +# %% +# Running PIMD calculations with ``i-PI`` +# --------------------------------------- +# +# `i-PI `_ is based on a client-server model, with ``i-PI`` +# controlling the nuclear dynamics (in this case sampling the path Hamiltonian using +# molecular dynamics) while the calculation of energies and forces is delegated to +# an external client program, in this example ``LAMMPS``. +# +# An i-PI calculation is specified by an XML file. + +# Open and read the XML file +with open("data/input_pimd.xml", "r") as file: + xml_content = file.read() +print(xml_content) + +# %% +# NB1: In a realistic simulation you may want to increase the field +# ``total_steps``, to simulate at least a few 100s of picoseconds. +# +# NB2: To converge a simulation of water at room temperature, you +# typically need at least 32 beads. We will see later how to accelerate +# convergence using a colored-noise thermostat, but you can try to +# modify the input to check convergence with conventional PIMD + +# %% +# i-PI and lammps should be run separately, and it is possible to +# launch separate lammps processes to parallelize the evaluation over +# the beads. On the the command line, this amounts to launching +# +# .. code-block:: bash +# +# i-pi data/input_pimd.xml > log & +# sleep 2 +# lmp -in data/in.lmp & +# lmp -in data/in.lmp & +# +# Note how ``i-PI`` and ``LAMMPS`` are completely independent, and +# therefore need a separate set of input files. The client-side communication +# in ``LAMMPS`` is described in the ``fix_ipi`` section, that matches the socket +# name and mode defined in the ``ffsocket`` field in the ``i-PI`` file. +# +# We can launch the external processes from a Python script as follows + +ipi_process = subprocess.Popen(["i-pi", "data/input_pimd.xml"]) +time.sleep(2) # wait for i-PI to start +lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(2)] + +# %% +# If you run this in a notebook, you can go ahead and start loading +# output files *before* i-PI and lammps have finished running, by +# skipping this cell + +ipi_process.wait() +lmp_process[0].wait() +lmp_process[1].wait() + + +# %% +# Analyzing the simulation +# ~~~~~~~~~~~~~~~~~~~~~~~~ +# +# After the simulation has run, you can visualize and post-process the trajectory data. +# Note that i-PI prints a separate trajectory for each bead, as structural properties +# can be computed averaging over the configurations of any of the beads. + +# drops first frame where all atoms overlap +output_data, output_desc = ipi.read_output("simulation.out") +traj_data = [ipi.read_trajectory(f"simulation.pos_{i}.xyz")[1:] for i in range(8)] + + +# %% +# The simulation parameters are pushed at the limits: with the aggressive stochastic +# thermostatting and the high-frequency normal modes of the ring polymer, there are +# fairly large fluctuations of the conserved quantity. This is usually not affecting +# physical observables, but if you see this level of drift in a production run, check +# carefully for convergence and stability with a reduced time step. + +fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["potential"] - output_data["potential"][0], + "b-", + label="Potential, $V$", +) +ax.plot( + output_data["time"], + output_data["conserved"] - output_data["conserved"][0], + "r-", + label="Conserved, $H$", +) +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"energy / eV") +ax.legend() +plt.show() + +# %% +# While the potential energy is simply the mean over the beads of the +# energy of individual replicas, computing the kinetic energy requires +# averaging special quantities that involve also the correlations between beads. +# Here we compare two of these *estimators*: the 'thermodynamic' estimator becomes +# statistically inefficient when increasing the number of beads, whereas the +# 'centroid virial' estimator remains well-behaved. Note how quickly these estimators +# equilibrate to roughly their stationary value, much faster than the equilibration +# of the potential energy above. This is thanks to the ``pile_g`` thermostat +# (see `DOI:10.1063/1.3489925 `_) that is +# optimally coupled to the normal modes of the ring polymer. + +fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["kinetic_cv"], + "b-", + label="Centroid virial, $K_{CV}$", +) +ax.plot( + output_data["time"], + output_data["kinetic_td"], + "r-", + label="Thermodynamic, $K_{TD}$", +) +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"energy / eV") +ax.legend() +plt.show() + +# %% +# You can also visualize the (very short) trajectory in a way that highlights the +# fast spreading out of the beads of the ring polymer. ``chemiscope`` provides a +# utility function to interleave the trajectories of the beads, forming a trajectory +# that shows the connecttions between the replicas of each atom. Each atom and its +# connections are color-coded. + +traj_pimd = chemiscope.ase_merge_pi_frames(traj_data) +# we also tweak the visualization options, and then show the viewer +traj_pimd["shapes"]["paths"]["parameters"]["global"]["radius"] = 0.05 +traj_pimd["settings"]["structure"][0].update( + dict( + atoms=False, + keepOrientation=True, + color={"property": "bead_id", "palette": "hsv (periodic)"}, + ) +) + +chemiscope.show(**traj_pimd, mode="structure") + +# %% +# Accelerating PIMD with a PIGLET thermostat +# ------------------------------------------ +# +# The simulations in the previous sections are very far from converged -- typically +# one would need approximately 32 replicas to converge a simulation of +# room-temperature water. To address this problem we will use a method based on +# generalized Langevin equations, called +# `PIGLET `_ +# +# The input file is ``input_piglet.xml``, that only differs by the definition of +# the thermostat, that uses a ``nm_gle`` mode in which each normal mode +# of the ring polymer is attached to a different colored-noise Generalized Langevin +# equation. This makes it possible to converge exactly the simulation results with +# a small number of replicas, and to accelerate greatly convergence for realistic +# systems such as this. The thermostat parameters can be generated on +# `the GLE4MD website `_ +# + +ipi_process = subprocess.Popen(["i-pi", "data/input_piglet.xml"]) +time.sleep(2) # wait for i-PI to start +lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(2)] + +ipi_process.wait() +lmp_process[0].wait() +lmp_process[1].wait() + +# %% +# The mean potential energy from the PIGLET trajectory is higher than that for the +# PIMD one, because it is closer to the converged value (try to run a PIMD trajectory +# with 64 beads for comparison) + +# drops first frame +output_gle, desc_gle = ipi.read_output("simulation_piglet.out") +traj_gle = [ipi.read_trajectory(f"simulation_piglet.pos_{i}.xyz")[1:] for i in range(8)] + +fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["potential"] - output_data["potential"][0], + "b--", + label="PIMD", +) +ax.plot( + output_gle["time"], + output_gle["potential"] - output_gle["potential"][0], + "b-", + label="PIGLET", +) +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"energy / eV") +ax.legend() +plt.show() + +# %% +# However, you should be somewhat careful: PIGLET converges *some* but not all the +# correlations within a path. For instance, it is designed to converge the +# centroid-virial estimator for the kinetic energy, but not the thermodynamic +# estimator. For the same reason, don't try to look at equilibration in terms of +# the mean temperature: it won't match the target value, because PIGLET uses a +# Langevin equation that breaks the classical fluctuation-dissipation theorem, and +# generates a steady-state distribution that mimics quantum fluctuations. + +fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot(output_data["time"], output_data["kinetic_cv"], "b--", label="PIMD, $K_{CV}$") +ax.plot(output_gle["time"], output_gle["kinetic_cv"], "b", label="PIGLET, $K_{CV}$") +ax.plot(output_data["time"], output_data["kinetic_td"], "r--", label="PIMD, $K_{TD}$") +ax.plot(output_gle["time"], output_gle["kinetic_td"], "r", label="PIGLET, $K_{TD}$") +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"energy / eV") +ax.legend() +plt.show() + +# %% +# Kinetic energy tensors +# ~~~~~~~~~~~~~~~~~~~~~~ +# +# While we're at it, let's do something more complicated (and instructive). +# Classically, the momentum distribution of any atom is isotropic, so the +# kinetic energy tensor (KET) :math:`\mathbf{p}\mathbf{p}^T/2m` is a constant +# times the identity matrix. Quantum mechanically, the kinetic energy tensor +# has more structure, that reflects the higher kinetic energy of particles +# along directions with stiff bonds. We can compute a moving average of the +# centroid virial estimator of the KET, and plot it to show the direction +# of anisotropy. Note that there are some subtleties connected with the +# evaluation of the moving average, see e.g. +# `DOI:10.1103/PhysRevLett.109.100604 `_ + +# %% +# We first need to postprocess the components of the kinetic energy tensors +# (that i-PI prints out separating the diagonal and off-diagonal bits), averaging +# them over the last 10 frames and combining them with the centroid configuration +# from the last frame in the trajectory. + +kinetic_cv = ipi.read_trajectory("simulation_piglet.kin.xyz")[1:] +kinetic_od = ipi.read_trajectory("simulation_piglet.kod.xyz")[1:] +kinetic_tens = np.hstack( + [ + np.asarray([k.positions for k in kinetic_cv[-10:]]).mean(axis=0), + np.asarray([k.positions for k in kinetic_od[-10:]]).mean(axis=0), + ] +) + +centroid = traj_gle[-1][-1].copy() +centroid.positions = np.asarray([t[-1].positions for t in traj_gle]).mean(axis=0) +centroid.arrays["kinetic_cv"] = kinetic_tens + +# %% +# We can then view these in ``chemiscope``, setting the proper parameters to +# visualize the ellipsoids associated with the KET. Note that some KETs have +# negative eigenvalues, because we are averaging over a few frames, which is +# insufficient to converge the estimator fully. + +ellipsoids = chemiscope.ase_tensors_to_ellipsoids( + [centroid], "kinetic_cv", scale=15, force_positive=True +) + +chemiscope.show( + [centroid], + shapes={"kinetic_cv": ellipsoids}, + mode="structure", + settings=chemiscope.quick_settings( + structure_settings={ + "shape": ["kinetic_cv"], + "unitCell": True, + } + ), +) diff --git a/_downloads/eca45738d1778be3da4e8dd6885e2b1b/sample-selection.zip b/_downloads/eca45738d1778be3da4e8dd6885e2b1b/sample-selection.zip new file mode 100644 index 00000000..9dfde77c Binary files /dev/null and b/_downloads/eca45738d1778be3da4e8dd6885e2b1b/sample-selection.zip differ diff --git a/_downloads/ecc5d2823a1b00229494ffc2024c524d/dos-align.py b/_downloads/ecc5d2823a1b00229494ffc2024c524d/dos-align.py new file mode 100644 index 00000000..7b789a3e --- /dev/null +++ b/_downloads/ecc5d2823a1b00229494ffc2024c524d/dos-align.py @@ -0,0 +1,951 @@ +""" +A ML model for the electron density of states +============================================= +:Authors: How Wei Bin `@HowWeiBin `_ + +This tutorial would go through the entire machine learning framework for the electronic +density of states (DOS). It will cover the construction of the DOS and SOAP +descriptors from ase Atoms and eigenenergy results. A simple neural network will +then be constructed and the model parameters, along with the energy reference will be +optimized during training. A total of three energy reference will be used, the average +Hartree potential, the Fermi level, and an optimized energy reference starting from +the Fermi level energy reference. The performance of each model is then compared. + +First, lets begin by importing the necessary packages and helper functions +""" + +# %% + +import os +import zipfile + +import ase +import ase.io +import matplotlib.pyplot as plt +import numpy as np +import requests +import torch +from rascaline import SoapPowerSpectrum +from scipy.interpolate import CubicHermiteSpline, interp1d +from scipy.optimize import brentq +from torch.utils.data import BatchSampler, DataLoader, Dataset, RandomSampler + + +# %% +# +# Step 0: Load Structures and Eigenenergies +# ------------------------------------------------ +# 1) Downloading and Extracting Data +# 2) Loading Data +# 3) Find range of eigenenergies +# +# We take a small subset of 104 structures in the Si dataset from `Bartok et al., +# 2018 `. +# Each structure in the dataset contains two atoms. +# +# + + +# %% +# 1) Downloading and Extracting Data +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +filename = "dataset.zip" +if not os.path.exists(filename): + url = "https://github.com/HowWeiBin/datasets/archive/refs/tags/Silicon-Diamonds.zip" + response = requests.get(url) + response.raise_for_status() + with open(filename, "wb") as f: + f.write(response.content) + +with zipfile.ZipFile("./dataset.zip", "r") as zip_ref: + zip_ref.extractall("./") +# %% +# 2) Loading Data +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +structures = ase.io.read("./datasets-Silicon-Diamonds/diamonds.xyz", ":") +n_structures = len(structures) +n_atoms = torch.tensor([len(i) for i in structures]) +eigenenergies = torch.load("./datasets-Silicon-Diamonds/diamond_energies.pt") +k_normalization = torch.tensor( + [len(i) for i in eigenenergies] +) # Calculates number of kpoints sampled per structure +print(f"Total number of structures: {len(structures)}") + +# %% +# 3) Find range of eigenenergies +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +# Process eigenenergies to flattened torch tensors + +total_eigenenergies = [torch.flatten(torch.tensor(i)) for i in eigenenergies] + +# Get lowest and highest value of eigenenergies to know the range of eigenenergies + +all_eigenenergies = torch.hstack(total_eigenenergies) +minE = torch.min(all_eigenenergies) +maxE = torch.max(all_eigenenergies) +print(f"The lowest eigenenergy in the dataset is {minE:.3}") +print(f"The highest eigenenergy in the dataset is {maxE:.3}") +# %% +# +# Step 1: Constructing the DOS with different energy references +# ------------------------------------------------------------------------------------------ +# 1) Construct the DOS using the original reference +# 2) Calculate the Fermi level from the DOS +# 3) Build a set of eigenenergies, with the energy reference set to the fermi level +# 4) Truncate the DOS energy window so that the DOS is well-defined at each point +# 5) Construct the DOS in the truncated energy window under both references +# 6) Construct Splines for the DOS to facilitate interpolation during model training +# +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +# %% +# 1) Construct the DOS using the original reference +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# The DOS will first be constructed from the full set of eigenenergies to +# determine the Fermi level of each structure. The original reference is the +# Average Hartree Potential in this example. + +# To ensure that all the eigenenergies are fully represented after +# gaussian broadening, the energy axis of the DOS extends +# 3eV wider than the range of values for the eigenenergies +energy_lower_bound = minE - 1.5 +energy_upper_bound = maxE + 1.5 + +# Gaussian Smearing for the eDOS, 0.3eV is the appropriate value for this dataset + +sigma = torch.tensor(0.3) +energy_interval = 0.05 +# energy axis, with a grid interval of 0.05 eV + +x_dos = torch.arange(energy_lower_bound, energy_upper_bound, energy_interval) +print( + f"The energy axis ranges from {energy_lower_bound:.3} to \ +{energy_upper_bound:.3}, consisting of {len(x_dos)} grid points" +) + +# normalization factor for each DOS, factor of 2 is included +# because each eigenenergy can be occupied by 2 electrons + +normalization = 2 * ( + 1 / torch.sqrt(2 * torch.tensor(np.pi) * sigma**2) / n_atoms / k_normalization +) + +total_edos = [] + +for structure_eigenenergies in total_eigenenergies: + e_dos = torch.sum( + # Builds a gaussian on each eigenenergy + # and calculates the value on each grid point + torch.exp(-0.5 * ((x_dos - structure_eigenenergies.view(-1, 1)) / sigma) ** 2), + dim=0, + ) + total_edos.append(e_dos) + +total_edos = torch.vstack(total_edos) +total_edos = (total_edos.T * normalization).T + +print(f"The final shape of all the DOS in the dataset is: {list(total_edos.shape)}") + +# %% +# 2) Calculate the Fermi level from the DOS +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Now we integration the DOS, and then use cubic interpolation and brentq +# to calculate the fermi level. Since only the 4 valence electrons in Silicon +# are represented in this energy range, we take the point where the DOS integrates +# to 4 as the fermi level. + +fermi_levels = [] +total_i_edos = torch.cumulative_trapezoid( + total_edos, x_dos, axis=1 +) # Integrate the DOS along the energy axis +for i in total_i_edos: + interpolated = interp1d( + x_dos[:-1], i - 4, kind="cubic", copy=True, assume_sorted=True + ) # We use i-4 because Silicon has 4 electrons in this energy range + Ef = brentq( + interpolated, x_dos[0] + 0.1, x_dos[-1] - 0.1 + ) # Fermi Level is the point where the (integrated DOS - 4) = 0 + # 0.1 is added and subtracted to prevent brentq from going out of range + fermi_levels.append(Ef) +fermi_levels = torch.tensor(fermi_levels) +# %% +# 3) Build a set of eigenenergies, with the energy reference set to the fermi level +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Using the fermi levels, we are now able to change the energy reference +# of the eigenenergies to the fermi level + +total_eigenenergies_Ef = [] +for index, energies in enumerate(total_eigenenergies): + total_eigenenergies_Ef.append(energies - fermi_levels[index]) + +all_eigenenergies_Ef = torch.hstack(total_eigenenergies_Ef) + +minE_Ef = torch.min(all_eigenenergies_Ef) +maxE_Ef = torch.max(all_eigenenergies_Ef) +print(f"The lowest eigenenergy using the fermi level energy reference is {minE_Ef:.3}") +print(f"The highest eigenenergy using the fermi level energy reference is {maxE_Ef:.3}") + + +# %% +# 4) Truncate the DOS energy window so that the DOS is well-defined at each point +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# With the fermi levels, we can also truncate the energy window for DOS prediction. +# In this example, we truncate the energy window such that it is 3eV above +# the highest Fermi level in the dataset. + +# For the Average Hartree Potential energy reference +x_dos_H = torch.arange(minE - 1.5, max(fermi_levels) + 3, energy_interval) + +# For the Fermi Level Energy Reference, all the Fermi levels in the dataset is 0eV +x_dos_Ef = torch.arange(minE_Ef - 1.5, 3, energy_interval) +# %% +# 5) Construct the DOS in the truncated energy window under both references +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Here we construct 2 different targets where they differ in the energy reference +# chosen. These targets will then be treated as different datasets for the model +# to learn on. + +# For the Average Hartree Potential energy reference + +total_edos_H = [] + +for structure_eigenenergies_H in total_eigenenergies: + e_dos = torch.sum( + torch.exp( + -0.5 * ((x_dos_H - structure_eigenenergies_H.view(-1, 1)) / sigma) ** 2 + ), + dim=0, + ) + total_edos_H.append(e_dos) + +total_edos_H = torch.vstack(total_edos_H) +total_edos_H = (total_edos_H.T * normalization).T + + +# For the Fermi Level Energy Reference + +total_edos_Ef = [] + +for structure_eigenenergies_Ef in total_eigenenergies_Ef: + e_dos = torch.sum( + torch.exp( + -0.5 * ((x_dos_Ef - structure_eigenenergies_Ef.view(-1, 1)) / sigma) ** 2 + ), + dim=0, + ) + total_edos_Ef.append(e_dos) + +total_edos_Ef = torch.vstack(total_edos_Ef) +total_edos_Ef = (total_edos_Ef.T * normalization).T + +# %% +# 6) Construct Splines for the DOS to facilitate interpolation during model training +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# Building Cubic Hermite Splines on the DOS on the truncated energy window +# to facilitate interpolation during training. Cubic Hermite Splines takes +# in information on the value and derivative of a function at a point to build splines. +# Thus, we will have to compute both the value and derivative at each spline position + + +# Functions to compute the value and derivative of the DOS at each energy value, x +def edos_value(x, eigenenergies, normalization): + e_dos_E = ( + torch.sum( + torch.exp(-0.5 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2), dim=0 + ) + * normalization + ) + + return e_dos_E + + +def edos_derivative(x, eigenenergies, normalization): + dfn_dos_E = ( + torch.sum( + torch.exp(-0.5 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2) + * (-1 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2), + dim=0, + ) + * normalization + ) + + return dfn_dos_E + + +total_splines_H = [] +# the splines have a higher energy range in case the shift is high +spline_positions_H = torch.arange(minE - 2, max(fermi_levels) + 6, energy_interval) + +for index, structure_eigenenergies_H in enumerate(total_eigenenergies): + e_dos_H = edos_value( + spline_positions_H, structure_eigenenergies_H, normalization[index] + ) + e_dos_H_grad = edos_derivative( + spline_positions_H, structure_eigenenergies_H, normalization[index] + ) + spliner = CubicHermiteSpline(spline_positions_H, e_dos_H, e_dos_H_grad) + total_splines_H.append(torch.tensor(spliner.c)) + +total_splines_H = torch.stack(total_splines_H) + +total_splines_Ef = [] +spline_positions_Ef = torch.arange(minE_Ef - 2, 6, energy_interval) + +for index, structure_eigenenergies_Ef in enumerate(total_eigenenergies_Ef): + e_dos_Ef = edos_value( + spline_positions_Ef, structure_eigenenergies_Ef, normalization[index] + ) + e_dos_Ef_grad = edos_derivative( + spline_positions_Ef, structure_eigenenergies_Ef, normalization[index] + ) + spliner = CubicHermiteSpline(spline_positions_Ef, e_dos_Ef, e_dos_Ef_grad) + total_splines_Ef.append(torch.tensor(spliner.c)) + +total_splines_Ef = torch.stack(total_splines_Ef) + + +# %% +# We have stored the splines coefficients (spliner.c) as torch tensors, +# as such as we will need to write a function to evaluate the DOS from +# the splines positions and coefficients. + + +def evaluate_spline(spline_coefs, spline_positions, x): + """ + spline_coefs: shape of (n x 4 x spline_positions) + + return value: shape of (n x x) + + x : shape of (n x n_points) + """ + interval = torch.round( + spline_positions[1] - spline_positions[0], decimals=4 + ) # get spline grid intervals + x = torch.clamp( + x, min=spline_positions[0], max=spline_positions[-1] - 0.0005 + ) # restrict x to fall within the spline interval + # 0.0005 is substracted to combat errors arising from precision + indexes = torch.floor( + (x - spline_positions[0]) / interval + ).long() # Obtain the index for the appropriate spline coefficients + expanded_index = indexes.unsqueeze(dim=1).expand(-1, 4, -1) + x_1 = x - spline_positions[indexes] + x_2 = x_1 * x_1 + x_3 = x_2 * x_1 + x_0 = torch.ones_like(x_1) + x_powers = torch.stack([x_3, x_2, x_1, x_0]).permute(1, 0, 2) + value = torch.sum( + torch.mul(x_powers, torch.gather(spline_coefs, 2, expanded_index)), axis=1 + ) + + return value # returns the value of the DOS at the energy positions, x. + + +# %% +# Lets look at the accuracy of the splines. +# Test 1: Ability to reproduce the correct values at the default x_dos positions + +shifts = torch.zeros(n_structures) +x_dos_splines = x_dos_H + shifts.view(-1, 1) +spline_dos_H = evaluate_spline(total_splines_H, spline_positions_H, x_dos_splines) + +plt.plot(x_dos_H, total_edos_H[0], color="red", label="True DOS") +plt.plot(x_dos_H, spline_dos_H[0], color="blue", linestyle="--", label="Spline DOS") +plt.legend() +plt.xlabel("Energy [eV]") +plt.ylabel("DOS") +print("Both lines lie on each other") +# %% +# Test 2: Ability to reproduce the correct values at the shifted x_dos positions + +shifts = torch.zeros(n_structures) + 0.3 +x_dos_splines = x_dos_Ef + shifts.view(-1, 1) +spline_dos_Ef = evaluate_spline(total_splines_Ef, spline_positions_Ef, x_dos_splines) + +plt.plot(x_dos_Ef, total_edos_Ef[0], color="red", label="True DOS") +plt.plot(x_dos_Ef, spline_dos_Ef[0], color="blue", linestyle="--", label="Spline DOS") +plt.legend() +plt.xlabel("Energy [eV]") +plt.ylabel("DOS") +print("Both spectras look very similar") +# %% +# +# Step 2: Compute SOAP power spectrum for the dataset +# ------------------------------------------------------------------------------------------ +# +# We first define the hyperparameters to compute the +# SOAP power spectrum using rascaline. + +HYPER_PARAMETERS = { + "cutoff": 4.0, + "max_radial": 8, + "max_angular": 6, + "atomic_gaussian_width": 0.45, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {}}, + "cutoff_function": { + "Step": {}, + }, + "radial_scaling": { + "Willatt2018": { + "exponent": 5, + "rate": 1, + "scale": 3.0, + }, + }, +} + +# %% +# +# We feed the Hyperparameters into rascaline to compute the SOAP Power spectrum + + +calculator = SoapPowerSpectrum(**HYPER_PARAMETERS) +R_total_soap = calculator.compute(structures) +# Transform the tensormap to a single block containing a dense representation +R_total_soap.keys_to_samples("species_center") +R_total_soap.keys_to_properties(["species_neighbor_1", "species_neighbor_2"]) + +# Now we extract the data tensor from the single block +total_atom_soap = [] +for structure_i in range(n_structures): + a_i = R_total_soap.block(0).samples["structure"] == structure_i + total_atom_soap.append(torch.tensor(R_total_soap.block(0).values[a_i, :])) + +total_soap = torch.stack(total_atom_soap) +# %% +# +# Step 3: Building a Simple MLP Model +# --------------------------------------------------------------------- +# +# 1) Split the data into Training, Validation and Test +# 2) Define the dataloader and the Model Architecture +# 3) Define relevant loss functions for training and inference +# 4) Define the training loop +# 5) Evaluate the model +# +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +# %% +# 1) Split the data into Training, Validation and Test +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# We will first split the data in a 7:1:2 manner, corresponding to train, val and test. +np.random.seed(0) +train_index = np.arange(n_structures) +np.random.shuffle(train_index) +test_mark = int(0.8 * n_structures) +val_mark = int(0.7 * n_structures) +test_index = train_index[test_mark:] +val_index = train_index[val_mark:test_mark] +train_index = train_index[:val_mark] + +# %% +# 2) Define the dataloader and the Model Architecture +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# We will now build a dataloader and dataset to facillitate training the model batchwise + + +def generate_atomstructure_index(n_atoms_per_structure): + """Generate a sequence of indices for each atom in the structure. + The indices correspond to index of the structure that the atom belongs to + + Args: + n_atoms_per_structure ([array]): + [Array containing the number of atoms each structure contains] + + Return s: + [tensor]: [Total index, matching atoms to structure] + """ + # n_structures = len(n_atoms_per_structure) + total_index = [] + for i, atoms in enumerate(n_atoms_per_structure): + indiv_index = torch.zeros(atoms) + i + total_index.append(indiv_index) + total_index = torch.hstack(total_index) + return total_index.long() + + +class AtomicDataset(Dataset): + def __init__(self, features, n_atoms_per_structure): + self.features = features + self.n_structures = len(n_atoms_per_structure) + self.n_atoms_per_structure = n_atoms_per_structure + self.index = generate_atomstructure_index(self.n_atoms_per_structure) + assert torch.sum(n_atoms_per_structure) == len(features) + + def __len__(self): + return self.n_structures + + def __getitem__(self, idx): + if isinstance(idx, list): # If a list of indexes is given + feature_indexes = [] + + for i in idx: + feature_indexes.append((self.index == i).nonzero(as_tuple=True)[0]) + + feature_indexes = torch.hstack(feature_indexes) + + return ( + self.features[feature_indexes], + idx, + generate_atomstructure_index(self.n_atoms_per_structure[idx]), + ) + + else: + feature_indexes = (self.index == idx).nonzero(as_tuple=True)[0] + return ( + self.features[feature_indexes], + idx, + self.n_atoms_per_structure[idx], + ) + + +def collate( + batch, +): # Defines how to collate the outputs of the __getitem__ function at each batch + for x, idx, index in batch: + return (x, idx, index) + + +x_train = torch.flatten(total_soap[train_index], 0, 1).float() +total_atomic_soaps = torch.vstack(total_atom_soap).float() +train_features = AtomicDataset(x_train, n_atoms[train_index]) +full_atomstructure_index = generate_atomstructure_index(n_atoms) +# Will be required later to collate atomic predictions into structural predictions + +# Build a Dataloader that samples from the AtomicDataset in random batches +Sampler = RandomSampler(train_features) +BSampler = BatchSampler(Sampler, batch_size=32, drop_last=False) +traindata_loader = DataLoader(train_features, sampler=BSampler, collate_fn=collate) + + +# %% +# +# We will now define a simple three layer MLP model, consisting of three layers. +# The align keyword is used to indicate that the energy reference will be optimized +# during training. The alignment parameter refers to the adjustments made to the +# initial energy referenced and will be initialized as zeros. +# + + +class SOAP_NN(torch.nn.Module): + def __init__(self, input_dims, L1, n_train, target_dims, align): + super(SOAP_NN, self).__init__() + self.target_dims = target_dims + self.fc1 = torch.nn.Linear(input_dims, L1) + self.fc2 = torch.nn.Linear(L1, target_dims) + self.silu = torch.nn.SiLU() + self.align = align + if align: + initial_alignment = torch.zeros(n_train) + self.alignment = torch.nn.parameter.Parameter(initial_alignment) + + def forward(self, x): + result = self.fc1(x) + result = self.silu(result) + result = self.fc2(result) + return result + + +# %% +# We will use a small network architecture, whereby the input layer corresponds +# to the size of the SOAP features, 448, the intermediate layer corresponds to +# a tenth size of the input layer and the final layer corresponds +# to the number of outputs. +# +# As a shorthand, the model that optimizes the energy reference during +# training will be called the alignment model +# + +n_outputs_H = len(x_dos_H) +n_outputs_Ef = len(x_dos_Ef) + + +Model_H = SOAP_NN( + x_train.shape[1], + x_train.shape[1] // 10, + len(train_index), + n_outputs_H, + align=False, +) +Model_Ef = SOAP_NN( + x_train.shape[1], + x_train.shape[1] // 10, + len(train_index), + n_outputs_Ef, + align=False, +) +Model_Align = SOAP_NN( + x_train.shape[1], + x_train.shape[1] // 10, + len(train_index), + n_outputs_Ef, + align=True, +) +# The alignment model takes the fermi level energy reference as the starting point + +# %% +# 3) Define relevant loss functions for training and inference +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# We will now define some loss functions that will be useful when we implement +# the model training loop later and during model evaluation on the test set. + + +def t_get_mse(a, b, xdos): + """Compute mean error between two Density of States. + The mean error is integrated across the entire energy grid + to provide a single value to characterize the error + + Args: + a ([tensor]): [Predicted DOS] + b ([tensor]): [True DOS] + xdos ([tensor], optional): [Energy axis of DOS] + + Returns: + [float]: [MSE] + """ + if len(a.size()) > 1: + mse = (torch.trapezoid((a - b) ** 2, xdos, axis=1)).mean() + else: + mse = (torch.trapezoid((a - b) ** 2, xdos, axis=0)).mean() + return mse + + +def t_get_rmse(a, b, xdos): + """Compute root mean squared error between two Density of States . + + Args: + a ([tensor]): [Predicted DOS] + b ([tensor]): [True DOS] + xdos ([tensor], optional): [Energy axis of DOS] + + Raises: + ValueError: [Occurs if tensor shapes are mismatched] + + Returns: + [float]: [RMSE or %RMSE] + """ + + if len(a.size()) > 1: + rmse = torch.sqrt((torch.trapezoid((a - b) ** 2, xdos, axis=1)).mean()) + else: + rmse = torch.sqrt((torch.trapezoid((a - b) ** 2, xdos, axis=0)).mean()) + return rmse + + +def Opt_RMSE_spline(y_pred, xdos, target_splines, spline_positions, n_epochs): + """Evaluates RMSE on the optimal shift of energy axis. + The optimal shift is found via gradient descent after a gridsearch is performed. + + Args: + y_pred ([tensor]): [Prediction/s of DOS] + xdos ([tensor]): [Energy axis] + target_splines ([tensor]): [Contains spline coefficients] + spline_positions ([tensor]): [Contains spline positions] + n_epochs ([int]): [Number of epochs to run for Gradient Descent] + + Returns: + [rmse([float]), optimal_shift[tensor]]: + [RMSE on optimal shift, the optimal shift itself] + + """ + optim_search_mse = [] + offsets = torch.arange(-2, 2, 0.1) + # Grid-search is first done to reduce number of epochs needed for + # gradient descent, typically 50 epochs will be sufficient + # if searching within 0.1 + with torch.no_grad(): + for offset in offsets: + shifts = torch.zeros(y_pred.shape[0]) + offset + shifted_target = evaluate_spline( + target_splines, spline_positions, xdos + shifts.view(-1, 1) + ) + loss_i = ((y_pred - shifted_target) ** 2).mean(dim=1) + optim_search_mse.append(loss_i) + optim_search_mse = torch.vstack(optim_search_mse) + min_index = torch.argmin(optim_search_mse, dim=0) + optimal_offset = offsets[min_index] + + offset = optimal_offset + + shifts = torch.nn.parameter.Parameter(offset.float()) + opt_adam = torch.optim.Adam([shifts], lr=1e-2) + best_error = torch.zeros(len(shifts)) + 100 + best_shifts = shifts.clone() + for _ in range(n_epochs): + shifted_target = evaluate_spline( + target_splines, spline_positions, xdos + shifts.view(-1, 1) + ).detach() + + def closure(): + opt_adam.zero_grad() + shifted_target = evaluate_spline( + target_splines, spline_positions, xdos + shifts.view(-1, 1) + ) + loss_i = ((y_pred - shifted_target) ** 2).mean() + loss_i.backward(gradient=torch.tensor(1), inputs=shifts) + return loss_i + + opt_adam.step(closure) + + with torch.no_grad(): + each_loss = ((y_pred - shifted_target) ** 2).mean(dim=1).float() + index = each_loss < best_error + best_error[index] = each_loss[index].clone() + best_shifts[index] = shifts[index].clone() + + # Evaluate + + optimal_shift = best_shifts + shifted_target = evaluate_spline( + target_splines, spline_positions, xdos + optimal_shift.view(-1, 1) + ) + rmse = t_get_rmse(y_pred, shifted_target, xdos) + return rmse, optimal_shift + + +# %% +# +# 4) Define the training loop +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# We will now define the model training loop, for simplicity we will only +# train each model for a fixed number of epochs, learning rate, and batch_size. +# The training and validation error at each epoch will be saved. + + +def train_model(model_to_train, fixed_DOS, structure_splines, spline_positions, x_dos): + """Trains a model for 500 epochs + + Args: + model_to_train ([torch.nn.Module]): [ML Model] + fixed_DOS ([tensor]): [Contains the DOS at a fixed energy reference, + useful for models that don't optimize the energy reference] + structure_splines ([tensor]): [Contains spline coefficients] + spline_positions ([tensor]): [Contains spline positions] + x_dos ([tensor]): [Energy axis for the prediction] + + Returns: + [train_loss_history([tensor]), + val_loss_history[tensor], + structure_results[tensor]]: + + [Respective loss histories and final structure predictions] + """ + lr = 1e-2 + n_epochs = 500 + + opt = torch.optim.Adam(model_to_train.parameters(), lr=lr) + + train_loss_history = [] + val_loss_history = [] + + for _epoch in range(n_epochs): + for x_data, idx, index in traindata_loader: + opt.zero_grad() + predictions = model_to_train.forward(x_data) + structure_results = torch.zeros([len(idx), model_to_train.target_dims]) + # Sum atomic predictions in each structure + structure_results = structure_results.index_add_( + 0, index, predictions + ) / n_atoms[train_index[idx]].view(-1, 1) + if model_to_train.align: + alignment = model_to_train.alignment + alignment = alignment - torch.mean(alignment) + # Enforce that the alignments have a mean of zero since a constant + # value across the dataset is meaningless when optimizing the + # relative energy reference + target = evaluate_spline( + structure_splines[train_index[idx]], + spline_positions, + x_dos + alignment[idx].view(-1, 1), + ) # Shifts the target based on the alignment value + pred_loss = t_get_mse(structure_results, target, x_dos) + pred_loss.backward() + else: + pred_loss = t_get_mse( + structure_results, fixed_DOS[train_index[idx]], x_dos + ) + pred_loss.backward() + + opt.step() + with torch.no_grad(): + all_pred = model_to_train.forward(total_atomic_soaps.float()) + structure_results = torch.zeros([n_structures, model_to_train.target_dims]) + structure_results = structure_results.index_add_( + 0, full_atomstructure_index, all_pred + ) / (n_atoms).view(-1, 1) + if model_to_train.align: + # Evaluate model on optimal shift as there is no information + # regarding the shift from the fermi level energy reference + # during inference + + alignment = model_to_train.alignment + alignment = alignment - torch.mean(alignment) + target = evaluate_spline( + structure_splines[train_index], + spline_positions, + x_dos + alignment.view(-1, 1), + ) + + train_loss = t_get_rmse(structure_results[train_index], target, x_dos) + val_loss, val_shifts = Opt_RMSE_spline( + structure_results[val_index], + x_dos, + structure_splines[val_index], + spline_positions, + 50, + ) + + else: + train_loss = t_get_rmse( + structure_results[train_index], fixed_DOS[train_index], x_dos + ) + val_loss = t_get_rmse( + structure_results[val_index], fixed_DOS[val_index], x_dos + ) + + train_loss_history.append(train_loss) + val_loss_history.append(val_loss) + train_loss_history = torch.tensor(train_loss_history) + val_loss_history = torch.tensor(val_loss_history) + return ( + train_loss_history, + val_loss_history, + structure_results, + ) + # returns the loss history and the final set of predictions + + +# %% We will now train the respective models + +H_trainloss, H_valloss, H_predictions = train_model( + Model_H, total_edos_H, total_splines_H, spline_positions_H, x_dos_H +) + +Ef_trainloss, Ef_valloss, Ef_predictions = train_model( + Model_Ef, total_edos_Ef, total_splines_Ef, spline_positions_Ef, x_dos_Ef +) + +Align_trainloss, Align_valloss, Align_predictions = train_model( + Model_Align, total_edos_Ef, total_splines_Ef, spline_positions_Ef, x_dos_Ef +) +# %% +# Lets plot the train loss histories to compare their learning behaviour +# + +epochs = np.arange(500) + + +plt.plot(epochs, H_trainloss, color="red", label="Avg Hartree Potential") +plt.plot(epochs, Ef_trainloss, color="blue", label="Fermi Level") +plt.plot(epochs, Align_trainloss, color="green", label="Optimized Reference") +plt.legend() +plt.yscale(value="log") +plt.xlabel("Epochs") +plt.ylabel("RMSE") +plt.title("Train Loss vs Epoch") +plt.show() +# %% +# Lets plot the val loss histories to compare their learning behaviour +# + + +plt.plot(epochs, H_valloss, color="red", label="Avg Hartree Potential") +plt.plot(epochs, Ef_valloss, color="blue", label="Fermi Level") +plt.plot(epochs, Align_valloss, color="green", label="Optimized Reference") +plt.legend() +plt.yscale(value="log") +plt.xlabel("Epochs") +plt.ylabel("RMSE") +plt.title("Validation Loss vs Epoch") +plt.show() + + +# %% +# +# 5) Evaluate the model +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# We will now evaluate the model performance on the test set +# based on the model predictions we obtained previously +# + +H_testloss = Opt_RMSE_spline( + H_predictions[test_index], + x_dos_H, + total_splines_H[test_index], + spline_positions_H, + 200, +) # We use 200 epochs just so it the error a little bit more converged +Ef_testloss = Opt_RMSE_spline( + Ef_predictions[test_index], + x_dos_Ef, + total_splines_Ef[test_index], + spline_positions_Ef, + 200, +) # We use 200 epochs just so it the error a little bit more converged +Align_testloss = Opt_RMSE_spline( + Align_predictions[test_index], + x_dos_Ef, + total_splines_Ef[test_index], + spline_positions_Ef, + 200, +) # We use 200 epochs just so it the error a little bit more converged + +print(f"Test RMSE for average Hartree Potential: {H_testloss[0].item():.3}") +print(f"Test RMSE for Fermi Level: {Ef_testloss[0].item():.3}") +print(f"Test RMSE for Optimized Reference: {Align_testloss[0].item():.3}") + +print( + "The difference in effectiveness between the Optimized Reference \ +and the Fermi Level will increase with more epochs" +) +# %% +# +# Plot Training DOSes at different energy reference to visualize +# the impact of the energy reference. From the plots we can see +# that the optimized energy reference has better alignment of +# common spectral patterns across the dataset +# +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# Average Hartree Energy Reference +# + +for i in total_edos_H[train_index]: + plt.plot(x_dos_H, i, color="C0", alpha=0.6) +plt.title("Energy Reference - Average Hartree Potential") +plt.xlabel("Energy [eV]") +plt.ylabel("DOS") +plt.show() +print("The DOSes, despite looking similar, are offset along the energy axis") + +# %% +# Fermi Level Energy Reference +for i in total_edos_Ef[train_index]: + plt.plot(x_dos_Ef, i, color="C0", alpha=0.6) +plt.title("Energy Reference - Fermi Level") +plt.xlabel("Energy [eV]") +plt.ylabel("DOS") +plt.show() + +print("It is better aligned but still quite some offset") +# %% +# Optimized Energy Reference +shifts = Model_Align.alignment.detach() +shifts = shifts - torch.mean(shifts) +x_dos_splines = x_dos_Ef + shifts.view(-1, 1) +total_edos_align = evaluate_spline( + total_splines_Ef[train_index], spline_positions_Ef, x_dos_splines +) + +for i in total_edos_align: + plt.plot(x_dos_Ef, i, color="C0", alpha=0.6) +plt.title("Energy Reference - Optimized") +plt.xlabel("Energy [eV]") +plt.ylabel("DOS") +plt.show() +print("The DOS alignment is better under the optimized energy reference") +print("The difference will increase with more training epochs") +# %% diff --git a/_downloads/edc4de60777e3b3373ed9e627d585459/environment.yml b/_downloads/edc4de60777e3b3373ed9e627d585459/environment.yml new file mode 100644 index 00000000..cb6cafe4 --- /dev/null +++ b/_downloads/edc4de60777e3b3373ed9e627d585459/environment.yml @@ -0,0 +1,14 @@ +channels: + - conda-forge +dependencies: + - python=3.11 + - pip + - rust >=1.65 + - pip: + - ase==3.22.1 + - chemiscope>=0.7 + - matplotlib + - metatensor + - rascaline @ git+https://github.com/Luthaf/rascaline@ca957642f512e141c7570e987aadc05c7ac71983 + - scikit-learn==1.4.0 + - skmatter diff --git a/_downloads/f04a73ec1916d97f905162a40b2a3dd0/heat-capacity.py b/_downloads/f04a73ec1916d97f905162a40b2a3dd0/heat-capacity.py new file mode 100644 index 00000000..dd574c7a --- /dev/null +++ b/_downloads/f04a73ec1916d97f905162a40b2a3dd0/heat-capacity.py @@ -0,0 +1,296 @@ +""" +Quantum heat capacity of water +============================== + +:Authors: + Filippo Bigi `@frostedoyster `_; + Michele Ceriotti `@ceriottm `_ + +This example shows how to estimate the heat capacity of liquid water +from a path integral molecular dynamics simulation. The dynamics are +run with `i-PI `_, and +`LAMMPS `_ is used +as the driver to simulate the `q-TIP4P/f water +model `_. +""" + +import os +import subprocess +import time +import xml.etree.ElementTree as ET + +import ipi +import matplotlib.pyplot as plt +import numpy as np + + +# %% +# A non-trivial energy estimator +# ------------------------------ +# +# As introduced in the +# `path-integrals example +# `_, +# path-integral estimators +# for observables that depend on momenta are generally not trivial to compute. +# +# In this example, we will focus on the constant-volume heat capacity, +# :math:`c_V`, which is one such +# observable, and we will calculate it for liquid water at room temperature. +# Because of the presence of high-frequency vibrations, many of the nuclear +# degrees of freedom are trapped in the vibrational ground state, which reduces +# substantially the heat capacity from the value that would be obtained +# in the classical limit. See `this review +# `_ +# for an overview of the impact of quantum nuclei on the properties of water. +# From a computational perspective, this means that it is necessary to use +# specialized simulations and estimators to evaluate the correct value. + + +# %% +# Running the PIMD calculation +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# This follows the same steps as the ``path-integrals`` example. One important +# difference is that we will request the ``scaledcoords`` output to the relevant +# section of the ``i-PI`` input XML file, which +# contains estimators that can be used to calculate the total energy and +# heat capacity as following +# `Yamamoto, J. Chem. Phys. (2005) `_. +# +# The input file is shown below. It should be noted that ``scaledcoords`` +# is given a finite differences displacement as a parameter. This is necessary +# as the estimators require higher order derivatives of the potential energy, +# which are calculated using finite differences. This also means that +# evaluating the estimator adds substantial overhead (so it is wise to only +# compute it every few simulation steps, to eliminate correlations between +# snapshots) and that one should be careful to use well-converged simulation +# parameters to avoid discontinuities and noise (for instance, we increase +# the accuracy of the particle-mesh electrostatic calculation, and use a +# shifted Lennard-Jones potential to avoid a discontinuity at the cutoff). + +# Open and show the relevant part of the input +xmlroot = ET.parse("data/input.xml").getroot() +print(" " + ET.tostring(xmlroot.find(".//properties"), encoding="unicode")) + +# %% +# We launch the i-PI and LAMMPS processes, exactly as in the +# ``path-integrals`` example. + +# don't rerun if the outputs already exist +ipi_process = None +if not os.path.exists("water-cv.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input.xml"]) + time.sleep(2) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(2)] + +# %% +# Skip this cell if you want to run in the background +if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + lmp_process[1].wait() + +# %% +# Analyzing the results +# ~~~~~~~~~~~~~~~~~~~~~ +# Let's plot the potential and conserved energy as a function of time, +# just to check that the simulation ran sensibly. + +output_data, output_desc = ipi.read_output("water-cv.out") +fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + output_data["potential"] - output_data["potential"][0], + "b-", + label="Potential, $V$", +) +ax.plot( + output_data["time"], + output_data["conserved"] - output_data["conserved"][0], + "r-", + label="Conserved, $H$", +) +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"energy / a.u.") +ax.legend() +plt.show() + +# %% +# As described in the `i-PI documentation +# `_, +# the two quantities returned by the ``scaledcoords`` output are ``eps_v`` +# and ``eps_v'``, defined in the aforementioned +# `paper `_. +# +# These estimators (:math:`\epsilon_v` and :math:`\epsilon_v'`) are derived in the +# "scaled coordinates" formalism, which is a useful trick to avoid the +# growth of the error in the instantaneous values of the estimators with +# the number of beads used in the path integral simulation. +# +# The same paper contains the formulas to calculate the total energy and +# heat capacity from these estimators: +# +# .. math:: +# E = \langle \epsilon_v \rangle \quad +# C_V = k_B \beta^2 \left( \langle \epsilon_v^2 \rangle - \langle +# \epsilon_v \rangle^2 - \langle \epsilon_v' \rangle \right) +# +# First the energy, whose estimator will be compared to the total energy +# calculated as the sum of the potential and kinetic energy estimators. +# Since the kinetic energy is itself calculated from a scaled-coordinates +# estimator (the "centroid virial" estimator), the two total energies are +# the same. + +eps_v = output_data["scaledcoords(fd_delta=5e-3)"][:, 0] +eps_v_prime = output_data["scaledcoords(fd_delta=5e-3)"][:, 1] + +energy_estimator = eps_v # first formula + +fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) +ax.plot( + output_data["time"], + energy_estimator - energy_estimator[0], + "b-", + label="scaled coordinates estimator", +) +ax.plot( + output_data["time"][:], + ( + output_data["potential"] + - output_data["potential"][0] + + output_data["kinetic_cv"] + - output_data["kinetic_cv"][0] + ), + "r.", + label="potential + virial kinetic", +) +ax.set_xlabel(r"$t$ / ps") +ax.set_ylabel(r"total energy / a.u.") +ax.legend() +plt.show() + + +# %% +# And, finally, the heat capacity. Note that normally the simulation +# requires a few ps for equilibration. Here we discard a few dozen steps +# to eliminate the initial jump, which is due to the relaxation of the +# ring polymers starting from a single atomic configuration. + +# i-PI scaledcoords outputs are in atomic units (see docs) +kB = 3.16681e-6 # Boltzmann constant in atomic units +T = 298.0 # temperature in K, as defined in the input file +beta = 1.0 / (kB * T) + +skip = 20 +heat_capacity = ( # second formula + kB + * (beta**2) + * ( + np.mean(eps_v[skip:] ** 2) + - np.mean(eps_v[skip:]) ** 2 + - np.mean(eps_v_prime[skip:]) + ) +) +heat_capacity_per_molecule = heat_capacity / 32 # 32 molecules in the simulation +print(f"Heat capacity (per water molecule): {(heat_capacity_per_molecule/kB):.2f} kB") + +# %% +# You may recognize that the first part of the estimator is reminiscent +# of the classical estimator for the heat capacity as the fluctuations of the +# (quantum) total energy, which in this case however requires a correction given +# by the mean of the second part of the scaled-coordinates estimator. + +# %% +# Estimating the statistical error +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# Especially with such an underconverged simulation, it is important to +# estimate the statistical error in the heat capacity. +# +# Generally, errors on measurements are computed +# as "standard errors", i.e. the standard deviation of a series of data points +# divided by the square root of the number of data points. In our case, +# however, this is made more complicated by the correlation between +# close steps in the molecular dynamics trajectory, which would lead to an +# overestimation of the number of independent samples. To fix this, we can +# calculate the autocorrelation time of the estimators whose errors we +# want to estimate, and apply a correction factor to the number of samples. + + +def autocorrelate(x): + n = len(x) + xo = x - x.mean() # remove mean + acov = (np.correlate(xo, xo, "full"))[n - 1 :] + return acov[: len(acov) // 2] + + +def autocorrelation_time(x): + acov = autocorrelate(x) + return 1.0 + np.sum(acov) / acov[0] + + +# %% +# Using these helper functions, we can now calculate the error on the various +# parts of the heat capacity estimator. Note also the autocorrelation times, that +# are just a little larger than one, indicating that the stride used to print out +# the estimators is appropriate (as there is little correlation between the samples). + +# Autocorrelation times (i.e. number of steps needed to have independent samples) +autocorr_time_error_delta_eps_v = autocorrelation_time( + (eps_v[skip:] - eps_v[skip:].mean()) ** 2 +) +autocorr_time_error_eps_v_prime = autocorrelation_time(eps_v_prime[skip:]) + +print( + f""" +Autocorrelation times (in number of samples): +(eps-)^2: {autocorr_time_error_delta_eps_v:.2f} +eps': {autocorr_time_error_eps_v_prime:.2f} +""" +) + +# Effective number of samples +effective_samples_delta_eps_v = len(eps_v[skip:]) / autocorr_time_error_delta_eps_v +effective_samples_eps_v_prime = len(eps_v[skip:]) / autocorr_time_error_eps_v_prime + +# Standard errors using the effective number of samples +error_delta_eps_v = np.std((eps_v[skip:] - eps_v[skip:].mean()) ** 2) / np.sqrt( + effective_samples_delta_eps_v +) +error_eps_v_prime = np.std(eps_v_prime[skip:]) / np.sqrt(effective_samples_eps_v_prime) + +# Error on the heat capacity (assuming quadrature sum) +error_heat_capacity = ( + kB * (beta**2) * np.sqrt(error_delta_eps_v**2 + error_eps_v_prime**2) +) + +error_heat_capacity_per_molecule = ( + error_heat_capacity / 32 +) # 32 molecules in the simulation + +print( + "Error on the heat capacity (per water molecule): " + f"{(error_heat_capacity_per_molecule/kB):.2f} kB" +) + + +# %% +# The obtained heat capacity is consistent with the values from the literature +# (see e.g. `Ceriotti et al., J. Chem. Phys. (2011) +# `_ +# where the convergence of the heat capacity with number of beads is shown for the same +# water model used in this example). +# However, the error is quite large, which is expected given the short simulation time. +# To reduce the error, one would need to run a longer simulation. Other important error +# sources, which are not accounted for in the error estimate, are the finite size of the +# system and number of beads. Both of these are too small in this example to give +# reliable results. +# +# In a realistic simulation, up to a few 100s of picoseconds might be needed to reduce +# the sampling error to a small value (1-2% of the heat capacity). For water at room +# temperature, you will need 32 beads at the very least (8 were used in this example). +# It is more difficult to give a general rule for the system size: (quantum) energy +# fluctuations are usually localized, but to guarantee accurate sampling of the +# liquid structure, a few hundred water molecules would be a reasonable guess +# (32 were used in this example). diff --git a/_downloads/f6d6590267d583b5f0e9a7ca3a9f8439/lpr.zip b/_downloads/f6d6590267d583b5f0e9a7ca3a9f8439/lpr.zip new file mode 100644 index 00000000..1ead8c7f Binary files /dev/null and b/_downloads/f6d6590267d583b5f0e9a7ca3a9f8439/lpr.zip differ diff --git a/_downloads/fe6711aca3f0f5f2cec13f8a8ebe3462/example.xyz b/_downloads/fe6711aca3f0f5f2cec13f8a8ebe3462/example.xyz new file mode 100644 index 00000000..c0031e2d --- /dev/null +++ b/_downloads/fe6711aca3f0f5f2cec13f8a8ebe3462/example.xyz @@ -0,0 +1,8 @@ +6 +Lattice="3.9111732301689224 0.0 0.0 0.0 3.9111732301689224 0.0 0.0 0.0 3.9111732301689224" Properties=species:S:1:pos:R:3 #=T CELL(abcABC):=T 3.91117=T 90.00000=T Step:=T 1975600=T Bead:=T 0=T x_centroidangstrom=T cellangstrom=T count=0 pbc="T T T" +H 2.55799292 0.30476323 0.67883354 +H 1.46739292 0.53584100 3.59015677 +O 1.78619292 3.82685646 0.31171354 +H 3.52058031 2.55936677 2.71091323 +H 0.84863385 2.05009677 1.85452646 +O 0.09813385 1.75660677 2.33837646 diff --git a/_downloads/fece03724daaa69643cea3d483b9c18e/path-integrals.ipynb b/_downloads/fece03724daaa69643cea3d483b9c18e/path-integrals.ipynb new file mode 100644 index 00000000..97025c2a --- /dev/null +++ b/_downloads/fece03724daaa69643cea3d483b9c18e/path-integrals.ipynb @@ -0,0 +1,280 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Path integral molecular dynamics\n\n:Authors: Michele Ceriotti [@ceriottm](https://github.com/ceriottm/)\n\nThis example shows how to run a path integral molecular dynamics\nsimulation using ``i-PI``, analyze the output and visualize the\ntrajectory in ``chemiscope``. It uses [LAMMPS](http://lammps.org)\nas the driver to simulate the [q-TIP4P/f water\nmodel](http://doi.org/10.1063/1.3167790).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import subprocess\nimport time\n\nimport chemiscope\nimport ipi\nimport matplotlib.pyplot as plt\nimport numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum nuclear effects and path integral methods\n\nThe Born-Oppenheimer approximation separates the joint quantum mechanical\nproblem for electrons and nuclei into two independent problems. Even though\noften one makes the additional approximation of treating nuclei as classical\nparticles, this is not necessary, and in some cases (typically when H atoms are\npresent) can add considerable error.\n\n\n.. figure:: pimd-slices-round.png\n :align: center\n :width: 600px\n\n A representation of ther ring-polymer Hamiltonian for a water molecule.\n\nIn order to describe the quantum mechanical nature of light nuclei\n(nuclear quantum effects) one of the most widely-applicable methods uses\nthe *path integral formalism* to map the quantum partition function of a\nset of distinguishable particles onto the classical partition function of\n*ring polymers* composed by multiple beads (replicas) with\ncorresponding atoms in adjacent replicas being connected by harmonic\nsprings.\n[The textbook by Tuckerman](https://tinyurl.com/bdfhk2tx)\ncontains a pedagogic introduction to the topic, while\n[this paper](https://doi.org/10.1063/1.3489925) outlines the implementation\nused in ``i-PI``.\n\nThe classical partition function of the path converges to quantum statistics\nin the limit of a large number of replicas. In this example, we will use a\ntechnique based on generalized Langevin dynamics, known as\n[PIGLET](http://doi.org/10.1103/PhysRevLett.109.100604) to accelerate the\nconvergence.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running PIMD calculations with ``i-PI``\n\n[i-PI](http://ipi-code.org) is based on a client-server model, with ``i-PI``\ncontrolling the nuclear dynamics (in this case sampling the path Hamiltonian using\nmolecular dynamics) while the calculation of energies and forces is delegated to\nan external client program, in this example ``LAMMPS``.\n\nAn i-PI calculation is specified by an XML file.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Open and read the XML file\nwith open(\"data/input_pimd.xml\", \"r\") as file:\n xml_content = file.read()\nprint(xml_content)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "NB1: In a realistic simulation you may want to increase the field\n``total_steps``, to simulate at least a few 100s of picoseconds.\n\nNB2: To converge a simulation of water at room temperature, you\ntypically need at least 32 beads. We will see later how to accelerate\nconvergence using a colored-noise thermostat, but you can try to\nmodify the input to check convergence with conventional PIMD\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "i-PI and lammps should be run separately, and it is possible to\nlaunch separate lammps processes to parallelize the evaluation over\nthe beads. On the the command line, this amounts to launching\n\n```bash\ni-pi data/input_pimd.xml > log &\nsleep 2\nlmp -in data/in.lmp &\nlmp -in data/in.lmp &\n```\nNote how ``i-PI`` and ``LAMMPS`` are completely independent, and\ntherefore need a separate set of input files. The client-side communication\nin ``LAMMPS`` is described in the ``fix_ipi`` section, that matches the socket\nname and mode defined in the ``ffsocket`` field in the ``i-PI`` file.\n\nWe can launch the external processes from a Python script as follows\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi_process = subprocess.Popen([\"i-pi\", \"data/input_pimd.xml\"])\ntime.sleep(2) # wait for i-PI to start\nlmp_process = [subprocess.Popen([\"lmp\", \"-in\", \"data/in.lmp\"]) for i in range(2)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you run this in a notebook, you can go ahead and start loading\noutput files *before* i-PI and lammps have finished running, by\nskipping this cell\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi_process.wait()\nlmp_process[0].wait()\nlmp_process[1].wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analyzing the simulation\n\nAfter the simulation has run, you can visualize and post-process the trajectory data.\nNote that i-PI prints a separate trajectory for each bead, as structural properties\ncan be computed averaging over the configurations of any of the beads.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# drops first frame where all atoms overlap\noutput_data, output_desc = ipi.read_output(\"simulation.out\")\ntraj_data = [ipi.read_trajectory(f\"simulation.pos_{i}.xyz\")[1:] for i in range(8)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The simulation parameters are pushed at the limits: with the aggressive stochastic\nthermostatting and the high-frequency normal modes of the ring polymer, there are\nfairly large fluctuations of the conserved quantity. This is usually not affecting\nphysical observables, but if you see this level of drift in a production run, check\ncarefully for convergence and stability with a reduced time step.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"potential\"] - output_data[\"potential\"][0],\n \"b-\",\n label=\"Potential, $V$\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"conserved\"] - output_data[\"conserved\"][0],\n \"r-\",\n label=\"Conserved, $H$\",\n)\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"energy / eV\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While the potential energy is simply the mean over the beads of the\nenergy of individual replicas, computing the kinetic energy requires\naveraging special quantities that involve also the correlations between beads.\nHere we compare two of these *estimators*: the 'thermodynamic' estimator becomes\nstatistically inefficient when increasing the number of beads, whereas the\n'centroid virial' estimator remains well-behaved. Note how quickly these estimators\nequilibrate to roughly their stationary value, much faster than the equilibration\nof the potential energy above. This is thanks to the ``pile_g`` thermostat\n(see [DOI:10.1063/1.3489925](http://doi.org/10.1063/1.3489925)) that is\noptimally coupled to the normal modes of the ring polymer.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"kinetic_cv\"],\n \"b-\",\n label=\"Centroid virial, $K_{CV}$\",\n)\nax.plot(\n output_data[\"time\"],\n output_data[\"kinetic_td\"],\n \"r-\",\n label=\"Thermodynamic, $K_{TD}$\",\n)\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"energy / eV\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can also visualize the (very short) trajectory in a way that highlights the\nfast spreading out of the beads of the ring polymer. ``chemiscope`` provides a\nutility function to interleave the trajectories of the beads, forming a trajectory\nthat shows the connecttions between the replicas of each atom. Each atom and its\nconnections are color-coded.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "traj_pimd = chemiscope.ase_merge_pi_frames(traj_data)\n# we also tweak the visualization options, and then show the viewer\ntraj_pimd[\"shapes\"][\"paths\"][\"parameters\"][\"global\"][\"radius\"] = 0.05\ntraj_pimd[\"settings\"][\"structure\"][0].update(\n dict(\n atoms=False,\n keepOrientation=True,\n color={\"property\": \"bead_id\", \"palette\": \"hsv (periodic)\"},\n )\n)\n\nchemiscope.show(**traj_pimd, mode=\"structure\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Accelerating PIMD with a PIGLET thermostat\n\nThe simulations in the previous sections are very far from converged -- typically\none would need approximately 32 replicas to converge a simulation of\nroom-temperature water. To address this problem we will use a method based on\ngeneralized Langevin equations, called\n[PIGLET](http://doi.org/10.1103/PhysRevLett.109.100604)\n\nThe input file is ``input_piglet.xml``, that only differs by the definition of\nthe thermostat, that uses a ``nm_gle`` mode in which each normal mode\nof the ring polymer is attached to a different colored-noise Generalized Langevin\nequation. This makes it possible to converge exactly the simulation results with\na small number of replicas, and to accelerate greatly convergence for realistic\nsystems such as this. The thermostat parameters can be generated on\n[the GLE4MD website](https://tinyurl.com/4y2e45jx)\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ipi_process = subprocess.Popen([\"i-pi\", \"data/input_piglet.xml\"])\ntime.sleep(2) # wait for i-PI to start\nlmp_process = [subprocess.Popen([\"lmp\", \"-in\", \"data/in.lmp\"]) for i in range(2)]\n\nipi_process.wait()\nlmp_process[0].wait()\nlmp_process[1].wait()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The mean potential energy from the PIGLET trajectory is higher than that for the\nPIMD one, because it is closer to the converged value (try to run a PIMD trajectory\nwith 64 beads for comparison)\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# drops first frame\noutput_gle, desc_gle = ipi.read_output(\"simulation_piglet.out\")\ntraj_gle = [ipi.read_trajectory(f\"simulation_piglet.pos_{i}.xyz\")[1:] for i in range(8)]\n\nfig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(\n output_data[\"time\"],\n output_data[\"potential\"] - output_data[\"potential\"][0],\n \"b--\",\n label=\"PIMD\",\n)\nax.plot(\n output_gle[\"time\"],\n output_gle[\"potential\"] - output_gle[\"potential\"][0],\n \"b-\",\n label=\"PIGLET\",\n)\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"energy / eV\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "However, you should be somewhat careful: PIGLET converges *some* but not all the\ncorrelations within a path. For instance, it is designed to converge the\ncentroid-virial estimator for the kinetic energy, but not the thermodynamic\nestimator. For the same reason, don't try to look at equilibration in terms of\nthe mean temperature: it won't match the target value, because PIGLET uses a\nLangevin equation that breaks the classical fluctuation-dissipation theorem, and\ngenerates a steady-state distribution that mimics quantum fluctuations.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True)\nax.plot(output_data[\"time\"], output_data[\"kinetic_cv\"], \"b--\", label=\"PIMD, $K_{CV}$\")\nax.plot(output_gle[\"time\"], output_gle[\"kinetic_cv\"], \"b\", label=\"PIGLET, $K_{CV}$\")\nax.plot(output_data[\"time\"], output_data[\"kinetic_td\"], \"r--\", label=\"PIMD, $K_{TD}$\")\nax.plot(output_gle[\"time\"], output_gle[\"kinetic_td\"], \"r\", label=\"PIGLET, $K_{TD}$\")\nax.set_xlabel(r\"$t$ / ps\")\nax.set_ylabel(r\"energy / eV\")\nax.legend()\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Kinetic energy tensors\n\nWhile we're at it, let's do something more complicated (and instructive).\nClassically, the momentum distribution of any atom is isotropic, so the\nkinetic energy tensor (KET) $\\mathbf{p}\\mathbf{p}^T/2m$ is a constant\ntimes the identity matrix. Quantum mechanically, the kinetic energy tensor\nhas more structure, that reflects the higher kinetic energy of particles\nalong directions with stiff bonds. We can compute a moving average of the\ncentroid virial estimator of the KET, and plot it to show the direction\nof anisotropy. Note that there are some subtleties connected with the\nevaluation of the moving average, see e.g.\n[DOI:10.1103/PhysRevLett.109.100604](http://doi.org/10.1103/PhysRevLett.109.100604)\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We first need to postprocess the components of the kinetic energy tensors\n(that i-PI prints out separating the diagonal and off-diagonal bits), averaging\nthem over the last 10 frames and combining them with the centroid configuration\nfrom the last frame in the trajectory.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "kinetic_cv = ipi.read_trajectory(\"simulation_piglet.kin.xyz\")[1:]\nkinetic_od = ipi.read_trajectory(\"simulation_piglet.kod.xyz\")[1:]\nkinetic_tens = np.hstack(\n [\n np.asarray([k.positions for k in kinetic_cv[-10:]]).mean(axis=0),\n np.asarray([k.positions for k in kinetic_od[-10:]]).mean(axis=0),\n ]\n)\n\ncentroid = traj_gle[-1][-1].copy()\ncentroid.positions = np.asarray([t[-1].positions for t in traj_gle]).mean(axis=0)\ncentroid.arrays[\"kinetic_cv\"] = kinetic_tens" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then view these in ``chemiscope``, setting the proper parameters to\nvisualize the ellipsoids associated with the KET. Note that some KETs have\nnegative eigenvalues, because we are averaging over a few frames, which is\ninsufficient to converge the estimator fully.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ellipsoids = chemiscope.ase_tensors_to_ellipsoids(\n [centroid], \"kinetic_cv\", scale=15, force_positive=True\n)\n\nchemiscope.show(\n [centroid],\n shapes={\"kinetic_cv\": ellipsoids},\n mode=\"structure\",\n settings=chemiscope.quick_settings(\n structure_settings={\n \"shape\": [\"kinetic_cv\"],\n \"unitCell\": True,\n }\n ),\n)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": 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+ :text-align: center + :shadow: md + + .. image:: examples/dos-align/images/thumb/sphx_glr_dos-align_thumb.png + :alt: This tutorial would go through the entire machine learning framework for the electronic density of states (DOS). It will cover the construction of the DOS and SOAP descriptors from ase Atoms and eigenenergy results. A simple neural network will then be constructed and the model parameters, along with the energy reference will be optimized during training. A total of three energy reference will be used, the average Hartree potential, the Fermi level, and an optimized energy reference starting from the Fermi level energy reference. The performance of each model is then compared. + :class: gallery-img + + + .. grid-item:: + .. card:: Batch run of CP2K calculations + :link: examples/batch-cp2k/reference-trajectory + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/batch-cp2k/images/thumb/sphx_glr_reference-trajectory_thumb.png + :alt: This is an example how to perform single point calculations based on list of structures using CP2K using its reftraj functionality. The inputs are a set of structures in :download:`example.xyz` using the DFT parameters defined in :download:`reftraj_template.cp2k`. The reference DFT parameters are taken from Cheng et al. Ab initio thermodynamics of liquid and solid water 2019. Due to the small size of the test structure and convergence issues, we have decreased the size of the CUTOFF_RADIUS from 6.0\,\mathrm{Å} to 3.0\,\mathrm{Å}. For actual production calculations adapt the template! + :class: gallery-img + + + .. grid-item:: + .. card:: Constant-temperature MD and thermostats + :link: examples/thermostats/thermostats + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/thermostats/images/thumb/sphx_glr_thermostats_thumb.png + :alt: This recipe gives a practical introduction to finite-temperature molecular dynamics simulations, and provides a guide to choose the most appropriate thermostat for the simulation at hand. + :class: gallery-img + + + .. grid-item:: + .. card:: Generalized Convex Hull construction for the polymorphs of ROY + :link: examples/roy-gch/roy-gch + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/roy-gch/images/thumb/sphx_glr_roy-gch_thumb.png + :alt: This notebook analyzes the structures of 264 polymorphs of ROY, from Beran et Al, Chemical Science (2022), comparing the conventional density-energy convex hull with a Generalized Convex Hull (GCH) analysis (see Anelli et al., Phys. Rev. Materials (2018)). It uses features computed with rascaline and uses the directional convex hull function from scikit-matter to make the figure. + :class: gallery-img + + + .. grid-item:: + .. card:: Local Prediction Rigidity analysis + :link: examples/lpr/lpr + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/lpr/images/thumb/sphx_glr_lpr_thumb.png + :alt: In this tutorial, we calculate the SOAP descriptors of an amorphous silicon dataset using rascaline, then compute the local prediction rigidity (LPR) for the atoms of a "test" set before and after modifications to the "training" dataset has been made. + :class: gallery-img + + + .. grid-item:: + .. card:: Long-distance Equivariants: a tutorial + :link: examples/lode-linear/lode-linear + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/lode-linear/images/thumb/sphx_glr_lode-linear_thumb.png + :alt: This tutorial explains how Long range equivariant descriptors can be constructed using rascaline and the resulting descriptors be used to construct a linear model with equisolve + :class: gallery-img + + + .. grid-item:: + .. card:: PCA/PCovR Visualization of a training dataset for a potential + :link: examples/gaas-map/gaas-map + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/gaas-map/images/thumb/sphx_glr_gaas-map_thumb.png + :alt: This example uses rascaline and metatensor to compute structural properties for the structures in a training dataset for a ML potential. These are then used with simple dimensionality reduction algorithms (implemented in sklearn and skmatter) to obtain a simplified description of the dataset, that is then visualized using chemiscope. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral metadynamics + :link: examples/pi-metad/pi-metad + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/pi-metad/images/thumb/sphx_glr_pi-metad_thumb.png + :alt: This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral molecular dynamics + :link: examples/path-integrals/path-integrals + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/path-integrals/images/thumb/sphx_glr_path-integrals_thumb.png + :alt: This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + + .. grid-item:: + .. card:: Periodic Hamiltonian learning + :link: examples/periodic-hamiltonian/periodic-hamiltonian + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/periodic-hamiltonian/images/thumb/sphx_glr_periodic-hamiltonian_thumb.png + :alt: This tutorial explains how to train a machine learning model for the electronic Hamiltonian of a periodic system. Even though we focus on periodic systems, the code and techniques presented here can be directly transferred to molecules. + :class: gallery-img + + + .. grid-item:: + .. card:: Quantum heat capacity of water + :link: examples/heat-capacity/heat-capacity + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/heat-capacity/images/thumb/sphx_glr_heat-capacity_thumb.png + :alt: This example shows how to estimate the heat capacity of liquid water from a path integral molecular dynamics simulation. The dynamics are run with i-PI, and LAMMPS is used as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + + .. grid-item:: + .. card:: Sample and Feature Selection with FPS and CUR + :link: examples/sample-selection/sample-selection + :link-type: doc + :text-align: center + :shadow: md + + .. image:: examples/sample-selection/images/thumb/sphx_glr_sample-selection_thumb.png + :alt: In this tutorial we generate descriptors using rascaline, then select a subset of structures using both the farthest-point sampling (FPS) and CUR algorithms implemented in scikit-matter. Finally, we also generate a selection of the most important features using the same techniques. + :class: gallery-img + + +.. toctree:: + :maxdepth: 1 + :hidden: + :titlesonly: + + examples/dos-align/dos-align + examples/batch-cp2k/reference-trajectory + examples/thermostats/thermostats + examples/roy-gch/roy-gch + examples/lpr/lpr + examples/lode-linear/lode-linear + examples/gaas-map/gaas-map + examples/pi-metad/pi-metad + examples/path-integrals/path-integrals + examples/periodic-hamiltonian/periodic-hamiltonian + examples/heat-capacity/heat-capacity + examples/sample-selection/sample-selection diff --git a/_sources/contributing.rst.txt b/_sources/contributing.rst.txt new file mode 100644 index 00000000..d197ee0b --- /dev/null +++ b/_sources/contributing.rst.txt @@ -0,0 +1,7 @@ +Contributing a recipe +===================== + +.. include:: ../../CONTRIBUTING.rst + :start-after: marker-contrib-start + :end-before: marker-contrib-end + diff --git a/_sources/downloading.rst.txt b/_sources/downloading.rst.txt new file mode 100644 index 00000000..aa5b09d2 --- /dev/null +++ b/_sources/downloading.rst.txt @@ -0,0 +1,6 @@ +Downloading and running the recipes +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. include:: ../../INSTALLING.rst + :start-after: marker-install-start + :end-before: marker-install-end diff --git a/_sources/examples/batch-cp2k/reference-trajectory.rst.txt b/_sources/examples/batch-cp2k/reference-trajectory.rst.txt new file mode 100644 index 00000000..e65bf0d9 --- /dev/null +++ b/_sources/examples/batch-cp2k/reference-trajectory.rst.txt @@ -0,0 +1,529 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/batch-cp2k/reference-trajectory.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_batch-cp2k_reference-trajectory.py: + + +Batch run of CP2K calculations +============================== + +:Authors: Matthias Kellner `@bananenpampe `_, + Philip Loche `@PicoCentauri `_ + +This is an example how to perform single point calculations based on list of structures +using `CP2K `_ using its `reftraj functionality +`_. The inputs are a +set of structures in :download:`example.xyz` using the DFT parameters defined in +:download:`reftraj_template.cp2k`. The reference DFT parameters are taken from `Cheng et +al. Ab initio thermodynamics of liquid and solid water 2019 +`_. Due to the small size of the test +structure and convergence issues, we have decreased the size of the ``CUTOFF_RADIUS`` +from :math:`6.0\,\mathrm{Å}` to :math:`3.0\,\mathrm{Å}`. For actual production +calculations adapt the template! + +.. GENERATED FROM PYTHON SOURCE LINES 21-22 + +We start the example by importing the required packages. + +.. GENERATED FROM PYTHON SOURCE LINES 22-35 + +.. code-block:: Python + + + import os + import platform + import subprocess + from typing import List, Union + + import ase.io + import ase.visualize.plot + import matplotlib.pyplot as plt + import numpy as np + import requests + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 36-42 + +Install CP2K +------------ + +We'll need a working installation of cp2k. The best way to do so depends on your +platform, here are some possible solutions, but feel free to replace them with another +installation method. + +.. GENERATED FROM PYTHON SOURCE LINES 43-54 + +.. code-block:: Python + + + if platform.system() == "Linux": + # use conda on Linux + subprocess.run(["conda", "install", "cp2k", "-c", "conda-forge", "-y"], check=True) + elif platform.system() == "Darwin": + # use homebrew on macOS + subprocess.run(["brew", "install", "cp2k"], check=True) + else: + print("no known way to install cp2k, skipping installation") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 55-58 + +Define necessary functions +-------------------------- +Next we below define necessary helper functions to run the example. + +.. GENERATED FROM PYTHON SOURCE LINES 58-92 + +.. code-block:: Python + + + + def write_reftraj(fname: str, frames: Union[ase.Atoms, List[ase.Atoms]]) -> None: + """Writes a list of ase atoms objects to a reference trajectory. + + A reference trajectory is the CP2K compatible format for the compuation of batches. + All frames must have the stoichiometry/composition. + """ + + if isinstance(frames, ase.Atoms): + frames = [frames] + + out = "" + for i, atoms in enumerate(frames): + if ( + len(atoms) != len(frames[0]) + or atoms.get_chemical_formula() != frames[0].get_chemical_formula() + ): + raise ValueError( + f"Atom symbols in frame {i},{atoms.get_chemical_formula()} are " + f"different compared to inital frame " + f"{frames[0].get_chemical_formula()}. " + "CP2K does not support changing atom types within a reftraj run!" + ) + + out += f"{len(atoms):>8}\n i = {i + 1:>8}, time = {0:>12.3f}\n" + for atom in atoms: + pos = atom.position + out += f"{atom.symbol}{pos[0]:24.15f}{pos[1]:24.15f}{pos[2]:24.15f}\n" + out += "\n" + with open(fname, "w") as f: + f.write(out) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 93-129 + +.. code-block:: Python + + + + def write_cellfile(fname: str, frames: Union[ase.Atoms, List[ase.Atoms]]) -> None: + """Writes a cellfile for a list of ``ase.Atoms``. + + A Cellfile accompanies a reftraj containing the cell parameters. + """ + if isinstance(frames, ase.Atoms): + frames = [frames] + + out = ( + "# " + "Step " + "Time [fs] " + "Ax [Angstrom] " + "Ay [Angstrom] " + "Az [Angstrom] " + "Bx [Angstrom] " + "By [Angstrom] " + "Bz [Angstrom] " + "Cx [Angstrom] " + "Cy [Angstrom] " + "Cz [Angstrom] " + "Volume [Angstrom^3]\n" + ) + + for i, atoms in enumerate(frames): + out += f"{i + 1:>8}{0:>12.3f}" + out += "".join([f"{c:>20.10f}" for c in atoms.cell.flatten()]) + out += f"{atoms.cell.volume:>25.10f}" + out += "\n" + + with open(fname, "w") as f: + f.write(out) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 130-151 + +.. code-block:: Python + + + + def write_cp2k_in( + fname: str, project_name: str, last_snapshot: int, cell: List[float] + ) -> None: + """Writes a cp2k input file from a template. + + Importantly, it writes the location of the basis set definitions, + determined from the path of the system CP2K install to the input file. + """ + + cp2k_in = open("reftraj_template.cp2k", "r").read() + + cp2k_in = cp2k_in.replace("//PROJECT//", project_name) + cp2k_in = cp2k_in.replace("//LAST_SNAPSHOT//", str(last_snapshot)) + cp2k_in = cp2k_in.replace("//CELL//", " ".join([f"{c:.6f}" for c in cell])) + + with open(fname, "w") as f: + f.write(cp2k_in) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 152-154 + +We will now download basis set files from CP2K website. Depending on your CP2K +installation, this might not be necessary! + +.. GENERATED FROM PYTHON SOURCE LINES 155-173 + +.. code-block:: Python + + + + def download_parameter(file): + path = os.path.join("parameters", file) + + if not os.path.exists(path): + url = f"https://raw.githubusercontent.com/cp2k/cp2k/support/v2024.1/data/{file}" + response = requests.get(url) + response.raise_for_status() + with open(path, "wb") as f: + f.write(response.content) + + + os.makedirs("parameters", exist_ok=True) + for file in ["GTH_BASIS_SETS", "BASIS_ADMM", "POTENTIAL", "dftd3.dat", "t_c_g.dat"]: + download_parameter(file) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 174-186 + +Prepare calculation inputs +-------------------------- +During this example we will create a directory named ``project_directory`` containing +the subdirectories for each stoichiometry. This is necessary, because CP2K can only +run calculations using a fixed stoichiometry at a time, using its ``reftraj`` +functionality. + +Below we define the general information for the CP2K run. This includes the reference +files for the structures, the ``project_name`` used to build the name of the +trajectory during the CP2K run, the ``project_directory`` where we store all +simulation output as well as the path ``write_to_file`` which is the name of the file +containing the computed energies and forces of the simulation. + +.. GENERATED FROM PYTHON SOURCE LINES 186-192 + +.. code-block:: Python + + + frames_full = ase.io.read("example.xyz", ":") + project_name = "test_calcs" # name of the global PROJECT + project_directory = "production" + write_to_file = "out.xyz" + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 193-195 + +Below we show the initial configuration of two water molecules in a cubic box with a +side length of :math:`\approx 4\,\mathrm{Å}`. + +.. GENERATED FROM PYTHON SOURCE LINES 195-203 + +.. code-block:: Python + + + ase.visualize.plot.plot_atoms(frames_full[0]) + + plt.xlabel("Å") + plt.ylabel("Å") + + plt.show() + + + + +.. image-sg:: /examples/batch-cp2k/images/sphx_glr_reference-trajectory_001.png + :alt: reference trajectory + :srcset: /examples/batch-cp2k/images/sphx_glr_reference-trajectory_001.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 204-206 + +We now extract the stoichiometry from the input dataset using ASE's +:py:meth:`ase.symbols.Symbols.get_chemical_formula` method. + +.. GENERATED FROM PYTHON SOURCE LINES 206-218 + +.. code-block:: Python + + + frames_dict = {} + + for atoms in frames_full: + chemical_formula = atoms.get_chemical_formula() + try: + frames_dict[chemical_formula] + except KeyError: + frames_dict[chemical_formula] = [] + + frames_dict[chemical_formula].append(atoms) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 219-223 + +Based on the stoichiometries we create one calculation subdirectories for the +calculations. (reftraj, input and cellfile). For our example this is only is one +directory named ``H4O2`` because our dataset consists only of a single structure with +two water molecules. + +.. GENERATED FROM PYTHON SOURCE LINES 223-239 + +.. code-block:: Python + + + for stoichiometry, frames in frames_dict.items(): + current_directory = f"{project_directory}/{stoichiometry}" + os.makedirs(current_directory, exist_ok=True) + + write_cp2k_in( + f"{current_directory}/in.cp2k", + project_name=project_name, + last_snapshot=len(frames), + cell=frames[0].cell.diagonal(), + ) + + ase.io.write(f"{current_directory}/init.xyz", frames[0]) + write_reftraj(f"{current_directory}/reftraj.xyz", frames) + write_cellfile(f"{current_directory}/reftraj.cell", frames) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 240-250 + +Run simulations +--------------- +Now we have all ingredients to run the simulations. Below we call the bash script +:download:`run_calcs.sh`. + +.. literalinclude:: run_calcs.sh + :language: bash + +This script will loop through all stoichiometry subdirectories and call the CP2K +engine. + +.. GENERATED FROM PYTHON SOURCE LINES 250-254 + +.. code-block:: Python + + + # run the bash script directly from this script + subprocess.run("bash run_calcs.sh", shell=True) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + CompletedProcess(args='bash run_calcs.sh', returncode=0) + + + +.. GENERATED FROM PYTHON SOURCE LINES 255-264 + +.. note:: + + For a usage on an HPC environment you can parallelize the loop over the + sub-directories and submit and single job per stoichiometry. + +Load results +------------ +After the simulation we load the results and perform a unit version from the default +CP2K output units (Bohr and Hartree) to Å and eV. + +.. GENERATED FROM PYTHON SOURCE LINES 264-269 + +.. code-block:: Python + + + cflength = 0.529177210903 # Bohr -> Å + cfenergy = 27.211386245988 # Hartree -> eV + cfforce = cfenergy / cflength # Hartree/Bohr -> eV/Å + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 270-273 + +Finally, we store the results as :class:`ase.Atoms` in the ``new_frames`` list and +write them to the ``project_directory`` using the ``new_fname``. Here it will be +written to ``production/out_dft.xyz``. + +.. GENERATED FROM PYTHON SOURCE LINES 273-305 + +.. code-block:: Python + + + new_frames = [] + + for stoichiometry, frames in frames_dict.items(): + current_directory = f"{project_directory}/{stoichiometry}" + + frames_dft = ase.io.read(f"{current_directory}/{project_name}-pos-1.xyz", ":") + forces_dft = ase.io.read(f"{current_directory}/{project_name}-frc-1.xyz", ":") + cell_dft = np.atleast_2d(np.loadtxt(f"{current_directory}/{project_name}-1.cell"))[ + :, 2:-1 + ] + + for i_atoms, atoms in enumerate(frames_dft): + frames_ref = frames[i_atoms] + + # Check consistent positions + if not np.allclose(atoms.positions, frames_ref.positions): + raise ValueError(f"Positions in frame {i_atoms} are not the same.") + + # Check consistent cell + if not np.allclose(frames_ref.cell.flatten(), cell_dft[i_atoms]): + raise ValueError(f"Cell dimensions in frame {i_atoms} are not the same.") + + atoms.info["E"] *= cfenergy + atoms.pbc = True + atoms.cell = frames_ref.cell + atoms.set_array("forces", cfforce * forces_dft[i_atoms].positions) + + new_frames += frames_dft + + new_fname = f"{os.path.splitext(os.path.basename(write_to_file))[0]}_dft.xyz" + ase.io.write(f"{project_directory}/{new_fname}", new_frames) + + + + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (0 minutes 31.608 seconds) + + +.. _sphx_glr_download_examples_batch-cp2k_reference-trajectory.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: reference-trajectory.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: reference-trajectory.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: reference-trajectory.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/dos-align/dos-align.rst.txt b/_sources/examples/dos-align/dos-align.rst.txt new file mode 100644 index 00000000..0c84c2f7 --- /dev/null +++ b/_sources/examples/dos-align/dos-align.rst.txt @@ -0,0 +1,1458 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/dos-align/dos-align.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_dos-align_dos-align.py: + + +A ML model for the electron density of states +============================================= +:Authors: How Wei Bin `@HowWeiBin `_ + +This tutorial would go through the entire machine learning framework for the electronic +density of states (DOS). It will cover the construction of the DOS and SOAP +descriptors from ase Atoms and eigenenergy results. A simple neural network will +then be constructed and the model parameters, along with the energy reference will be +optimized during training. A total of three energy reference will be used, the average +Hartree potential, the Fermi level, and an optimized energy reference starting from +the Fermi level energy reference. The performance of each model is then compared. + +First, lets begin by importing the necessary packages and helper functions + +.. GENERATED FROM PYTHON SOURCE LINES 18-34 + +.. code-block:: Python + + + import os + import zipfile + + import ase + import ase.io + import matplotlib.pyplot as plt + import numpy as np + import requests + import torch + from rascaline import SoapPowerSpectrum + from scipy.interpolate import CubicHermiteSpline, interp1d + from scipy.optimize import brentq + from torch.utils.data import BatchSampler, DataLoader, Dataset, RandomSampler + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 35-46 + +Step 0: Load Structures and Eigenenergies +------------------------------------------------ +1) Downloading and Extracting Data +2) Loading Data +3) Find range of eigenenergies + +We take a small subset of 104 structures in the Si dataset from `Bartok et al., +2018 `. +Each structure in the dataset contains two atoms. + + + +.. GENERATED FROM PYTHON SOURCE LINES 50-52 + +1) Downloading and Extracting Data +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 52-62 + +.. code-block:: Python + + filename = "dataset.zip" + if not os.path.exists(filename): + url = "https://github.com/HowWeiBin/datasets/archive/refs/tags/Silicon-Diamonds.zip" + response = requests.get(url) + response.raise_for_status() + with open(filename, "wb") as f: + f.write(response.content) + + with zipfile.ZipFile("./dataset.zip", "r") as zip_ref: + zip_ref.extractall("./") + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 63-65 + +2) Loading Data +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 65-74 + +.. code-block:: Python + + structures = ase.io.read("./datasets-Silicon-Diamonds/diamonds.xyz", ":") + n_structures = len(structures) + n_atoms = torch.tensor([len(i) for i in structures]) + eigenenergies = torch.load("./datasets-Silicon-Diamonds/diamond_energies.pt") + k_normalization = torch.tensor( + [len(i) for i in eigenenergies] + ) # Calculates number of kpoints sampled per structure + print(f"Total number of structures: {len(structures)}") + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + /home/runner/work/atomistic-cookbook/atomistic-cookbook/examples/dos-align/dos-align.py:68: FutureWarning: You are using `torch.load` with `weights_only=False` (the current default value), which uses the default pickle module implicitly. It is possible to construct malicious pickle data which will execute arbitrary code during unpickling (See https://github.com/pytorch/pytorch/blob/main/SECURITY.md#untrusted-models for more details). In a future release, the default value for `weights_only` will be flipped to `True`. This limits the functions that could be executed during unpickling. Arbitrary objects will no longer be allowed to be loaded via this mode unless they are explicitly allowlisted by the user via `torch.serialization.add_safe_globals`. We recommend you start setting `weights_only=True` for any use case where you don't have full control of the loaded file. Please open an issue on GitHub for any issues related to this experimental feature. + eigenenergies = torch.load("./datasets-Silicon-Diamonds/diamond_energies.pt") + Total number of structures: 104 + + + + +.. GENERATED FROM PYTHON SOURCE LINES 75-77 + +3) Find range of eigenenergies +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 77-89 + +.. code-block:: Python + + + # Process eigenenergies to flattened torch tensors + + total_eigenenergies = [torch.flatten(torch.tensor(i)) for i in eigenenergies] + + # Get lowest and highest value of eigenenergies to know the range of eigenenergies + + all_eigenenergies = torch.hstack(total_eigenenergies) + minE = torch.min(all_eigenenergies) + maxE = torch.max(all_eigenenergies) + print(f"The lowest eigenenergy in the dataset is {minE:.3}") + print(f"The highest eigenenergy in the dataset is {maxE:.3}") + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + The lowest eigenenergy in the dataset is -20.5 + The highest eigenenergy in the dataset is 8.65 + + + + +.. GENERATED FROM PYTHON SOURCE LINES 90-100 + +Step 1: Constructing the DOS with different energy references +------------------------------------------------------------------------------------------ +1) Construct the DOS using the original reference +2) Calculate the Fermi level from the DOS +3) Build a set of eigenenergies, with the energy reference set to the fermi level +4) Truncate the DOS energy window so that the DOS is well-defined at each point +5) Construct the DOS in the truncated energy window under both references +6) Construct Splines for the DOS to facilitate interpolation during model training + +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 103-108 + +1) Construct the DOS using the original reference +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +The DOS will first be constructed from the full set of eigenenergies to +determine the Fermi level of each structure. The original reference is the +Average Hartree Potential in this example. + +.. GENERATED FROM PYTHON SOURCE LINES 108-150 + +.. code-block:: Python + + + # To ensure that all the eigenenergies are fully represented after + # gaussian broadening, the energy axis of the DOS extends + # 3eV wider than the range of values for the eigenenergies + energy_lower_bound = minE - 1.5 + energy_upper_bound = maxE + 1.5 + + # Gaussian Smearing for the eDOS, 0.3eV is the appropriate value for this dataset + + sigma = torch.tensor(0.3) + energy_interval = 0.05 + # energy axis, with a grid interval of 0.05 eV + + x_dos = torch.arange(energy_lower_bound, energy_upper_bound, energy_interval) + print( + f"The energy axis ranges from {energy_lower_bound:.3} to \ + {energy_upper_bound:.3}, consisting of {len(x_dos)} grid points" + ) + + # normalization factor for each DOS, factor of 2 is included + # because each eigenenergy can be occupied by 2 electrons + + normalization = 2 * ( + 1 / torch.sqrt(2 * torch.tensor(np.pi) * sigma**2) / n_atoms / k_normalization + ) + + total_edos = [] + + for structure_eigenenergies in total_eigenenergies: + e_dos = torch.sum( + # Builds a gaussian on each eigenenergy + # and calculates the value on each grid point + torch.exp(-0.5 * ((x_dos - structure_eigenenergies.view(-1, 1)) / sigma) ** 2), + dim=0, + ) + total_edos.append(e_dos) + + total_edos = torch.vstack(total_edos) + total_edos = (total_edos.T * normalization).T + + print(f"The final shape of all the DOS in the dataset is: {list(total_edos.shape)}") + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + The energy axis ranges from -22.0 to 10.1, consisting of 644 grid points + The final shape of all the DOS in the dataset is: [104, 644] + + + + +.. GENERATED FROM PYTHON SOURCE LINES 151-157 + +2) Calculate the Fermi level from the DOS +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Now we integration the DOS, and then use cubic interpolation and brentq +to calculate the fermi level. Since only the 4 valence electrons in Silicon +are represented in this energy range, we take the point where the DOS integrates +to 4 as the fermi level. + +.. GENERATED FROM PYTHON SOURCE LINES 157-172 + +.. code-block:: Python + + + fermi_levels = [] + total_i_edos = torch.cumulative_trapezoid( + total_edos, x_dos, axis=1 + ) # Integrate the DOS along the energy axis + for i in total_i_edos: + interpolated = interp1d( + x_dos[:-1], i - 4, kind="cubic", copy=True, assume_sorted=True + ) # We use i-4 because Silicon has 4 electrons in this energy range + Ef = brentq( + interpolated, x_dos[0] + 0.1, x_dos[-1] - 0.1 + ) # Fermi Level is the point where the (integrated DOS - 4) = 0 + # 0.1 is added and subtracted to prevent brentq from going out of range + fermi_levels.append(Ef) + fermi_levels = torch.tensor(fermi_levels) + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 173-177 + +3) Build a set of eigenenergies, with the energy reference set to the fermi level +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Using the fermi levels, we are now able to change the energy reference +of the eigenenergies to the fermi level + +.. GENERATED FROM PYTHON SOURCE LINES 177-190 + +.. code-block:: Python + + + total_eigenenergies_Ef = [] + for index, energies in enumerate(total_eigenenergies): + total_eigenenergies_Ef.append(energies - fermi_levels[index]) + + all_eigenenergies_Ef = torch.hstack(total_eigenenergies_Ef) + + minE_Ef = torch.min(all_eigenenergies_Ef) + maxE_Ef = torch.max(all_eigenenergies_Ef) + print(f"The lowest eigenenergy using the fermi level energy reference is {minE_Ef:.3}") + print(f"The highest eigenenergy using the fermi level energy reference is {maxE_Ef:.3}") + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + The lowest eigenenergy using the fermi level energy reference is -13.8 + The highest eigenenergy using the fermi level energy reference is 14.9 + + + + +.. GENERATED FROM PYTHON SOURCE LINES 191-196 + +4) Truncate the DOS energy window so that the DOS is well-defined at each point +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +With the fermi levels, we can also truncate the energy window for DOS prediction. +In this example, we truncate the energy window such that it is 3eV above +the highest Fermi level in the dataset. + +.. GENERATED FROM PYTHON SOURCE LINES 196-202 + +.. code-block:: Python + + + # For the Average Hartree Potential energy reference + x_dos_H = torch.arange(minE - 1.5, max(fermi_levels) + 3, energy_interval) + + # For the Fermi Level Energy Reference, all the Fermi levels in the dataset is 0eV + x_dos_Ef = torch.arange(minE_Ef - 1.5, 3, energy_interval) + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 203-208 + +5) Construct the DOS in the truncated energy window under both references +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Here we construct 2 different targets where they differ in the energy reference +chosen. These targets will then be treated as different datasets for the model +to learn on. + +.. GENERATED FROM PYTHON SOURCE LINES 208-242 + +.. code-block:: Python + + + # For the Average Hartree Potential energy reference + + total_edos_H = [] + + for structure_eigenenergies_H in total_eigenenergies: + e_dos = torch.sum( + torch.exp( + -0.5 * ((x_dos_H - structure_eigenenergies_H.view(-1, 1)) / sigma) ** 2 + ), + dim=0, + ) + total_edos_H.append(e_dos) + + total_edos_H = torch.vstack(total_edos_H) + total_edos_H = (total_edos_H.T * normalization).T + + + # For the Fermi Level Energy Reference + + total_edos_Ef = [] + + for structure_eigenenergies_Ef in total_eigenenergies_Ef: + e_dos = torch.sum( + torch.exp( + -0.5 * ((x_dos_Ef - structure_eigenenergies_Ef.view(-1, 1)) / sigma) ** 2 + ), + dim=0, + ) + total_edos_Ef.append(e_dos) + + total_edos_Ef = torch.vstack(total_edos_Ef) + total_edos_Ef = (total_edos_Ef.T * normalization).T + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 243-249 + +6) Construct Splines for the DOS to facilitate interpolation during model training +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Building Cubic Hermite Splines on the DOS on the truncated energy window +to facilitate interpolation during training. Cubic Hermite Splines takes +in information on the value and derivative of a function at a point to build splines. +Thus, we will have to compute both the value and derivative at each spline position + +.. GENERATED FROM PYTHON SOURCE LINES 249-308 + +.. code-block:: Python + + + + # Functions to compute the value and derivative of the DOS at each energy value, x + def edos_value(x, eigenenergies, normalization): + e_dos_E = ( + torch.sum( + torch.exp(-0.5 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2), dim=0 + ) + * normalization + ) + + return e_dos_E + + + def edos_derivative(x, eigenenergies, normalization): + dfn_dos_E = ( + torch.sum( + torch.exp(-0.5 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2) + * (-1 * ((x - eigenenergies.view(-1, 1)) / sigma) ** 2), + dim=0, + ) + * normalization + ) + + return dfn_dos_E + + + total_splines_H = [] + # the splines have a higher energy range in case the shift is high + spline_positions_H = torch.arange(minE - 2, max(fermi_levels) + 6, energy_interval) + + for index, structure_eigenenergies_H in enumerate(total_eigenenergies): + e_dos_H = edos_value( + spline_positions_H, structure_eigenenergies_H, normalization[index] + ) + e_dos_H_grad = edos_derivative( + spline_positions_H, structure_eigenenergies_H, normalization[index] + ) + spliner = CubicHermiteSpline(spline_positions_H, e_dos_H, e_dos_H_grad) + total_splines_H.append(torch.tensor(spliner.c)) + + total_splines_H = torch.stack(total_splines_H) + + total_splines_Ef = [] + spline_positions_Ef = torch.arange(minE_Ef - 2, 6, energy_interval) + + for index, structure_eigenenergies_Ef in enumerate(total_eigenenergies_Ef): + e_dos_Ef = edos_value( + spline_positions_Ef, structure_eigenenergies_Ef, normalization[index] + ) + e_dos_Ef_grad = edos_derivative( + spline_positions_Ef, structure_eigenenergies_Ef, normalization[index] + ) + spliner = CubicHermiteSpline(spline_positions_Ef, e_dos_Ef, e_dos_Ef_grad) + total_splines_Ef.append(torch.tensor(spliner.c)) + + total_splines_Ef = torch.stack(total_splines_Ef) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 309-312 + +We have stored the splines coefficients (spliner.c) as torch tensors, +as such as we will need to write a function to evaluate the DOS from +the splines positions and coefficients. + +.. GENERATED FROM PYTHON SOURCE LINES 312-345 + +.. code-block:: Python + + + + def evaluate_spline(spline_coefs, spline_positions, x): + """ + spline_coefs: shape of (n x 4 x spline_positions) + + return value: shape of (n x x) + + x : shape of (n x n_points) + """ + interval = torch.round( + spline_positions[1] - spline_positions[0], decimals=4 + ) # get spline grid intervals + x = torch.clamp( + x, min=spline_positions[0], max=spline_positions[-1] - 0.0005 + ) # restrict x to fall within the spline interval + # 0.0005 is substracted to combat errors arising from precision + indexes = torch.floor( + (x - spline_positions[0]) / interval + ).long() # Obtain the index for the appropriate spline coefficients + expanded_index = indexes.unsqueeze(dim=1).expand(-1, 4, -1) + x_1 = x - spline_positions[indexes] + x_2 = x_1 * x_1 + x_3 = x_2 * x_1 + x_0 = torch.ones_like(x_1) + x_powers = torch.stack([x_3, x_2, x_1, x_0]).permute(1, 0, 2) + value = torch.sum( + torch.mul(x_powers, torch.gather(spline_coefs, 2, expanded_index)), axis=1 + ) + + return value # returns the value of the DOS at the energy positions, x. + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 346-348 + +Lets look at the accuracy of the splines. +Test 1: Ability to reproduce the correct values at the default x_dos positions + +.. GENERATED FROM PYTHON SOURCE LINES 348-359 + +.. code-block:: Python + + + shifts = torch.zeros(n_structures) + x_dos_splines = x_dos_H + shifts.view(-1, 1) + spline_dos_H = evaluate_spline(total_splines_H, spline_positions_H, x_dos_splines) + + plt.plot(x_dos_H, total_edos_H[0], color="red", label="True DOS") + plt.plot(x_dos_H, spline_dos_H[0], color="blue", linestyle="--", label="Spline DOS") + plt.legend() + plt.xlabel("Energy [eV]") + plt.ylabel("DOS") + print("Both lines lie on each other") + + + +.. image-sg:: /examples/dos-align/images/sphx_glr_dos-align_001.png + :alt: dos align + :srcset: /examples/dos-align/images/sphx_glr_dos-align_001.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Both lines lie on each other + + + + +.. GENERATED FROM PYTHON SOURCE LINES 360-361 + +Test 2: Ability to reproduce the correct values at the shifted x_dos positions + +.. GENERATED FROM PYTHON SOURCE LINES 361-372 + +.. code-block:: Python + + + shifts = torch.zeros(n_structures) + 0.3 + x_dos_splines = x_dos_Ef + shifts.view(-1, 1) + spline_dos_Ef = evaluate_spline(total_splines_Ef, spline_positions_Ef, x_dos_splines) + + plt.plot(x_dos_Ef, total_edos_Ef[0], color="red", label="True DOS") + plt.plot(x_dos_Ef, spline_dos_Ef[0], color="blue", linestyle="--", label="Spline DOS") + plt.legend() + plt.xlabel("Energy [eV]") + plt.ylabel("DOS") + print("Both spectras look very similar") + + + +.. image-sg:: /examples/dos-align/images/sphx_glr_dos-align_002.png + :alt: dos align + :srcset: /examples/dos-align/images/sphx_glr_dos-align_002.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Both spectras look very similar + + + + +.. GENERATED FROM PYTHON SOURCE LINES 373-378 + +Step 2: Compute SOAP power spectrum for the dataset +------------------------------------------------------------------------------------------ + +We first define the hyperparameters to compute the +SOAP power spectrum using rascaline. + +.. GENERATED FROM PYTHON SOURCE LINES 379-399 + +.. code-block:: Python + + + HYPER_PARAMETERS = { + "cutoff": 4.0, + "max_radial": 8, + "max_angular": 6, + "atomic_gaussian_width": 0.45, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {}}, + "cutoff_function": { + "Step": {}, + }, + "radial_scaling": { + "Willatt2018": { + "exponent": 5, + "rate": 1, + "scale": 3.0, + }, + }, + } + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 400-401 + +We feed the Hyperparameters into rascaline to compute the SOAP Power spectrum + +.. GENERATED FROM PYTHON SOURCE LINES 402-417 + +.. code-block:: Python + + + + calculator = SoapPowerSpectrum(**HYPER_PARAMETERS) + R_total_soap = calculator.compute(structures) + # Transform the tensormap to a single block containing a dense representation + R_total_soap.keys_to_samples("species_center") + R_total_soap.keys_to_properties(["species_neighbor_1", "species_neighbor_2"]) + + # Now we extract the data tensor from the single block + total_atom_soap = [] + for structure_i in range(n_structures): + a_i = R_total_soap.block(0).samples["structure"] == structure_i + total_atom_soap.append(torch.tensor(R_total_soap.block(0).values[a_i, :])) + + total_soap = torch.stack(total_atom_soap) + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 418-428 + +Step 3: Building a Simple MLP Model +--------------------------------------------------------------------- + +1) Split the data into Training, Validation and Test +2) Define the dataloader and the Model Architecture +3) Define relevant loss functions for training and inference +4) Define the training loop +5) Evaluate the model + +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. GENERATED FROM PYTHON SOURCE LINES 431-434 + +1) Split the data into Training, Validation and Test +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +We will first split the data in a 7:1:2 manner, corresponding to train, val and test. + +.. GENERATED FROM PYTHON SOURCE LINES 434-443 + +.. code-block:: Python + + np.random.seed(0) + train_index = np.arange(n_structures) + np.random.shuffle(train_index) + test_mark = int(0.8 * n_structures) + val_mark = int(0.7 * n_structures) + test_index = train_index[test_mark:] + val_index = train_index[val_mark:test_mark] + train_index = train_index[:val_mark] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 444-447 + +2) Define the dataloader and the Model Architecture +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +We will now build a dataloader and dataset to facillitate training the model batchwise + +.. GENERATED FROM PYTHON SOURCE LINES 447-523 + +.. code-block:: Python + + + + def generate_atomstructure_index(n_atoms_per_structure): + """Generate a sequence of indices for each atom in the structure. + The indices correspond to index of the structure that the atom belongs to + + Args: + n_atoms_per_structure ([array]): + [Array containing the number of atoms each structure contains] + + Return s: + [tensor]: [Total index, matching atoms to structure] + """ + # n_structures = len(n_atoms_per_structure) + total_index = [] + for i, atoms in enumerate(n_atoms_per_structure): + indiv_index = torch.zeros(atoms) + i + total_index.append(indiv_index) + total_index = torch.hstack(total_index) + return total_index.long() + + + class AtomicDataset(Dataset): + def __init__(self, features, n_atoms_per_structure): + self.features = features + self.n_structures = len(n_atoms_per_structure) + self.n_atoms_per_structure = n_atoms_per_structure + self.index = generate_atomstructure_index(self.n_atoms_per_structure) + assert torch.sum(n_atoms_per_structure) == len(features) + + def __len__(self): + return self.n_structures + + def __getitem__(self, idx): + if isinstance(idx, list): # If a list of indexes is given + feature_indexes = [] + + for i in idx: + feature_indexes.append((self.index == i).nonzero(as_tuple=True)[0]) + + feature_indexes = torch.hstack(feature_indexes) + + return ( + self.features[feature_indexes], + idx, + generate_atomstructure_index(self.n_atoms_per_structure[idx]), + ) + + else: + feature_indexes = (self.index == idx).nonzero(as_tuple=True)[0] + return ( + self.features[feature_indexes], + idx, + self.n_atoms_per_structure[idx], + ) + + + def collate( + batch, + ): # Defines how to collate the outputs of the __getitem__ function at each batch + for x, idx, index in batch: + return (x, idx, index) + + + x_train = torch.flatten(total_soap[train_index], 0, 1).float() + total_atomic_soaps = torch.vstack(total_atom_soap).float() + train_features = AtomicDataset(x_train, n_atoms[train_index]) + full_atomstructure_index = generate_atomstructure_index(n_atoms) + # Will be required later to collate atomic predictions into structural predictions + + # Build a Dataloader that samples from the AtomicDataset in random batches + Sampler = RandomSampler(train_features) + BSampler = BatchSampler(Sampler, batch_size=32, drop_last=False) + traindata_loader = DataLoader(train_features, sampler=BSampler, collate_fn=collate) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 524-529 + +We will now define a simple three layer MLP model, consisting of three layers. +The align keyword is used to indicate that the energy reference will be optimized +during training. The alignment parameter refers to the adjustments made to the +initial energy referenced and will be initialized as zeros. + + +.. GENERATED FROM PYTHON SOURCE LINES 530-551 + +.. code-block:: Python + + + + class SOAP_NN(torch.nn.Module): + def __init__(self, input_dims, L1, n_train, target_dims, align): + super(SOAP_NN, self).__init__() + self.target_dims = target_dims + self.fc1 = torch.nn.Linear(input_dims, L1) + self.fc2 = torch.nn.Linear(L1, target_dims) + self.silu = torch.nn.SiLU() + self.align = align + if align: + initial_alignment = torch.zeros(n_train) + self.alignment = torch.nn.parameter.Parameter(initial_alignment) + + def forward(self, x): + result = self.fc1(x) + result = self.silu(result) + result = self.fc2(result) + return result + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 552-560 + +We will use a small network architecture, whereby the input layer corresponds +to the size of the SOAP features, 448, the intermediate layer corresponds to +a tenth size of the input layer and the final layer corresponds +to the number of outputs. + +As a shorthand, the model that optimizes the energy reference during +training will be called the alignment model + + +.. GENERATED FROM PYTHON SOURCE LINES 560-588 + +.. code-block:: Python + + + n_outputs_H = len(x_dos_H) + n_outputs_Ef = len(x_dos_Ef) + + + Model_H = SOAP_NN( + x_train.shape[1], + x_train.shape[1] // 10, + len(train_index), + n_outputs_H, + align=False, + ) + Model_Ef = SOAP_NN( + x_train.shape[1], + x_train.shape[1] // 10, + len(train_index), + n_outputs_Ef, + align=False, + ) + Model_Align = SOAP_NN( + x_train.shape[1], + x_train.shape[1] // 10, + len(train_index), + n_outputs_Ef, + align=True, + ) + # The alignment model takes the fermi level energy reference as the starting point + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 589-593 + +3) Define relevant loss functions for training and inference +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +We will now define some loss functions that will be useful when we implement +the model training loop later and during model evaluation on the test set. + +.. GENERATED FROM PYTHON SOURCE LINES 593-708 + +.. code-block:: Python + + + + def t_get_mse(a, b, xdos): + """Compute mean error between two Density of States. + The mean error is integrated across the entire energy grid + to provide a single value to characterize the error + + Args: + a ([tensor]): [Predicted DOS] + b ([tensor]): [True DOS] + xdos ([tensor], optional): [Energy axis of DOS] + + Returns: + [float]: [MSE] + """ + if len(a.size()) > 1: + mse = (torch.trapezoid((a - b) ** 2, xdos, axis=1)).mean() + else: + mse = (torch.trapezoid((a - b) ** 2, xdos, axis=0)).mean() + return mse + + + def t_get_rmse(a, b, xdos): + """Compute root mean squared error between two Density of States . + + Args: + a ([tensor]): [Predicted DOS] + b ([tensor]): [True DOS] + xdos ([tensor], optional): [Energy axis of DOS] + + Raises: + ValueError: [Occurs if tensor shapes are mismatched] + + Returns: + [float]: [RMSE or %RMSE] + """ + + if len(a.size()) > 1: + rmse = torch.sqrt((torch.trapezoid((a - b) ** 2, xdos, axis=1)).mean()) + else: + rmse = torch.sqrt((torch.trapezoid((a - b) ** 2, xdos, axis=0)).mean()) + return rmse + + + def Opt_RMSE_spline(y_pred, xdos, target_splines, spline_positions, n_epochs): + """Evaluates RMSE on the optimal shift of energy axis. + The optimal shift is found via gradient descent after a gridsearch is performed. + + Args: + y_pred ([tensor]): [Prediction/s of DOS] + xdos ([tensor]): [Energy axis] + target_splines ([tensor]): [Contains spline coefficients] + spline_positions ([tensor]): [Contains spline positions] + n_epochs ([int]): [Number of epochs to run for Gradient Descent] + + Returns: + [rmse([float]), optimal_shift[tensor]]: + [RMSE on optimal shift, the optimal shift itself] + + """ + optim_search_mse = [] + offsets = torch.arange(-2, 2, 0.1) + # Grid-search is first done to reduce number of epochs needed for + # gradient descent, typically 50 epochs will be sufficient + # if searching within 0.1 + with torch.no_grad(): + for offset in offsets: + shifts = torch.zeros(y_pred.shape[0]) + offset + shifted_target = evaluate_spline( + target_splines, spline_positions, xdos + shifts.view(-1, 1) + ) + loss_i = ((y_pred - shifted_target) ** 2).mean(dim=1) + optim_search_mse.append(loss_i) + optim_search_mse = torch.vstack(optim_search_mse) + min_index = torch.argmin(optim_search_mse, dim=0) + optimal_offset = offsets[min_index] + + offset = optimal_offset + + shifts = torch.nn.parameter.Parameter(offset.float()) + opt_adam = torch.optim.Adam([shifts], lr=1e-2) + best_error = torch.zeros(len(shifts)) + 100 + best_shifts = shifts.clone() + for _ in range(n_epochs): + shifted_target = evaluate_spline( + target_splines, spline_positions, xdos + shifts.view(-1, 1) + ).detach() + + def closure(): + opt_adam.zero_grad() + shifted_target = evaluate_spline( + target_splines, spline_positions, xdos + shifts.view(-1, 1) + ) + loss_i = ((y_pred - shifted_target) ** 2).mean() + loss_i.backward(gradient=torch.tensor(1), inputs=shifts) + return loss_i + + opt_adam.step(closure) + + with torch.no_grad(): + each_loss = ((y_pred - shifted_target) ** 2).mean(dim=1).float() + index = each_loss < best_error + best_error[index] = each_loss[index].clone() + best_shifts[index] = shifts[index].clone() + + # Evaluate + + optimal_shift = best_shifts + shifted_target = evaluate_spline( + target_splines, spline_positions, xdos + optimal_shift.view(-1, 1) + ) + rmse = t_get_rmse(y_pred, shifted_target, xdos) + return rmse, optimal_shift + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 709-715 + +4) Define the training loop +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +We will now define the model training loop, for simplicity we will only +train each model for a fixed number of epochs, learning rate, and batch_size. +The training and validation error at each epoch will be saved. + +.. GENERATED FROM PYTHON SOURCE LINES 716-821 + +.. code-block:: Python + + + + def train_model(model_to_train, fixed_DOS, structure_splines, spline_positions, x_dos): + """Trains a model for 500 epochs + + Args: + model_to_train ([torch.nn.Module]): [ML Model] + fixed_DOS ([tensor]): [Contains the DOS at a fixed energy reference, + useful for models that don't optimize the energy reference] + structure_splines ([tensor]): [Contains spline coefficients] + spline_positions ([tensor]): [Contains spline positions] + x_dos ([tensor]): [Energy axis for the prediction] + + Returns: + [train_loss_history([tensor]), + val_loss_history[tensor], + structure_results[tensor]]: + + [Respective loss histories and final structure predictions] + """ + lr = 1e-2 + n_epochs = 500 + + opt = torch.optim.Adam(model_to_train.parameters(), lr=lr) + + train_loss_history = [] + val_loss_history = [] + + for _epoch in range(n_epochs): + for x_data, idx, index in traindata_loader: + opt.zero_grad() + predictions = model_to_train.forward(x_data) + structure_results = torch.zeros([len(idx), model_to_train.target_dims]) + # Sum atomic predictions in each structure + structure_results = structure_results.index_add_( + 0, index, predictions + ) / n_atoms[train_index[idx]].view(-1, 1) + if model_to_train.align: + alignment = model_to_train.alignment + alignment = alignment - torch.mean(alignment) + # Enforce that the alignments have a mean of zero since a constant + # value across the dataset is meaningless when optimizing the + # relative energy reference + target = evaluate_spline( + structure_splines[train_index[idx]], + spline_positions, + x_dos + alignment[idx].view(-1, 1), + ) # Shifts the target based on the alignment value + pred_loss = t_get_mse(structure_results, target, x_dos) + pred_loss.backward() + else: + pred_loss = t_get_mse( + structure_results, fixed_DOS[train_index[idx]], x_dos + ) + pred_loss.backward() + + opt.step() + with torch.no_grad(): + all_pred = model_to_train.forward(total_atomic_soaps.float()) + structure_results = torch.zeros([n_structures, model_to_train.target_dims]) + structure_results = structure_results.index_add_( + 0, full_atomstructure_index, all_pred + ) / (n_atoms).view(-1, 1) + if model_to_train.align: + # Evaluate model on optimal shift as there is no information + # regarding the shift from the fermi level energy reference + # during inference + + alignment = model_to_train.alignment + alignment = alignment - torch.mean(alignment) + target = evaluate_spline( + structure_splines[train_index], + spline_positions, + x_dos + alignment.view(-1, 1), + ) + + train_loss = t_get_rmse(structure_results[train_index], target, x_dos) + val_loss, val_shifts = Opt_RMSE_spline( + structure_results[val_index], + x_dos, + structure_splines[val_index], + spline_positions, + 50, + ) + + else: + train_loss = t_get_rmse( + structure_results[train_index], fixed_DOS[train_index], x_dos + ) + val_loss = t_get_rmse( + structure_results[val_index], fixed_DOS[val_index], x_dos + ) + + train_loss_history.append(train_loss) + val_loss_history.append(val_loss) + train_loss_history = torch.tensor(train_loss_history) + val_loss_history = torch.tensor(val_loss_history) + return ( + train_loss_history, + val_loss_history, + structure_results, + ) + # returns the loss history and the final set of predictions + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 822-834 + +.. code-block:: Python + + + H_trainloss, H_valloss, H_predictions = train_model( + Model_H, total_edos_H, total_splines_H, spline_positions_H, x_dos_H + ) + + Ef_trainloss, Ef_valloss, Ef_predictions = train_model( + Model_Ef, total_edos_Ef, total_splines_Ef, spline_positions_Ef, x_dos_Ef + ) + + Align_trainloss, Align_valloss, Align_predictions = train_model( + Model_Align, total_edos_Ef, total_splines_Ef, spline_positions_Ef, x_dos_Ef + ) + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 835-837 + +Lets plot the train loss histories to compare their learning behaviour + + +.. GENERATED FROM PYTHON SOURCE LINES 837-850 + +.. code-block:: Python + + + epochs = np.arange(500) + + + plt.plot(epochs, H_trainloss, color="red", label="Avg Hartree Potential") + plt.plot(epochs, Ef_trainloss, color="blue", label="Fermi Level") + plt.plot(epochs, Align_trainloss, color="green", label="Optimized Reference") + plt.legend() + plt.yscale(value="log") + plt.xlabel("Epochs") + plt.ylabel("RMSE") + plt.title("Train Loss vs Epoch") + plt.show() + + + +.. image-sg:: /examples/dos-align/images/sphx_glr_dos-align_003.png + :alt: Train Loss vs Epoch + :srcset: /examples/dos-align/images/sphx_glr_dos-align_003.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 851-853 + +Lets plot the val loss histories to compare their learning behaviour + + +.. GENERATED FROM PYTHON SOURCE LINES 853-866 + +.. code-block:: Python + + + + plt.plot(epochs, H_valloss, color="red", label="Avg Hartree Potential") + plt.plot(epochs, Ef_valloss, color="blue", label="Fermi Level") + plt.plot(epochs, Align_valloss, color="green", label="Optimized Reference") + plt.legend() + plt.yscale(value="log") + plt.xlabel("Epochs") + plt.ylabel("RMSE") + plt.title("Validation Loss vs Epoch") + plt.show() + + + + + +.. image-sg:: /examples/dos-align/images/sphx_glr_dos-align_004.png + :alt: Validation Loss vs Epoch + :srcset: /examples/dos-align/images/sphx_glr_dos-align_004.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 867-872 + +5) Evaluate the model +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +We will now evaluate the model performance on the test set +based on the model predictions we obtained previously + + +.. GENERATED FROM PYTHON SOURCE LINES 873-904 + +.. code-block:: Python + + + H_testloss = Opt_RMSE_spline( + H_predictions[test_index], + x_dos_H, + total_splines_H[test_index], + spline_positions_H, + 200, + ) # We use 200 epochs just so it the error a little bit more converged + Ef_testloss = Opt_RMSE_spline( + Ef_predictions[test_index], + x_dos_Ef, + total_splines_Ef[test_index], + spline_positions_Ef, + 200, + ) # We use 200 epochs just so it the error a little bit more converged + Align_testloss = Opt_RMSE_spline( + Align_predictions[test_index], + x_dos_Ef, + total_splines_Ef[test_index], + spline_positions_Ef, + 200, + ) # We use 200 epochs just so it the error a little bit more converged + + print(f"Test RMSE for average Hartree Potential: {H_testloss[0].item():.3}") + print(f"Test RMSE for Fermi Level: {Ef_testloss[0].item():.3}") + print(f"Test RMSE for Optimized Reference: {Align_testloss[0].item():.3}") + + print( + "The difference in effectiveness between the Optimized Reference \ + and the Fermi Level will increase with more epochs" + ) + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Test RMSE for average Hartree Potential: 0.0558 + Test RMSE for Fermi Level: 0.0398 + Test RMSE for Optimized Reference: 0.0378 + The difference in effectiveness between the Optimized Reference and the Fermi Level will increase with more epochs + + + + +.. GENERATED FROM PYTHON SOURCE LINES 905-914 + +Plot Training DOSes at different energy reference to visualize +the impact of the energy reference. From the plots we can see +that the optimized energy reference has better alignment of +common spectral patterns across the dataset + +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Average Hartree Energy Reference + + +.. GENERATED FROM PYTHON SOURCE LINES 915-924 + +.. code-block:: Python + + + for i in total_edos_H[train_index]: + plt.plot(x_dos_H, i, color="C0", alpha=0.6) + plt.title("Energy Reference - Average Hartree Potential") + plt.xlabel("Energy [eV]") + plt.ylabel("DOS") + plt.show() + print("The DOSes, despite looking similar, are offset along the energy axis") + + + + +.. image-sg:: /examples/dos-align/images/sphx_glr_dos-align_005.png + :alt: Energy Reference - Average Hartree Potential + :srcset: /examples/dos-align/images/sphx_glr_dos-align_005.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + The DOSes, despite looking similar, are offset along the energy axis + + + + +.. GENERATED FROM PYTHON SOURCE LINES 925-926 + +Fermi Level Energy Reference + +.. GENERATED FROM PYTHON SOURCE LINES 926-934 + +.. code-block:: Python + + for i in total_edos_Ef[train_index]: + plt.plot(x_dos_Ef, i, color="C0", alpha=0.6) + plt.title("Energy Reference - Fermi Level") + plt.xlabel("Energy [eV]") + plt.ylabel("DOS") + plt.show() + + print("It is better aligned but still quite some offset") + + + +.. image-sg:: /examples/dos-align/images/sphx_glr_dos-align_006.png + :alt: Energy Reference - Fermi Level + :srcset: /examples/dos-align/images/sphx_glr_dos-align_006.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + It is better aligned but still quite some offset + + + + +.. GENERATED FROM PYTHON SOURCE LINES 935-936 + +Optimized Energy Reference + +.. GENERATED FROM PYTHON SOURCE LINES 936-951 + +.. code-block:: Python + + shifts = Model_Align.alignment.detach() + shifts = shifts - torch.mean(shifts) + x_dos_splines = x_dos_Ef + shifts.view(-1, 1) + total_edos_align = evaluate_spline( + total_splines_Ef[train_index], spline_positions_Ef, x_dos_splines + ) + + for i in total_edos_align: + plt.plot(x_dos_Ef, i, color="C0", alpha=0.6) + plt.title("Energy Reference - Optimized") + plt.xlabel("Energy [eV]") + plt.ylabel("DOS") + plt.show() + print("The DOS alignment is better under the optimized energy reference") + print("The difference will increase with more training epochs") + + + +.. image-sg:: /examples/dos-align/images/sphx_glr_dos-align_007.png + :alt: Energy Reference - Optimized + :srcset: /examples/dos-align/images/sphx_glr_dos-align_007.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + The DOS alignment is better under the optimized energy reference + The difference will increase with more training epochs + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (1 minutes 47.626 seconds) + + +.. _sphx_glr_download_examples_dos-align_dos-align.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: dos-align.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: dos-align.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: dos-align.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/gaas-map/gaas-map.rst.txt b/_sources/examples/gaas-map/gaas-map.rst.txt new file mode 100644 index 00000000..f36ec5ca --- /dev/null +++ b/_sources/examples/gaas-map/gaas-map.rst.txt @@ -0,0 +1,453 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/gaas-map/gaas-map.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_gaas-map_gaas-map.py: + + +PCA/PCovR Visualization of a training dataset for a potential +============================================================= + +:Authors: Michele Ceriotti `@ceriottm `_, + Giulio Imbalzano + +This example uses ``rascaline`` and ``metatensor`` to compute +structural properties for the structures in a training dataset +for a ML potential. +These are then used with simple dimensionality reduction algorithms +(implemented in ``sklearn`` and ``skmatter``) to obtain a simplified +description of the dataset, that is then visualized using +``chemiscope``. + +This example uses the dataset from +`Imbalzano (2021) `_ +and the principal covariate regression scheme as implemented in +`Helfrecht (2020) `_. + +.. GENERATED FROM PYTHON SOURCE LINES 21-40 + +.. code-block:: Python + + + import os + + import ase + import ase.io + import chemiscope + import numpy as np + import requests + from matplotlib import pyplot as plt + from metatensor import mean_over_samples + from rascaline import AtomicComposition, SoapPowerSpectrum + from sklearn.decomposition import PCA + from sklearn.linear_model import RidgeCV + from skmatter.decomposition import PCovR + from skmatter.preprocessing import StandardFlexibleScaler + + + # sphinx_gallery_thumbnail_number = 2 + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 41-47 + +First, we load the structures, extracting some of the properties for +more convenient manipulation. These are +:math:`\mathrm{Ga}_x\mathrm{As}_{1-x}` structures used in `Imbalzano & +Ceriotti (2021) `__ to +train a ML potential to describe the full composition range. + + +.. GENERATED FROM PYTHON SOURCE LINES 47-61 + +.. code-block:: Python + + + filename = "gaas_training.xyz" + if not os.path.exists(filename): + url = f"https://zenodo.org/records/10566825/files/{filename}" + response = requests.get(url) + response.raise_for_status() + with open(filename, "wb") as f: + f.write(response.content) + + structures = ase.io.read(filename, ":") + energy = np.array([f.info["energy"] for f in structures]) + natoms = np.array([len(f) for f in structures]) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 62-75 + +Remove atomic energy baseline +----------------------------- + +Energies from an electronic structure calculation contain a very large +“self” contributions from the atoms, which can obscure the important +differences in cohesive energies between structures. We can build an +approximate model based on the chemical nature of the atoms, :math:`a_i` + +.. math:: E(A) = \sum_{i\in A} e_{a_i} + +where :math:`e_a` are atomic energies that can be determined by linear +regression. + + +.. GENERATED FROM PYTHON SOURCE LINES 75-98 + +.. code-block:: Python + + + # rascaline has an `AtomicComposition` calculator that streamlines + # this (simple) calculation + calculator = AtomicComposition(**{"per_structure": True}) + rho0 = calculator.compute(structures) + + # the descriptors are returned as a `TensorMap` object, that contains + # the composition data in a sparse storage format + rho0 + + # for easier manipulation, we extract the features as a dense vector + # of composition weights + comp_feats = rho0.keys_to_properties(["species_center"]).block(0).values + + # a one-liner to fit a linear model and compute "dressed energies" + atom_energy = ( + RidgeCV(alphas=np.geomspace(1e-8, 1e2, 20)) + .fit(comp_feats, energy) + .predict(comp_feats) + ) + cohesive_peratom = (energy - atom_energy) / natoms + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 99-102 + +The baseline makes up a large fraction of the total energy, but actually +the residual (which is the part that matters) is still large. + + +.. GENERATED FROM PYTHON SOURCE LINES 102-111 + +.. code-block:: Python + + + fig, ax = plt.subplots(1, 1, figsize=(6, 4)) + ax.plot(energy / natoms, atom_energy / natoms, "b.") + ax.set_xlabel("Energy / (eV/atom)") + ax.set_ylabel("Atomic e. / (eV/atom)") + plt.show() + print(f"RMSE / (eV/atom): {np.sqrt(np.mean((cohesive_peratom)**2))}") + + + + + +.. image-sg:: /examples/gaas-map/images/sphx_glr_gaas-map_001.png + :alt: gaas map + :srcset: /examples/gaas-map/images/sphx_glr_gaas-map_001.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + RMSE / (eV/atom): 0.25095652580859984 + + + + +.. GENERATED FROM PYTHON SOURCE LINES 112-119 + +Compute structural descriptors +------------------------------ + +In order to visualize the structures as a low-dimensional map, we start +by computing suitable ML descriptors. Here we have used ``rascaline`` to +evaluate average SOAP features for the structures. + + +.. GENERATED FROM PYTHON SOURCE LINES 119-146 + +.. code-block:: Python + + + # hypers for evaluating rascaline features + hypers = { + "cutoff": 4.5, + "max_radial": 6, + "max_angular": 4, + "atomic_gaussian_width": 0.3, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + "radial_basis": {"Gto": {"accuracy": 1e-6}}, + "center_atom_weight": 1.0, + } + calculator = SoapPowerSpectrum(**hypers) + rho2i = calculator.compute(structures) + + # neighbor types go to the keys for sparsity (this way one can + # compute a heterogeneous dataset without having blocks of zeros) + rho2i = rho2i.keys_to_samples(["species_center"]).keys_to_properties( + ["species_neighbor_1", "species_neighbor_2"] + ) + + # computes structure-level descriptors and then extracts + # the features as a dense array + rho2i_structure = mean_over_samples(rho2i, sample_names=["center", "species_center"]) + rho2i = None # releases memory + features = rho2i_structure.block(0).values + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 147-150 + +We standardize (per atom) energy and features (computed as a *mean* over +atomic environments) so that they can be combined on the same footings. + + +.. GENERATED FROM PYTHON SOURCE LINES 150-155 + +.. code-block:: Python + + + sf_energy = StandardFlexibleScaler().fit_transform(cohesive_peratom.reshape(-1, 1)) + sf_feats = StandardFlexibleScaler().fit_transform(features) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 156-168 + +PCA and PCovR projection +------------------------ + +Computes PCA projection to generate low-dimensional descriptors that +reflect structural diversity. Any other dimensionality reduction scheme +could be used in a similar fashion. + +We also compute the principal covariate regression (PCovR) descriptors, +that reduce dimensionality while combining a variance preserving +criterion with the requirement that the low-dimensional features are +capable of estimating a target quantity (here, the energy). + + +.. GENERATED FROM PYTHON SOURCE LINES 168-194 + +.. code-block:: Python + + + # PCA + pca = PCA(n_components=4) + pca_features = pca.fit_transform(sf_feats) + + fig, ax = plt.subplots(1, 1, figsize=(6, 4)) + scatter = ax.scatter(pca_features[:, 0], pca_features[:, 1], c=cohesive_peratom) + ax.set_xlabel("PCA[1]") + ax.set_ylabel("PCA[2]") + cbar = fig.colorbar(scatter, ax=ax) + cbar.set_label("energy / eV/at.") + plt.show() + + # computes PCovR map + pcovr = PCovR(n_components=4) + pcovr_features = pcovr.fit_transform(sf_feats, sf_energy) + + fig, ax = plt.subplots(1, 1, figsize=(6, 4)) + scatter = ax.scatter(pcovr_features[:, 0], pcovr_features[:, 1], c=cohesive_peratom) + ax.set_xlabel("PCovR[1]") + ax.set_ylabel("PCovR[2]") + cbar = fig.colorbar(scatter, ax=ax) + cbar.set_label("energy / (eV/at.)") + plt.show() + + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image-sg:: /examples/gaas-map/images/sphx_glr_gaas-map_002.png + :alt: gaas map + :srcset: /examples/gaas-map/images/sphx_glr_gaas-map_002.png + :class: sphx-glr-multi-img + + * + + .. image-sg:: /examples/gaas-map/images/sphx_glr_gaas-map_003.png + :alt: gaas map + :srcset: /examples/gaas-map/images/sphx_glr_gaas-map_003.png + :class: sphx-glr-multi-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 195-202 + +Chemiscope visualization +------------------------ + +Visualizes the structure-property map using a chemiscope widget (and +generates a .json file that can be viewed on +`chemiscope.org `__). + + +.. GENERATED FROM PYTHON SOURCE LINES 202-262 + +.. code-block:: Python + + + # extracts force data (adding considerably to the dataset size...) + force_vectors = chemiscope.ase_vectors_to_arrows(structures, scale=1) + force_vectors["parameters"]["global"]["color"] = 0x505050 + + # adds properties to the ASE frames + for i, f in enumerate(structures): + for j in range(len(pca_features[i])): + f.info["pca_" + str(j + 1)] = pca_features[i, j] + for i, f in enumerate(structures): + for j in range(len(pcovr_features[i])): + f.info["pcovr_" + str(j + 1)] = pcovr_features[i, j] + for i, f in enumerate(structures): + f.info["cohesive_energy"] = cohesive_peratom[i] + f.info["x_ga"] = comp_feats[i, 0] / comp_feats[i].sum() + + # it would also be easy to add the properties manually, this is just a dictionary + structure_properties = chemiscope.extract_properties(structures) + + cs = chemiscope.show( + frames=structures, + properties=structure_properties, + shapes={"forces": force_vectors}, + # the settings are a tad verbose, but give full control over the visualization + settings={ + "map": { + "x": {"property": "pcovr_1"}, + "y": {"property": "pcovr_2"}, + "color": {"property": "x_ga"}, + }, + "structure": [ + { + "bonds": True, + "unitCell": True, + "shape": ["forces"], + "keepOrientation": False, + } + ], + }, + meta={ + "name": "GaAs training data", + "description": """ + A collection of Ga(x)As(1-x) structures to train a MLIP, + including force and energy data. + """, + "authors": ["Giulio Imbalzano", "Michele Ceriotti"], + "references": [ + """ + G. Imbalzano and M. Ceriotti, 'Modeling the Ga/As binary system across + temperatures and compositions from first principles,' + Phys. Rev. Materials 5(6), 063804 (2021). + """, + "Original dataset: https://archive.materialscloud.org/record/2021.226", + ], + }, + ) + + cs.save("gaas_map.chemiscope.json.gz") + + cs # display if in a notebook + + +.. chemiscope:: _datasets/fig_gaas-map_001.json.gz + :mode: default + + + +.. raw:: html + +
+ +
+
+
+ + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (1 minutes 2.675 seconds) + + +.. _sphx_glr_download_examples_gaas-map_gaas-map.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: gaas-map.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: gaas-map.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: gaas-map.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/heat-capacity/heat-capacity.rst.txt b/_sources/examples/heat-capacity/heat-capacity.rst.txt new file mode 100644 index 00000000..0ad7a65c --- /dev/null +++ b/_sources/examples/heat-capacity/heat-capacity.rst.txt @@ -0,0 +1,509 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/heat-capacity/heat-capacity.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_heat-capacity_heat-capacity.py: + + +Quantum heat capacity of water +============================== + +:Authors: + Filippo Bigi `@frostedoyster `_; + Michele Ceriotti `@ceriottm `_ + +This example shows how to estimate the heat capacity of liquid water +from a path integral molecular dynamics simulation. The dynamics are +run with `i-PI `_, and +`LAMMPS `_ is used +as the driver to simulate the `q-TIP4P/f water +model `_. + +.. GENERATED FROM PYTHON SOURCE LINES 16-27 + +.. code-block:: Python + + + import os + import subprocess + import time + import xml.etree.ElementTree as ET + + import ipi + import matplotlib.pyplot as plt + import numpy as np + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 28-48 + +A non-trivial energy estimator +------------------------------ + +As introduced in the +`path-integrals example +`_, +path-integral estimators +for observables that depend on momenta are generally not trivial to compute. + +In this example, we will focus on the constant-volume heat capacity, +:math:`c_V`, which is one such +observable, and we will calculate it for liquid water at room temperature. +Because of the presence of high-frequency vibrations, many of the nuclear +degrees of freedom are trapped in the vibrational ground state, which reduces +substantially the heat capacity from the value that would be obtained +in the classical limit. See `this review +`_ +for an overview of the impact of quantum nuclei on the properties of water. +From a computational perspective, this means that it is necessary to use +specialized simulations and estimators to evaluate the correct value. + +.. GENERATED FROM PYTHON SOURCE LINES 51-71 + +Running the PIMD calculation +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This follows the same steps as the ``path-integrals`` example. One important +difference is that we will request the ``scaledcoords`` output to the relevant +section of the ``i-PI`` input XML file, which +contains estimators that can be used to calculate the total energy and +heat capacity as following +`Yamamoto, J. Chem. Phys. (2005) `_. + +The input file is shown below. It should be noted that ``scaledcoords`` +is given a finite differences displacement as a parameter. This is necessary +as the estimators require higher order derivatives of the potential energy, +which are calculated using finite differences. This also means that +evaluating the estimator adds substantial overhead (so it is wise to only +compute it every few simulation steps, to eliminate correlations between +snapshots) and that one should be careful to use well-converged simulation +parameters to avoid discontinuities and noise (for instance, we increase +the accuracy of the particle-mesh electrostatic calculation, and use a +shifted Lennard-Jones potential to avoid a discontinuity at the cutoff). + +.. GENERATED FROM PYTHON SOURCE LINES 71-76 + +.. code-block:: Python + + + # Open and show the relevant part of the input + xmlroot = ET.parse("data/input.xml").getroot() + print(" " + ET.tostring(xmlroot.find(".//properties"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + [ step, time{picosecond}, conserved, potential, kinetic_cv, + scaledcoords(fd_delta=5e-3) ] + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 77-79 + +We launch the i-PI and LAMMPS processes, exactly as in the +``path-integrals`` example. + +.. GENERATED FROM PYTHON SOURCE LINES 79-87 + +.. code-block:: Python + + + # don't rerun if the outputs already exist + ipi_process = None + if not os.path.exists("water-cv.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input.xml"]) + time.sleep(2) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(2)] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 88-89 + +Skip this cell if you want to run in the background + +.. GENERATED FROM PYTHON SOURCE LINES 89-94 + +.. code-block:: Python + + if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + lmp_process[1].wait() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 95-99 + +Analyzing the results +~~~~~~~~~~~~~~~~~~~~~ +Let's plot the potential and conserved energy as a function of time, +just to check that the simulation ran sensibly. + +.. GENERATED FROM PYTHON SOURCE LINES 99-119 + +.. code-block:: Python + + + output_data, output_desc = ipi.read_output("water-cv.out") + fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["potential"] - output_data["potential"][0], + "b-", + label="Potential, $V$", + ) + ax.plot( + output_data["time"], + output_data["conserved"] - output_data["conserved"][0], + "r-", + label="Conserved, $H$", + ) + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"energy / a.u.") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/heat-capacity/images/sphx_glr_heat-capacity_001.png + :alt: heat capacity + :srcset: /examples/heat-capacity/images/sphx_glr_heat-capacity_001.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 120-144 + +As described in the `i-PI documentation +`_, +the two quantities returned by the ``scaledcoords`` output are ``eps_v`` +and ``eps_v'``, defined in the aforementioned +`paper `_. + +These estimators (:math:`\epsilon_v` and :math:`\epsilon_v'`) are derived in the +"scaled coordinates" formalism, which is a useful trick to avoid the +growth of the error in the instantaneous values of the estimators with +the number of beads used in the path integral simulation. + +The same paper contains the formulas to calculate the total energy and +heat capacity from these estimators: + +.. math:: + E = \langle \epsilon_v \rangle \quad + C_V = k_B \beta^2 \left( \langle \epsilon_v^2 \rangle - \langle + \epsilon_v \rangle^2 - \langle \epsilon_v' \rangle \right) + +First the energy, whose estimator will be compared to the total energy +calculated as the sum of the potential and kinetic energy estimators. +Since the kinetic energy is itself calculated from a scaled-coordinates +estimator (the "centroid virial" estimator), the two total energies are +the same. + +.. GENERATED FROM PYTHON SOURCE LINES 144-174 + +.. code-block:: Python + + + eps_v = output_data["scaledcoords(fd_delta=5e-3)"][:, 0] + eps_v_prime = output_data["scaledcoords(fd_delta=5e-3)"][:, 1] + + energy_estimator = eps_v # first formula + + fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + energy_estimator - energy_estimator[0], + "b-", + label="scaled coordinates estimator", + ) + ax.plot( + output_data["time"][:], + ( + output_data["potential"] + - output_data["potential"][0] + + output_data["kinetic_cv"] + - output_data["kinetic_cv"][0] + ), + "r.", + label="potential + virial kinetic", + ) + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"total energy / a.u.") + ax.legend() + plt.show() + + + + + +.. image-sg:: /examples/heat-capacity/images/sphx_glr_heat-capacity_002.png + :alt: heat capacity + :srcset: /examples/heat-capacity/images/sphx_glr_heat-capacity_002.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 175-179 + +And, finally, the heat capacity. Note that normally the simulation +requires a few ps for equilibration. Here we discard a few dozen steps +to eliminate the initial jump, which is due to the relaxation of the +ring polymers starting from a single atomic configuration. + +.. GENERATED FROM PYTHON SOURCE LINES 179-198 + +.. code-block:: Python + + + # i-PI scaledcoords outputs are in atomic units (see docs) + kB = 3.16681e-6 # Boltzmann constant in atomic units + T = 298.0 # temperature in K, as defined in the input file + beta = 1.0 / (kB * T) + + skip = 20 + heat_capacity = ( # second formula + kB + * (beta**2) + * ( + np.mean(eps_v[skip:] ** 2) + - np.mean(eps_v[skip:]) ** 2 + - np.mean(eps_v_prime[skip:]) + ) + ) + heat_capacity_per_molecule = heat_capacity / 32 # 32 molecules in the simulation + print(f"Heat capacity (per water molecule): {(heat_capacity_per_molecule/kB):.2f} kB") + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Heat capacity (per water molecule): 15.17 kB + + + + +.. GENERATED FROM PYTHON SOURCE LINES 199-203 + +You may recognize that the first part of the estimator is reminiscent +of the classical estimator for the heat capacity as the fluctuations of the +(quantum) total energy, which in this case however requires a correction given +by the mean of the second part of the scaled-coordinates estimator. + +.. GENERATED FROM PYTHON SOURCE LINES 205-219 + +Estimating the statistical error +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Especially with such an underconverged simulation, it is important to +estimate the statistical error in the heat capacity. + +Generally, errors on measurements are computed +as "standard errors", i.e. the standard deviation of a series of data points +divided by the square root of the number of data points. In our case, +however, this is made more complicated by the correlation between +close steps in the molecular dynamics trajectory, which would lead to an +overestimation of the number of independent samples. To fix this, we can +calculate the autocorrelation time of the estimators whose errors we +want to estimate, and apply a correction factor to the number of samples. + +.. GENERATED FROM PYTHON SOURCE LINES 219-233 + +.. code-block:: Python + + + + def autocorrelate(x): + n = len(x) + xo = x - x.mean() # remove mean + acov = (np.correlate(xo, xo, "full"))[n - 1 :] + return acov[: len(acov) // 2] + + + def autocorrelation_time(x): + acov = autocorrelate(x) + return 1.0 + np.sum(acov) / acov[0] + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 234-238 + +Using these helper functions, we can now calculate the error on the various +parts of the heat capacity estimator. Note also the autocorrelation times, that +are just a little larger than one, indicating that the stride used to print out +the estimators is appropriate (as there is little correlation between the samples). + +.. GENERATED FROM PYTHON SOURCE LINES 238-278 + +.. code-block:: Python + + + # Autocorrelation times (i.e. number of steps needed to have independent samples) + autocorr_time_error_delta_eps_v = autocorrelation_time( + (eps_v[skip:] - eps_v[skip:].mean()) ** 2 + ) + autocorr_time_error_eps_v_prime = autocorrelation_time(eps_v_prime[skip:]) + + print( + f""" + Autocorrelation times (in number of samples): + (eps-)^2: {autocorr_time_error_delta_eps_v:.2f} + eps': {autocorr_time_error_eps_v_prime:.2f} + """ + ) + + # Effective number of samples + effective_samples_delta_eps_v = len(eps_v[skip:]) / autocorr_time_error_delta_eps_v + effective_samples_eps_v_prime = len(eps_v[skip:]) / autocorr_time_error_eps_v_prime + + # Standard errors using the effective number of samples + error_delta_eps_v = np.std((eps_v[skip:] - eps_v[skip:].mean()) ** 2) / np.sqrt( + effective_samples_delta_eps_v + ) + error_eps_v_prime = np.std(eps_v_prime[skip:]) / np.sqrt(effective_samples_eps_v_prime) + + # Error on the heat capacity (assuming quadrature sum) + error_heat_capacity = ( + kB * (beta**2) * np.sqrt(error_delta_eps_v**2 + error_eps_v_prime**2) + ) + + error_heat_capacity_per_molecule = ( + error_heat_capacity / 32 + ) # 32 molecules in the simulation + + print( + "Error on the heat capacity (per water molecule): " + f"{(error_heat_capacity_per_molecule/kB):.2f} kB" + ) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + Autocorrelation times (in number of samples): + (eps-)^2: 1.94 + eps': 1.31 + + Error on the heat capacity (per water molecule): 2.06 kB + + + + +.. GENERATED FROM PYTHON SOURCE LINES 279-297 + +The obtained heat capacity is consistent with the values from the literature +(see e.g. `Ceriotti et al., J. Chem. Phys. (2011) +`_ +where the convergence of the heat capacity with number of beads is shown for the same +water model used in this example). +However, the error is quite large, which is expected given the short simulation time. +To reduce the error, one would need to run a longer simulation. Other important error +sources, which are not accounted for in the error estimate, are the finite size of the +system and number of beads. Both of these are too small in this example to give +reliable results. + +In a realistic simulation, up to a few 100s of picoseconds might be needed to reduce +the sampling error to a small value (1-2% of the heat capacity). For water at room +temperature, you will need 32 beads at the very least (8 were used in this example). +It is more difficult to give a general rule for the system size: (quantum) energy +fluctuations are usually localized, but to guarantee accurate sampling of the +liquid structure, a few hundred water molecules would be a reasonable guess +(32 were used in this example). + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (0 minutes 40.552 seconds) + + +.. _sphx_glr_download_examples_heat-capacity_heat-capacity.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + + .. container:: sphx-glr-download + + :download:`Download data files: data.zip ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: heat-capacity.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: heat-capacity.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: heat-capacity.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/lode-linear/lode-linear.rst.txt b/_sources/examples/lode-linear/lode-linear.rst.txt new file mode 100644 index 00000000..ea3e3458 --- /dev/null +++ b/_sources/examples/lode-linear/lode-linear.rst.txt @@ -0,0 +1,742 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/lode-linear/lode-linear.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_lode-linear_lode-linear.py: + + +Long-distance Equivariants: a tutorial +====================================== + +:Authors: Philip Loche `@PicoCentauri `_, + Kevin Huguenin-Dumittan `@kvhuguenin `_ + +This tutorial explains how Long range equivariant descriptors can be constructed using +rascaline and the resulting descriptors be used to construct a linear model with +equisolve + +First, import all the necessary packages + +.. GENERATED FROM PYTHON SOURCE LINES 16-27 + +.. code-block:: Python + + + import ase.io + import matplotlib.pyplot as plt + import metatensor + import numpy as np + from equisolve.numpy.models.linear_model import Ridge + from equisolve.utils.convert import ase_to_tensormap + from rascaline import AtomicComposition, LodeSphericalExpansion, SphericalExpansion + from rascaline.utils import PowerSpectrum + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 28-43 + +Step 0: Prepare Data Set +------------------------ + +Get structures +~~~~~~~~~~~~~~ + +We take a small subset of the dimer dataset from `A. Grisafi et al., +2021 `_ +for which we additionally calculated the forces. Each structure in the +dataset contains two small organic molecules which are extended along a +certain direction in the subsequent structures. + +For speeding up the calculations we already selected the first 130 +:download:`structures ` of the charge-charge molecule +pairs. + +.. GENERATED FROM PYTHON SOURCE LINES 44-48 + +.. code-block:: Python + + + frames = ase.io.read("charge-charge.xyz", ":") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 49-56 + +Convert target properties to metatensor format +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +If we want to train models using the +`equisolve `_ package, we need to +convert the target properties (in this case, the energies and forces) +into the appropriate format #justequistorethings + +.. GENERATED FROM PYTHON SOURCE LINES 57-61 + +.. code-block:: Python + + + y = ase_to_tensormap(frames, energy="energy", forces="forces") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 62-73 + +Step 1: Compute short-range and LODE features +--------------------------------------------- + +Define hypers and get the expansion coefficients :math:`\langle anlm | \rho_i \rangle` +and :math:`\langle anlm | V_i \rangle` + +The short-range and long-range descriptors have very similar hyperparameters. We +highlight the differences below. + +We first define the hyperparameters for the short-range (SR) part. These will be used +to create SOAP features. + +.. GENERATED FROM PYTHON SOURCE LINES 74-86 + +.. code-block:: Python + + + SR_HYPERS = { + "cutoff": 3.0, + "max_radial": 6, + "max_angular": 2, + "atomic_gaussian_width": 0.3, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {}}, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + } + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 87-88 + +And next the hyperparaters for the LODE / long-range (LR) part + +.. GENERATED FROM PYTHON SOURCE LINES 89-107 + +.. code-block:: Python + + + + LR_HYPERS = { + # Cutoff on which to project potential density + "cutoff": 3.0, + # keep max_radial slightly smaller than for SR part + "max_radial": 3, + # max_angular should be <= 4, more precisely, max_angular + potential_exponent < 10 + "max_angular": 2, + # keep at >=1, WARNING: CUBIC SCALING, do not use values <0.5 + "atomic_gaussian_width": 3.0, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {}}, + # the exponent p that determines the 1/r^p potential + "potential_exponent": 1, + } + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 108-110 + +We then use the above defined hyperparaters to define the per atom short range (sr) +and long range (sr) descriptors. + +.. GENERATED FROM PYTHON SOURCE LINES 110-115 + +.. code-block:: Python + + + calculator_sr = SphericalExpansion(**SR_HYPERS) + calculator_lr = LodeSphericalExpansion(**LR_HYPERS) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 116-136 + +Note that LODE requires periodic systems. Therefore, if the data set does not come +with periodic boundary conditions by default you can not use the data set and you will +face an error if you try to compute the features. + +As you notices the calculation of the long range features takes significant more time +compared to the sr features. + +Taking a look at the output we find that the resulting +:py:class:`metatensor.TensorMap` are quite similar in their structure. The short range +:py:class:`metatensor.TensorMap` contains more blocks due to the higher +``max_angular`` paramater we choosed above. + +Generate the rotational invariants (power spectra) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Rotationally invariant features can be obtained by taking two of the calculators that +were defines above. + +For the short-range part, we use the SOAP vector which is obtained by computing the +invariant combinations of the form :math:`\rho \otimes \rho`. + +.. GENERATED FROM PYTHON SOURCE LINES 137-142 + +.. code-block:: Python + + + ps_calculator_sr = PowerSpectrum(calculator_sr, calculator_sr) + ps_sr = ps_calculator_sr.compute(frames, gradients=["positions"]) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 143-149 + +We calculate gradients with respect to pistions by providing the +``gradients=["positions"]`` option to the +:py:meth:`rascaline.calculators.CalculatorBase.compute()` method. + +For the long-range part, we combine the long-range descriptor :math:`V` with one a +short-range density :math:`\rho` to get :math:`\rho \otimes V` features. + +.. GENERATED FROM PYTHON SOURCE LINES 150-155 + +.. code-block:: Python + + + ps_calculator_lr = PowerSpectrum(calculator_sr, calculator_lr) + ps_lr = ps_calculator_lr.compute(systems=frames, gradients=["positions"]) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 156-165 + +Step 2: Building a Simple Linear SR + LR Model with energy baselining +--------------------------------------------------------------------- + +Preprocessing (model dependent) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +For our current model, we do not wish to treat the individual center and +neighbor species separately. Thus, we move the ``"species_center"`` key +into the ``sample`` direction, over which we will later sum over. + +.. GENERATED FROM PYTHON SOURCE LINES 166-171 + +.. code-block:: Python + + + ps_sr = ps_sr.keys_to_samples("species_center") + ps_lr = ps_lr.keys_to_samples("species_center") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 172-174 + +For linear models only: Sum features up over atoms (``samples``) in the same +structure. + +.. GENERATED FROM PYTHON SOURCE LINES 175-182 + +.. code-block:: Python + + + sample_names_to_sum = ["center", "species_center"] + + ps_sr = metatensor.sum_over_samples(ps_sr, sample_names=sample_names_to_sum) + ps_lr = metatensor.sum_over_samples(ps_lr, sample_names=sample_names_to_sum) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 183-189 + +Initialize tensormaps for energy baselining +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +We add a simple extra descriptor :py:class:`rascaline.AtomicComposition` that stores +how many atoms of each chemical species are contained in the structures. This is used +for energy baselining. + +.. GENERATED FROM PYTHON SOURCE LINES 190-197 + +.. code-block:: Python + + + calculator_co = AtomicComposition(per_structure=False) + descriptor_co = calculator_co.compute(frames, gradients=["positions"]) + + co = descriptor_co.keys_to_properties(["species_center"]) + co = metatensor.sum_over_samples(co, sample_names=["center"]) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 198-219 + +The :py:class:`rascaline.AtomicComposition` calculator also allows to directly perform +the the sum over center atoms by using the following lines. + +.. code:: python + + descriptor_co = AtomicComposition(per_structure=True).compute(**compute_args) + co = descriptor_co.keys_to_properties(["species_center"]) + +Stack all the features together for linear model +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A linear model on SR + LR features can be thought of as a linear model +built on a feature vector that is simply the concatenation of the SR and +LR features. + +Furthermore, energy baselining can be performed by concatenating the information about +chemical species as well. There is an metatensor function called +:py:func:`metatensor.join()` for this purpose. Formally, we can write for the SR +model. + +X_sr: :math:`1 \oplus \left(\rho \otimes \rho\right)` + +.. GENERATED FROM PYTHON SOURCE LINES 220-224 + +.. code-block:: Python + + + X_sr = metatensor.join([co, ps_sr], axis="properties") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 225-232 + +We used the ``axis="properties"`` parameter since we want to concatenate along the +features/properties dimensions. + +For the long range model we can formerly write + +X_lr: :math:`1 \oplus \left(\rho \otimes \rho\right) \oplus \left(\rho \otimes +V\right)` + +.. GENERATED FROM PYTHON SOURCE LINES 233-237 + +.. code-block:: Python + + + X_lr = metatensor.join([co, ps_sr, ps_lr], axis="properties") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 238-245 + +The features are now ready! Let us now perform some actual learning. Below we +initialize two instances of the :py:class:`equisolve.numpy.models.linear_model.Ridge` +class. :py:class:`equisolve.numpy.models.linear_model.Ridge` will perform a regression +with respect to ``"values"`` (energies) and ``"positions"`` gradients (forces). + +If you only want a fit with respect to energies you can remove the gradients with +``metatensor.remove_gradients()`` + +.. GENERATED FROM PYTHON SOURCE LINES 246-251 + +.. code-block:: Python + + + clf_sr = Ridge() + clf_lr = Ridge() + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 252-258 + +Split training and target data into train and test dat +------------------------------------------------------ + +Split the training and the test data by the distance :math:`r_{\rm +train}=6\,\mathrm{Å}` between the center of mass of the two molecules. A structure +with a :math:`r_{\rm train}<6 {\rm Å}` is used for training. + +.. GENERATED FROM PYTHON SOURCE LINES 259-263 + +.. code-block:: Python + + + r_cut = 6.0 + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 264-266 + +We calculate the indices from the dataset by list comprehension. The center of mass +distance is stored in the ``"distance""`` attribute. + +.. GENERATED FROM PYTHON SOURCE LINES 267-272 + +.. code-block:: Python + + + idx_train = [i for i, f in enumerate(frames) if f.info["distance"] < r_cut] + idx_test = [i for i, f in enumerate(frames) if f.info["distance"] >= r_cut] + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 273-275 + +For doing the split we define two ``Labels`` instances and combine them in a +:py:class:`List`. + +.. GENERATED FROM PYTHON SOURCE LINES 276-282 + +.. code-block:: Python + + + samples_train = metatensor.Labels(["structure"], np.reshape(idx_train, (-1, 1))) + samples_test = metatensor.Labels(["structure"], np.reshape(idx_test, (-1, 1))) + grouped_labels = [samples_train, samples_test] + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 283-284 + +That we use as input to the :py:func:`metatensor.split()` function + +.. GENERATED FROM PYTHON SOURCE LINES 285-297 + +.. code-block:: Python + + + X_sr_train, X_sr_test = metatensor.split( + X_sr, axis="samples", grouped_labels=grouped_labels + ) + + X_lr_train, X_lr_test = metatensor.split( + X_lr, axis="samples", grouped_labels=grouped_labels + ) + + y_train, y_test = metatensor.split(y, axis="samples", grouped_labels=grouped_labels) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 298-305 + +Fit the model +------------- + +For this model, we use a very simple regularization scheme where all features are +regularized in the same way (the amount being controlled by the parameter ``alpha``). +For more advanced regularization schemes (regularizing energies and forces differently +and/or the SR and LR parts differently), see further down. + +.. GENERATED FROM PYTHON SOURCE LINES 306-311 + +.. code-block:: Python + + + clf_sr.fit(X_sr_train, y_train, alpha=1e-6) + clf_lr.fit(X_lr_train, y_train, alpha=1e-6) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 312-317 + +Evaluation +---------- + +For evaluating the model we calculate the RMSEs using the ``score()`` method. With the +``parameter_key`` parameter we select which RMSE should be calculated. + +.. GENERATED FROM PYTHON SOURCE LINES 318-338 + +.. code-block:: Python + + + print( + "SR: RMSE energies = " + f"{clf_sr.score(X_sr_test, y_test, parameter_key='values')[0]:.3f} eV" + ) + print( + "SR: RMSE forces = " + f"{clf_sr.score(X_sr_test, y_test, parameter_key='positions')[0]:.3f} eV/Å" + ) + + print( + "LR: RMSE energies = " + f"{clf_lr.score(X_lr_test, y_test, parameter_key='values')[0]:.3f} eV" + ) + print( + "LR: RMSE forces = " + f"{clf_lr.score(X_lr_test, y_test, parameter_key='positions')[0]:.3f} eV/Å" + ) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + SR: RMSE energies = 0.557 eV + SR: RMSE forces = 0.188 eV/Å + LR: RMSE energies = 0.158 eV + LR: RMSE forces = 0.178 eV/Å + + + + +.. GENERATED FROM PYTHON SOURCE LINES 339-345 + +We find that the RMSE of the energy and the force of the LR model is smaller compared +to the SR model. From this we conclude that the LR model performs better for the +selection of the dataset. + +We additionally, can plot of the binding energy as a function of the distance. For the +plot we select some properties from the dataset + +.. GENERATED FROM PYTHON SOURCE LINES 346-352 + +.. code-block:: Python + + + dist = np.array([f.info["distance"] for f in frames]) + energies = np.array([f.info["energy"] for f in frames]) + monomer_energies = np.array([f.info["energyA"] + f.info["energyB"] for f in frames]) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 353-354 + +and select only the indices corresponding to our test set. + +.. GENERATED FROM PYTHON SOURCE LINES 358-359 + +Next we calculate the predicted SR and LR ``TensorMaps``. + +.. GENERATED FROM PYTHON SOURCE LINES 360-365 + +.. code-block:: Python + + + y_sr_pred = clf_sr.predict(X_sr) + y_lr_pred = clf_lr.predict(X_lr) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 366-367 + +And, finally perform the plot. + +.. GENERATED FROM PYTHON SOURCE LINES 368-396 + +.. code-block:: Python + + + plt.scatter( + dist, y.block().values[:, 0] - monomer_energies, label="target data", color="black" + ) + + plt.scatter( + dist, + y_sr_pred.block().values[:, 0] - monomer_energies, + label="short range model", + marker="x", + ) + + plt.scatter( + dist, + y_lr_pred.block().values[:, 0] - monomer_energies, + label="long range model", + marker="s", + facecolor="None", + edgecolor="orange", + ) + + plt.xlabel("center of mass distance in Å") + plt.ylabel(r"$E - E_\mathrm{monomer}$ in eV") + plt.axvline(r_cut, c="red", label=r"$r_\mathrm{train}$") + + plt.legend() + plt.tight_layout() + plt.show() + + + +.. image-sg:: /examples/lode-linear/images/sphx_glr_lode-linear_001.png + :alt: lode linear + :srcset: /examples/lode-linear/images/sphx_glr_lode-linear_001.png + :class: sphx-glr-single-img + + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (0 minutes 9.031 seconds) + + +.. _sphx_glr_download_examples_lode-linear_lode-linear.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: lode-linear.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: lode-linear.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: lode-linear.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/lpr/lpr.rst.txt b/_sources/examples/lpr/lpr.rst.txt new file mode 100644 index 00000000..eafaf2ea --- /dev/null +++ b/_sources/examples/lpr/lpr.rst.txt @@ -0,0 +1,441 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/lpr/lpr.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_lpr_lpr.py: + + +Local Prediction Rigidity analysis +================================== + +:Authors: Sanggyu "Raymond" Chong `@SanggyuChong `_; + Federico Grasselli `@fgrassel `_ + +In this tutorial, we calculate the SOAP descriptors of an amorphous +silicon dataset using rascaline, then compute the local prediction +rigidity (LPR) for the atoms of a "test" set before and after +modifications to the "training" dataset has been made. + +First, we import all the necessary packages: + +.. GENERATED FROM PYTHON SOURCE LINES 17-30 + +.. code-block:: Python + + import os + import tarfile + + import numpy as np + import requests + from ase.io import read + from matplotlib import pyplot as plt + from matplotlib.colors import LogNorm + from rascaline import SoapPowerSpectrum + from sklearn.decomposition import PCA + from skmatter.metrics import local_prediction_rigidity as lpr + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 31-38 + +Load and prepare amorphous silicon data +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + +We first download the dataset associated with LPR +analysis from Materials Cloud and load the the amorphous +silicon structures using `ASE `_. + +.. GENERATED FROM PYTHON SOURCE LINES 38-65 + +.. code-block:: Python + + + filename = "LPR_supp_notebook_dataset.tar.gz" + if not os.path.exists(filename): + url = "https://rb.gy/wxsrug" # shortened URL + response = requests.get(url) + response.raise_for_status() + with open(filename, "wb") as f: + f.write(response.content) + + with tarfile.open(filename) as tar: + tar.extractall(path=".") + + frames_pristine = read("datasets/Si_amo_defect_free.xyz", ":") + frames_defect = read("datasets/Si_amo_defect_containing.xyz", ":") + + # Randomly shuffle the structures + + np.random.seed(20230215) + + ids = list(range(len(frames_pristine))) + np.random.shuffle(ids) + frames_pristine = [frames_pristine[ii] for ii in ids] + + ids = list(range(len(frames_defect))) + np.random.shuffle(ids) + frames_defect = [frames_defect[ii] for ii in ids] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 66-74 + +We now further refine the loaded datasets according the the +number of coordinated atoms that each atomic environment exhibits. +"Pristine" refers to structures where all of the atoms have strictly +4 coordinating atoms. "Defect" refers to structures that contain +atoms with coordination numbers other than 4. + +We use :code:`get_all_distances` funciton of :code:`ase.Atoms` to detect the +number of coordinated atoms. + +.. GENERATED FROM PYTHON SOURCE LINES 74-92 + +.. code-block:: Python + + + cur_cutoff = 2.7 + refined_pristine_frames = [] + for frame in frames_pristine: + neighs = (frame.get_all_distances(mic=True) < cur_cutoff).sum(axis=0) - 1 + if neighs.max() > 4 or neighs.min() < 4: + continue + else: + refined_pristine_frames.append(frame) + + refined_defect_frames = [] + for frame in frames_defect: + neighs = (frame.get_all_distances(mic=True) < cur_cutoff).sum(axis=0) - 1 + num_defects = (neighs > 4).sum() + (neighs < 4).sum() + if num_defects > 4: + refined_defect_frames.append(frame) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 93-103 + +Compute SOAP descriptors using rascaline +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Now, we move on and compute the SOAP descriptors for the refined +structures. First, define the rascaline hyperparameters used to +compute SOAP. Among the hypers, notice that the cutoff is chosen +to be 2.85 Å, and the radial scaling is turned off. These were +heuristic choices made to accentuate the difference in the LPR +based on the nearest-neighbor coordination. (Do not blindly +use this set of hypers for production-quality model training!) + +.. GENERATED FROM PYTHON SOURCE LINES 103-129 + +.. code-block:: Python + + + # Hypers dictionary + hypers = { + "cutoff": 2.85, + "max_radial": 10, + "max_angular": 12, + "atomic_gaussian_width": 0.5, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {"spline_accuracy": 1e-8}}, + "cutoff_function": {"ShiftedCosine": {"width": 0.1}}, + "radial_scaling": None, + } + # Define rascaline calculator + calculator = SoapPowerSpectrum(**hypers) + + # Calculate the SOAP power spectrum + Xlist_pristine = [] + for frame in refined_pristine_frames: + descriptor = calculator.compute(frame) + Xlist_pristine.append(np.array(descriptor.block().values)) + + Xlist_defect = [] + for frame in refined_defect_frames: + descriptor = calculator.compute(frame) + Xlist_defect.append(np.array(descriptor.block().values)) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 130-141 + +Organize structures into "training" and "test" sets +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Now we move on and compute the SOAP descriptors for the refined +structures. First, define the rascaline hyperparameters used to +compute SOAP. + +Notice that the format in which we handle the descriptors is as a +list of :code:`np.array` descriptor blocks. This is to ensure +compatibility with how things have been implemented in the LPR +module of :code:`scikit-matter`. + +.. GENERATED FROM PYTHON SOURCE LINES 141-157 + +.. code-block:: Python + + + n_train = 400 + n_add = 50 + n_test = 50 + + X_pristine = [Xlist for Xlist in Xlist_pristine[: n_train + n_add]] + X_defect = [Xlist for Xlist in Xlist_defect[:n_add]] + X_test = [Xlist for Xlist in Xlist_defect[n_add : n_add + n_test]] + + # Save coordination values for visualization + test_coord = [] + for frame in refined_defect_frames[n_add : n_add + n_test]: + coord = (frame.get_all_distances(mic=True) < cur_cutoff - 0.05).sum(axis=0) - 1 + test_coord += coord.tolist() + test_coord = np.array(test_coord) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 158-172 + +Compute the LPR for the test set +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Next, we will use the :code:`local_prediction_rigidity` module of +`scikit-matter `_ +to compute the LPRs for the test set that we have set apart. + +LPR reflects how the ML model perceives a local environment, +given a collection of other structures, similar or different. +It should then carry over some of the details involved in training +the model, in this case the regularization strength. + +For this example, we have foregone on the actual model training, +and so we define an arbitrary value for the alpha. + +.. GENERATED FROM PYTHON SOURCE LINES 172-177 + +.. code-block:: Python + + + alpha = 1e-4 + LPR_test, rank = lpr(X_pristine, X_test, alpha) + LPR_test = np.hstack(LPR_test) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 178-184 + +Visualizing the LPR on a PCA map +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +We now visualize the LPRs of the test set on a PCA map, +where the PCA is performed on the SOAP descriptors of +defect-containing dataset. + +.. GENERATED FROM PYTHON SOURCE LINES 184-211 + +.. code-block:: Python + + + pca = PCA(n_components=5) + descriptors_all = calculator.compute(refined_defect_frames) + pca.fit_transform(descriptors_all.block().values) + PCA_test = pca.transform(np.vstack(X_test)) + + rmin = np.log10(LPR_test.min()) + 0.5 + rmax = np.log10(LPR_test.max()) - 0.5 + + fig = plt.figure(figsize=(5, 4), dpi=200) + ax = fig.add_subplot() + im = ax.scatter( + PCA_test[:, 0], + PCA_test[:, 1], + c=LPR_test, + s=20, + linewidths=0, + norm=LogNorm(vmin=10**rmin, vmax=10**rmax), + cmap="viridis", + ) + + ax.set_xlabel("PC1") + ax.set_ylabel("PC2") + fig.colorbar(im, ax=ax, label="LPR") + ax.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False) + plt.show() + + + + +.. image-sg:: /examples/lpr/images/sphx_glr_lpr_001.png + :alt: lpr + :srcset: /examples/lpr/images/sphx_glr_lpr_001.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 212-220 + +In the PCA map, where each point corresponds to an +atomic environment of the test set structures, one +can observe 4 different clusters of points, arranged +along PC1. This corresponds to the coordination numbers +ranging from 3 to 6. Since the training set contains +structures exclusively composed of 4-coordinated atoms, +LPR is distinctly high for the second, main cluster of +points, and quite low for the three other clusters. + +.. GENERATED FROM PYTHON SOURCE LINES 223-230 + +Studying the LPR after dataset modification +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +We now want to see what would happen when defect structures +are included into the training set of the model. For this, +we first create a modified dataset that incorporates in the +defect structures, and recompute the LPR. + +.. GENERATED FROM PYTHON SOURCE LINES 230-235 + +.. code-block:: Python + + + X_new = X_pristine[:n_train] + X_defect[:n_add] + LPR_test_new, rank = lpr(X_new, X_test, alpha) + LPR_test_new = np.hstack(LPR_test_new) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 236-241 + +We then visualize the change in the LPR with the +modification of the dataset by plotting the same PCA +map, but now colored by the ratio of new set of LPR +values (after dataset modification) over the original +one. + +.. GENERATED FROM PYTHON SOURCE LINES 241-259 + +.. code-block:: Python + + + fig = plt.figure(figsize=(5, 4), dpi=200) + ax = fig.add_subplot() + im = ax.scatter( + PCA_test[:, 0], + PCA_test[:, 1], + c=LPR_test_new / LPR_test, + s=20, + linewidths=0, + # norm=LogNorm(vmin=10**rmin, vmax=10**rmax), + cmap="OrRd", + ) + ax.set_xlabel("PC1") + ax.set_ylabel("PC2") + fig.colorbar(im, ax=ax, label=r"LPR$_{\mathrm{new}}$ / LPR$_{\mathrm{old}}$") + ax.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False) + plt.show() + + + + +.. image-sg:: /examples/lpr/images/sphx_glr_lpr_002.png + :alt: lpr + :srcset: /examples/lpr/images/sphx_glr_lpr_002.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 260-263 + +It is apparent that while the LPR stays more or less consistent for the +4-coordinated atoms, it is significantly enhanced for the defective environments +as a result of the inclusion of defective structures in the training set. + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (0 minutes 16.406 seconds) + + +.. _sphx_glr_download_examples_lpr_lpr.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: lpr.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: lpr.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: lpr.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/path-integrals/path-integrals.rst.txt b/_sources/examples/path-integrals/path-integrals.rst.txt new file mode 100644 index 00000000..765f9995 --- /dev/null +++ b/_sources/examples/path-integrals/path-integrals.rst.txt @@ -0,0 +1,648 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/path-integrals/path-integrals.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_path-integrals_path-integrals.py: + + +Path integral molecular dynamics +================================ + +:Authors: Michele Ceriotti `@ceriottm `_ + +This example shows how to run a path integral molecular dynamics +simulation using ``i-PI``, analyze the output and visualize the +trajectory in ``chemiscope``. It uses `LAMMPS `_ +as the driver to simulate the `q-TIP4P/f water +model `_. + +.. GENERATED FROM PYTHON SOURCE LINES 13-23 + +.. code-block:: Python + + + import subprocess + import time + + import chemiscope + import ipi + import matplotlib.pyplot as plt + import numpy as np + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 24-57 + +Quantum nuclear effects and path integral methods +------------------------------------------------- + +The Born-Oppenheimer approximation separates the joint quantum mechanical +problem for electrons and nuclei into two independent problems. Even though +often one makes the additional approximation of treating nuclei as classical +particles, this is not necessary, and in some cases (typically when H atoms are +present) can add considerable error. + + +.. figure:: pimd-slices-round.png + :align: center + :width: 600px + + A representation of ther ring-polymer Hamiltonian for a water molecule. + +In order to describe the quantum mechanical nature of light nuclei +(nuclear quantum effects) one of the most widely-applicable methods uses +the *path integral formalism* to map the quantum partition function of a +set of distinguishable particles onto the classical partition function of +*ring polymers* composed by multiple beads (replicas) with +corresponding atoms in adjacent replicas being connected by harmonic +springs. +`The textbook by Tuckerman `_ +contains a pedagogic introduction to the topic, while +`this paper `_ outlines the implementation +used in ``i-PI``. + +The classical partition function of the path converges to quantum statistics +in the limit of a large number of replicas. In this example, we will use a +technique based on generalized Langevin dynamics, known as +`PIGLET `_ to accelerate the +convergence. + +.. GENERATED FROM PYTHON SOURCE LINES 60-69 + +Running PIMD calculations with ``i-PI`` +--------------------------------------- + +`i-PI `_ is based on a client-server model, with ``i-PI`` +controlling the nuclear dynamics (in this case sampling the path Hamiltonian using +molecular dynamics) while the calculation of energies and forces is delegated to +an external client program, in this example ``LAMMPS``. + +An i-PI calculation is specified by an XML file. + +.. GENERATED FROM PYTHON SOURCE LINES 69-75 + +.. code-block:: Python + + + # Open and read the XML file + with open("data/input_pimd.xml", "r") as file: + xml_content = file.read() + print(xml_content) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + + [ step, time{picosecond}, conserved{electronvolt}, temperature{kelvin}, kinetic_cv{electronvolt}, potential{electronvolt}, pressure_cv{megapascal}, kinetic_td{electronvolt} ] + positions + kinetic_cv + kinetic_od + + 200 + + 32342 + + +
h2o-lammps
1e-4 + + + + data/water_32.pdb + 298 + + + lmpserial + + + 298 + + + + + 5.0 + + 0.5 + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 76-83 + +NB1: In a realistic simulation you may want to increase the field +``total_steps``, to simulate at least a few 100s of picoseconds. + +NB2: To converge a simulation of water at room temperature, you +typically need at least 32 beads. We will see later how to accelerate +convergence using a colored-noise thermostat, but you can try to +modify the input to check convergence with conventional PIMD + +.. GENERATED FROM PYTHON SOURCE LINES 85-102 + +i-PI and lammps should be run separately, and it is possible to +launch separate lammps processes to parallelize the evaluation over +the beads. On the the command line, this amounts to launching + +.. code-block:: bash + + i-pi data/input_pimd.xml > log & + sleep 2 + lmp -in data/in.lmp & + lmp -in data/in.lmp & + +Note how ``i-PI`` and ``LAMMPS`` are completely independent, and +therefore need a separate set of input files. The client-side communication +in ``LAMMPS`` is described in the ``fix_ipi`` section, that matches the socket +name and mode defined in the ``ffsocket`` field in the ``i-PI`` file. + +We can launch the external processes from a Python script as follows + +.. GENERATED FROM PYTHON SOURCE LINES 102-107 + +.. code-block:: Python + + + ipi_process = subprocess.Popen(["i-pi", "data/input_pimd.xml"]) + time.sleep(2) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(2)] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 108-111 + +If you run this in a notebook, you can go ahead and start loading +output files *before* i-PI and lammps have finished running, by +skipping this cell + +.. GENERATED FROM PYTHON SOURCE LINES 111-117 + +.. code-block:: Python + + + ipi_process.wait() + lmp_process[0].wait() + lmp_process[1].wait() + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + 1 + + + +.. GENERATED FROM PYTHON SOURCE LINES 118-124 + +Analyzing the simulation +~~~~~~~~~~~~~~~~~~~~~~~~ + +After the simulation has run, you can visualize and post-process the trajectory data. +Note that i-PI prints a separate trajectory for each bead, as structural properties +can be computed averaging over the configurations of any of the beads. + +.. GENERATED FROM PYTHON SOURCE LINES 124-130 + +.. code-block:: Python + + + # drops first frame where all atoms overlap + output_data, output_desc = ipi.read_output("simulation.out") + traj_data = [ipi.read_trajectory(f"simulation.pos_{i}.xyz")[1:] for i in range(8)] + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 131-136 + +The simulation parameters are pushed at the limits: with the aggressive stochastic +thermostatting and the high-frequency normal modes of the ring polymer, there are +fairly large fluctuations of the conserved quantity. This is usually not affecting +physical observables, but if you see this level of drift in a production run, check +carefully for convergence and stability with a reduced time step. + +.. GENERATED FROM PYTHON SOURCE LINES 136-155 + +.. code-block:: Python + + + fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["potential"] - output_data["potential"][0], + "b-", + label="Potential, $V$", + ) + ax.plot( + output_data["time"], + output_data["conserved"] - output_data["conserved"][0], + "r-", + label="Conserved, $H$", + ) + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"energy / eV") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/path-integrals/images/sphx_glr_path-integrals_001.png + :alt: path integrals + :srcset: /examples/path-integrals/images/sphx_glr_path-integrals_001.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 156-166 + +While the potential energy is simply the mean over the beads of the +energy of individual replicas, computing the kinetic energy requires +averaging special quantities that involve also the correlations between beads. +Here we compare two of these *estimators*: the 'thermodynamic' estimator becomes +statistically inefficient when increasing the number of beads, whereas the +'centroid virial' estimator remains well-behaved. Note how quickly these estimators +equilibrate to roughly their stationary value, much faster than the equilibration +of the potential energy above. This is thanks to the ``pile_g`` thermostat +(see `DOI:10.1063/1.3489925 `_) that is +optimally coupled to the normal modes of the ring polymer. + +.. GENERATED FROM PYTHON SOURCE LINES 166-185 + +.. code-block:: Python + + + fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["kinetic_cv"], + "b-", + label="Centroid virial, $K_{CV}$", + ) + ax.plot( + output_data["time"], + output_data["kinetic_td"], + "r-", + label="Thermodynamic, $K_{TD}$", + ) + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"energy / eV") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/path-integrals/images/sphx_glr_path-integrals_002.png + :alt: path integrals + :srcset: /examples/path-integrals/images/sphx_glr_path-integrals_002.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 186-191 + +You can also visualize the (very short) trajectory in a way that highlights the +fast spreading out of the beads of the ring polymer. ``chemiscope`` provides a +utility function to interleave the trajectories of the beads, forming a trajectory +that shows the connecttions between the replicas of each atom. Each atom and its +connections are color-coded. + +.. GENERATED FROM PYTHON SOURCE LINES 191-205 + +.. code-block:: Python + + + traj_pimd = chemiscope.ase_merge_pi_frames(traj_data) + # we also tweak the visualization options, and then show the viewer + traj_pimd["shapes"]["paths"]["parameters"]["global"]["radius"] = 0.05 + traj_pimd["settings"]["structure"][0].update( + dict( + atoms=False, + keepOrientation=True, + color={"property": "bead_id", "palette": "hsv (periodic)"}, + ) + ) + + chemiscope.show(**traj_pimd, mode="structure") + + + +.. chemiscope:: _datasets/fig_path-integrals_001.json.gz + :mode: structure + + + +.. raw:: html + +
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 206-223 + +Accelerating PIMD with a PIGLET thermostat +------------------------------------------ + +The simulations in the previous sections are very far from converged -- typically +one would need approximately 32 replicas to converge a simulation of +room-temperature water. To address this problem we will use a method based on +generalized Langevin equations, called +`PIGLET `_ + +The input file is ``input_piglet.xml``, that only differs by the definition of +the thermostat, that uses a ``nm_gle`` mode in which each normal mode +of the ring polymer is attached to a different colored-noise Generalized Langevin +equation. This makes it possible to converge exactly the simulation results with +a small number of replicas, and to accelerate greatly convergence for realistic +systems such as this. The thermostat parameters can be generated on +`the GLE4MD website `_ + + +.. GENERATED FROM PYTHON SOURCE LINES 223-232 + +.. code-block:: Python + + + ipi_process = subprocess.Popen(["i-pi", "data/input_piglet.xml"]) + time.sleep(2) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(2)] + + ipi_process.wait() + lmp_process[0].wait() + lmp_process[1].wait() + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + 1 + + + +.. GENERATED FROM PYTHON SOURCE LINES 233-236 + +The mean potential energy from the PIGLET trajectory is higher than that for the +PIMD one, because it is closer to the converged value (try to run a PIMD trajectory +with 64 beads for comparison) + +.. GENERATED FROM PYTHON SOURCE LINES 236-259 + +.. code-block:: Python + + + # drops first frame + output_gle, desc_gle = ipi.read_output("simulation_piglet.out") + traj_gle = [ipi.read_trajectory(f"simulation_piglet.pos_{i}.xyz")[1:] for i in range(8)] + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["potential"] - output_data["potential"][0], + "b--", + label="PIMD", + ) + ax.plot( + output_gle["time"], + output_gle["potential"] - output_gle["potential"][0], + "b-", + label="PIGLET", + ) + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"energy / eV") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/path-integrals/images/sphx_glr_path-integrals_003.png + :alt: path integrals + :srcset: /examples/path-integrals/images/sphx_glr_path-integrals_003.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 260-267 + +However, you should be somewhat careful: PIGLET converges *some* but not all the +correlations within a path. For instance, it is designed to converge the +centroid-virial estimator for the kinetic energy, but not the thermodynamic +estimator. For the same reason, don't try to look at equilibration in terms of +the mean temperature: it won't match the target value, because PIGLET uses a +Langevin equation that breaks the classical fluctuation-dissipation theorem, and +generates a steady-state distribution that mimics quantum fluctuations. + +.. GENERATED FROM PYTHON SOURCE LINES 267-278 + +.. code-block:: Python + + + fix, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot(output_data["time"], output_data["kinetic_cv"], "b--", label="PIMD, $K_{CV}$") + ax.plot(output_gle["time"], output_gle["kinetic_cv"], "b", label="PIGLET, $K_{CV}$") + ax.plot(output_data["time"], output_data["kinetic_td"], "r--", label="PIMD, $K_{TD}$") + ax.plot(output_gle["time"], output_gle["kinetic_td"], "r", label="PIGLET, $K_{TD}$") + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"energy / eV") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/path-integrals/images/sphx_glr_path-integrals_004.png + :alt: path integrals + :srcset: /examples/path-integrals/images/sphx_glr_path-integrals_004.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 279-292 + +Kinetic energy tensors +~~~~~~~~~~~~~~~~~~~~~~ + +While we're at it, let's do something more complicated (and instructive). +Classically, the momentum distribution of any atom is isotropic, so the +kinetic energy tensor (KET) :math:`\mathbf{p}\mathbf{p}^T/2m` is a constant +times the identity matrix. Quantum mechanically, the kinetic energy tensor +has more structure, that reflects the higher kinetic energy of particles +along directions with stiff bonds. We can compute a moving average of the +centroid virial estimator of the KET, and plot it to show the direction +of anisotropy. Note that there are some subtleties connected with the +evaluation of the moving average, see e.g. +`DOI:10.1103/PhysRevLett.109.100604 `_ + +.. GENERATED FROM PYTHON SOURCE LINES 294-298 + +We first need to postprocess the components of the kinetic energy tensors +(that i-PI prints out separating the diagonal and off-diagonal bits), averaging +them over the last 10 frames and combining them with the centroid configuration +from the last frame in the trajectory. + +.. GENERATED FROM PYTHON SOURCE LINES 298-312 + +.. code-block:: Python + + + kinetic_cv = ipi.read_trajectory("simulation_piglet.kin.xyz")[1:] + kinetic_od = ipi.read_trajectory("simulation_piglet.kod.xyz")[1:] + kinetic_tens = np.hstack( + [ + np.asarray([k.positions for k in kinetic_cv[-10:]]).mean(axis=0), + np.asarray([k.positions for k in kinetic_od[-10:]]).mean(axis=0), + ] + ) + + centroid = traj_gle[-1][-1].copy() + centroid.positions = np.asarray([t[-1].positions for t in traj_gle]).mean(axis=0) + centroid.arrays["kinetic_cv"] = kinetic_tens + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 313-317 + +We can then view these in ``chemiscope``, setting the proper parameters to +visualize the ellipsoids associated with the KET. Note that some KETs have +negative eigenvalues, because we are averaging over a few frames, which is +insufficient to converge the estimator fully. + +.. GENERATED FROM PYTHON SOURCE LINES 317-333 + +.. code-block:: Python + + + ellipsoids = chemiscope.ase_tensors_to_ellipsoids( + [centroid], "kinetic_cv", scale=15, force_positive=True + ) + + chemiscope.show( + [centroid], + shapes={"kinetic_cv": ellipsoids}, + mode="structure", + settings=chemiscope.quick_settings( + structure_settings={ + "shape": ["kinetic_cv"], + "unitCell": True, + } + ), + ) + + +.. chemiscope:: _datasets/fig_path-integrals_002.json.gz + :mode: structure + + + +.. raw:: html + +
+ +
+
+
+ + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (0 minutes 15.997 seconds) + + +.. _sphx_glr_download_examples_path-integrals_path-integrals.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + + .. container:: sphx-glr-download + + :download:`Download data files: data.zip ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: path-integrals.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: path-integrals.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: path-integrals.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/periodic-hamiltonian/periodic-hamiltonian.rst.txt b/_sources/examples/periodic-hamiltonian/periodic-hamiltonian.rst.txt new file mode 100644 index 00000000..954dc16e --- /dev/null +++ b/_sources/examples/periodic-hamiltonian/periodic-hamiltonian.rst.txt @@ -0,0 +1,83990 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/periodic-hamiltonian/periodic-hamiltonian.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_periodic-hamiltonian_periodic-hamiltonian.py: + + +Periodic Hamiltonian learning +============================= + +:Authors: Paolo Pegolo `@ppegolo `__, + Jigyasa Nigam `@curiosity54 `__ + +This tutorial explains how to train a machine learning model for the +electronic Hamiltonian of a periodic system. Even though we focus on +periodic systems, the code and techniques presented here can be directly +transferred to molecules. + +.. GENERATED FROM PYTHON SOURCE LINES 15-17 + +First, import the necessary packages + + +.. GENERATED FROM PYTHON SOURCE LINES 17-42 + +.. code-block:: Python + + + import os + import warnings + import zipfile + + import matplotlib.image as mpimg + import matplotlib.pyplot as plt + import numpy as np + import requests + import torch + from matplotlib.animation import FuncAnimation + from mlelec.data.derived_properties import compute_eigenvalues + from mlelec.data.mldataset import MLDataset + from mlelec.data.qmdataset import QMDataset + from mlelec.models.equivariant_lightning import LitEquivariantModel, MSELoss + from mlelec.utils.pbc_utils import blocks_to_matrix + from mlelec.utils.plot_utils import plot_bands_frame + + + warnings.filterwarnings("ignore") + torch.set_default_dtype(torch.float64) + + # sphinx_gallery_thumbnail_number = 3 + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/pyscf/dft/libxc.py:772: UserWarning: Since PySCF-2.3, B3LYP (and B3P86) are changed to the VWN-RPA variant, the same to the B3LYP functional in Gaussian and ORCA (issue 1480). To restore the VWN5 definition, you can put the setting "B3LYP_WITH_VWN5 = True" in pyscf_conf.py + warnings.warn('Since PySCF-2.3, B3LYP (and B3P86) are changed to the VWN-RPA variant, ' + + + + +.. GENERATED FROM PYTHON SOURCE LINES 43-46 + +Get Data and Prepare Data Set +----------------------------- + + +.. GENERATED FROM PYTHON SOURCE LINES 49-57 + +The data set contains 35 distorted graphene unit cells containing 2 +atoms. The reference density functional theory (DFT) calculations are +performed with `CP2K `__ using a minimal +`STO-3G `__ basis and +the `PBE `__ functional. +The Kohn-Sham equations are solved on a Monkhorst-Pack grid of +:math:`15\times 15\times 1` points in the Brillouin zone of the crystal. + + +.. GENERATED FROM PYTHON SOURCE LINES 60-68 + +Obtain structures and DFT data +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Generating training structures requires running a suitable DFT code, +and converting the output data in a format that can be processed by +the ML library ``mlelec``. Given that it takes some time to run even +these small calculations, we provide pre-computed data, but you can +also find instructions on how to generate data from scratch. + +.. GENERATED FROM PYTHON SOURCE LINES 70-83 + +Run your own cp2k calculations +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +If you have computational resources, you can run the DFT calculations +needed to produce the data set. `This other +tutorial `__ in the atomistic cookbook can +help you set up the CP2K calculations for this data set, using the +``reftraj_hamiltonian.cp2k`` file provided in ``data/``. To do the same +for another data set, adapt the reftraj file. +We will provide here some of the functions in the `batch-cp2k +tutorial `__ that need to be adapted to the +current data set. Note however you will have to modify these and combine +them with other tutorials to actually generate the data. + +.. GENERATED FROM PYTHON SOURCE LINES 86-93 + +Start by importing all the modules from the `batch-cp2k +tutorial `__ and run the cell to install +CP2K. Run also the cells up to the one defining ``write_cp2k_in``. +The following code snippet defines a slighly modified version of that function, +allowing for non-orthorombic supercell, and accounting for the reftraj file +name change. + + +.. GENERATED FROM PYTHON SOURCE LINES 95-122 + +.. code:: python + + def write_cp2k_in( + fname: str, + project_name: str, + last_snapshot: int, + cell_a: List[float], + cell_b: List[float], + cell_c: List[float], + ) -> None: + """Writes a cp2k input file from a template. + + Importantly, it writes the location of the basis set definitions, + determined from the path of the system CP2K install to the input file. + """ + + cp2k_in = open("reftraj_hamiltonian.cp2k", "r").read() + + cp2k_in = cp2k_in.replace("//PROJECT//", project_name) + cp2k_in = cp2k_in.replace("//LAST_SNAPSHOT//", str(last_snapshot)) + cp2k_in = cp2k_in.replace("//CELL_A//", " ".join([f"{c:.6f}" for c in cell_a])) + cp2k_in = cp2k_in.replace("//CELL_B//", " ".join([f"{c:.6f}" for c in cell_b])) + cp2k_in = cp2k_in.replace("//CELL_C//", " ".join([f"{c:.6f}" for c in cell_c])) + + with open(fname, "w") as f: + f.write(cp2k_in) + + +.. GENERATED FROM PYTHON SOURCE LINES 125-129 + +Unlike the `batch-cp2k tutorial `__, the +current data set includes a single stoichiometry, :math:`\mathrm{C_2}`. +Therefore, you can run this cell to set the calculation scripts up. + + +.. GENERATED FROM PYTHON SOURCE LINES 131-152 + +.. code:: python + + project_name = 'graphene' + frames = ase_read('C2.xyz', index=':') + os.makedirs(project_name, exist_ok=True) + os.makedirs(f"{project_name}/FOCK", exist_ok=True) + os.makedirs(f"{project_name}/OVER", exist_ok=True) + + write_cp2k_in( + f"{project_name}/in.cp2k", + project_name=project_name, + last_snapshot=len(frames), + cell_a=frames[0].cell.array[0], + cell_b=frames[0].cell.array[1], + cell_c=frames[0].cell.array[2], + ) + + ase_write(f"{project_name}/init.xyz", frames[0]) + write_reftraj(f"{project_name}/reftraj.xyz", frames) + write_cellfile(f"{project_name}/reftraj.cell", frames) + + +.. GENERATED FROM PYTHON SOURCE LINES 155-157 + +The CP2K calculations can be simply run using: + + +.. GENERATED FROM PYTHON SOURCE LINES 160-168 + +.. code:: python + + subprocess.run(( + f"cp2k.ssmp -i {project_name}/in.cp2k " + "> {project_name}/out.cp2k" + ), + shell=True) + + +.. GENERATED FROM PYTHON SOURCE LINES 171-173 + +Once the calculations are done, we can parse the results with: + + +.. GENERATED FROM PYTHON SOURCE LINES 176-238 + +.. code:: python + + from scipy.sparse import csr_matrix + + nao = 10 + ifr = 1 + fock = [] + over = [] + with open(f"{project_name}/out.cp2k", "r") as outfile: + T_lists = [] # List to hold all T_list instances + while True: + line = outfile.readline() + if not line: + break + if line.strip().split()[:3] != ["KS", "CSR", "write|"]: + continue + else: + nT = int(line.strip().split()[3]) + outfile.readline() # Skip the next line if necessary + T_list = [] # Initialize a new T_list for this block + for _ in range(nT): + line = outfile.readline() + if not line: + break + T_list.append([np.int32(j) for j in line.strip().split()[1:4]]) + T_list = np.array(T_list) + T_lists.append(T_list) # Append the T_list to T_lists + fock_ = {} + over_ = {} + for iT, T in enumerate( + T_list + ): # Loop through the translations and load matrices + T = T.tolist() + r, c, data = np.loadtxt( + ( + f"{project_name}/FOCK/{project_name}" + f"-KS_SPIN_1_R_{iT+1}-1_{ifr}.csr" + ), + unpack=True, + ) + r = np.int32(r - 1) + c = np.int32(c - 1) + fock_[tuple(T)] = csr_matrix( + (data, (r, c)), shape=(nao, nao) + ).toarray() + + r, c, data = np.loadtxt( + ( + f"{project_name}/OVER/{project_name}" + f"-S_SPIN_1_R_{iT+1}-1_{ifr}.csr" + ), + unpack=True, + ) + r = np.int32(r - 1) + c = np.int32(c - 1) + over_[tuple(T)] = csr_matrix( + (data, (r, c)), shape=(nao, nao) + ).toarray() + fock.append(fock_) + over.append(over_) + ifr += 1 + + +.. GENERATED FROM PYTHON SOURCE LINES 241-244 + +You can now save the matrices to ``.npy`` files, and a file with the +k-grids used in the calculations. + + +.. GENERATED FROM PYTHON SOURCE LINES 247-257 + +.. code:: python + + os.makedirs("data", exist_ok=True) + # Save the Hamiltonians + np.save("data/graphene_fock.npy", fock) + # Save the overlaps + np.save("data/graphene_ovlp.npy", over) + # Write a file with the k-grids, one line per structure + np.savetxt('data/kmesh.dat', [[15,15,1]]*len(frames), fmt='%d') + + +.. GENERATED FROM PYTHON SOURCE LINES 260-263 + +Download precomputed data +^^^^^^^^^^^^^^^^^^^^^^^^^ + + +.. GENERATED FROM PYTHON SOURCE LINES 266-269 + +For the sake of simplicity, you can also download precomputed data and +run just the machine learning part of the notebook using these data. + + +.. GENERATED FROM PYTHON SOURCE LINES 269-285 + +.. code-block:: Python + + + filename = "precomputed.zip" + if not os.path.exists(filename): + url = ( + "https://github.com/curiosity54/mlelec/raw/" + "tutorial_periodic/examples/periodic_tutorial/precomputed.zip" + ) + response = requests.get(url) + response.raise_for_status() + with open(filename, "wb") as f: + f.write(response.content) + + with zipfile.ZipFile(filename, "r") as zip_ref: + zip_ref.extractall("./") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 286-301 + +Periodic Hamiltonians in real and reciprocal space +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The DFT calculations for the dataset above were performed using a +*minimal* STO-3G basis. The basis set is specified for each species +using three quantum numbers, :math:`n`, :math:`l`, :math:`m`. :math:`n` +is usually a natural number relating to the *radial* extent or +resolution whereas :math:`l` and :math:`m` specify the *angular +components* determining the shape of the orbital and its orientation in +space. For example, :math:`1s` orbitals correspond to :math:`n=1`, +:math:`l=0` and :math:`m=0`, while a :math:`2p_z` orbital corresponds to +:math:`n=2`, :math:`l=1` and :math:`m=0`. For the STO-3G basis-set, +these quantum numbers for Carbon (identified by its atomic number) are +given as follows. + + +.. GENERATED FROM PYTHON SOURCE LINES 301-308 + +.. code-block:: Python + + + basis = "sto-3g" + orbitals = { + "sto-3g": {6: [[1, 0, 0], [2, 0, 0], [2, 1, -1], [2, 1, 0], [2, 1, 1]]}, + } + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 309-326 + +For each *frame* which of either train and test structures, the QM data +comprises the configuration, along with the corresponding *overlap* and +*Hamiltonian* (used interchangeably with *Fock*) matrices in the basis +specified above, as well as the :math:`k`-point grid that was used for the +calculation. + +Note that we are currently specifying these matrices in *real-space*, +:math:`\mathbf{H}(\mathbf{t})` , such that the element +:math:`\langle \mathbf{0} i nlm| \hat{H}| \mathbf{t} i' n'l'm'\rangle` +indicates the interaction between orbital :math:`nlm` on atom :math:`i` +in the undisplaced cell (denoted by the null lattice translation, +:math:`\mathbf{t}=\mathbf{0}`) and orbital :math:`n'l'm'` on atom +:math:`i'` in a periodic copy of the unit cell translated by +:math:`\mathbf{t}`. A short-hand notation for +:math:`\langle \mathbf{0} i nlm| \hat{H}| \mathbf{t} i' n'l'm'\rangle` +is :math:`H_{\small\substack{i,nlm\\i',n'l'm'}}(\mathbf{t})` + + +.. GENERATED FROM PYTHON SOURCE LINES 328-342 + +.. figure:: graphene_lattice.png + :alt: Representation of a graphene unit cell and some replicas. + :width: 600px + + Representation of a graphene unit cell and its + :math:`3 \times 3 \times 1` replicas in real space. The central cell + is denoted by :math:`\mathbf{t}=(0,0,0)`, while the cells translated + by a single lattice vector along directions 1 and 2 are denoted by + :math:`\mathbf{t}=(1,0,0)` and :math:`\mathbf{t}=(0,1,0)`, + respectively. The Hamiltonian matrix element between the :math:`1s` + orbital on atom :math:`i` in the central unit cell and the + :math:`2p_z` orbital on atom :math:`i'` in the + :math:`\mathbf{t}=(1,0,0)` cell is schematically represented. + + +.. GENERATED FROM PYTHON SOURCE LINES 345-358 + +Alternatively, we can provide the matrices in *reciprocal* (or +Fourier, :math:`k`) space. These are related to the real-space matrices +by a *Bloch sum*, + +.. math:: + + \mathbf{H}(\mathbf{k})=\sum_{\mathbf{t}}\ + e^{i\mathbf{k}\cdot\mathbf{t}} \mathbf{H}(\mathbf{t}). + + +In the case the input matrices are in reciprocal space, there should be +one matrix per :math:`k`-point in the grid. + + +.. GENERATED FROM PYTHON SOURCE LINES 360-366 + +A ``QMDataset`` to store the DFT data +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +The ``QMDataset`` class holds all the relevant data +obtained from a quantum-mechanical (in this case, DFT) calculation, +combining information from the files containing structures, +Hamiltonians and overlap matrices, and :math:`k`-point mesh. + +.. GENERATED FROM PYTHON SOURCE LINES 366-388 + +.. code-block:: Python + + + qmdata = QMDataset.from_file( + # File containing the atomistic structures + frames_path="data/C2.xyz", + # File containing the Hamiltonian (of Fock) matrices + fock_realspace_path="graphene_fock.npy", + # File containing the overlap matrices + overlap_realspace_path="graphene_ovlp.npy", + # File containing the k-point grids used for the DFT calculations + kmesh_path="kmesh.dat", + # Physical dimensionality of the system. Graphene is a 2D material + dimension=2, + # Device where to run the calculations + # (can be 'cpu' or 'cuda', if GPUs are available) + device="cpu", + # Name of the basis set used for the calculations + orbs_name=basis, + # List of quantum numbers associated with the basis set orbitals + orbs=orbitals[basis], + ) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 389-394 + +Quantities stored in ``QMDataset`` can be accessed as attributes, +e.g. ``qmdata.fock_realspace`` is a list (one element per structure) of +dictionaries labeled by the indices of the unit cell real-space +translations containing ``torch.Tensor``. + + +.. GENERATED FROM PYTHON SOURCE LINES 394-402 + +.. code-block:: Python + + + structure_idx = 0 + realspace_translation = 0, 0, 0 + print(f"The real-space Hamiltonian matrix for structure {structure_idx} labeled by") + print(f"translation T={realspace_translation} is:") + print(f"{qmdata.fock_realspace[structure_idx][realspace_translation]}") + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + The real-space Hamiltonian matrix for structure 0 labeled by + translation T=(0, 0, 0) is: + tensor([[-9.7210e+00, -2.6676e+00, 2.9317e-04, 3.2255e-04, 5.7009e-04, + -8.1646e-05, -4.6611e-01, -3.6897e-01, -1.2792e-02, 6.7660e-01], + [-2.6676e+00, -1.3880e+00, 3.2649e-03, 7.2985e-03, 1.0359e-02, + -4.6611e-01, -5.9615e-01, -2.5023e-01, -8.9866e-03, 4.5874e-01], + [ 2.9317e-04, 3.2649e-03, -4.2835e-01, -9.5326e-05, -1.2642e-02, + 3.6897e-01, 2.5023e-01, -1.0482e-01, 3.3322e-03, -1.6016e-01], + [ 3.2255e-04, 7.2985e-03, -9.5326e-05, -1.4549e-01, -2.8526e-04, + 1.2792e-02, 8.9865e-03, 3.3322e-03, -1.4956e-01, -6.0943e-03], + [ 5.7009e-04, 1.0359e-02, -1.2642e-02, -2.8526e-04, -4.4633e-01, + -6.7660e-01, -4.5874e-01, -1.6016e-01, -6.0944e-03, 1.0121e-01], + [-8.1646e-05, -4.6611e-01, 3.6897e-01, 1.2792e-02, -6.7660e-01, + -9.7210e+00, -2.6676e+00, -2.9113e-04, -3.2414e-04, -5.7176e-04], + [-4.6611e-01, -5.9615e-01, 2.5023e-01, 8.9865e-03, -4.5874e-01, + -2.6676e+00, -1.3880e+00, -3.2673e-03, -7.2983e-03, -1.0360e-02], + [-3.6897e-01, -2.5023e-01, -1.0482e-01, 3.3322e-03, -1.6016e-01, + -2.9113e-04, -3.2673e-03, -4.2835e-01, -9.5331e-05, -1.2644e-02], + [-1.2792e-02, -8.9866e-03, 3.3322e-03, -1.4956e-01, -6.0944e-03, + -3.2414e-04, -7.2983e-03, -9.5331e-05, -1.4549e-01, -2.8525e-04], + [ 6.7660e-01, 4.5874e-01, -1.6016e-01, -6.0943e-03, 1.0121e-01, + -5.7176e-04, -1.0360e-02, -1.2644e-02, -2.8525e-04, -4.4633e-01]]) + + + + +.. GENERATED FROM PYTHON SOURCE LINES 403-406 + +Machine learning data set +~~~~~~~~~~~~~~~~~~~~~~~~~ + + +.. GENERATED FROM PYTHON SOURCE LINES 409-412 + +Symmetries of the Hamiltonian matrix +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + +.. GENERATED FROM PYTHON SOURCE LINES 415-450 + +The data stored in ``QMDataset`` can be transformed into a format that +is optimal for machine learning modeling by leveraging the underlying +*physical symmetries* that characterize the atomistic structure, the +basis set, and their associated matrices. + +The Hamiltonian matrix is a complex learning target, indexed by two +atoms and the orbitals centered on them. Each +:math:`\mathbf{H}(\mathbf{k})` is a *Hermitian* matrix, while in real +space, periodicity introduces a *symmetry over translation pairs* such +that :math:`\mathbf{H}(-\mathbf{t}) = \mathbf{H}(\mathbf{t})^\dagger`, +where the dagger, :math:`\dagger`, denotes Hermitian conjugation. + +To address the symmetries associated with swapping atomic indices or +orbital labels, we divide the matrix into *blocks labeled by pairs of +atom types*. + +- ``block_type = 0``, or *on-site* blocks, consist of elements + corresponding to the interaction of orbitals on the same atom, + :math:`i = i'`. + +- ``block_type = 2``, or *cross-species* blocks, consist of elements + corresponding to orbitals centered on atoms of distinct species. + Since the two atoms can be distinguished, they can be consistently + arranged in a predetermined order. + +- ``block_type = 1, -1``, or *same-species* blocks, consist of + elements corresponding to orbitals centered on distinct atoms of the + same species. As these atoms are indistinguishable and cannot be + ordered definitively, the pair must be symmetrized for permutations. + We construct symmetric and antisymmetric combinations + :math:`(\mathbf{H}_{\small\substack{i,nlm\\i',n'l'm'}}(\mathbf{t})\pm\ + \mathbf{H}_{\small\substack{i',nlm\\i,n'l'm'}}(\mathbf{-t}))` + that correspond to ``block_type`` :math:`+1` and :math:`-1`, + respectively. + + +.. GENERATED FROM PYTHON SOURCE LINES 453-456 + +Equivariant structure of the Hamiltonians +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + +.. GENERATED FROM PYTHON SOURCE LINES 459-507 + +Even though the Hamiltonian operator under consideration is invariant, +*its representation transforms under the action of structural rotations +and inversions* due to the choice of the basis functions. Each of the +blocks has elements of the form +:math:`\langle\mathbf{0}inlm|\hat{H}|\mathbf{t}i'n'l'm'\rangle`, which +are in an *uncoupled* representation and transform as a product of +(real) spherical harmonics, :math:`Y_l^m \otimes Y_{l'}^{m'}`. + +This product can be decomposed into a direct sum of irreducible +representations (irreps) of :math:`\mathrm{SO(3)}`, + +.. math:: \lambda \mu:\lambda \in [|l_1-l_2|,l_1+l_2],\mu \in [-\lambda,\lambda], + +which express the Hamiltonian blocks in terms of contributions that +rotate independently and can be modeled using a feature that +geometrically describes the pair of atoms under consideration and shares +the same symmetry. We use the notation +:math:`H_{ii';nn'll'}^{\lambda\mu}` to indicate the elements of the +Hamiltonian in this coupled basis. + +The resulting irreps form a *coupled* representation, each of which +transforms as a spherical harmonic :math:`Y^\mu_\lambda` under +:math:`\mathrm{SO(3)}` rotations, but may exhibit more complex behavior +under inversions. For example, spherical harmonics transform under +inversion, :math:`\hat{i}`, as polar tensors: + +.. math:: \hat{i}Y^\mu_\lambda = (-1)^\lambda Y^\mu_\lambda. + +Some of the coupled basis terms transform like :math:`Y^\mu_\lambda`, +while others instead transform as pseudotensors, + +.. math:: \hat{i}H^{\lambda\mu}=(-1)^{\lambda+1}H^{\lambda\mu} + +where we omit for simplicity the indices that are not directly associated +with inversion and rotation symmetry. For more details about the block +decomposition, please refer to `Nigam et al., J. Chem. Phys. 156, 014115 +(2022) `__. + +The following is an animation of a trajectory along a `Lissajous +curve `__ in 3D space, +alongside a colormap representing the values of the real-space +Hamiltonian matrix elements of the graphene unit cell in a minimal +STO-3G basis. From the animation, it is evident how invariant elements, +such as those associated with interactions between :math:`s` orbitals, +do not change under structural rotations. On the other hand, +interactions allowing for equivariant components, such as the +:math:`s`-:math:`p` block, change under rotations. + + +.. GENERATED FROM PYTHON SOURCE LINES 507-529 + +.. code-block:: Python + + + image_files = sorted( + [ + f"frames/{f}" + for f in os.listdir("./frames") + if f.startswith("rot_") and f.endswith(".png") + ] + ) + images = [mpimg.imread(img) for img in image_files] + fig, ax = plt.subplots() + img_display = ax.imshow(images[0]) + ax.axis("off") + + + def update(frame): + img_display.set_data(images[frame]) + return [img_display] + + + ani = FuncAnimation(fig, update, frames=len(images), interval=20, blit=True) + + + + + +.. container:: sphx-glr-animation + + .. raw:: html + + + + + + + +
+ +
+ +
+ + + + + + + + + +
+
+ + + + + + +
+
+
+ + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 530-535 + +.. code:: python + + from IPython.display import HTML + HTML(ani.to_jshtml()) + + +.. GENERATED FROM PYTHON SOURCE LINES 538-541 + +Mapping geometric features to Hamiltonian targets +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + +.. GENERATED FROM PYTHON SOURCE LINES 544-567 + +Each Hamiltonian block obtained from the procedure `described +above <#symmetries-of-the-hamiltonian-matrix>`__ can be modeled using +symmetrized features. + +Elements of ``block_type=0`` are indexed by a single atom and are best +described by a symmetrized atom-centered density correlation +(`ACDC `__), denoted by +:math:`|\overline{\rho_{i}^{\otimes \nu}; \sigma; \lambda\mu }\rangle`, +where :math:`\nu` refers to the correlation (body)-order, and—just as +for the blocks—:math:`\lambda \mu` indicate the :math:`\mathrm{SO(3)}` +irrep to which the feature is symmetrized. The symbol :math:`\sigma` +denotes the inversion parity. + +For other blocks, such as ``block_type=2``, which explicitly reference +two atoms, we use `two-center `__ +ACDCs, :math:`|\overline{\rho_{ii'}^{\otimes \nu}; \lambda\mu }\rangle`. + +For ``block_type=1, -1``, we ensure equivariance with respect to atom +index permutation by constructing symmetric and antisymmetric pair +features: +:math:`(|\overline{\rho_{ii'}^{\otimes \nu};\lambda\mu }\rangle\pm\ +|\overline{\rho_{i'i}^{\otimes \nu};\lambda\mu }\rangle)`. + + +.. GENERATED FROM PYTHON SOURCE LINES 570-589 + +The features are discretized on a basis of radial functions and +spherical harmonics, and their performance may depend on the +*resolution* of the functions included in the model. There are +additional hyperparameters, such as the *cutoff* radius, which +controls the extent of the atomic environment, and Gaussian widths. In +the following, we allow for flexibility in discretizing the +atom-centered and two-centered ACDCs by defining the hyperparameters for +the single-center (SC) :math:`\lambda`-SOAP and two-center (TC) ACDC +descriptors. + +The single and two-center descriptors have very similar hyperparameters, +except for the cutoff radius, which is larger for the two-center +descriptors to explicitly include distant pairs of atoms. + +Note that the descriptors of pairs of atoms separated by distances +greater than the cutoff radius are identically zero. Thus, any model +based on these descriptors would predict an identically zero value for +these pairs. + + +.. GENERATED FROM PYTHON SOURCE LINES 589-611 + +.. code-block:: Python + + + SC_HYPERS = { + "cutoff": 3.0, + "max_radial": 6, + "max_angular": 6, + "atomic_gaussian_width": 0.5, + "center_atom_weight": 1, + "radial_basis": {"Gto": {}}, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + } + + TC_HYPERS = { + "cutoff": 6.0, + "max_radial": 6, + "max_angular": 6, + "atomic_gaussian_width": 0.3, + "center_atom_weight": 1.0, + "radial_basis": {"Gto": {}}, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + } + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 612-621 + +We then use the above defined hyperparameters to compute the descriptor +and initialize a ``MLDataset`` instance, which contains, among other +things, the Hamiltonian block decomposition and the geometric features +described above. + +In addition to computing the descriptors, ``MLDataset`` takes the data +stored in the ``QMDataset`` instance and puts it in a form required to +train a ML model. + + +.. GENERATED FROM PYTHON SOURCE LINES 624-634 + +The ``item_names`` argument is a list of names of the quantities we want +to compute and target in the ML model training, or that we want to be +able to access later. + +For example, ``fock_blocks`` is a +`metatensor.Tensormap `__ containing the +Hamiltonian coupled blocks. We also want to access the overlap matrices +in :math:`k`-space (``overlap_kspace``) to be able to compute the +Hamiltonian eigenvalues in the :math:`k`-grid. + + +.. GENERATED FROM PYTHON SOURCE LINES 634-658 + +.. code-block:: Python + + + + mldata = MLDataset( + # A QMDataset instance + qmdata, + # The names of the quantities to compute/initialize for the training + item_names=["fock_blocks", "overlap_kspace"], + # Hypers for the SC descriptors + hypers_atom=SC_HYPERS, + # Hypers for the TC descriptors + hypers_pair=TC_HYPERS, + # Cutoff for the angular quantum number to use in the Clebsh-Gordan iterations + lcut=4, + # Fraction of structures in the training set + train_frac=0.7, + # Fraction of structures in the validation set + val_frac=0.2, + # Fraction of structures in the test set + test_frac=0.1, + # Whether to shuffle or not the structure indices before splitting the data set + shuffle=True, + ) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + cpu pair features + cpu single center features + cpu single center features + + + + +.. GENERATED FROM PYTHON SOURCE LINES 659-662 + +The matrix decomposition into blocks and the calculations of geometric +features is performed by the ``MLDataset`` class. + + +.. GENERATED FROM PYTHON SOURCE LINES 665-668 + +``mldata.features`` is ``metatensor.TensorMap`` containing the +stuctures’ descriptors + + +.. GENERATED FROM PYTHON SOURCE LINES 668-672 + +.. code-block:: Python + + + mldata.features + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + TensorMap with 27 blocks + keys: order_nu inversion_sigma spherical_harmonics_l species_center species_neighbor block_type + 2 -1 1 6 6 -1 + 2 -1 1 6 6 0 + 2 -1 1 6 6 1 + 2 -1 2 6 6 -1 + 2 -1 2 6 6 0 + 2 -1 2 6 6 1 + 2 -1 3 6 6 -1 + 2 -1 3 6 6 0 + 2 -1 3 6 6 1 + 2 -1 4 6 6 -1 + 2 -1 4 6 6 0 + 2 -1 4 6 6 1 + 2 1 0 6 6 -1 + 2 1 0 6 6 0 + 2 1 0 6 6 1 + 2 1 1 6 6 -1 + 2 1 1 6 6 0 + 2 1 1 6 6 1 + 2 1 2 6 6 -1 + 2 1 2 6 6 0 + 2 1 2 6 6 1 + 2 1 3 6 6 -1 + 2 1 3 6 6 0 + 2 1 3 6 6 1 + 2 1 4 6 6 -1 + 2 1 4 6 6 0 + 2 1 4 6 6 1 + + + +.. GENERATED FROM PYTHON SOURCE LINES 673-676 + +``mldata.items`` is a ``namedtuple`` containing the quantities defined +in ``item_names``. e.g. the coupled Hamiltonian blocks: + + +.. GENERATED FROM PYTHON SOURCE LINES 676-681 + +.. code-block:: Python + + + print("The TensorMap containing the Hamiltonian coupled blocks is") + mldata.items.fock_blocks + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + The TensorMap containing the Hamiltonian coupled blocks is + + TensorMap with 9 blocks + keys: block_type species_i species_j L inversion_sigma + -1 6 6 0 1 + -1 6 6 1 -1 + -1 6 6 1 1 + 0 6 6 0 1 + 0 6 6 1 1 + 0 6 6 2 1 + 1 6 6 0 1 + 1 6 6 1 1 + 1 6 6 2 1 + + + +.. GENERATED FROM PYTHON SOURCE LINES 682-684 + +Or the overlap matrices: + + +.. GENERATED FROM PYTHON SOURCE LINES 684-691 + +.. code-block:: Python + + + structure_idx = 0 + k_idx = 0 + print(f"The overlap matrix for structure {structure_idx} at the {k_idx}-th k-point is") + mldata.items.overlap_kspace[structure_idx][k_idx] + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + The overlap matrix for structure 0 at the 0-th k-point is + + tensor([[ 1.0000e+00+0.j, 2.6471e-01+0.j, -8.6736e-19+0.j, -3.4717e-16+0.j, + 0.0000e+00+0.j, 8.4955e-06+0.j, 1.3441e-01+0.j, 8.8189e-04+0.j, + 3.7267e-03+0.j, 3.8015e-03+0.j], + [ 2.6471e-01+0.j, 1.4675e+00+0.j, 5.4607e-25+0.j, -2.2147e-16+0.j, + 2.6503e-23+0.j, 1.3441e-01+0.j, 1.3276e+00+0.j, -7.6212e-04+0.j, + 2.2394e-02+0.j, 4.7228e-03+0.j], + [ 8.6736e-19+0.j, -5.4607e-25+0.j, 6.5783e-01+0.j, 6.3610e-17+0.j, + 6.2688e-04+0.j, -8.8189e-04+0.j, 7.6212e-04+0.j, -2.4925e-01+0.j, + -2.1836e-05+0.j, -1.6848e-02+0.j], + [ 3.4717e-16+0.j, 2.2147e-16+0.j, 6.3610e-17+0.j, 1.2005e+00+0.j, + 3.4697e-17+0.j, -3.7267e-03+0.j, -2.2394e-02+0.j, -2.1836e-05+0.j, + 7.7122e-01+0.j, -2.4677e-04+0.j], + [ 0.0000e+00+0.j, -2.6503e-23+0.j, 6.2688e-04+0.j, 3.4697e-17+0.j, + 6.6397e-01+0.j, -3.8015e-03+0.j, -4.7228e-03+0.j, -1.6848e-02+0.j, + -2.4677e-04+0.j, -2.7830e-01+0.j], + [ 8.4955e-06+0.j, 1.3441e-01+0.j, -8.8189e-04+0.j, -3.7267e-03+0.j, + -3.8015e-03+0.j, 1.0000e+00+0.j, 2.6471e-01+0.j, 0.0000e+00+0.j, + 0.0000e+00+0.j, 0.0000e+00+0.j], + [ 1.3441e-01+0.j, 1.3276e+00+0.j, 7.6212e-04+0.j, -2.2394e-02+0.j, + -4.7228e-03+0.j, 2.6471e-01+0.j, 1.4675e+00+0.j, 5.4607e-25+0.j, + 0.0000e+00+0.j, 2.6501e-23+0.j], + [ 8.8189e-04+0.j, -7.6212e-04+0.j, -2.4925e-01+0.j, -2.1836e-05+0.j, + -1.6848e-02+0.j, 0.0000e+00+0.j, -5.4607e-25+0.j, 6.5783e-01+0.j, + 0.0000e+00+0.j, 6.2688e-04+0.j], + [ 3.7267e-03+0.j, 2.2394e-02+0.j, -2.1836e-05+0.j, 7.7122e-01+0.j, + -2.4677e-04+0.j, 0.0000e+00+0.j, 0.0000e+00+0.j, 0.0000e+00+0.j, + 1.2005e+00+0.j, 0.0000e+00+0.j], + [ 3.8015e-03+0.j, 4.7228e-03+0.j, -1.6848e-02+0.j, -2.4677e-04+0.j, + -2.7830e-01+0.j, 0.0000e+00+0.j, -2.6501e-23+0.j, 6.2688e-04+0.j, + 0.0000e+00+0.j, 6.6397e-01+0.j]]) + + + +.. GENERATED FROM PYTHON SOURCE LINES 692-695 + +A machine learning model for the electronic Hamiltonian of graphene +------------------------------------------------------------------- + + +.. GENERATED FROM PYTHON SOURCE LINES 698-726 + +Linear model +~~~~~~~~~~~~ + +In simple cases, such as the present one, it is convenient to start with +a linear model that directly maps the geometric descriptors to the +target coupled blocks. This can be achieved using `Ridge regression +`__ +as implemented in `scikit-learn `__. + +The linear regression model is expressed as + +.. math:: + + + H_{ii',\mathbf{Q}}^{\lambda\mu}(\mathbf{t}) = \ + \sum_\mathbf{q} w_{\mathbf{q}}^{\mathbf{Q},\lambda} \ + (\rho_{ii'}^{\otimes \nu}(\mathbf{t}))_{\mathbf{q}}^{\lambda\mu}, + +where a shorthand notation for the features has been introduced. Here, +:math:`\mathbf{Q}` includes all labels indicating the involved orbitals, +atomic species, and permutation symmetry, while :math:`\mathbf{q}` +represents the feature dimension. The quantities +:math:`w_{\mathbf{q}}^{\mathbf{Q},\lambda}` are the model’s weights. +Note that different weights are associated with different values of +:math:`\mathbf{Q}` and :math:`\lambda`, but not with specific atom pairs +or the translation vector, whose dependence arises only through the +descriptors. + + +.. GENERATED FROM PYTHON SOURCE LINES 729-735 + +In ``mlelec``, a linear model can be trained through the +``LitEquivariantModel`` class, which accepts an ``init_from_ridge`` +keyword. When set to ``True``, this initializes the weights of a more +general ``torch.nn.Module`` with the weights provided by Ridge +regression. + + +.. GENERATED FROM PYTHON SOURCE LINES 738-742 + +We will pass other keyword arguments to ``LitEquivariantModel``, to be +able to further train the weights on top to the initial Ridge +regression. + + +.. GENERATED FROM PYTHON SOURCE LINES 742-760 + +.. code-block:: Python + + + model = LitEquivariantModel( + mldata=mldata, # a MLDataset instance + nlayers=0, # The number of hidden layers + nhidden=1, # The number of neurons in each hidden layer + init_from_ridge=True, # If True, initialize the weights and biases of the + # purely linear model from Ridge regression + optimizer="LBFGS", # Type of optimizer. Adam is likely better for + # a more general neural network + activation="SiLU", # The nonlinear activation function + learning_rate=1e-3, # Initial learning rate (LR) + lr_scheduler_patience=10, + lr_scheduler_factor=0.7, + lr_scheduler_min_lr=1e-6, + loss_fn=MSELoss(), # Use the mean square error as loss function + ) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 761-764 + +Model’s accuracy in reproducing derived properties +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + +.. GENERATED FROM PYTHON SOURCE LINES 767-770 + +The Hamiltonian coupled blocks predicted by the ML model can be accessed +from ``model.forward()`` + + +.. GENERATED FROM PYTHON SOURCE LINES 770-774 + +.. code-block:: Python + + + predicted_blocks = model.forward(mldata.features) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 775-780 + +The real-space blocks can be transformed to Hamiltonian matrices via the +``mlelec.utils.pbc_utils.blocks_to_matrix`` function. The resulting +real-space Hamiltonians can be Fourier transformed to give the +:math:`k`-space ones. + + +.. GENERATED FROM PYTHON SOURCE LINES 780-790 + +.. code-block:: Python + + + HT = blocks_to_matrix( + predicted_blocks, + orbitals["sto-3g"], + {A: qmdata.structures[A] for A in range(len(qmdata))}, + detach=True, + ) + Hk = qmdata.bloch_sum(HT, is_tensor=True) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 791-794 + +Kohn-Sham eigenvalues +''''''''''''''''''''' + + +.. GENERATED FROM PYTHON SOURCE LINES 797-800 + +We can then compute the eigenvalues on the :math:`k`-grid used for the +calculation to assess the model accuracy in predicting band energies. + + +.. GENERATED FROM PYTHON SOURCE LINES 800-852 + +.. code-block:: Python + + + target_eigenvalues = compute_eigenvalues(qmdata.fock_kspace, qmdata.overlap_kspace) + predicted_eigenvalues = compute_eigenvalues(Hk, qmdata.overlap_kspace) + + Hartree = 27.211386024367243 # eV + + plt.rcParams["font.size"] = 14 + fig, ax = plt.subplots() + ax.set_aspect("equal") + + x_text = 0.38 + y_text = 0.2 + d = 0.06 + + for i, (idx, label) in enumerate( + zip( + [mldata.train_idx, mldata.val_idx, mldata.test_idx], + ["train", "validation", "test"], + ) + ): + + target = ( + torch.stack([target_eigenvalues[i] for i in idx]).flatten().detach() * Hartree + ) + prediction = ( + torch.stack([predicted_eigenvalues[i] for i in idx]).flatten().detach() + * Hartree + ) + + non_core_states = target > -100 + rmse = np.sqrt( + np.mean( + (target.numpy()[non_core_states] - prediction.numpy()[non_core_states]) ** 2 + ) + ) + ax.scatter(target, prediction, marker=".", label=label, alpha=0.5) + ax.text( + x=x_text, + y=y_text - d * i, + s=rf"$\mathrm{{RMSE_{{{label}}}={rmse:.2f}\,eV}}$", + transform=ax.transAxes, + ) + + xmin, xmax = ax.get_xlim() + ax.plot([xmin, xmax], [xmin, xmax], "--k") + ax.set_xlim(xmin, xmax) + ax.set_ylim(xmin, xmax) + ax.legend() + ax.set_xlabel("Target eigenvalues (eV)") + ax.set_ylabel("Predicted eigenvalues (eV)") + + + + + +.. image-sg:: /examples/periodic-hamiltonian/images/sphx_glr_periodic-hamiltonian_002.png + :alt: periodic hamiltonian + :srcset: /examples/periodic-hamiltonian/images/sphx_glr_periodic-hamiltonian_002.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + Text(74.4222222222222, 0.5, 'Predicted eigenvalues (eV)') + + + +.. GENERATED FROM PYTHON SOURCE LINES 853-856 + +Graphene band structure +''''''''''''''''''''''' + + +.. GENERATED FROM PYTHON SOURCE LINES 859-863 + +Apart from the eigenvalues on a mesh in the Brillouin zone, we can use +the real-space Hamiltonians predicted by the model to compute the band +structure along high-symmetry paths. + + +.. GENERATED FROM PYTHON SOURCE LINES 863-893 + +.. code-block:: Python + + + fig, ax = plt.subplots(figsize=(8, 4.8)) + + idx = 0 + + handles = [] + + with warnings.catch_warnings(): + warnings.filterwarnings("ignore", category=DeprecationWarning) + + # Plot reference + ax, h_ref = plot_bands_frame( + qmdata.fock_realspace[idx], idx, qmdata, ax=ax, color="blue", lw=2 + ) + + # Plot prediction + ax, h_pred = plot_bands_frame( + HT[idx], idx, qmdata, ax=ax, color="lime", ls="--", lw=2 + ) + + ax.set_ylim(-30, 30) + ax.legend( + [h_ref, h_pred], + ["Reference", "Prediction"], + loc="center left", + bbox_to_anchor=(1, 0.5), + ) + fig.tight_layout() + + + + + +.. image-sg:: /examples/periodic-hamiltonian/images/sphx_glr_periodic-hamiltonian_003.png + :alt: periodic hamiltonian + :srcset: /examples/periodic-hamiltonian/images/sphx_glr_periodic-hamiltonian_003.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['std_lattice']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['std_positions']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['std_types']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['number']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['transformation_matrix']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['international']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['std_rotation_matrix']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['std_lattice']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['std_positions']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['std_types']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['number']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['transformation_matrix']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['international']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/periodic-hamiltonian/lib/python3.11/site-packages/spglib/spglib.py:115: DeprecationWarning: dict interface (SpglibDataset['std_rotation_matrix']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead + warnings.warn( + + + + +.. GENERATED FROM PYTHON SOURCE LINES 894-897 + +Adding nonlinearities +--------------------- + + +.. GENERATED FROM PYTHON SOURCE LINES 900-911 + +The model used above consists of several submodels, one for each Hamiltonian +coupled block. Each submodel can be extended to a `multilayer +perceptron `__ +(MLP) that maps the corresponding set of geometric features to the +Hamiltonian coupled block. Nonlinearities are applied to the invariants +constructed from each equivariant feature block using the +``EquivariantNonlinearity`` module. This section outlines the process to +modify the model to introduce non-linear terms. Given that the time +to train and evaluate the model would then increase, this section +includes snippets of code, but is not a complete implementation and +is not executed when running this example. + +.. GENERATED FROM PYTHON SOURCE LINES 914-929 + +The architecture of ``EquivariantNonlinearity`` can be visualized with +``torchviz`` with the following snippet: + +.. code:: python + + import torch + from mlelec.models.equivariant_model import EquivariantNonLinearity + from torchviz import make_dot + m = EquivariantNonLinearity(torch.nn.SiLU(), layersize = 10) + y = m.forward(torch.randn(3,3,10)) + dot = make_dot(y, dict(m.named_parameters())) + dot.graph_attr.update(size='150,150') + dot.render("equivariantnonlinear", format="png") + dot + + +.. GENERATED FROM PYTHON SOURCE LINES 932-938 + +.. figure:: equivariantnonlinear.png + :alt: Graph representing the architecture of EquivariantNonLinearity + :width: 300px + + Graph representing the architecture of EquivariantNonLinearity + + +.. GENERATED FROM PYTHON SOURCE LINES 941-964 + +The global architecture of the MLP, implemented in ``simpleMLP``, can be +visualized with + +.. code:: python + + import torch + from mlelec.models.equivariant_model import simpleMLP + from torchviz import make_dot + mlp = simpleMLP( + nin=10, + nout=1, + nhidden=1, + nlayers=1, + bias=True, + activation='SiLU', + apply_layer_norm=True + ) + y = mlp.forward(torch.randn(1,1,10)) + dot = make_dot(y, dict(mlp.named_parameters())) + dot.graph_attr.update(size='150,150') + dot.render("simpleMLP", format="png") + dot + + +.. GENERATED FROM PYTHON SOURCE LINES 967-973 + +.. figure:: simpleMLP.png + :alt: Graph representing the architecture of simpleMLP + :width: 600px + + Graph representing the architecture of simpleMLP + + +.. GENERATED FROM PYTHON SOURCE LINES 976-979 + +Set up the training loop for stochastic gradient descent +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + +.. GENERATED FROM PYTHON SOURCE LINES 982-984 + +Import additional modules needed to monitor the training. + + +.. GENERATED FROM PYTHON SOURCE LINES 987-994 + +.. code:: python + + import lightning.pytorch as pl + from lightning.pytorch.callbacks import EarlyStopping + from mlelec.callbacks.logging import LoggingCallback + from mlelec.models.equivariant_lightning import MLDatasetDataModule + + +.. GENERATED FROM PYTHON SOURCE LINES 997-1000 + +We set up a callback for logging training information such as the +training and validation losses. + + +.. GENERATED FROM PYTHON SOURCE LINES 1003-1007 + +.. code:: python + + logger_callback = LoggingCallback(log_every_n_epochs=5) + + +.. GENERATED FROM PYTHON SOURCE LINES 1010-1013 + +We set up an early stopping criterion to stop the training when the +validation loss function stops decreasing. + + +.. GENERATED FROM PYTHON SOURCE LINES 1016-1022 + +.. code:: python + + early_stopping = EarlyStopping( + monitor="val_loss", min_delta=1e-3, patience=10, verbose=False, mode="min" + ) + + +.. GENERATED FROM PYTHON SOURCE LINES 1025-1033 + +We define a ``lighting.pytorch.Trainer`` instance to handle the training +loop. For example, we can further optimize the weights for 50 epochs using +the `LBFGS `__ +optimizer. + +Note that PyTorch Lightning requires the definition of a data module to +instantiate DataLoaders to be used during the training. + + +.. GENERATED FROM PYTHON SOURCE LINES 1036-1051 + +.. code:: python + + data_module = MLDatasetDataModule(mldata, batch_size=16, num_workers=0) + + trainer = pl.Trainer( + max_epochs=50, + accelerator="cpu", + check_val_every_n_epoch=10, + callbacks=[early_stopping, logger_callback], + logger=False, + enable_checkpointing=False, + ) + + trainer.fit(model, data_module) + + +.. GENERATED FROM PYTHON SOURCE LINES 1054-1057 + +We compute the test set loss to assess the model accuracy on an unseen +set of structures + + +.. GENERATED FROM PYTHON SOURCE LINES 1060-1064 + +.. code:: python + + trainer.test(model, data_module) + + +.. GENERATED FROM PYTHON SOURCE LINES 1067-1072 + +In this case, Ridge regression already provides good accuracy, so +further optimizing the weights offers limited improvement. However, for +more complex datasets, the benefits of additional optimization can be +significant. + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (1 minutes 53.471 seconds) + + +.. _sphx_glr_download_examples_periodic-hamiltonian_periodic-hamiltonian.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + + .. container:: sphx-glr-download + + :download:`Download data files: data.zip ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: periodic-hamiltonian.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: periodic-hamiltonian.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: periodic-hamiltonian.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/pi-metad/pi-metad.rst.txt b/_sources/examples/pi-metad/pi-metad.rst.txt new file mode 100644 index 00000000..3e975c11 --- /dev/null +++ b/_sources/examples/pi-metad/pi-metad.rst.txt @@ -0,0 +1,1366 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/pi-metad/pi-metad.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_pi-metad_pi-metad.py: + + +Path integral metadynamics +========================== + +:Authors: Michele Ceriotti `@ceriottm `_ + +This example shows how to run a free-energy sampling calculation that +combines path integral molecular dynamics to model nuclear quantum effects +and metadynamics to accelerate sampling of the high-free-energy regions. + +The rather complicated setup combines `i-PI `_ +to perform path integral +MD, its built-in driver to compute energy and forces for the Zundel +:math:`\mathrm{H_5O_2^+}` cation, and `PLUMED `_ +to perform metadynamics. +If you want to see an example in a more realistic scenario, you can look at +`this paper (Rossi et al., JCTC (2020)) +`_, +in which this +methodology is used to simulate the decomposition of methanesulphonic +acid in a solution of phenol and hydrogen peroxide. + +Note also that, in order to keep the execution time of this example as +low as possible, several parameters are set to values that would not be +suitable for an accurate, converged simulation. +They will be highlighted and more reasonable values will be provided. +"High-quality" runs can also be realized substituting the input files +used in this example with those labeled with the ``_hiq`` suffix, that +are also provided in the ``data/`` folder. + +.. GENERATED FROM PYTHON SOURCE LINES 33-48 + +.. code-block:: Python + + + import bz2 + import os + import subprocess + import time + import xml.etree.ElementTree as ET + + import ase + import ase.io + import chemiscope + import ipi + import matplotlib.pyplot as plt + import numpy as np + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 49-76 + +Metadynamics for the Zundel cation +---------------------------------- + +Metadynamics is a method to accelerate sampling of rare events - microscopic processes +that are too infrequent to be observed over the time scale (ns-µs) accessible to +molecular dynamics simulations. You can read one of the many excellent reviews +on metadynamics (see e.g. +`Bussi and Branduardi (2015) `_), +or follow a +`lecture from the PLUMED masterclass +`_. +In short, during a metadynamics simulation an adaptive biasing potential is +built as a superimposition of Gaussians centered over configurations that have +been previously visited by the trajectory. This discourages the system from remaining +in high-probability configurations and accelerates sampling of free-energy barriers. + +.. figure:: metad-scheme.png + :align: center + :width: 600px + + A schematic representation of how metadynamics work by adaptively building + a repulsive bias based on the trajectory of a molecule, compensating for + low-energy regions in the free energy surface. + +Crucially, the bias is *not* built relative to the Cartesian coordinates of the atoms, +but relative to a lower-dimensional description of the system (so-called collective +variables) that are suited to describe the processes being studied. + +.. GENERATED FROM PYTHON SOURCE LINES 78-85 + +The Zundel cation :math:`\mathrm{H_5O_2^+}` is one of the limiting +structures of the solvated proton, and in the gas phase leads to a +stable structure, with the additional proton shared between two water +molecules (see the structure below). +We will use a potential fitted on high-end quantum-chemistry calculations +`Huang et al. (2005) `_ to compute energy +and forces acting on the atoms. + +.. GENERATED FROM PYTHON SOURCE LINES 86-90 + +.. code-block:: Python + + + zundel = ase.io.read("data/h5o2+.xyz", ":") + chemiscope.show(frames=zundel, mode="structure") + + + +.. chemiscope:: _datasets/fig_pi-metad_001.json.gz + :mode: structure + + + +.. raw:: html + +
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 91-98 + +As the two water molecules are separated, the proton remains attached +to one of the two, effectively leading to a dissociated +:math:`\mathrm{H_2O+H_3O^+}` configuration. Thus, two natural +coordinates to describe the physics of this system are the distance +between the O atoms, and the difference in coordination number of +the two O atoms, which is 0 for a shared proton and ±1 for the +dissociated system. + +.. GENERATED FROM PYTHON SOURCE LINES 101-111 + +Running metadynamics calculations with ``i-PI`` and ``PLUMED`` +-------------------------------------------------------------- + +The client-server architecture `i-PI `_ is based on makes it easy +to combine multiple programs to realize complicated simulation workflows. +In this case we will use an implementation of the Zundel potential in a simple +driver code that is available in the i-PI repository, and use +`PLUMED `_ to compute collective variables and build +the adaptive bias. We will then perform some post-processing to +estimate the free energy. + +.. GENERATED FROM PYTHON SOURCE LINES 114-120 + +Installing the Python driver +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +i-PI comes with a FORTRAN driver, which however has to be installed +from source. We use a utility function to compile it. Note that this requires +a functioning build system with `gfortran` and `make`. + +.. GENERATED FROM PYTHON SOURCE LINES 120-123 + +.. code-block:: Python + + + ipi.install_driver() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 124-127 + +Defining the molecular dynamics setup +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +The `input-md.xml` file defines the way the MD simulation is performed. + +.. GENERATED FROM PYTHON SOURCE LINES 127-130 + +.. code-block:: Python + + + xmlroot = ET.parse("data/input-md.xml").getroot() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 131-133 + +The `` block describe the way communication will occur with the +driver code + +.. GENERATED FROM PYTHON SOURCE LINES 133-136 + +.. code-block:: Python + + + print(" " + ET.tostring(xmlroot.find("ffsocket"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + 1.00000000e-04
zundel
+ + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 137-145 + +... and the `` section describes the MD setup. +This is a relatively standard NVT setup, with an efficient +generalized Langevin equation thermostat (important to +compensate for the non-equilibrium nature of metadynamics). +Note that the time step is rather long (the recommended value for +aqueous systems is around 0.5 fs). This is done to improve +efficiency for this example, but you should check if it +affects results in a realistic scenario. + +.. GENERATED FROM PYTHON SOURCE LINES 145-148 + +.. code-block:: Python + + + print(" " + ET.tostring(xmlroot.find(".//motion"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + False + + 1.0 + + + + [ 8.191023526179e-4, 8.328506066524e-3, 1.657771834013e-3, 9.736989925341e-4, 2.841803794895e-4, -3.176846864198e-5, -2.967010478210e-4, + -8.389856546341e-4, 2.405526974742e-2, -1.507872374848e-2, 2.589784240185e-3, 1.516783633362e-3, -5.958833418565e-4, 4.198422349789e-4, + 7.798710586406e-4, 1.507872374848e-2, 8.569039501219e-3, 6.001000899602e-3, 1.062029383877e-3, 1.093939147968e-3, -2.661575532976e-3, + -9.676783161546e-4, -2.589784240185e-3, -6.001000899602e-3, 2.680459336535e-5, -5.214694469742e-5, 4.231304910751e-4, -2.104894919743e-5, + -2.841997149166e-4, -1.516783633362e-3, -1.062029383877e-3, 5.214694469742e-5, 1.433903506353e-9, -4.241574212449e-5, 7.910178912362e-5, + 3.333208286893e-5, 5.958833418565e-4, -1.093939147968e-3, -4.231304910751e-4, 4.241574212449e-5, 2.385554468441e-8, -3.139255482869e-5, + 2.967533789056e-4, -4.198422349789e-4, 2.661575532976e-3, 2.104894919743e-5, -7.910178912362e-5, 3.139255482869e-5, 2.432567259684e-11 + ] + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 149-157 + +The metadynamics setup requires three ingredients: +a `` forcefield that defines what input to use +(more on that later) and the file from which to initialize +the structural information (number of atoms, ...); +`` is an advanced feature, available from +PLUMED 2.10, that allows extracting internal variables +from plumed and integrate them into the outputs of +i-PI. + +.. GENERATED FROM PYTHON SOURCE LINES 157-160 + +.. code-block:: Python + + + print(" " + ET.tostring(xmlroot.find("ffplumed"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + data/h5o2+.xyz + data/plumed-md.dat + [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 161-166 + +The `` section contains a `` key that +specifies that energy and forces from PLUMED should be +treated as a bias (so that e.g. are not included in the +potential, even though they're used to propagate the +trajectory). + +.. GENERATED FROM PYTHON SOURCE LINES 166-176 + +.. code-block:: Python + + + print(" " + ET.tostring(xmlroot.find(".//ensemble"), encoding="unicode")) + + # The `` section contains a `` class that + # instructs i-PI to call the PLUMED action that adds hills + # along the trajectory. + + print(" " + ET.tostring(xmlroot.find("smotion"), encoding="unicode")) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + 300.0 + + + + + + + [ plumed ] + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 177-198 + +CVs and metadynamics +~~~~~~~~~~~~~~~~~~~~ + +The calculation of the collective variables and the +metadynamics bias is delegated to PLUMED, and controlled by +a separate `plumed-md.dat` input file. +Without going in detail into the syntax, one can recognize the +calculation of the distance between the O atoms `doo`, +the coordination of the two oxygens `co1` and `co2`, +and the difference between the two, `dc`. +The `METAD` action specifies the CVs to be used, the pace of +hill depositon (which is way too frequent here, but suitable for +this example), the width along the two CVs and the initial +height of the repulsive Gaussians (which are both too large to +guarantee high resolution in CV and energy). The `BIASFACTOR` keyword specifies +that the height of the hills will be progressively reduced +according to the "well-tempered metadynamics" protocol, see +`Barducci et al., Phys. Rev. Lett. (2008) +`_. +A repulsive static bias (`UPPER_WALLS`) prevents complete dissociation of the +cation by limiting the range of the O-O distance. + +.. GENERATED FROM PYTHON SOURCE LINES 198-203 + +.. code-block:: Python + + + with open("data/plumed-md.dat", "r") as file: + plumed_dat = file.read() + print(plumed_dat) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + # default units are LENGTH=nm ENERGY=kJ/mol TIME=ps + doo: DISTANCE ATOMS=1,2 + co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14} + co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14} + dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO + mtd: METAD ARG=doo,dc PACE=10 SIGMA=0.005,0.05 HEIGHT=4 FILE=HILLS-md BIASFACTOR=10 TEMP=300 + uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250 + + PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=10 FILE=COLVAR-md + FLUSH STRIDE=1 + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 204-222 + +Running the simulations +~~~~~~~~~~~~~~~~~~~~~~~ + +Now we can launch the actual calculations. On the the command line, +this requires launching i-PI first, and then the built-in driver, +specifying the appropriate communication mode, and the `zundel` potential. +PLUMED is called from within i-PI as a library, so there is no need to +launch a separate process. Note that the Zundel potential requires some data +files, with a hard-coded location in the current working directory, +which is why the driver should be run from within the ``data/`` folder. + +.. code-block:: bash + + i-pi data/input-md.xml > log & + sleep 2 + cd data; i-pi-driver -u -a zundel -m zundel + +The same can be achieved from Python using ``subprocess.Popen`` + +.. GENERATED FROM PYTHON SOURCE LINES 222-235 + +.. code-block:: Python + + + ipi_process = None + if not os.path.exists("meta-md.out"): + # don't rerun if the outputs already exist + ipi_process = subprocess.Popen(["i-pi", "data/input-md.xml"]) + time.sleep(2) # wait for i-PI to start + driver_process = [ + subprocess.Popen( + ["i-pi-driver", "-u", "-a", "zundel", "-m", "zundel"], cwd="data/" + ) + for i in range(1) + ] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 236-238 + +If you run this in a notebook, you can go ahead and start loading +output files *before* i-PI has finished running by skipping this cell + +.. GENERATED FROM PYTHON SOURCE LINES 238-245 + +.. code-block:: Python + + + # wait for simulations to finish + if ipi_process is not None: + ipi_process.wait() + for process in driver_process: + process.wait() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 246-253 + +Trajectory post-processing +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +We can now post-process the simulation to see metadynamics in action. + +First, we read the trajectory outputs. Note that these have all been +printed with the same stride + +.. GENERATED FROM PYTHON SOURCE LINES 253-260 + +.. code-block:: Python + + + output_data, output_desc = ipi.read_output("meta-md.out") + colvar_data = ipi.read_trajectory("meta-md.colvar_0", format="extras")[ + "doo,dc,mtd.bias" + ] + traj_data = ipi.read_trajectory("meta-md.pos_0.xyz") + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 261-262 + +then, assemble a visualization + +.. GENERATED FROM PYTHON SOURCE LINES 262-277 + +.. code-block:: Python + + chemiscope.show( + frames=traj_data, + properties=dict( + d_OO=10 * colvar_data[:, 0], # nm to Å + delta_coord=colvar_data[:, 1], + bias=27.211386 * output_data["ensemble_bias"], # Ha to eV + time=2.4188843e-05 * output_data["time"], # atomictime to ps + ), # attime to ps + settings=chemiscope.quick_settings( + x="d_OO", y="delta_coord", z="bias", color="time", trajectory=True + ), + mode="default", + ) + + + + +.. chemiscope:: _datasets/fig_pi-metad_002.json.gz + :mode: default + + + +.. raw:: html + +
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 278-283 + +The visualization above shows how the growing metadynamics bias pushes +progressively the atoms towards geometries with larger O-O separations, +and that for these distorted configurations the proton is not shared +symmetrically between the O atoms, but is preferentially attached to +one of the two water molecules. + +.. GENERATED FROM PYTHON SOURCE LINES 285-300 + +Trajectory diagnostics +...................... + +The time history of the bias is instructive, as it shows how the +bias grows until the trajectory gets pushed in a new region (where the +bias is zero) and then grows again. The envelope of the bias increase +slows down over time, because the "well-tempered" deposition strategy +reduces the height of the hills deposited in high-bias regions. + +Note that the potential energy has fluctuations that are larger than +the magnitude of the bias, although it shows a tendency to reach higher +values as the simulation progresses. This is because only two degrees +of freedom are affected by the bias, while all degrees of freedom +undergo thermal fluctuations, which are dominant even for this +small system. + +.. GENERATED FROM PYTHON SOURCE LINES 300-322 + +.. code-block:: Python + + + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + + ax.plot( + 2.4188843e-05 * output_data["time"], + 27.211386 * output_data["potential"], + "r", + label="potential", + ) + ax.plot( + 2.4188843e-05 * output_data["time"], + 27.211386 * output_data["ensemble_bias"], + "b", + label="bias", + ) + + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"energy / eV") + ax.legend(loc="upper left", ncols=1) + plt.show() + + + + +.. image-sg:: /examples/pi-metad/images/sphx_glr_pi-metad_001.png + :alt: pi metad + :srcset: /examples/pi-metad/images/sphx_glr_pi-metad_001.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 323-329 + +It's important to keep in mind that the growing metadynamics bias can +lead to deviations from the quasi-equilibrium sampling that is necessary +to recover the correct properties of the rare event. It is not easy +to verify this condition, but one simple diagnostics that can highlight +the most evident problems is looking at the kinetic temperature of different +portions of the system, computing a moving average to have a clearer signal. + +.. GENERATED FROM PYTHON SOURCE LINES 330-366 + +.. code-block:: Python + + + + def moving_average(arr, window_size): + # Create a window of the specified size with equal weights + window = np.ones(window_size) / window_size + # Use the 'valid' mode to only return elements where the window fully + # overlaps with the data + return np.convolve(arr, window, mode="valid") + + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + + ax.plot( + 2.4188843e-05 * output_data["time"][50:-49], + moving_average(output_data["temperature(O)"], 100), + "r", + label=r"$T_\mathrm{O}$", + ) + ax.plot( + 2.4188843e-05 * output_data["time"][50:-49], + moving_average(output_data["temperature(H)"], 100), + "gray", + label=r"$T_\mathrm{H}$", + ) + ax.plot( + 2.4188843e-05 * output_data["time"][50:-49], + moving_average(output_data["temperature"], 100), + "b", + label="T", + ) + + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"temperature / K") + ax.legend(loc="upper left", ncols=2) + plt.show() + + + + +.. image-sg:: /examples/pi-metad/images/sphx_glr_pi-metad_002.png + :alt: pi metad + :srcset: /examples/pi-metad/images/sphx_glr_pi-metad_002.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 367-377 + +It is clear that the very high rate of biasing used in this demonstrative +example leads to a temperature that is consistently higher than the target, +with spikes up to 380 K and O and H atoms reaching different temperatures +(i.e. equipartition is broken). While this does not affect the qualitative +nature of the results, these parameters are unsuitable for a production run. +NB: especially for small systems, the instantaneous kinetic temperature +can deviate by a large amount from the target temperature: only the mean +value has actual meaning. However, a kinetic temperature that is consistently +above the target value indicates that the thermostat cannot dissipate +efficiently the energy due to the growing bias. + +.. GENERATED FROM PYTHON SOURCE LINES 379-406 + +Free energy profiles +.................... + +One of the advantages of metadynamics is that it allows one to easily +estimate the free-energy associated with the collective variables +that are used to accelerate sampling by summing the repulsive hills +that have been deposited during the run and taking the negative of +the total bias at the end of the trajectory. + +Even though more sophisticated strategies exist that provide explicit +weighting factors to estimate the unbiased Boltzmann distribution +(see e.g. +`Giberti et al., JCTC 2020 +`_), +this simple approach is good enough for this example, and can be +realized as a post-processing step using the ``plumed sum_hills`` module, +that also applies a (simple) correction to the negative bias that +is needed when using the well-tempered bias scaling protocol. +On the command line, + +.. code-block:: bash + + plumed sum_hills --hills HILLS-md --min 0.21,-1 --max 0.31,1 --bin 100,100 \ + --outfile FES-md --stride 100 --mintozero < data/plumed-md.dat + +The ``--stride`` option generates a series of files showing the estimates +of :math:`F` at different times along the trajectory. + +.. GENERATED FROM PYTHON SOURCE LINES 406-444 + +.. code-block:: Python + + + with open("data/plumed-md.dat", "r") as file: + subprocess.run( + [ + "plumed", + "sum_hills", + "--hills", + "HILLS-md", + "--min", + "0.21,-1", + "--max", + "0.31,1", + "--bin", + "100,100", + "--outfile", + "FES-md", + "--stride", + "100", + "--mintozero", + ], + stdin=file, + text=True, + ) + + # rearrange data and converts to Å and eV + data = np.loadtxt("FES-md0.dat", comments="#")[:, :3] + xyz_0 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 + ) + data = np.loadtxt("FES-md2.dat", comments="#")[:, :3] + xyz_2 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 + ) + data = np.loadtxt("FES-md5.dat", comments="#")[:, :3] + xyz_5 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 + ) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 445-447 + +The plots show, left-to-right, the accumulation of the +metadynamics bias as simulation progresses. + +.. GENERATED FROM PYTHON SOURCE LINES 447-465 + +.. code-block:: Python + + + fig, ax = plt.subplots( + 1, 3, figsize=(8, 3), sharex=True, sharey=True, constrained_layout=True + ) + + cf_0 = ax[0].contourf(*xyz_0) + cf_1 = ax[1].contourf(*xyz_2) + cf_2 = ax[2].contourf(*xyz_5) + fig.colorbar(cf_2, ax=ax, orientation="vertical", label=r"$F$ / eV") + ax[0].set_ylabel(r"$\Delta C_\mathrm{H}$") + ax[0].set_xlabel(r"$d_\mathrm{OO}$ / Å") + ax[1].set_xlabel(r"$d_\mathrm{OO}$ / Å") + ax[2].set_xlabel(r"$d_\mathrm{OO}$ / Å") + ax[0].set_title(r"$t=0.8$ ps") + ax[1].set_title(r"$t=2.5$ ps") + ax[2].set_title(r"$t=5.0$ ps") + plt.show() + + + + +.. image-sg:: /examples/pi-metad/images/sphx_glr_pi-metad_003.png + :alt: $t=0.8$ ps, $t=2.5$ ps, $t=5.0$ ps + :srcset: /examples/pi-metad/images/sphx_glr_pi-metad_003.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 466-474 + +Biasing a path integral calculation +----------------------------------- + +You can see `this recipe +`_ +for a brief introduction to path integral simulations with `i-PI`. +From a practical perspective, very little needs to change with respect +to the classical case. + +.. GENERATED FROM PYTHON SOURCE LINES 474-477 + +.. code-block:: Python + + + xmlroot = ET.parse("data/input-pimd.xml").getroot() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 478-486 + +The `nbeads` option determines the number of path integral +replicas. The value of 8 used here is not sufficient to converge +quantum statistics at 300 K (a more typical value would be +around 32). There are methods to reduce the number of replicas +needed for convergence, see e.g. +`Ceriotti and Markland, Nat. Rev. Chem. (2018) +`_ +but we keep it simple here. + +.. GENERATED FROM PYTHON SOURCE LINES 486-489 + +.. code-block:: Python + + + print(" " + ET.tostring(xmlroot.find(".//initialize"), encoding="unicode")[:23]) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 490-520 + +Centroid bias +~~~~~~~~~~~~~ + +Another detail worth discussing is that the metadynamics bias +is computed exclusively on the *centroid*, the mean position of +the ring-polymer beads. This is an extreme form of +ring polymer contraction +`(Markland and Manolopoulos, J. Chem. Phys. (2008) +`_ +that avoids computing for each replica the slowly-varying +parts of the potential, but is not applied for computational +savings. When performing a quantum free-energy calculation it +is important to distinguish between the free-energy computed +as the logarithm of the probability of observing a given +configuration (that depends on the distribution of the +replicas) and the free-energy taken as a tool to estimate +reaction rates :math:`k` in a transition-state theory +fashion :math:`k\propto e^{-\Delta E^\ddagger/kT}`, +where the energy barrier :math:`\Delta E^\ddagger` +is better estimated from the distribution of the centroid. +See e.g. +`Habershon et al., Annu. Rev. Phys. Chem. (2013) +`_ +for a discussion of the subtleties involved in estimating +transition rates. +In practice, performing this contraction step is very easy +in `i-PI`, because for each `` section - including +that corresponding to the bias - it is possible to specify +a different number of replicas. The configurations will +be automatically computed by Fourier interpolation. + +.. GENERATED FROM PYTHON SOURCE LINES 520-523 + +.. code-block:: Python + + + print(" " + ET.tostring(xmlroot.find(".//bias"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + + [ doo, dc, mtd.bias ] + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 524-531 + +Running the calculation +~~~~~~~~~~~~~~~~~~~~~~~ + +The other changes are purely cosmetic, and the calculation +can be launched very easily, using several drivers to parallelize +the energy evaluation over the beads (although this kind of calculations +is not limited by the evaluation of the forces). + +.. GENERATED FROM PYTHON SOURCE LINES 531-544 + +.. code-block:: Python + + + # don't rerun if the outputs already exist + ipi_process = None + if not os.path.exists("meta-pimd.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input-pimd.xml"]) + time.sleep(2) # wait for i-PI to start + driver_process = [ + subprocess.Popen( + ["i-pi-driver", "-u", "-a", "zundel", "-m", "zundel"], cwd="data/" + ) + for i in range(4) + ] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 545-547 + +If you run this in a notebook, you can go ahead and start loading +output files _before_ i-PI has finished running by skipping this cell + +.. GENERATED FROM PYTHON SOURCE LINES 548-555 + +.. code-block:: Python + + + # wait for simulations to finish + if ipi_process is not None: + ipi_process.wait() + for process in driver_process: + process.wait() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 556-565 + +Analysis of the simulation +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A path integral simulation evolves multiple configurations at the same +time, forming a `ring polymer`. Each replica provides a sample of the +quantum mechanical configuration distribution of the atoms. To provide +an overall visualization of the path integral dynamics, we load all the +replicas and combine them using a utility function from the +`chemiscope` library.` + +.. GENERATED FROM PYTHON SOURCE LINES 565-600 + +.. code-block:: Python + + + + output_data, output_desc = ipi.read_output("meta-pimd.out") + colvar_data = ipi.read_trajectory("meta-pimd.colvar_0", format="extras")[ + "doo,dc,mtd.bias" + ] + pimd_traj_data = [ipi.read_trajectory(f"meta-pimd.pos_{i}.xyz") for i in range(8)] + + # combines the PI beads and sets up the visualization options + traj_pimd = chemiscope.ase_merge_pi_frames(pimd_traj_data) + traj_pimd["shapes"]["paths"]["parameters"]["global"]["radius"] = 0.05 + traj_pimd["properties"] = dict( + d_OO=10 * colvar_data[:, 0], # nm to Å + delta_coord=colvar_data[:, 1], + bias=27.211386 * output_data["ensemble_bias"], # Ha to eV + time=2.4188843e-05 * output_data["time"], + ) + traj_pimd["settings"] = chemiscope.quick_settings( + x="d_OO", + y="delta_coord", + z="bias", + color="time", + trajectory=True, + structure_settings=dict( + bonds=False, + atoms=False, + keepOrientation=True, + unitCell=False, + shape=[ + "paths", + ], + ), + ) + traj_pimd["settings"]["target"] = "structure" + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 601-603 + +Visualize the trajectory. Note the similar behavior as for the classical +trajectory, and the delocalization of the protons + +.. GENERATED FROM PYTHON SOURCE LINES 604-608 + +.. code-block:: Python + + + chemiscope.show(**traj_pimd) + + + + +.. chemiscope:: _datasets/fig_pi-metad_003.json.gz + :mode: default + + + +.. raw:: html + +
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 609-615 + +Free energy plots +~~~~~~~~~~~~~~~~~ + +The free energy profiles relative to :math:`\Delta C_\mathrm{H}` +and :math:`d_\mathrm{OO}` can be computed exactly as for the +classical trajectory, using the `sum_hills` module. + +.. GENERATED FROM PYTHON SOURCE LINES 615-653 + +.. code-block:: Python + + + with open("data/plumed-pimd.dat", "r") as file: + subprocess.run( + [ + "plumed", + "sum_hills", + "--hills", + "HILLS-pimd", + "--min", + "0.21,-1", + "--max", + "0.31,1", + "--bin", + "100,100", + "--outfile", + "FES-pimd", + "--stride", + "100", + "--mintozero", + ], + stdin=file, + text=True, + ) + + # rearrange data and converts to Å and eV + data = np.loadtxt("FES-pimd0.dat", comments="#")[:, :3] + xyz_pi_0 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 + ) + data = np.loadtxt("FES-pimd2.dat", comments="#")[:, :3] + xyz_pi_2 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 + ) + data = np.loadtxt("FES-pimd5.dat", comments="#")[:, :3] + xyz_pi_5 = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 + ) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 654-657 + +Just as for a classical run, the metadynamics bias progressively +pushes the centroid (and the beads that are distributed around it) +to sample a wider portion of the collective-variable space. + +.. GENERATED FROM PYTHON SOURCE LINES 657-675 + +.. code-block:: Python + + + fig, ax = plt.subplots( + 1, 3, figsize=(8, 3), sharex=True, sharey=True, constrained_layout=True + ) + + cf_0 = ax[0].contourf(*xyz_pi_0) + cf_1 = ax[1].contourf(*xyz_pi_2) + cf_2 = ax[2].contourf(*xyz_pi_5) + fig.colorbar(cf_2, ax=ax, orientation="vertical", label=r"$F$ / eV") + ax[0].set_ylabel(r"$\Delta C_\mathrm{H}$") + ax[0].set_xlabel(r"$d_\mathrm{OO}$ / Å") + ax[1].set_xlabel(r"$d_\mathrm{OO}$ / Å") + ax[2].set_xlabel(r"$d_\mathrm{OO}$ / Å") + ax[0].set_title(r"$t=0.8$ ps") + ax[1].set_title(r"$t=2.5$ ps") + ax[2].set_title(r"$t=5.0$ ps") + plt.show() + + + + +.. image-sg:: /examples/pi-metad/images/sphx_glr_pi-metad_004.png + :alt: $t=0.8$ ps, $t=2.5$ ps, $t=5.0$ ps + :srcset: /examples/pi-metad/images/sphx_glr_pi-metad_004.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 676-685 + +Assessing quantum nuclear effects +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The effect of nuclear quantization on the centroid free-energy +is relatively small, despite the large delocalization of the +protons in the PIMD calculation. Looking more +carefully at the two distributions, one can notice that +in the high-:math:`d_\mathrm{OO}` region there is higher +delocalisation of the proton. + +.. GENERATED FROM PYTHON SOURCE LINES 685-703 + +.. code-block:: Python + + + fig, ax = plt.subplots( + 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True + ) + + levels = np.linspace(0, 0.5, 6) + cp1 = ax.contour(*xyz_5, colors="b", levels=levels) + cp2 = ax.contour(*xyz_pi_5, colors="r", levels=levels) + ax.set_ylabel(r"$\Delta C_\mathrm{H}$") + ax.set_xlabel(r"$d_\mathrm{OO}$ / Å") + ax.legend( + handles=[ + plt.Line2D([0], [0], color="b", label="MD"), + plt.Line2D([0], [0], color="r", label="PIMD"), + ] + ) + plt.show() + + + + +.. image-sg:: /examples/pi-metad/images/sphx_glr_pi-metad_005.png + :alt: pi metad + :srcset: /examples/pi-metad/images/sphx_glr_pi-metad_005.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 704-710 + +To get a clear signal, we need better-converged calculations; +the `data/` folder contains inputs for these "high quality" runs, +and free-energies obtained from them. +The results confirm the lowering of the free-energy barrier for +the :math:`\mathrm{H_3O^+ + H_2O} \rightarrow \mathrm{H_2O + H_3O^+}` +transition. + +.. GENERATED FROM PYTHON SOURCE LINES 711-740 + +.. code-block:: Python + + + with bz2.open("data/FES-md_hiq.bz2", "rt") as f: + data = np.loadtxt(f, comments="#")[:, :3] + xyz_md_hiq = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 + ) + with bz2.open("data/FES-pimd_hiq.bz2", "rt") as f: + data = np.loadtxt(f, comments="#")[:, :3] + xyz_pi_hiq = np.array([10, 1, 0.01036427])[:, np.newaxis, np.newaxis] * data.T.reshape( + 3, 101, 101 + ) + + fig, ax = plt.subplots( + 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True + ) + + levels = np.linspace(0, 0.5, 6) + cp1 = ax.contour(*xyz_md_hiq, colors="b", levels=levels) + cp2 = ax.contour(*xyz_pi_hiq, colors="r", levels=levels) + ax.set_ylabel(r"$\Delta C_\mathrm{H}$") + ax.set_xlabel(r"$d_\mathrm{OO}$ / Å") + ax.legend( + handles=[ + plt.Line2D([0], [0], color="b", label="MD"), + plt.Line2D([0], [0], color="r", label="PIMD"), + ] + ) + plt.show() + + + + +.. image-sg:: /examples/pi-metad/images/sphx_glr_pi-metad_006.png + :alt: pi metad + :srcset: /examples/pi-metad/images/sphx_glr_pi-metad_006.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 741-743 + +The lowering of the barrier for proton hopping is clearly +seen by taking 1D slices of the free energy at different O-O separations. + +.. GENERATED FROM PYTHON SOURCE LINES 744-776 + +.. code-block:: Python + + + fig, ax = plt.subplots( + 1, 1, figsize=(4, 3), sharex=True, sharey=True, constrained_layout=True + ) + + ax.plot( + xyz_md_hiq[1, :, 50], xyz_md_hiq[2, :, 50], "b", label=r"MD, $d_\mathrm{OO}=2.6 $Å" + ) + ax.plot( + xyz_pi_hiq[1, :, 50], + xyz_pi_hiq[2, :, 50], + "r", + label=r"PIMD, $d_\mathrm{OO}=2.6 $Å", + ) + ax.plot( + xyz_md_hiq[1, :, 60], + xyz_md_hiq[2, :, 60], + "b--", + label=r"MD, $d_\mathrm{OO}=2.7 $Å", + ) + ax.plot( + xyz_pi_hiq[1, :, 60], + xyz_pi_hiq[2, :, 60], + "r--", + label=r"PIMD, $d_\mathrm{OO}=2.7 $Å", + ) + ax.set_ylim(0.08, 0.6) + ax.legend(ncols=2, loc="upper right", fontsize=9) + ax.set_ylabel(r"$F$ / eV") + ax.set_xlabel(r"$\Delta C_\mathrm{H}$") + plt.show() + + + + +.. image-sg:: /examples/pi-metad/images/sphx_glr_pi-metad_007.png + :alt: pi metad + :srcset: /examples/pi-metad/images/sphx_glr_pi-metad_007.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 777-784 + +This model system is representative of the behavior of protons +along a hydrogen bond in different conditions, where the environment +determines the typical O-O separation, and whether the proton is shared +(as in high pressure ice X) or preferentially attached to one of the two +molecules. Zero-point energy (and to a lesser extent tunneling) +increases the delocalization, and reduces the barrier for an excess +proton to hop between water molecues. + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (1 minutes 53.200 seconds) + + +.. _sphx_glr_download_examples_pi-metad_pi-metad.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + + .. container:: sphx-glr-download + + :download:`Download data files: data.zip ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: pi-metad.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: pi-metad.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: pi-metad.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/roy-gch/roy-gch.rst.txt b/_sources/examples/roy-gch/roy-gch.rst.txt new file mode 100644 index 00000000..97d50daa --- /dev/null +++ b/_sources/examples/roy-gch/roy-gch.rst.txt @@ -0,0 +1,586 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/roy-gch/roy-gch.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_roy-gch_roy-gch.py: + + +Generalized Convex Hull construction for the polymorphs of ROY +============================================================== + +:Authors: Michele Ceriotti `@ceriottm `_ + +This notebook analyzes the structures of 264 polymorphs of ROY, from +`Beran et Al, Chemical Science (2022) `__, +comparing the conventional density-energy convex hull with a Generalized Convex Hull +(GCH) analysis (see `Anelli et al., Phys. Rev. Materials +(2018) `__). +It uses features computed with `rascaline `__ +and uses the directional convex hull function from +`scikit-matter `__ +to make the figure. + +The GCH construction aims at determining structures, among a collection of +candidate configurations, that are stable or have the potential of being stabilized +by appropriate thermodynamic boundary conditions (pressure, doping, external fields, +...). It does so by using microscopic descriptors to determine the diversity of +structures, and assumes that configurations that are stable relative to other +configurations with similar descriptors are those that could be made +"locally" stable by suitable synthesis conditions. + +.. GENERATED FROM PYTHON SOURCE LINES 25-38 + +.. code-block:: Python + + + # sphinx_gallery_thumbnail_number = 3 + import chemiscope + import matplotlib.tri + import numpy as np + from matplotlib import pyplot as plt + from metatensor import mean_over_samples + from rascaline import SoapPowerSpectrum + from sklearn.decomposition import PCA + from skmatter.datasets import load_roy_dataset + from skmatter.sample_selection import DirectionalConvexHull + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 39-40 + +Loads the structures (that also contain properties in the ``info`` field) + +.. GENERATED FROM PYTHON SOURCE LINES 40-52 + +.. code-block:: Python + + + roy_data = load_roy_dataset() + + structures = roy_data["structures"] + + density = np.array([s.info["density"] for s in structures]) + energy = np.array([s.info["energy"] for s in structures]) + structype = np.array([s.info["type"] for s in structures]) + iknown = np.where(structype == "known")[0] + iothers = np.where(structype != "known")[0] + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 53-62 + +Energy-density hull +------------------- + +The Directional Convex Hull routines can be used to compute a +conventional density-energy hull (see +`Hautier (2014) +`_ for a pedagogic +introduction to the convex hull construction in the context +of atomistic simulations). + +.. GENERATED FROM PYTHON SOURCE LINES 62-66 + +.. code-block:: Python + + + dch_builder = DirectionalConvexHull(low_dim_idx=[0]) + dch_builder.fit(density.reshape(-1, 1), energy) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 67-69 + +We can get the indices of the selection, and compute the distance from +the hull + +.. GENERATED FROM PYTHON SOURCE LINES 69-74 + +.. code-block:: Python + + + sel = dch_builder.selected_idx_ + dch_dist = dch_builder.score_samples(density.reshape(-1, 1), energy) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 75-86 + +Hull energies +^^^^^^^^^^^^^ + +Structures on the hull are stable with respect to synthesis at constant +molar volume. Any other structure would lower the energy by decomposing +into a mixture of the two nearest structures along the hull. Given that +the lattice energy is an imperfect proxy for the free energy, and that +synthesis can be performed in other ways than by fixing the density, +structures that are not exactly on the hull might also be stable. One +can compute a “hull energy” as an indication of how close these +structures are to being stable. + +.. GENERATED FROM PYTHON SOURCE LINES 87-102 + +.. code-block:: Python + + + fig, ax = plt.subplots(1, 1, figsize=(6, 4)) + ax.scatter(density, energy, c=dch_dist, marker=".") + ssel = sel[np.argsort(density[sel])] + ax.plot(density[ssel], energy[ssel], "k--") + ax.set_xlabel("density / g/cm$^3$") + ax.set_ylabel("energy / kJ/mol") + plt.show() + + print( + f"Mean hull energy for 'known' stable structures {dch_dist[iknown].mean()} kJ/mol" + ) + print(f"Mean hull energy for 'other' structures {dch_dist[iothers].mean()} kJ/mol") + + + + + +.. image-sg:: /examples/roy-gch/images/sphx_glr_roy-gch_001.png + :alt: roy gch + :srcset: /examples/roy-gch/images/sphx_glr_roy-gch_001.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Mean hull energy for 'known' stable structures 1.816657381014075 kJ/mol + Mean hull energy for 'other' structures 6.312730486304906 kJ/mol + + + + +.. GENERATED FROM PYTHON SOURCE LINES 103-108 + +Interactive visualization +^^^^^^^^^^^^^^^^^^^^^^^^^ + +You can also visualize the hull with ``chemiscope`` in a juptyer notebook. + + +.. GENERATED FROM PYTHON SOURCE LINES 108-130 + +.. code-block:: Python + + + cs = chemiscope.show( + structures, + dict( + energy=energy, + density=density, + hull_energy=dch_dist, + structure_type=structype, + ), + settings={ + "map": { + "x": {"property": "density"}, + "y": {"property": "energy"}, + "color": {"property": "hull_energy"}, + "symbol": "structure_type", + "size": {"factor": 35}, + }, + "structure": [{"unitCell": True, "supercell": {"0": 2, "1": 2, "2": 2}}], + }, + ) + cs + + + +.. chemiscope:: _datasets/fig_roy-gch_001.json.gz + :mode: default + + + +.. raw:: html + +
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 131-132 + +Save chemiscope file in a format that can be shared and viewed on `chemiscope.org` + +.. GENERATED FROM PYTHON SOURCE LINES 133-135 + +.. code-block:: Python + + cs.save("roy_ch.json.gz") + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 136-148 + +Generalized Convex Hull +----------------------- + +A GCH is a similar construction, in which generic structural descriptors +are used in lieu of composition, density or other thermodynamic +constraints. The idea is that configurations that are found close to the +GCH are locally stable with respect to structurally-similar +configurations. In other terms, one can hope to find a thermodynamic +constraint (i.e. synthesis conditions) that act differently on these +structures in comparison with the others, and may potentially stabilize +them. + + +.. GENERATED FROM PYTHON SOURCE LINES 151-159 + +Compute structural descriptors +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +A first step is to computes suitable ML descriptors. Here we have used +``rascaline`` to evaluate average SOAP features for the structures. +If you don't want to install these dependencies for this example you +can also use the pre-computed features, but you can use this as a stub +to apply this analysis to other chemical systems + +.. GENERATED FROM PYTHON SOURCE LINES 159-182 + +.. code-block:: Python + + + hypers = { + "cutoff": 4, + "max_radial": 6, + "max_angular": 4, + "atomic_gaussian_width": 0.7, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + "radial_basis": {"Gto": {"accuracy": 1e-6}}, + "center_atom_weight": 1.0, + } + calculator = SoapPowerSpectrum(**hypers) + rho2i = calculator.compute(structures) + rho2i = rho2i.keys_to_samples(["species_center"]).keys_to_properties( + ["species_neighbor_1", "species_neighbor_2"] + ) + rho2i_structure = mean_over_samples(rho2i, sample_names=["center", "species_center"]) + np.savez("roy_features.npz", feats=rho2i_structure.block(0).values) + + + # features = roy_data["features"] + features = rho2i_structure.block(0).values + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 183-189 + +PCA projection +^^^^^^^^^^^^^^ + +Computes PCA projection to generate low-dimensional descriptors that +reflect structural diversity. Any other dimensionality reduction scheme +could be used in a similar fashion. + +.. GENERATED FROM PYTHON SOURCE LINES 189-202 + +.. code-block:: Python + + + pca = PCA(n_components=4) + pca_features = pca.fit_transform(features) + + fig, ax = plt.subplots(1, 1, figsize=(6, 4)) + scatter = ax.scatter(pca_features[:, 0], pca_features[:, 1], c=energy) + ax.set_xlabel("PCA[1]") + ax.set_ylabel("PCA[2]") + cbar = fig.colorbar(scatter, ax=ax) + cbar.set_label("energy / kJ/mol") + plt.show() + + + + + +.. image-sg:: /examples/roy-gch/images/sphx_glr_roy-gch_002.png + :alt: roy gch + :srcset: /examples/roy-gch/images/sphx_glr_roy-gch_002.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 203-207 + +Builds the Generalized Convex Hull +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Builds a convex hull on the first two PCA features + +.. GENERATED FROM PYTHON SOURCE LINES 207-214 + +.. code-block:: Python + + + dch_builder = DirectionalConvexHull(low_dim_idx=[0, 1]) + dch_builder.fit(pca_features, energy) + sel = dch_builder.selected_idx_ + dch_dist = dch_builder.score_samples(pca_features, energy) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 215-217 + +Generates a 3D Plot + + +.. GENERATED FROM PYTHON SOURCE LINES 217-230 + +.. code-block:: Python + + + triang = matplotlib.tri.Triangulation(pca_features[sel, 0], pca_features[sel, 1]) + fig = plt.figure(figsize=(7, 5), tight_layout=True) + ax = fig.add_subplot(projection="3d") + ax.plot_trisurf(triang, energy[sel], color="gray") + ax.scatter(pca_features[:, 0], pca_features[:, 1], energy, c=dch_dist) + ax.set_xlabel("PCA[1]") + ax.set_ylabel("PCA[2]") + ax.set_zlabel("energy / kJ/mol\n \n", labelpad=11) + ax.view_init(25, 110) + plt.show() + + + + + +.. image-sg:: /examples/roy-gch/images/sphx_glr_roy-gch_003.png + :alt: roy gch + :srcset: /examples/roy-gch/images/sphx_glr_roy-gch_003.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 231-234 + +The GCH construction improves the separation between the hull energies +of “known” and hypothetical polymorphs (compare with the density-energy +values above) + +.. GENERATED FROM PYTHON SOURCE LINES 234-241 + +.. code-block:: Python + + + print( + f"Mean hull energy for 'known' stable structures {dch_dist[iknown].mean()} kJ/mol" + ) + print(f"Mean hull energy for 'other' structures {dch_dist[iothers].mean()} kJ/mol") + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Mean hull energy for 'known' stable structures 0.8537845044740536 kJ/mol + Mean hull energy for 'other' structures 5.19887158185163 kJ/mol + + + + +.. GENERATED FROM PYTHON SOURCE LINES 242-243 + +Visualize in a ``chemiscope`` widget + +.. GENERATED FROM PYTHON SOURCE LINES 243-300 + +.. code-block:: Python + + + for i, f in enumerate(structures): + for j in range(len(pca_features[i])): + f.info["pca_" + str(j + 1)] = pca_features[i, j] + structure_properties = chemiscope.extract_properties(structures) + structure_properties.update({"per_atom_energy": energy, "hull_energy": dch_dist}) + + # You can save a chemiscope file to disk (for viewing on chemiscope.org) + + chemiscope.write_input( + "roy_gch.json.gz", + frames=structures, + properties=structure_properties, + meta={ + "name": "GCH for ROY polymorphs", + "description": """ + Demonstration of the Generalized Convex Hull construction for + polymorphs of the ROY molecule. Molecules that are closest to + the hull built on PCA-based structural descriptors and having the + internal energy predicted by electronic-structure calculations as + the z axis are the most thermodynamically stable. Indeed most of the + known polymorphs of ROY are on (or very close) to this hull. + """, + "authors": ["Michele Ceriotti "], + "references": [ + 'A. Anelli, E. A. Engel, C. J. Pickard, and M. Ceriotti, \ + "Generalized convex hull construction for materials discovery," \ + Physical Review Materials 2(10), 103804 (2018).', + 'G. J. O. Beran, I. J. Sugden, C. Greenwell, D. H. Bowskill, \ + C. C. Pantelides, and C. S. Adjiman, "How many more polymorphs of \ + ROY remain undiscovered," Chem. Sci. 13(5), 1288–1297 (2022).', + ], + }, + settings={ + "map": { + "x": {"property": "pca_1"}, + "y": {"property": "pca_2"}, + "z": {"property": "energy"}, + "symbol": "type", + "color": {"property": "hull_energy"}, + "size": { + "factor": 35, + "mode": "linear", + "property": "", + "reverse": True, + }, + }, + "structure": [ + { + "bonds": True, + "unitCell": True, + "keepOrientation": True, + } + ], + }, + ) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 301-302 + +... and also load one as an interactive viewer + +.. GENERATED FROM PYTHON SOURCE LINES 303-305 + +.. code-block:: Python + + + chemiscope.show_input("roy_gch.json.gz") + + +.. chemiscope:: _datasets/fig_roy-gch_002.json.gz + :mode: default + + + +.. raw:: html + +
+ +
+
+
+ + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (0 minutes 17.619 seconds) + + +.. _sphx_glr_download_examples_roy-gch_roy-gch.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: roy-gch.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: roy-gch.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: roy-gch.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/sample-selection/sample-selection.rst.txt b/_sources/examples/sample-selection/sample-selection.rst.txt new file mode 100644 index 00000000..f572d946 --- /dev/null +++ b/_sources/examples/sample-selection/sample-selection.rst.txt @@ -0,0 +1,771 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/sample-selection/sample-selection.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_sample-selection_sample-selection.py: + + +Sample and Feature Selection with FPS and CUR +============================================= + +:Authors: Davide Tisi `@DavideTisi `_ + +In this tutorial we generate descriptors using rascaline, then select a subset +of structures using both the farthest-point sampling (FPS) and CUR algorithms +implemented in scikit-matter. Finally, we also generate a selection of +the most important features using the same techniques. + +First, import all the necessary packages + +.. GENERATED FROM PYTHON SOURCE LINES 16-28 + +.. code-block:: Python + + + import ase.io + import chemiscope + import metatensor + import numpy as np + from equisolve.numpy import feature_selection, sample_selection + from matplotlib import pyplot as plt + from rascaline import SoapPowerSpectrum + from sklearn.decomposition import PCA + from skmatter import feature_selection as skfeat_selection + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 29-34 + +Load molecular data +------------------- + +Load 500 example BTO structures from file, reading them using +`ASE `_. + +.. GENERATED FROM PYTHON SOURCE LINES 34-39 + +.. code-block:: Python + + + # Load a subset of :download:`structures ` of the example dataset + n_frames = 500 + frames = ase.io.read("input-fps.xyz", f":{n_frames}", format="extxyz") + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 40-44 + +Compute SOAP descriptors using rascaline +---------------------------------------- + +First, define the rascaline hyperparameters used to compute SOAP. + +.. GENERATED FROM PYTHON SOURCE LINES 44-82 + +.. code-block:: Python + + + + # rascaline hyperparameters + hypers = { + "cutoff": 6.0, + "max_radial": 8, + "max_angular": 6, + "atomic_gaussian_width": 0.3, + "cutoff_function": {"ShiftedCosine": {"width": 0.5}}, + "radial_basis": {"Gto": {"accuracy": 1e-6}}, + "radial_scaling": {"Willatt2018": {"exponent": 4, "rate": 1, "scale": 3.5}}, + "center_atom_weight": 1.0, + } + + # Generate a SOAP power spectrum + calculator = SoapPowerSpectrum(**hypers) + rho2i = calculator.compute(frames) + + + # Makes a dense block + atom_soap = rho2i.keys_to_properties(["species_neighbor_1", "species_neighbor_2"]) + + atom_soap_single_block = atom_soap.keys_to_samples(keys_to_move=["species_center"]) + + # Sum over atomic centers to compute structure features + struct_soap = metatensor.sum_over_samples( + atom_soap_single_block, sample_names=["center", "species_center"] + ) + + + print("atom feature descriptor shape:", atom_soap.block(0).values.shape) + print( + "atom feature descriptor (all in one block) shape:", + atom_soap_single_block.block(0).values.shape, + ) + print("structure feature descriptor shape:", struct_soap.block(0).values.shape) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + atom feature descriptor shape: (12000, 2688) + atom feature descriptor (all in one block) shape: (20000, 2688) + structure feature descriptor shape: (500, 2688) + + + + +.. GENERATED FROM PYTHON SOURCE LINES 83-99 + +Perform atomic environment (i.e. sample) selection +--------------------------------------------------- + +Using FPS and CUR algorithms, we can perform selection of atomic environments. +These are implemented in equisolve, which provides a wrapper around +scikit-matter to allow for interfacing with data stored in the metatensor +format. + +Suppose we want to select the 10 most diverse environments for each chemical +species. + +First, we can use the `keys_to_properties` operation in metatensor to move the +neighbour species indices to the properties of the TensorBlocks. The resulting +descriptor will be a TensorMap comprised of three blocks, one for each +chemical species, where the chemical species indices are solely present in the +keys. + +.. GENERATED FROM PYTHON SOURCE LINES 99-108 + +.. code-block:: Python + + + + print("----Atomic environment selection-----") + # Define the number of structures to select using FPS/CUR + n_envs = 25 + + print(atom_soap) + print(atom_soap.block(0)) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + ----Atomic environment selection----- + TensorMap with 3 blocks + keys: species_center + 8 + 22 + 56 + TensorBlock + samples (12000): ['structure', 'center'] + components (): [] + properties (2688): ['species_neighbor_1', 'species_neighbor_2', 'l', 'n1', 'n2'] + gradients: None + + + + +.. GENERATED FROM PYTHON SOURCE LINES 109-110 + +select 10 atomic environments for each chemical species. + +.. GENERATED FROM PYTHON SOURCE LINES 110-131 + +.. code-block:: Python + + + # Define the number of structures *per block* to select using FPS + n_envs = 10 + + # FPS sample selection + selector_atomic_fps = sample_selection.FPS(n_to_select=n_envs, initialize="random").fit( + atom_soap + ) + + # Print the selected envs for each block + print("atomic envs selected with FPS:\n") + for key, block in selector_atomic_fps.support.items(): + print("species_center:", key, "\n(struct_idx, atom_idx)\n", block.samples.values) + + selector_atomic_cur = sample_selection.CUR(n_to_select=n_envs).fit(atom_soap) + # Print the selected envs for each block + print("atomic envs selected with CUR:\n") + for key, block in selector_atomic_cur.support.items(): + print("species_center:", key, "\n(struct_idx, atom_idx)\n", block.samples.values) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + atomic envs selected with FPS: + + species_center: LabelsEntry(species_center=8) + (struct_idx, atom_idx) + [[ 68 18] + [113 36] + [140 21] + [285 20] + [339 16] + [339 23] + [339 24] + [341 17] + [347 37] + [436 22]] + species_center: LabelsEntry(species_center=22) + (struct_idx, atom_idx) + [[ 19 11] + [ 55 13] + [166 15] + [198 12] + [216 8] + [285 9] + [324 8] + [341 12] + [433 13] + [466 9]] + species_center: LabelsEntry(species_center=56) + (struct_idx, atom_idx) + [[ 40 7] + [140 2] + [238 3] + [289 6] + [339 3] + [341 4] + [407 0] + [407 7] + [436 6] + [451 7]] + atomic envs selected with CUR: + + species_center: LabelsEntry(species_center=8) + (struct_idx, atom_idx) + [[ 55 21] + [ 68 20] + [ 77 30] + [198 36] + [267 32] + [336 33] + [339 24] + [339 36] + [341 17] + [436 19]] + species_center: LabelsEntry(species_center=22) + (struct_idx, atom_idx) + [[ 10 39] + [ 40 10] + [ 70 10] + [130 10] + [166 15] + [170 14] + [216 8] + [285 9] + [326 10] + [466 10]] + species_center: LabelsEntry(species_center=56) + (struct_idx, atom_idx) + [[ 40 7] + [ 77 3] + [172 3] + [219 7] + [289 6] + [296 2] + [339 5] + [339 6] + [407 0] + [436 2]] + + + + +.. GENERATED FROM PYTHON SOURCE LINES 132-141 + +Selecting from a combined pool of atomic environments +----------------------------------------------------- + +One can also select from a combined pool of atomic environments and +structures, instead of selecting an equal number of atomic environments for +each chemical species. In this case, we can move the 'species_center' key to samples +such that our descriptor is a TensorMap consisting of a single block. Upon +sample selection, the most diverse atomic environments will be selected, +regardless of their chemical species. + +.. GENERATED FROM PYTHON SOURCE LINES 141-163 + +.. code-block:: Python + + print("----All atomic environment selection-----") + + print("keys", atom_soap.keys) + print("blocks", atom_soap[0]) + print("samples in first block", atom_soap[0].samples) + + # Using the original SOAP descriptor, move all keys to properties. + + + # Define the number of structures to select using FPS + n_envs = 10 + + # FPS sample selection + selector_atomic_fps = sample_selection.FPS(n_to_select=n_envs, initialize="random").fit( + atom_soap_single_block + ) + print( + "atomic envs selected with FPS: \n (struct_idx, atom_idx, species_center) \n", + selector_atomic_fps.support.block(0).samples.values, + ) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + ----All atomic environment selection----- + keys Labels( + species_center + 8 + 22 + 56 + ) + blocks TensorBlock + samples (12000): ['structure', 'center'] + components (): [] + properties (2688): ['species_neighbor_1', 'species_neighbor_2', 'l', 'n1', 'n2'] + gradients: None + samples in first block Labels( + structure center + 0 16 + 0 17 + ... + 499 30 + 499 31 + ) + atomic envs selected with FPS: + (struct_idx, atom_idx, species_center) + [[ 68 12 22] + [ 77 30 8] + [140 21 8] + [166 15 22] + [216 8 22] + [289 6 56] + [339 18 8] + [407 0 56] + [460 4 56] + [466 34 8]] + + + + +.. GENERATED FROM PYTHON SOURCE LINES 164-175 + +Perform structure (i.e. sample) selection with FPS/CUR +--------------------------------------------------------- + +Instead of atomic environments, one can also select diverse structures. We can +use the `sum_over_samples` operation in metatensor to define features in the +structural basis instead of the atomic basis. This is done by summing over the +atomic environments, labeled by the 'center' index in the samples of the +TensorMap. + +Alternatively, one could use the `mean_over_samples` operation, depending on +the specific inhomogeneity of the size of the structures in the training set. + +.. GENERATED FROM PYTHON SOURCE LINES 175-205 + +.. code-block:: Python + + + print("----Structure selection-----") + + # Define the number of structures to select *per block* using FPS + n_structures = 10 + + # FPS structure selection + selector_struct_fps = sample_selection.FPS( + n_to_select=n_structures, initialize="random" + ).fit(struct_soap) + struct_fps_idxs = selector_struct_fps.support.block(0).samples.values.flatten() + + print("structures selected with FPS:\n", struct_fps_idxs) + + # CUR structure selection + selector_struct_cur = sample_selection.CUR(n_to_select=n_structures).fit(struct_soap) + struct_cur_idxs = selector_struct_cur.support.block(0).samples.values.flatten() + print("structures selected with CUR:\n", struct_cur_idxs) + + + # Slice structure descriptor along axis 0 to contain only the selected structures + struct_soap_fps = struct_soap.block(0).values[struct_fps_idxs, :] + struct_soap_cur = struct_soap.block(0).values[struct_cur_idxs, :] + assert struct_soap_fps.shape == struct_soap_cur.shape + + print("Structure descriptor shape before selection ", struct_soap.block(0).values.shape) + print("Structure descriptor shape after selection (FPS)", struct_soap_fps.shape) + print("Structure descriptor shape after selection (CUR)", struct_soap_cur.shape) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + ----Structure selection----- + structures selected with FPS: + [ 15 71 140 167 172 257 317 326 356 496] + structures selected with CUR: + [ 39 40 68 110 140 289 326 386 398 438] + Structure descriptor shape before selection (500, 2688) + Structure descriptor shape after selection (FPS) (10, 2688) + Structure descriptor shape after selection (CUR) (10, 2688) + + + + +.. GENERATED FROM PYTHON SOURCE LINES 206-213 + +Visualize selected structures +----------------------------- + +sklearn can be used to perform PCA dimensionality reduction on the SOAP +descriptors. The resulting PC coordinates can be used to visualize the the +data alongside their structures in a chemiscope widget. + + +.. GENERATED FROM PYTHON SOURCE LINES 213-219 + +.. code-block:: Python + + + # Generate a structure PCA + struct_soap_pca = PCA(n_components=2).fit_transform(struct_soap.block(0).values) + assert struct_soap_pca.shape == (n_frames, 2) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 220-225 + +Plot the PCA map +~~~~~~~~~~~~~~~~ + +Notice how the selected points avoid the densely-sampled area, and cover +the periphery of the dataset + +.. GENERATED FROM PYTHON SOURCE LINES 225-242 + +.. code-block:: Python + + + # Matplotlib plot + fig, ax = plt.subplots(1, 1, figsize=(6, 4)) + scatter = ax.scatter(struct_soap_pca[:, 0], struct_soap_pca[:, 1], c="red") + ax.plot( + struct_soap_pca[struct_cur_idxs, 0], + struct_soap_pca[struct_cur_idxs, 1], + "ko", + fillstyle="none", + label="FPS selection", + ) + ax.set_xlabel("PCA[1]") + ax.set_ylabel("PCA[2]") + ax.legend() + fig.show() + + + + + +.. image-sg:: /examples/sample-selection/images/sphx_glr_sample-selection_001.png + :alt: sample selection + :srcset: /examples/sample-selection/images/sphx_glr_sample-selection_001.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 243-246 + +Creates a chemiscope viewer +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + +.. GENERATED FROM PYTHON SOURCE LINES 246-294 + +.. code-block:: Python + + + # Selected level + selection_levels = [] + for i in range(len(frames)): + level = 0 + if i in struct_cur_idxs: + level += 1 + if i in struct_fps_idxs: + level += 2 + if level == 0: + level = "Not selected" + elif level == 1: + level = "CUR" + elif level == 2: + level = "FPS" + else: + level = "FPS+CUR" + selection_levels.append(level) + + properties = chemiscope.extract_properties(frames) + + properties.update( + { + "PC1": struct_soap_pca[:, 0], + "PC2": struct_soap_pca[:, 1], + "selection": np.array(selection_levels), + } + ) + + widget = chemiscope.show( + frames, + properties=properties, + settings={ + "map": { + "x": {"property": "PC1"}, + "y": {"property": "PC2"}, + "color": {"property": "energy"}, + "symbol": "selection", + "size": {"factor": 50}, + }, + "structure": [{"unitCell": True}], + }, + ) + widget.save("sample-selection.json.gz") + + # display, if in notebook or sphinx + widget + + + +.. chemiscope:: _datasets/fig_sample-selection_001.json.gz + :mode: default + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/sample-selection/lib/python3.11/site-packages/chemiscope/structures/_ase.py:134: UserWarning: the following structure properties are only defined for a subset of frames: ['stress']; they will be ignored + all_names = _ase_list_structure_properties(frames) + /home/runner/work/atomistic-cookbook/atomistic-cookbook/.nox/sample-selection/lib/python3.11/site-packages/chemiscope/structures/__init__.py:93: UserWarning: the following structure properties are only defined for a subset of frames: ['stress']; they will be ignored + return _ase_list_structure_properties(frames) + + +.. raw:: html + +
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 295-301 + +Perform feature selection +------------------------- + +Now perform feature selection. In this example we will go back to using the +descriptor decomposed into atomic environments, as opposed to the one +decomposed into structure environments, but only use FPS for brevity. + +.. GENERATED FROM PYTHON SOURCE LINES 301-328 + +.. code-block:: Python + + print("----Feature selection-----") + + # Define the number of features to select + n_features = 200 + + # FPS feature selection + feat_fps = feature_selection.FPS(n_to_select=n_features, initialize="random").fit( + atom_soap_single_block + ) + + # Slice atomic descriptor along axis 1 to contain only the selected features + # atom_soap_single_block_fps = atom_soap_single_block.block(0).values[:, feat_fps_idxs] + atom_soap_single_block_fps = metatensor.slice( + atom_soap_single_block, + axis="properties", + labels=feat_fps.support.block(0).properties, + ) + + print( + "atomic descriptor shape before selection ", + atom_soap_single_block.block(0).values.shape, + ) + print( + "atomic descriptor shape after selection ", + atom_soap_single_block_fps.block(0).values.shape, + ) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + ----Feature selection----- + atomic descriptor shape before selection (20000, 2688) + atomic descriptor shape after selection (20000, 200) + + + + +.. GENERATED FROM PYTHON SOURCE LINES 331-337 + +Perform feature selection (skmatter) +------------------------------------ + +Now perform feature selection. In this example we will go back to using the +descriptor decomposed into atomic environments, as opposed to the one +decomposed into structure environments, but only use FPS for brevity. + +.. GENERATED FROM PYTHON SOURCE LINES 337-360 + +.. code-block:: Python + + + print("----Feature selection (skmatter)-----") + + # Define the number of features to select + n_features = 200 + + # FPS feature selection + feat_fps = skfeat_selection.FPS(n_to_select=n_features, initialize="random").fit( + atom_soap_single_block.block(0).values + ) + feat_fps_idxs = feat_fps.selected_idx_ + + print("Feature indices obtained with FPS ", feat_fps_idxs) + + # Slice atomic descriptor along axis 1 to contain only the selected features + atom_dscrptr_fps = atom_soap_single_block.block(0).values[:, feat_fps_idxs] + + print( + "atomic descriptor shape before selection ", + atom_soap_single_block.block(0).values.shape, + ) + print("atomic descriptor shape after selection ", atom_dscrptr_fps.shape) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + ----Feature selection (skmatter)----- + Feature indices obtained with FPS [2607 0 920 464 3 411 1 488 1824 921 5 465 29 1179 + 27 2240 468 1344 4 2244 602 923 489 274 1825 45 916 1180 + 28 1308 475 470 731 924 46 283 1828 474 450 30 491 2241 + 730 412 2084 12 477 1835 1636 859 476 1827 1796 496 413 931 + 936 21 453 1345 899 466 939 940 11 1816 1324 934 900 948 + 861 928 1490 19 860 925 2 1170 2276 456 1347 1819 1181 1310 + 13 858 1380 36 210 1372 1812 926 929 2195 947 458 1196 451 + 1307 492 2267 472 2212 915 462 449 733 725 922 18 37 2523 + 2532 1365 932 1746 347 473 868 912 502 275 927 1362 2246 1172 + 485 54 504 484 285 866 395 31 499 1348 480 1316 2092 38 + 1805 901 913 1941 723 944 2213 898 1187 1939 941 402 907 1364 + 6 1947 469 1309 467 490 1940 10 905 498 2242 1637 908 904 + 452 2083 942 1820 937 724 1171 500 933 338 420 2524 1682 2254 + 483 2221 22 1792 1764 494 7 738 949 9 2268 1832 1618 1323 + 478 482 950 461] + atomic descriptor shape before selection (20000, 2688) + atomic descriptor shape after selection (20000, 200) + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (0 minutes 22.357 seconds) + + +.. _sphx_glr_download_examples_sample-selection_sample-selection.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: sample-selection.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: sample-selection.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: sample-selection.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/examples/thermostats/thermostats.rst.txt b/_sources/examples/thermostats/thermostats.rst.txt new file mode 100644 index 00000000..5ba4274e --- /dev/null +++ b/_sources/examples/thermostats/thermostats.rst.txt @@ -0,0 +1,1604 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/thermostats/thermostats.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + :ref:`Go to the end ` + to download the full example code. + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_examples_thermostats_thermostats.py: + + +Constant-temperature MD and thermostats +======================================= + +:Authors: Michele Ceriotti `@ceriottm `_ + +This recipe gives a practical introduction to finite-temperature +molecular dynamics simulations, and provides a guide to choose the +most appropriate thermostat for the simulation at hand. + +As for other examples in the cookbook, a small simulation of liquid +water is used as an archetypal example. Molecular dynamics, sampling, +and constant-temperature simulations are discussed in much detail in +the book "Understanding Molecular Simulations" by Daan Frenkel and Berend Smit. +This +`seminal paper by H.C.Andersen `_ +provides a good historical introduction to the problem of +thermostatting, and this +`PhD thesis +`_ +provides a more detailed background to several of the techniques +discussed in this recipe. + +.. GENERATED FROM PYTHON SOURCE LINES 24-27 + +.. code-block:: Python + + + import os + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 28-41 + +.. code-block:: Python + + import subprocess + import time + import xml.etree.ElementTree as ET + + import chemiscope + import ipi + import matplotlib as mpl + import matplotlib.pyplot as plt + import numpy as np + from ipi.utils.tools.acf_xyz import compute_acf_xyz + from ipi.utils.tools.gle import get_gle_matrices, gle_frequency_kernel, isra_deconvolute + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 42-67 + +Constant-temperature sampling of (thermo)dynamics +------------------------------------------------- + +Even though Hamilton's equations in classical mechanics conserve the total +energy of the group of atoms in a simulation, experimental boundary conditions +usually involve exchange of heat with the surroundings, especially when considering +the relatively small supercells that are often used in simulations. + +The goal of a constant-temperature MD simulation is to compute efficiently thermal +averages of the form :math:`\langle A(q,p)\rangle_\beta`, where the average +of the observable :math:`A(q,p)` is +evaluated over the Boltzmann distribution at inverse temperature +:math:`\beta=1/k_\mathrm{B}T`, +:math:`P(q,p)=Q^{-1} \exp(-\beta(p^2/2m + V(q)))` +In all these scenarios, optimizing the simulation involves reducing as much as +possible the *autocorrelation time* of the observable. + +Constant-temperature sampling is also important when one wants to compute +*dynamical* properties. In principle these would require +constant-energy trajectories, as any thermostatting procedure modifies +the dynamics of the system. However, the initial conditions +should usually be determined from constant-temperature conditions, +averaging over multiple constant-energy trajectories. +As we shall see, this protocol can often be simplified greatly, by choosing +thermostats that don't interfere with the natural microscopic dynamics. + +.. GENERATED FROM PYTHON SOURCE LINES 69-87 + +Running simulations +~~~~~~~~~~~~~~~~~~~ + +We use `i-PI `_ together with a ``LAMMPS`` driver to run +all the simulations in this recipe. The two codes need to be run separately, +and communicate atomic positions, energy and forces through a socket interface. + +The LAMMPS input defines the parameters of the +`q-TIP4P/f water model `_, +while the XML-formatted input of i-PI describes the setup of the +MD simulation. + +We begin running a constant-energy calculation, that +we will use to illustrate the metrics that can be applied to +assess the performance of a thermostatting scheme. If it is the +first time you see an ``i-PI`` input, you may want to look at +the input file side-by-sidewith the +`input reference `_. + +.. GENERATED FROM PYTHON SOURCE LINES 87-93 + +.. code-block:: Python + + + # Open and read the XML file + with open("data/input_nve.xml", "r") as file: + xml_content = file.read() + print(xml_content) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + + + [ step, time{picosecond}, conserved{electronvolt}, + temperature{kelvin}, kinetic_md{electronvolt}, potential{electronvolt}, + temperature(H){kelvin}, temperature(O){kelvin} ] + positions + velocities + + 2000 + + 32342 + + +
h2o-lammps
1e-4 + + + + data/water_32.pdb + 300 + + + lmpserial + + + 300 + + + + 1.0 + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 94-97 + +The part of the input that describes the molecular dynamics integrator +is the ``motion`` class. For this run, it specifies an *NVE* ensemble, and +a ``timestep`` of 1 fs for the integrator. + +.. GENERATED FROM PYTHON SOURCE LINES 97-101 + +.. code-block:: Python + + + xmlroot = ET.parse("data/input_nve.xml").getroot() + print(" " + ET.tostring(xmlroot.find(".//motion"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + + 1.0 + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 102-108 + +Note that this -- and other runs in this example -- are too short to +provide quantitative results, and you may want to increase the +```` parameter so that the simulation runs for at least +a few tens of ps. The time step of 1 fs is also at the limit of what +is acceptable for running simulations of water. 0.5 fs would be a +safer, stabler value. + +.. GENERATED FROM PYTHON SOURCE LINES 111-122 + +To launch i-PI and LAMMPS from the command line you can just +execute the following commands + +.. code-block:: bash + + i-pi data/input_nve.xml > log & + sleep 2 + lmp -in data/in.lmp & + +To launch the external processes from a Python script +proceed as follows: + +.. GENERATED FROM PYTHON SOURCE LINES 122-129 + +.. code-block:: Python + + + ipi_process = None + if not os.path.exists("simulation_nve.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input_nve.xml"]) + time.sleep(4) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(1)] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 130-133 + +If you run this in a notebook, you can go ahead and start loading +output files *before* i-PI and LAMMPS have finished running, by +skipping this cell + +.. GENERATED FROM PYTHON SOURCE LINES 133-139 + +.. code-block:: Python + + + if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 140-146 + +Analyzing the simulation +~~~~~~~~~~~~~~~~~~~~~~~~ + +After the simulation is finished, we can look at the outputs. +The outputs include the trajectory of positions, the velocities +and a number of energetic observables + +.. GENERATED FROM PYTHON SOURCE LINES 146-150 + +.. code-block:: Python + + + output_data, output_desc = ipi.read_output("simulation_nve.out") + traj_data = ipi.read_trajectory("simulation_nve.pos_0.xyz") + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 151-154 + +The trajectory shows mostly local vibrations on this short time scale, +but if you re-run with a longer ```` settings you should be +able to observe diffusing molecules in the liquid. + +.. GENERATED FROM PYTHON SOURCE LINES 154-163 + +.. code-block:: Python + + + chemiscope.show( + traj_data, + mode="structure", + settings=chemiscope.quick_settings( + trajectory=True, structure_settings={"unitCell": True} + ), + ) + + + +.. chemiscope:: _datasets/fig_thermostats_001.json.gz + :mode: structure + + + +.. raw:: html + +
+ +
+
+
+ +.. GENERATED FROM PYTHON SOURCE LINES 164-170 + +Potential and kinetic energy fluctuate, but the total energy is +(almost) constant, the small fluctuations being due to integration +errors, that are quite large with the long time step used for this +example. If you run with smaller ```` values, you should +see that the energy conservation condition is fulfilled with higher +accuracy. + +.. GENERATED FROM PYTHON SOURCE LINES 170-195 + +.. code-block:: Python + + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["potential"] - output_data["potential"][0], + "b-", + label="Potential, $V$", + ) + ax.plot( + output_data["time"], + output_data["kinetic_md"], + "r-", + label="Kinetic, $K$", + ) + ax.plot( + output_data["time"], + output_data["conserved"] - output_data["conserved"][0], + "k-", + label="Conserved, $H$", + ) + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"energy / eV") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_001.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_001.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 196-209 + +In a classical MD simulation, based on the momentum :math:`\mathbf{p}` +of each atom, it is possible to evaluate its *kinetic temperature +estimator* :math:`T=\langle \mathbf{p}^2/m \rangle /3k_B` the average is to +be intended over a converged trajectory. Keep in mind that + +1. The *instantaneous* value of this estimator is meaningless +2. It is only well-defined in a constant-temperature simulation, so here + it only gives a sense of whether atomic momenta are close to what one + would expect at 300 K. + +With these caveats in mind, we can observe that the simulation has higher +velocities than expected at 300 K, and that there is no equipartition, the +O atoms having on average a higher energy than the H atoms. + +.. GENERATED FROM PYTHON SOURCE LINES 209-229 + +.. code-block:: Python + + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["temperature(O)"], + "r-", + label="O atoms", + ) + ax.plot( + output_data["time"], + output_data["temperature(H)"], + "c-", + label="H atoms", + ) + ax.plot(output_data["time"], output_data["temperature"], "k-", label="All atoms") + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"$\tilde{T}$ / K") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_002.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_002.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 230-239 + +In order to investigate the dynamics more carefully, we +compute the velocity-velocity autocorrelation function +:math:`c_{vv}(t)=\sum_i \langle \mathbf{v}_i(t) \cdot \mathbf{v}_i(0) \rangle`. +We use a utility function that reads the outputs of ``i-PI`` +and computes both the autocorrelation function and its Fourier +transform. +:math:`c_{vv}(t)` contains information on the time scale and amplitude +of molecular motion, and is closely related to the vibrational density +of states and to spectroscopic observables such as IR and Raman spectra. + +.. GENERATED FROM PYTHON SOURCE LINES 239-260 + +.. code-block:: Python + + + acf_nve = compute_acf_xyz( + "simulation_nve.vel_0.xyz", + maximum_lag=600, + length_zeropadding=2000, + spectral_windowing="cosine-blackman", + timestep=1, + time_units="femtosecond", + skip=100, + ) + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + acf_nve[0][:1200] * 2.4188843e-05, # atomic time to ps + acf_nve[1][:1200] * 1e5, + "r-", + ) + ax.set_xlabel(r"$t$ / ps$") + ax.set_ylabel(r"$c_{vv}$ / arb. units") + plt.show() + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_003.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_003.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 261-271 + +The power spectrum (that can be computed as the Fourier transform of +:math:`c_{vv}`) reveals the frequencies of stretching, bending and libration +modes of water; the :math:`\omega\rightarrow 0` limit is proportional +to the diffusion coefficient. +We also load the results from a reference calculation (average of 8 +trajectories initiated from NVT-equilibrated samples, shown as the +confidence interval). You can see how to run these reference calculations +from the script ``data/run_traj.sh``. +The differences are due to the short trajectory, and to the fact that the +NVE trajectory is not equilibrated at 300 K. + +.. GENERATED FROM PYTHON SOURCE LINES 271-293 + +.. code-block:: Python + + + ha2cm1 = 219474.63 + + # Loads reference trajectory + acf_ref = np.loadtxt("data/traj-all_facf.data") + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + + ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", + ) + + ax.loglog(acf_nve[3][:1200] * ha2cm1, acf_nve[4][:1200] * 1e5, "r-", label="NVE") + ax.set_xlabel(r"$\omega$ / cm$^{-1}$") + ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_004.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_004.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 294-329 + +Langevin thermostatting +----------------------- + +In order to perform a simulations that samples configurations +consistent with a Boltzmann distribution :math:`e^{-V(x)/k_B T}` +one needs to modify the equations of motion. There are many +different approaches to do this, some of which lead to deterministic +dynamics; the two more widely used deterministic thermostats +are the +`Berendsen thermostat `_ +which does not sample the Boltzmann distribution exactly and +should never be used given the many more rigorous alternatives, +and the Nosé-Hoover thermostat, that requires a +`"chain" implementation `_ +to be ergodic, which amounts essentially to a complicated way +to generate poor-quality pseudo-random numbers. + +Given the limitations of deterministic thermostats, in this +recipe we focus on stochastic thermostats, that model the +coupling to the chaotic dynamics of an external bath through +explicit random numbers. Langevin dynamics amounts to adding +to Hamilton's equations of motion, for each degree of freedom, +a term of the form + +.. math:: + + \dot{p} = -\gamma p + \sqrt{2\gamma m k_B T} \, \xi(t) + +where :math:` +\gamma` is a friction coefficient, and :math:`\xi` +uncorrelated random numbers that mimic collisions with the bath +particles. The friction can be seen as the inverse of a +characteristic *coupling time scale* +:math:`\tau=1/\gamma` that describes how strongly the bath +interacts with the system. + +.. GENERATED FROM PYTHON SOURCE LINES 331-339 + +Setting up a thermostat in ``i-PI`` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +In order to set up a thermostat in ``i-PI``, one simply needs +to adjust the ```` block, to perform ``nvt`` dynamics +and include an appropriate ```` section. +Here we use a very-strongly coupled Langevin thermostat, +with :math:`\tau=10~fs`. + +.. GENERATED FROM PYTHON SOURCE LINES 339-343 + +.. code-block:: Python + + + xmlroot = ET.parse("data/input_higamma.xml").getroot() + print(" " + ET.tostring(xmlroot.find(".//dynamics"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + 1.0 + + 10 + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 344-345 + +``i-PI`` and ``LAMMPS`` are launched as above ... + +.. GENERATED FROM PYTHON SOURCE LINES 345-352 + +.. code-block:: Python + + + ipi_process = None + if not os.path.exists("simulation_higamma.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input_higamma.xml"]) + time.sleep(4) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(1)] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 353-355 + +... and you should probably wait until they're done, +it'll take less than a minute. + +.. GENERATED FROM PYTHON SOURCE LINES 355-360 + +.. code-block:: Python + + + if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 361-368 + +Analysis of the trajectory +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The temperature converges very quickly to the target value +(fluctuations are to be expected, given that as discussed above +the temperature estimator is just the instantaneous kinetic energy, +that is not constant). There is also equipartition between O and H. + +.. GENERATED FROM PYTHON SOURCE LINES 368-392 + +.. code-block:: Python + + + output_data, output_desc = ipi.read_output("simulation_higamma.out") + traj_data = ipi.read_trajectory("simulation_higamma.pos_0.xyz") + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["temperature(O)"], + "r-", + label="O atoms", + ) + ax.plot( + output_data["time"], + output_data["temperature(H)"], + "c-", + label="H atoms", + ) + ax.plot(output_data["time"], output_data["temperature"], "k-", label="All atoms") + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"$\tilde{T}$ / K") + ax.legend() + plt.show() + + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_005.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_005.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 393-412 + +The velocity-velocity correlation function shows how much +this thermostat affects the system dynamics. The high-frequency peaks, +corresponding to stretches and bending, are +greatly broadened, and the :math:`\omega\rightarrow 0` +limit of :math:`\hat{c}_{vv}`, corresponding to the +diffusion coefficient, is reduced by almost a factor of 5. +This last observation highlights that a too-aggressive +thermostat is not only disrupting the dynamics: +it also slows down diffusion through phase space, +making the dynamics less efficient at sampling slow, +collective motions. We shall see further down various +methods to counteract this effect, but in general one should +use a weaker coupling, that improves the sampling of configuration +space even though it slows down the convergence of the +kinetic energy. If you want a thermostat that equilibrates +aggressively the temperature while disturbing less the diffusive +modes, you may try the *fast-forward Langevin* thermostat +`(Hijazi et al., JCP (2018)) `_ +that can be activated with the option ``mode="ffl"``. + +.. GENERATED FROM PYTHON SOURCE LINES 412-444 + +.. code-block:: Python + + + # compute the v-v acf + acf_higamma = compute_acf_xyz( + "simulation_higamma.vel_0.xyz", + maximum_lag=600, + length_zeropadding=2000, + spectral_windowing="cosine-blackman", + timestep=1, + time_units="femtosecond", + skip=100, + ) + + # and plot + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", + ) + ax.loglog( + acf_higamma[3][:1200] * ha2cm1, + acf_higamma[4][:1200] * 1e5, + "b-", + label=r"Langevin, $\tau=10$fs", + ) + ax.set_xlabel(r"$\omega$ / cm$^{-1}$") + ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_006.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_006.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 445-457 + +Global thermostats: stochastic velocity rescaling +------------------------------------------------- + +An alternative approach to sample the canonical Boltzmann +distribution while introducing fewer disturbances to the system +dynamics is to use a *global* thermostat, i.e. a scheme that +targets the *total* kinetic energy of the system, rather than that +of individual degrees of freedom. +We recommend the "stochastic velocity rescaling" thermostat +`(Bussi, Donadio, Parrinello, JCP (2007)) `_ +that acts by rescaling the total momentum vector, adding a +suitably distributed random noise term. + +.. GENERATED FROM PYTHON SOURCE LINES 460-467 + +Setting up a thermostat in ``i-PI`` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Stochastic velocity rescaling is implemented in ``i-PI`` +can be selected by setting ``mode="svr"``, and has a +``tau`` parameter that corresponds to the time scale of the +coupling. + +.. GENERATED FROM PYTHON SOURCE LINES 467-471 + +.. code-block:: Python + + + xmlroot = ET.parse("data/input_svr.xml").getroot() + print(" " + ET.tostring(xmlroot.find(".//thermostat"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + 10 + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 472-473 + +We run a simulation with the usual set up ... + +.. GENERATED FROM PYTHON SOURCE LINES 473-480 + +.. code-block:: Python + + + ipi_process = None + if not os.path.exists("simulation_svr.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input_svr.xml"]) + time.sleep(4) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(1)] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 481-482 + +... and wait for it to finish. + +.. GENERATED FROM PYTHON SOURCE LINES 482-487 + +.. code-block:: Python + + + if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 488-504 + +Analysis of the trajectory +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The kinetic temperature of the trajectory equilibrates very +rapidly to the target value. However, it takes a bit longer +(approximately 0.5 ps) to reach equipartition between O and H +atoms. This is an important shortcoming of global thermostats: +since they only target the total kinetic energy, they must rely +on internal energy redistribution to reach equilibrium between +different degrees of freedom. +Liquid water is a very ergodic system, in which all degrees of +freedom are strongly coupled, so this is not a major issue. However +care must be taken when modeling a quasi-harmonic crystal (e.g. +diamond, a metal, or an inorganic crystal), or a molecular system +in which the coupling between molecules is weaker (e.g. methane, +or another apolar compound). + +.. GENERATED FROM PYTHON SOURCE LINES 504-528 + +.. code-block:: Python + + + output_data, output_desc = ipi.read_output("simulation_svr.out") + traj_data = ipi.read_trajectory("simulation_svr.pos_0.xyz") + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["temperature(O)"], + "r-", + label="O atoms", + ) + ax.plot( + output_data["time"], + output_data["temperature(H)"], + "c-", + label="H atoms", + ) + ax.plot(output_data["time"], output_data["temperature"], "k-", label="All atoms") + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"$\tilde{T}$ / K") + ax.legend() + plt.show() + + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_007.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_007.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 529-540 + +The velocity-velocity autocorrelation function is +essentially indistinguishable from the reference, computed +with an ensemble of NVE trajectories starting from canonical +samples. In fact, the small discrepancies are mostly due to +incomplete convergence of the averages in the short trajectory. + +This highlights the advantages of a global thermostat, that +does not disrupt the natural diffusion in configuration space, +and can often be used to compute dynamical, time-dependent +observables out of a single trajectory -- which is far more +practical than performing a collection of NVE trajectories. + +.. GENERATED FROM PYTHON SOURCE LINES 540-570 + +.. code-block:: Python + + + acf_svr = compute_acf_xyz( + "simulation_svr.vel_0.xyz", + maximum_lag=600, + length_zeropadding=2000, + spectral_windowing="cosine-blackman", + timestep=1, + time_units="femtosecond", + skip=100, + ) + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", + ) + ax.loglog( + acf_svr[3][:1200] * ha2cm1, + acf_svr[4][:1200] * 1e5, + "b-", + label=r"SVR, $\tau=10$fs", + ) + ax.set_xlabel(r"$\omega$ / cm$^{-1}$") + ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_008.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_008.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 571-603 + +Generalized Langevin Equation thermostat +---------------------------------------- + +The issue with a Langevin thermostat is that, for a given coupling +time :math:`\tau`, only molecular motions with a comparable time scale +are sampled efficiently: faster modes are *underdamped*, and slower modes +are *overdamped*, cf. the slowing down of diffusive behavior. + +A possible solution to this problem is using a +*Generalized Langevin Equation (GLE)* thermostat. A GLE +thermostat uses a matrix generalization of the Langevin term, +in which the physical momentum is supplemented by a few fictitious +momenta :math:`\mathbf{s}`, i.e. + +.. math:: + + (\dot{p},\dot{\mathbf{s}}) = -\mathbf{A}_p (p,\mathbf{s})\ + +\mathbf{B}_p (\xi,\boldsymbol{\xi}) + + +Here :math:`\mathbf{A}_p` is the *drift matrix* and :math:`\mathbf{B}_p` +is a diffusion matrix which, for canonical sampling, is determined by the target +temperature and the drift matrix through a fluctuation-dissipation relation. +The key idea is that :math:`\mathbf{A}_p` provides a lot of flexibility in defining +the behavior of the GLE, that can be tuned to achieve near-optimal sampling +for every degree of freedom (effectively acting as if the coupling constant was +tuned separately for slow and fast molecular motions). +The general idea and the practical implementation are discussed in +`(Ceriotti et al. JCTC (2010)) `_ +which also discusses other applications of the same principle, including +performing simulations with a non-equilibrium *quantum thermostat* that +mimics the quantum the quantum mechanical behavior of light nuclei. + +.. GENERATED FROM PYTHON SOURCE LINES 605-620 + +Setting up a thermostat in ``i-PI`` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A GLE thermostat can be activated using ``mode="gle"``. +The drift matrix used here has been generated from the +`GLE4MD website `_, using parameters that +aim for the most efficient sampling possible with the short +simulation time (2 ps). The `online generator +`_ +can be tuned to provide the best possible sampling for the system +of interest, the most important parameter being the slowest time scale +that one is interested in sampling (typically a fraction of the total +simulation time). The range of frequencies that is optimized can then +be tuned so as to reach, roughly, the maximum frequency present in the +system. + +.. GENERATED FROM PYTHON SOURCE LINES 620-624 + +.. code-block:: Python + + + xmlroot = ET.parse("data/input_gle.xml").getroot() + print(" " + ET.tostring(xmlroot.find(".//thermostat"), encoding="unicode")) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + + [ 8.191023526179e-4, 8.328506066524e-3, 1.657771834013e-3, 9.736989925341e-4, 2.841803794895e-4, -3.176846864198e-5, -2.967010478210e-4, + -8.389856546341e-4, 2.405526974742e-2, -1.507872374848e-2, 2.589784240185e-3, 1.516783633362e-3, -5.958833418565e-4, 4.198422349789e-4, + 7.798710586406e-4, 1.507872374848e-2, 8.569039501219e-3, 6.001000899602e-3, 1.062029383877e-3, 1.093939147968e-3, -2.661575532976e-3, + -9.676783161546e-4, -2.589784240185e-3, -6.001000899602e-3, 2.680459336535e-5, -5.214694469742e-5, 4.231304910751e-4, -2.104894919743e-5, + -2.841997149166e-4, -1.516783633362e-3, -1.062029383877e-3, 5.214694469742e-5, 1.433903506353e-9, -4.241574212449e-5, 7.910178912362e-5, + 3.333208286893e-5, 5.958833418565e-4, -1.093939147968e-3, -4.231304910751e-4, 4.241574212449e-5, 2.385554468441e-8, -3.139255482869e-5, + 2.967533789056e-4, -4.198422349789e-4, 2.661575532976e-3, 2.104894919743e-5, -7.910178912362e-5, 3.139255482869e-5, 2.432567259684e-11 + ] + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 625-626 + +We launch ``i-PI`` as usual ... + +.. GENERATED FROM PYTHON SOURCE LINES 626-633 + +.. code-block:: Python + + + ipi_process = None + if not os.path.exists("simulation_gle.out"): + ipi_process = subprocess.Popen(["i-pi", "data/input_gle.xml"]) + time.sleep(4) # wait for i-PI to start + lmp_process = [subprocess.Popen(["lmp", "-in", "data/in.lmp"]) for i in range(1)] + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 634-635 + +... and wait for simulations to finish. + +.. GENERATED FROM PYTHON SOURCE LINES 635-640 + +.. code-block:: Python + + + if ipi_process is not None: + ipi_process.wait() + lmp_process[0].wait() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 641-649 + +Analysis of the trajectory +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The kinetic temperature equilibrates quickly to the target value. +Since the GLE is a local thermostat, targeting each degree of freedom +separately, equipartition is also reached quickly. Sampling is less +fast than with an aggressive Langevin thermostat, because the GLE targets +each vibrational frequency separately, to minimize the impact on diffusion. + +.. GENERATED FROM PYTHON SOURCE LINES 649-672 + +.. code-block:: Python + + output_data, output_desc = ipi.read_output("simulation_gle.out") + traj_data = ipi.read_trajectory("simulation_gle.pos_0.xyz") + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + output_data["time"], + output_data["temperature(O)"], + "r-", + label="O atoms", + ) + ax.plot( + output_data["time"], + output_data["temperature(H)"], + "c-", + label="H atoms", + ) + ax.plot(output_data["time"], output_data["temperature"], "k-", label="All atoms") + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"$\tilde{T}$ / K") + ax.legend() + plt.show() + + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_009.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_009.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 673-681 + +:math:`\hat{c}_{vv}` reflects the adaptive behavior of the GLE. +The fast modes are damped aggressively, leading to a large +broadening of the high frequency peaks, but librations and diffusive +modes are much less dampened than in the high-coupling Langevin case. +An optimal-coupling GLE is a safe choice to sample any system, from +molecular liquids to harmonic crystals, although a stochastic velocity +rescaling is preferable if one is interested in preserving the natural +dynamics. + +.. GENERATED FROM PYTHON SOURCE LINES 681-711 + +.. code-block:: Python + + + acf_gle = compute_acf_xyz( + "simulation_gle.vel_0.xyz", + maximum_lag=600, + length_zeropadding=2000, + spectral_windowing="cosine-blackman", + timestep=1, + time_units="femtosecond", + skip=100, + ) + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", + ) + ax.loglog( + acf_gle[3][:1200] * ha2cm1, + acf_gle[4][:1200] * 1e5, + "b-", + label=r"GLE", + ) + ax.set_xlabel(r"$\omega$ / cm$^{-1}$") + ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_010.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_010.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 712-735 + +R-L purification +~~~~~~~~~~~~~~~~ + +What if you also want to extract dynamical information from a GLE +(or Langevin) trajectory? It is actually possible to post-process the +power spectrum, performing a deconvolution based on the amount of +disturbance introduced by the GLE, that can be predicted analytically +in the harmonic limit. +The idea, discussed in `(Rossi et al., JCP (2018)) +`_ +is that if :math:`\hat{y}(\omega)` is the "natural" NVE power +spectrum, and :math:`k_{\mathrm{GLE}}(\omega_0, \omega)` is the power +spectrum predicted for a harmonic oscillator of frequency :math:`\omega_0`, +then the spectrum from the GLE dynamics will be approximately + +.. math:: + + \hat{y}_{\mathrm{GLE}}(\omega) = \int \mathrm{d}\omega' + k_{\mathrm{GLE}}(\omega', \omega) \hat{y}(\omega') + +The kernel can be computed analytically for all frequencies that +are relevant for the power spectrum, based on the GLE parameters +extracted from the input of ``i-PI``. + +.. GENERATED FROM PYTHON SOURCE LINES 735-753 + +.. code-block:: Python + + + n_omega = 1200 + Ap, Cp, Dp = get_gle_matrices("data/input_gle.xml") + gle_kernel = gle_frequency_kernel(acf_gle[3][:n_omega], Ap, Dp) + + + lomega = acf_gle[3][:n_omega] * ha2cm1 + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + levels = np.logspace(np.log10(gle_kernel.min()), np.log10(gle_kernel.max()), num=50) + contour = ax.contourf(lomega, lomega, gle_kernel, norm=mpl.colors.LogNorm()) + ax.set_xscale("log") + ax.set_yscale("log") + ax.set_xlabel(r"$\omega_0$ / cm$^{-1}$") + ax.set_ylabel(r"$\omega$ / cm$^{-1}$") + ax.set_xlim(10, 5000) + ax.set_ylim(10, 5000) + cbar = fig.colorbar(contour, ticks=[1e1, 1e3, 1e5, 1e7]) + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_011.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_011.png + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + + # Initializing system object + # Initializing simulation object + # Initializing from file data/water_32.pdb. Dimension: length, units: angstrom, cell_units: automatic + # Initializing from file data/water_32.pdb. Dimension: length, units: automatic, cell_units: automatic + # Initializing from file data/water_32.pdb. Dimension: length, units: automatic, cell_units: automatic + # Initializing from file data/water_32.pdb. Dimension: length, units: automatic, cell_units: automatic + # Initializing from file data/water_32.pdb. Dimension: length, units: automatic, cell_units: automatic + # Resampling velocities at temperature 300.0 kelvin + + + + +.. GENERATED FROM PYTHON SOURCE LINES 754-757 + +The deconvolution is based on the Iterative Image Space +Reconstruction Algorithm, which preserves the positive-definiteness +of the spectrum + +.. GENERATED FROM PYTHON SOURCE LINES 757-762 + +.. code-block:: Python + + + isra_acf, history, errors, laplace = isra_deconvolute( + acf_gle[3][:n_omega], acf_gle[4][:n_omega], gle_kernel, 64, 4 + ) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + # error, laplacian = 2.0035857194608525e-08, 5.597931268407369e-11 + # error, laplacian = 2.2056080818736523e-08, 1.7376945463460065e-10 + # error, laplacian = 2.3108219158631213e-08, 4.09763216849384e-10 + # error, laplacian = 2.369196704921211e-08, 7.780582324317745e-10 + # error, laplacian = 2.403580322791337e-08, 1.2694726433106536e-09 + # error, laplacian = 2.4249416522217333e-08, 1.8613480357225975e-09 + # error, laplacian = 2.438911224963073e-08, 2.5265424831388664e-09 + # error, laplacian = 2.4485109864354932e-08, 3.239103110728055e-09 + # error, laplacian = 2.4554211808525377e-08, 3.976973254686062e-09 + # error, laplacian = 2.4606081167050248e-08, 4.722765353502745e-09 + # error, laplacian = 2.4646468346077778e-08, 5.463509169214063e-09 + # error, laplacian = 2.467891320726097e-08, 6.189975719656217e-09 + # error, laplacian = 2.470566688914048e-08, 6.895908466753566e-09 + # error, laplacian = 2.472820607594879e-08, 7.577316415575888e-09 + # error, laplacian = 2.4747528979283516e-08, 8.231884533278532e-09 + + + + +.. GENERATED FROM PYTHON SOURCE LINES 763-767 + +Even though the ISRA algorithm is less prone to enhancing noise than +other deconvolution algorithms, successive iterations sharpen the spectrum +but introduce higher and higher levles of noise, particularly on the +low-frequency end of the spectrum so one has to choose when to stop. + +.. GENERATED FROM PYTHON SOURCE LINES 767-809 + +.. code-block:: Python + + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.loglog( + acf_gle[3][:1200] * ha2cm1, + acf_gle[4][:1200] * 1e5, + "b-", + label=r"GLE", + ) + ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[0] * 1e5, + ":", + color="#4000D0", + label=r"iter[1]", + ) + ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[2] * 1e5, + ":", + color="#A000A0", + label=r"iter[9]", + ) + ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[4] * 1e5, + ":", + color="#D00040", + label=r"iter[17]", + ) + ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[12] * 1e5, + ":", + color="#FF0000", + label=r"iter[49]", + ) + + ax.set_xlabel(r"$\omega$ / cm$^{-1}$") + ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") + ax.legend() + plt.show() + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_012.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_012.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 810-815 + +Especially in the high-frequency region, the deconvolution +algorithm succees in recovering the underlying NVE dynamics, +which can be useful whenever one wants to optimize statistical +efficiency while still being able to estimate dynamical +properties. + +.. GENERATED FROM PYTHON SOURCE LINES 815-842 + +.. code-block:: Python + + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.fill_between( + acf_ref[:1200, 0] * ha2cm1, + (acf_ref[:1200, 1] - acf_ref[:1200, 2]) * 1e5, + (acf_ref[:1200, 1] + acf_ref[:1200, 2]) * 1e5, + color="gray", + label="reference", + ) + ax.loglog( + acf_gle[3][:1200] * ha2cm1, + acf_gle[4][:1200] * 1e5, + "b-", + label=r"GLE", + ) + ax.loglog( + acf_gle[3][:1200] * ha2cm1, + history[2] * 1e5, + "r-", + label=r"GLE$\rightarrow$ NVE (iter[5])", + ) + ax.set_xlabel(r"$\omega$ / cm$^{-1}$") + ax.set_ylabel(r"$\hat{c}_{vv}$ / arb. units") + ax.legend() + plt.show() + + + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_013.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_013.png + :class: sphx-glr-single-img + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 843-864 + +Running with LAMMPS +~~~~~~~~~~~~~~~~~~~ + +GLE thermostats (as well as conventional Langevin, and +stochastic velocity rescaling) are also implemented natively +in ``LAMMPS``. + +An example of ``LAMMPS`` input containing a GLE thermostat can +be found in ``data/gle.lmp``. See also the +`documentation of the fix gle command +`_ + +.. code-block:: text + + fix 1 all gle 6 300 300 31415 data/smart.A + +The drift matrix can be obtained from the same website, simply +asking to output the matrix in raw format, choosing units consistent +with the ``LAMMPS`` settings, e.g. for this `optimal sampling setup +`_ + + +.. GENERATED FROM PYTHON SOURCE LINES 866-873 + +We can run ``LAMMPS`` from the command line + +.. code-block:: bash + + lmp -in data/gle.lmp & + +or from Python + +.. GENERATED FROM PYTHON SOURCE LINES 873-878 + +.. code-block:: Python + + + lmp_process = None + if not os.path.exists("lammps_out.dat"): + lmp_process = subprocess.Popen(["lmp", "-in", "data/gle.lmp"]) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 879-881 + +... and wait + + +.. GENERATED FROM PYTHON SOURCE LINES 881-885 + +.. code-block:: Python + + + if lmp_process is not None: + lmp_process.wait() + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 886-890 + +The simulation is much faster (for such a small system and +cheap potential the overhead of ``i-PI``'s client-server mechanism +is substantial) and leads to similar results for the kinetic temperature + + +.. GENERATED FROM PYTHON SOURCE LINES 890-904 + +.. code-block:: Python + + + traj_data = np.loadtxt("lammps_out.dat") + + fig, ax = plt.subplots(1, 1, figsize=(4, 3), constrained_layout=True) + ax.plot( + traj_data[:, 0] * 1e-3, + traj_data[:, 1], + "k-", + label="All atoms", + ) + ax.set_xlabel(r"$t$ / ps") + ax.set_ylabel(r"$\tilde{T}$ / K") + ax.legend() + plt.show() + + + +.. image-sg:: /examples/thermostats/images/sphx_glr_thermostats_014.png + :alt: thermostats + :srcset: /examples/thermostats/images/sphx_glr_thermostats_014.png + :class: sphx-glr-single-img + + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** (1 minutes 14.142 seconds) + + +.. _sphx_glr_download_examples_thermostats_thermostats.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + + .. container:: sphx-glr-download + + :download:`Download Conda environment file: environment.yml ` + + .. container:: sphx-glr-download + + :download:`Download data files: data.zip ` + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: thermostats.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: thermostats.py ` + + .. container:: sphx-glr-download sphx-glr-download-zip + + :download:`Download zipped: thermostats.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ + diff --git a/_sources/index.rst.txt b/_sources/index.rst.txt new file mode 100644 index 00000000..94d6983b --- /dev/null +++ b/_sources/index.rst.txt @@ -0,0 +1,35 @@ +.. meta:: + :description: Computational recipes for modeling matter at the atomic scale. + Interactive guides that you can also run locally and use as templates for + your own simulations. + :keywords: Atomistic simulations, statistical mechanics, machine learning, + molecular dynamics, quantum chemistry, materials modeling + +The Atomistic Cookbook +====================== + +.. include:: ../../README.rst + :start-after: marker-intro-start + :end-before: marker-intro-end + +Table of contents +~~~~~~~~~~~~~~~~~ + +.. toctree:: + :maxdepth: 1 + + topics/index + software/index + all-examples + downloading + contributing + +Recipe of the day +~~~~~~~~~~~~~~~~~ + +Want to try something new? Each day, one of the recipes in the cookbook +is highlighted on the front page. There is one to suit everyone's taste! + +.. raw:: html + +
diff --git a/_sources/software/chemiscope.rst.txt b/_sources/software/chemiscope.rst.txt new file mode 100644 index 00000000..37b6ed03 --- /dev/null +++ b/_sources/software/chemiscope.rst.txt @@ -0,0 +1,79 @@ +.. _chemiscope: + +chemiscope +========== + +Chemiscope is a tool for interactive exploration of databases of materials and +molecules, correlating local and global structural representations with the +properties of the systems. Chemiscope files can be viewed `online +`_, generated using a `python library +`_ and used inside jupyter notebooks or +sphinx documentations, which is how it's used in the cookbook examples. You can +check the `documentation `_ and the `github +repository `_. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: Generalized Convex Hull construction for the polymorphs of ROY + :link: ../examples/roy-gch/roy-gch + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/roy-gch/images/thumb/sphx_glr_roy-gch_thumb.png + :alt: This notebook analyzes the structures of 264 polymorphs of ROY, from Beran et Al, Chemical Science (2022), comparing the conventional density-energy convex hull with a Generalized Convex Hull (GCH) analysis (see Anelli et al., Phys. Rev. Materials (2018)). It uses features computed with rascaline and uses the directional convex hull function from scikit-matter to make the figure. + :class: gallery-img + + + .. grid-item:: + .. card:: PCA/PCovR Visualization of a training dataset for a potential + :link: ../examples/gaas-map/gaas-map + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/gaas-map/images/thumb/sphx_glr_gaas-map_thumb.png + :alt: This example uses rascaline and metatensor to compute structural properties for the structures in a training dataset for a ML potential. These are then used with simple dimensionality reduction algorithms (implemented in sklearn and skmatter) to obtain a simplified description of the dataset, that is then visualized using chemiscope. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral metadynamics + :link: ../examples/pi-metad/pi-metad + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/pi-metad/images/thumb/sphx_glr_pi-metad_thumb.png + :alt: This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral molecular dynamics + :link: ../examples/path-integrals/path-integrals + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/path-integrals/images/thumb/sphx_glr_path-integrals_thumb.png + :alt: This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + + .. grid-item:: + .. card:: Constant-temperature MD and thermostats + :link: ../examples/thermostats/thermostats + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/thermostats/images/thumb/sphx_glr_thermostats_thumb.png + :alt: This recipe gives a practical introduction to finite-temperature molecular dynamics simulations, and provides a guide to choose the most appropriate thermostat for the simulation at hand. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/software/cp2k.rst.txt b/_sources/software/cp2k.rst.txt new file mode 100644 index 00000000..8af5aeb1 --- /dev/null +++ b/_sources/software/cp2k.rst.txt @@ -0,0 +1,37 @@ +cp2k +==== + +CP2K is a quantum chemistry and solid state physics software package that can +perform atomistic simulations of solid state, liquid, molecular, periodic, +material, crystal, and biological systems. Learn more about it on its `homepage +`_. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: Batch run of CP2K calculations + :link: ../examples/batch-cp2k/reference-trajectory + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/batch-cp2k/images/thumb/sphx_glr_reference-trajectory_thumb.png + :alt: This is an example how to perform single point calculations based on list of structures using CP2K using its reftraj functionality. The inputs are a set of structures in :download:`example.xyz` using the DFT parameters defined in :download:`reftraj_template.cp2k`. The reference DFT parameters are taken from Cheng et al. Ab initio thermodynamics of liquid and solid water 2019. Due to the small size of the test structure and convergence issues, we have decreased the size of the CUTOFF_RADIUS from 6.0\,\mathrm{Å} to 3.0\,\mathrm{Å}. For actual production calculations adapt the template! + :class: gallery-img + + + .. grid-item:: + .. card:: Periodic Hamiltonian learning + :link: ../examples/periodic-hamiltonian/periodic-hamiltonian + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/periodic-hamiltonian/images/thumb/sphx_glr_periodic-hamiltonian_thumb.png + :alt: This tutorial explains how to train a machine learning model for the electronic Hamiltonian of a periodic system. Even though we focus on periodic systems, the code and techniques presented here can be directly transferred to molecules. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/software/i-pi.rst.txt b/_sources/software/i-pi.rst.txt new file mode 100644 index 00000000..95580f0a --- /dev/null +++ b/_sources/software/i-pi.rst.txt @@ -0,0 +1,63 @@ +i-PI +==== + +i-PI is a universal force engine interface written in Python, designed to be +used together with an ab-initio, machine-learned, or force-field based +evaluation of the interactions between the atoms. You can see learn more about +it on the `ipi-code website `_, the `documentation pages +`_ or `the github repository +`_. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: Constant-temperature MD and thermostats + :link: ../examples/thermostats/thermostats + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/thermostats/images/thumb/sphx_glr_thermostats_thumb.png + :alt: This recipe gives a practical introduction to finite-temperature molecular dynamics simulations, and provides a guide to choose the most appropriate thermostat for the simulation at hand. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral molecular dynamics + :link: ../examples/path-integrals/path-integrals + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/path-integrals/images/thumb/sphx_glr_path-integrals_thumb.png + :alt: This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral metadynamics + :link: ../examples/pi-metad/pi-metad + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/pi-metad/images/thumb/sphx_glr_pi-metad_thumb.png + :alt: This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions. + :class: gallery-img + + + .. grid-item:: + .. card:: Quantum heat capacity of water + :link: ../examples/heat-capacity/heat-capacity + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/heat-capacity/images/thumb/sphx_glr_heat-capacity_thumb.png + :alt: This example shows how to estimate the heat capacity of liquid water from a path integral molecular dynamics simulation. The dynamics are run with i-PI, and LAMMPS is used as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/software/index.rst.txt b/_sources/software/index.rst.txt new file mode 100644 index 00000000..c742851b --- /dev/null +++ b/_sources/software/index.rst.txt @@ -0,0 +1,18 @@ +Recipes grouped by software used +================================ + +Cookbook recipes often combine multiple modeling tools. +Here you can find them organized based on the software +they use. They may give you ideas on how to use them +in your own atomistic cooking. + +.. toctree:: + :maxdepth: 1 + + i-pi + chemiscope + rascaline + scikit-matter + cp2k + lammps + plumed diff --git a/_sources/software/lammps.rst.txt b/_sources/software/lammps.rst.txt new file mode 100644 index 00000000..540c39e2 --- /dev/null +++ b/_sources/software/lammps.rst.txt @@ -0,0 +1,50 @@ +LAMMPS +====== + +LAMMPS is a classical molecular dynamics (MD) code, with a focus on materials +simulations. It includes a wealth of interatomic potentials, and of basic and +advanced molecular simulations techniques, and is highly parallelized using an +efficient domain decomposition scheme. Learn more about LAMMPS on its `homepage +`_. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: Constant-temperature MD and thermostats + :link: ../examples/thermostats/thermostats + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/thermostats/images/thumb/sphx_glr_thermostats_thumb.png + :alt: This recipe gives a practical introduction to finite-temperature molecular dynamics simulations, and provides a guide to choose the most appropriate thermostat for the simulation at hand. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral molecular dynamics + :link: ../examples/path-integrals/path-integrals + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/path-integrals/images/thumb/sphx_glr_path-integrals_thumb.png + :alt: This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + + .. grid-item:: + .. card:: Quantum heat capacity of water + :link: ../examples/heat-capacity/heat-capacity + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/heat-capacity/images/thumb/sphx_glr_heat-capacity_thumb.png + :alt: This example shows how to estimate the heat capacity of liquid water from a path integral molecular dynamics simulation. The dynamics are run with i-PI, and LAMMPS is used as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/software/plumed.rst.txt b/_sources/software/plumed.rst.txt new file mode 100644 index 00000000..b46204b3 --- /dev/null +++ b/_sources/software/plumed.rst.txt @@ -0,0 +1,29 @@ +PLUMED +====== + +PLUMED is an open-source, community-developed library that provides a wide range +of different methods, which include enhanced-sampling algorithms, free-energy +methods, tools to analyze the vast amounts of data produced by molecular +dynamics (MD) simulations. These techniques can be used in combination with a +large toolbox of collective variables that describe complex processes in +physics, chemistry, material science, and biology. Documentation, examples and +installation instructions for the various packages are discussed on the `PLUMED +website `_. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: Path integral metadynamics + :link: ../examples/pi-metad/pi-metad + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/pi-metad/images/thumb/sphx_glr_pi-metad_thumb.png + :alt: This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/software/rascaline.rst.txt b/_sources/software/rascaline.rst.txt new file mode 100644 index 00000000..aed8fa94 --- /dev/null +++ b/_sources/software/rascaline.rst.txt @@ -0,0 +1,99 @@ +rascaline +========= + +Rascaline is a library for the efficient computing of representations for +atomistic machine learning also called “descriptors” or “fingerprints”. These +representation can be used for atomistic machine learning (ML) models including +ML potentials, visualization or similarity analysis. You can learn how to use it +reading the `documentation `_, and get the latest +version from the `github repository `_ + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: PCA/PCovR Visualization of a training dataset for a potential + :link: ../examples/gaas-map/gaas-map + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/gaas-map/images/thumb/sphx_glr_gaas-map_thumb.png + :alt: This example uses rascaline and metatensor to compute structural properties for the structures in a training dataset for a ML potential. These are then used with simple dimensionality reduction algorithms (implemented in sklearn and skmatter) to obtain a simplified description of the dataset, that is then visualized using chemiscope. + :class: gallery-img + + + .. grid-item:: + .. card:: Local Prediction Rigidity analysis + :link: ../examples/lpr/lpr + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/lpr/images/thumb/sphx_glr_lpr_thumb.png + :alt: In this tutorial, we calculate the SOAP descriptors of an amorphous silicon dataset using rascaline, then compute the local prediction rigidity (LPR) for the atoms of a "test" set before and after modifications to the "training" dataset has been made. + :class: gallery-img + + + .. grid-item:: + .. card:: A ML model for the electron density of states + :link: ../examples/dos-align/dos-align + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/dos-align/images/thumb/sphx_glr_dos-align_thumb.png + :alt: This tutorial would go through the entire machine learning framework for the electronic density of states (DOS). It will cover the construction of the DOS and SOAP descriptors from ase Atoms and eigenenergy results. A simple neural network will then be constructed and the model parameters, along with the energy reference will be optimized during training. A total of three energy reference will be used, the average Hartree potential, the Fermi level, and an optimized energy reference starting from the Fermi level energy reference. The performance of each model is then compared. + :class: gallery-img + + + .. grid-item:: + .. card:: Long-distance Equivariants: a tutorial + :link: ../examples/lode-linear/lode-linear + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/lode-linear/images/thumb/sphx_glr_lode-linear_thumb.png + :alt: This tutorial explains how Long range equivariant descriptors can be constructed using rascaline and the resulting descriptors be used to construct a linear model with equisolve + :class: gallery-img + + + .. grid-item:: + .. card:: Generalized Convex Hull construction for the polymorphs of ROY + :link: ../examples/roy-gch/roy-gch + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/roy-gch/images/thumb/sphx_glr_roy-gch_thumb.png + :alt: This notebook analyzes the structures of 264 polymorphs of ROY, from Beran et Al, Chemical Science (2022), comparing the conventional density-energy convex hull with a Generalized Convex Hull (GCH) analysis (see Anelli et al., Phys. Rev. Materials (2018)). It uses features computed with rascaline and uses the directional convex hull function from scikit-matter to make the figure. + :class: gallery-img + + + .. grid-item:: + .. card:: Sample and Feature Selection with FPS and CUR + :link: ../examples/sample-selection/sample-selection + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/sample-selection/images/thumb/sphx_glr_sample-selection_thumb.png + :alt: In this tutorial we generate descriptors using rascaline, then select a subset of structures using both the farthest-point sampling (FPS) and CUR algorithms implemented in scikit-matter. Finally, we also generate a selection of the most important features using the same techniques. + :class: gallery-img + + + .. grid-item:: + .. card:: Periodic Hamiltonian learning + :link: ../examples/periodic-hamiltonian/periodic-hamiltonian + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/periodic-hamiltonian/images/thumb/sphx_glr_periodic-hamiltonian_thumb.png + :alt: This tutorial explains how to train a machine learning model for the electronic Hamiltonian of a periodic system. Even though we focus on periodic systems, the code and techniques presented here can be directly transferred to molecules. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/software/scikit-matter.rst.txt b/_sources/software/scikit-matter.rst.txt new file mode 100644 index 00000000..142057a2 --- /dev/null +++ b/_sources/software/scikit-matter.rst.txt @@ -0,0 +1,63 @@ +scikit-matter +============= + +scikit-matter is a toolbox of methods developed in the computational chemical +and materials science community, following the scikit-learn API and coding +guidelines to promote usability and interoperability with existing workflows. +You can get the latest version from its `github repository +`_ and learn how to use +it from its `documentation `_. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: Sample and Feature Selection with FPS and CUR + :link: ../examples/sample-selection/sample-selection + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/sample-selection/images/thumb/sphx_glr_sample-selection_thumb.png + :alt: In this tutorial we generate descriptors using rascaline, then select a subset of structures using both the farthest-point sampling (FPS) and CUR algorithms implemented in scikit-matter. Finally, we also generate a selection of the most important features using the same techniques. + :class: gallery-img + + + .. grid-item:: + .. card:: Generalized Convex Hull construction for the polymorphs of ROY + :link: ../examples/roy-gch/roy-gch + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/roy-gch/images/thumb/sphx_glr_roy-gch_thumb.png + :alt: This notebook analyzes the structures of 264 polymorphs of ROY, from Beran et Al, Chemical Science (2022), comparing the conventional density-energy convex hull with a Generalized Convex Hull (GCH) analysis (see Anelli et al., Phys. Rev. Materials (2018)). It uses features computed with rascaline and uses the directional convex hull function from scikit-matter to make the figure. + :class: gallery-img + + + .. grid-item:: + .. card:: Local Prediction Rigidity analysis + :link: ../examples/lpr/lpr + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/lpr/images/thumb/sphx_glr_lpr_thumb.png + :alt: In this tutorial, we calculate the SOAP descriptors of an amorphous silicon dataset using rascaline, then compute the local prediction rigidity (LPR) for the atoms of a "test" set before and after modifications to the "training" dataset has been made. + :class: gallery-img + + + .. grid-item:: + .. card:: PCA/PCovR Visualization of a training dataset for a potential + :link: ../examples/gaas-map/gaas-map + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/gaas-map/images/thumb/sphx_glr_gaas-map_thumb.png + :alt: This example uses rascaline and metatensor to compute structural properties for the structures in a training dataset for a ML potential. These are then used with simple dimensionality reduction algorithms (implemented in sklearn and skmatter) to obtain a simplified description of the dataset, that is then visualized using chemiscope. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/topics/analysis.rst.txt b/_sources/topics/analysis.rst.txt new file mode 100644 index 00000000..6c6b4880 --- /dev/null +++ b/_sources/topics/analysis.rst.txt @@ -0,0 +1,47 @@ +Analysis and post-processing +============================ + +This section contains recipes that analyze the output of a simulation, +for analysis or visualization purposes. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: PCA/PCovR Visualization of a training dataset for a potential + :link: ../examples/gaas-map/gaas-map + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/gaas-map/images/thumb/sphx_glr_gaas-map_thumb.png + :alt: This example uses rascaline and metatensor to compute structural properties for the structures in a training dataset for a ML potential. These are then used with simple dimensionality reduction algorithms (implemented in sklearn and skmatter) to obtain a simplified description of the dataset, that is then visualized using chemiscope. + :class: gallery-img + + + .. grid-item:: + .. card:: Local Prediction Rigidity analysis + :link: ../examples/lpr/lpr + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/lpr/images/thumb/sphx_glr_lpr_thumb.png + :alt: In this tutorial, we calculate the SOAP descriptors of an amorphous silicon dataset using rascaline, then compute the local prediction rigidity (LPR) for the atoms of a "test" set before and after modifications to the "training" dataset has been made. + :class: gallery-img + + + .. grid-item:: + .. card:: Generalized Convex Hull construction for the polymorphs of ROY + :link: ../examples/roy-gch/roy-gch + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/roy-gch/images/thumb/sphx_glr_roy-gch_thumb.png + :alt: This notebook analyzes the structures of 264 polymorphs of ROY, from Beran et Al, Chemical Science (2022), comparing the conventional density-energy convex hull with a Generalized Convex Hull (GCH) analysis (see Anelli et al., Phys. Rev. Materials (2018)). It uses features computed with rascaline and uses the directional convex hull function from scikit-matter to make the figure. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/topics/index.rst.txt b/_sources/topics/index.rst.txt new file mode 100644 index 00000000..6b9f5be9 --- /dev/null +++ b/_sources/topics/index.rst.txt @@ -0,0 +1,15 @@ +Recipes grouped by topic +======================== + +You can navigate through the various recipes grouped +in thematic areas, including classes of simulation problems +and of modeling techniques. Recipes may be listed in +more than one area, when relevant. + +.. toctree:: + :maxdepth: 1 + + sampling + analysis + ml-models + nqes diff --git a/_sources/topics/ml-models.rst.txt b/_sources/topics/ml-models.rst.txt new file mode 100644 index 00000000..f2fe93d3 --- /dev/null +++ b/_sources/topics/ml-models.rst.txt @@ -0,0 +1,60 @@ +Machine learning models +======================= + +This section contains recipes that concern the training of machine-learning +models, or the pre-processing of data to optimize the model architecture or +data. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: A ML model for the electron density of states + :link: ../examples/dos-align/dos-align + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/dos-align/images/thumb/sphx_glr_dos-align_thumb.png + :alt: This tutorial would go through the entire machine learning framework for the electronic density of states (DOS). It will cover the construction of the DOS and SOAP descriptors from ase Atoms and eigenenergy results. A simple neural network will then be constructed and the model parameters, along with the energy reference will be optimized during training. A total of three energy reference will be used, the average Hartree potential, the Fermi level, and an optimized energy reference starting from the Fermi level energy reference. The performance of each model is then compared. + :class: gallery-img + + + .. grid-item:: + .. card:: Long-distance Equivariants: a tutorial + :link: ../examples/lode-linear/lode-linear + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/lode-linear/images/thumb/sphx_glr_lode-linear_thumb.png + :alt: This tutorial explains how Long range equivariant descriptors can be constructed using rascaline and the resulting descriptors be used to construct a linear model with equisolve + :class: gallery-img + + + .. grid-item:: + .. card:: Sample and Feature Selection with FPS and CUR + :link: ../examples/sample-selection/sample-selection + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/sample-selection/images/thumb/sphx_glr_sample-selection_thumb.png + :alt: In this tutorial we generate descriptors using rascaline, then select a subset of structures using both the farthest-point sampling (FPS) and CUR algorithms implemented in scikit-matter. Finally, we also generate a selection of the most important features using the same techniques. + :class: gallery-img + + + .. grid-item:: + .. card:: Periodic Hamiltonian learning + :link: ../examples/periodic-hamiltonian/periodic-hamiltonian + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/periodic-hamiltonian/images/thumb/sphx_glr_periodic-hamiltonian_thumb.png + :alt: This tutorial explains how to train a machine learning model for the electronic Hamiltonian of a periodic system. Even though we focus on periodic systems, the code and techniques presented here can be directly transferred to molecules. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/topics/nqes.rst.txt b/_sources/topics/nqes.rst.txt new file mode 100644 index 00000000..03072b8d --- /dev/null +++ b/_sources/topics/nqes.rst.txt @@ -0,0 +1,49 @@ +Nuclear quantum effects +======================= + +Most atomistic simulations treat nuclei as classical particles, that sample a +Boltzmann distribution. This approximation breaks down for light nuclei +(hydrogen above all) and high-frequency vibrations, requiring more sophisticated +statistical sampling to compute accurate statistical and dynamical properties. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: Path integral molecular dynamics + :link: ../examples/path-integrals/path-integrals + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/path-integrals/images/thumb/sphx_glr_path-integrals_thumb.png + :alt: This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral metadynamics + :link: ../examples/pi-metad/pi-metad + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/pi-metad/images/thumb/sphx_glr_pi-metad_thumb.png + :alt: This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions. + :class: gallery-img + + + .. grid-item:: + .. card:: Quantum heat capacity of water + :link: ../examples/heat-capacity/heat-capacity + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/heat-capacity/images/thumb/sphx_glr_heat-capacity_thumb.png + :alt: This example shows how to estimate the heat capacity of liquid water from a path integral molecular dynamics simulation. The dynamics are run with i-PI, and LAMMPS is used as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + \ No newline at end of file diff --git a/_sources/topics/sampling.rst.txt b/_sources/topics/sampling.rst.txt new file mode 100644 index 00000000..129cdb8b --- /dev/null +++ b/_sources/topics/sampling.rst.txt @@ -0,0 +1,72 @@ +Statistical sampling and dynamics +================================= + +This section contains recipes that compute thermodynamic averages by sampling, +evaluates dynamical properties, or otherwise computes the properties of a +set of configurations of an atomistic system. + + + +.. grid:: 1 2 2 3 + :gutter: 1 1 2 3 + + .. grid-item:: + .. card:: Constant-temperature MD and thermostats + :link: ../examples/thermostats/thermostats + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/thermostats/images/thumb/sphx_glr_thermostats_thumb.png + :alt: This recipe gives a practical introduction to finite-temperature molecular dynamics simulations, and provides a guide to choose the most appropriate thermostat for the simulation at hand. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral molecular dynamics + :link: ../examples/path-integrals/path-integrals + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/path-integrals/images/thumb/sphx_glr_path-integrals_thumb.png + :alt: This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + + .. grid-item:: + .. card:: Path integral metadynamics + :link: ../examples/pi-metad/pi-metad + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/pi-metad/images/thumb/sphx_glr_pi-metad_thumb.png + :alt: This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions. + :class: gallery-img + + + .. grid-item:: + .. card:: Batch run of CP2K calculations + :link: ../examples/batch-cp2k/reference-trajectory + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/batch-cp2k/images/thumb/sphx_glr_reference-trajectory_thumb.png + :alt: This is an example how to perform single point calculations based on list of structures using CP2K using its reftraj functionality. The inputs are a set of structures in :download:`example.xyz` using the DFT parameters defined in :download:`reftraj_template.cp2k`. The reference DFT parameters are taken from Cheng et al. Ab initio thermodynamics of liquid and solid water 2019. Due to the small size of the test structure and convergence issues, we have decreased the size of the CUTOFF_RADIUS from 6.0\,\mathrm{Å} to 3.0\,\mathrm{Å}. For actual production calculations adapt the template! + :class: gallery-img + + + .. grid-item:: + .. card:: Quantum heat capacity of water + :link: ../examples/heat-capacity/heat-capacity + :link-type: doc + :text-align: center + :shadow: md + + .. image:: ../examples/heat-capacity/images/thumb/sphx_glr_heat-capacity_thumb.png + :alt: This example shows how to estimate the heat capacity of liquid water from a path integral molecular dynamics simulation. The dynamics are run with i-PI, and LAMMPS is used as the driver to simulate the q-TIP4P/f water model. + :class: gallery-img + + \ No newline at end of file diff --git a/_sphinx_design_static/design-tabs.js b/_sphinx_design_static/design-tabs.js new file mode 100644 index 00000000..b25bd6a4 --- /dev/null +++ b/_sphinx_design_static/design-tabs.js @@ -0,0 +1,101 @@ +// @ts-check + +// Extra JS capability for selected tabs to be synced +// The selection is stored in local storage so that it persists across page loads. + +/** + * @type {Record} + */ +let sd_id_to_elements = {}; +const storageKeyPrefix = "sphinx-design-tab-id-"; + +/** + * Create a key for a tab element. + * @param {HTMLElement} el - The tab element. + * @returns {[string, string, string] | null} - The key. + * + */ +function create_key(el) { + let syncId = el.getAttribute("data-sync-id"); + let syncGroup = el.getAttribute("data-sync-group"); + if (!syncId || !syncGroup) return null; + return [syncGroup, syncId, syncGroup + "--" + syncId]; +} + +/** + * Initialize the tab selection. + * + */ +function ready() { + // Find all tabs with sync data + + /** @type {string[]} */ + let groups = []; + + document.querySelectorAll(".sd-tab-label").forEach((label) => { + if (label instanceof HTMLElement) { + let data = create_key(label); + if (data) { + let [group, id, key] = data; + + // add click event listener + // @ts-ignore + label.onclick = onSDLabelClick; + + // store map of key to elements + if (!sd_id_to_elements[key]) { + sd_id_to_elements[key] = []; + } + sd_id_to_elements[key].push(label); + + if (groups.indexOf(group) === -1) { + groups.push(group); + // Check if a specific tab has been selected via URL parameter + const tabParam = new URLSearchParams(window.location.search).get( + group + ); + if (tabParam) { + console.log( + "sphinx-design: Selecting tab id for group '" + + group + + "' from URL parameter: " + + tabParam + ); + window.sessionStorage.setItem(storageKeyPrefix + group, tabParam); + } + } + + // Check is a specific tab has been selected previously + let previousId = window.sessionStorage.getItem( + storageKeyPrefix + group + ); + if (previousId === id) { + // console.log( + // "sphinx-design: Selecting tab from session storage: " + id + // ); + // @ts-ignore + label.previousElementSibling.checked = true; + } + } + } + }); +} + +/** + * Activate other tabs with the same sync id. + * + * @this {HTMLElement} - The element that was clicked. + */ +function onSDLabelClick() { + let data = create_key(this); + if (!data) return; + let [group, id, key] = data; + for (const label of sd_id_to_elements[key]) { + if (label === this) continue; + // @ts-ignore + label.previousElementSibling.checked = true; + } + window.sessionStorage.setItem(storageKeyPrefix + group, id); +} + +document.addEventListener("DOMContentLoaded", ready, false); diff --git a/_sphinx_design_static/sphinx-design.min.css b/_sphinx_design_static/sphinx-design.min.css new file mode 100644 index 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[{"title": "A ML model for the electron density of states", "description": "This tutorial would go through the entire machine learning framework for the electronic density of states (DOS). It will cover the construction of the DOS and SOAP descriptors from ase Atoms and eigenenergy results. A simple neural network will then be constructed and the model parameters, along with the energy reference will be optimized during training. A total of three energy reference will be used, the average Hartree potential, the Fermi level, and an optimized energy reference starting from the Fermi level energy reference. The performance of each model is then compared.", "html": "

This tutorial would go through the entire machine learning framework for the electronic density of states (DOS). It will cover the construction of the DOS and SOAP descriptors from ase Atoms and eigenenergy results. A simple neural network will then be constructed and the model parameters, along with the energy reference will be optimized during training. A total of three energy reference will be used, the average Hartree potential, the Fermi level, and an optimized energy reference starting from the Fermi level energy reference. The performance of each model is then compared.

\n", "thumbnail": "_images/sphx_glr_dos-align_thumb.png", "ref": "examples/dos-align/dos-align.html"}, {"title": "Batch run of CP2K calculations", "description": "This is an example how to perform single point calculations based on list of structures using CP2K using its reftraj functionality. The inputs are a set of structures in :download:`example.xyz` using the DFT parameters defined in :download:`reftraj_template.cp2k`. The reference DFT parameters are taken from Cheng et al. Ab initio thermodynamics of liquid and solid water 2019. Due to the small size of the test structure and convergence issues, we have decreased the size of the CUTOFF_RADIUS from 6.0\\,\\mathrm{\u00c5} to 3.0\\,\\mathrm{\u00c5}. For actual production calculations adapt the template!", "html": "

This is an example how to perform single point calculations based on list of structures using CP2K using its reftraj functionality. The inputs are a set of structures in :download:`example.xyz` using the DFT parameters defined in :download:`reftraj_template.cp2k`. The reference DFT parameters are taken from Cheng et al. Ab initio thermodynamics of liquid and solid water 2019. Due to the small size of the test structure and convergence issues, we have decreased the size of the CUTOFF_RADIUS from 6.0,mathrm{\u00c5} to 3.0,mathrm{\u00c5}. For actual production calculations adapt the template!

\n", "thumbnail": "_images/sphx_glr_reference-trajectory_thumb.png", "ref": "examples/batch-cp2k/reference-trajectory.html"}, {"title": "Constant-temperature MD and thermostats", "description": "This recipe gives a practical introduction to finite-temperature molecular dynamics simulations, and provides a guide to choose the most appropriate thermostat for the simulation at hand.", "html": "

This recipe gives a practical introduction to finite-temperature molecular dynamics simulations, and provides a guide to choose the most appropriate thermostat for the simulation at hand.

\n", "thumbnail": "_images/sphx_glr_thermostats_thumb.png", "ref": "examples/thermostats/thermostats.html"}, {"title": "Generalized Convex Hull construction for the polymorphs of ROY", "description": "This notebook analyzes the structures of 264 polymorphs of ROY, from Beran et Al, Chemical Science (2022), comparing the conventional density-energy convex hull with a Generalized Convex Hull (GCH) analysis (see Anelli et al., Phys. Rev. Materials (2018)). It uses features computed with rascaline and uses the directional convex hull function from scikit-matter to make the figure.", "html": "

This notebook analyzes the structures of 264 polymorphs of ROY, from Beran et Al, Chemical Science (2022), comparing the conventional density-energy convex hull with a Generalized Convex Hull (GCH) analysis (see Anelli et al., Phys. Rev. Materials (2018)). It uses features computed with rascaline and uses the directional convex hull function from scikit-matter to make the figure.

\n", "thumbnail": "_images/sphx_glr_roy-gch_thumb.png", "ref": "examples/roy-gch/roy-gch.html"}, {"title": "Local Prediction Rigidity analysis", "description": "In this tutorial, we calculate the SOAP descriptors of an amorphous silicon dataset using rascaline, then compute the local prediction rigidity (LPR) for the atoms of a \"test\" set before and after modifications to the \"training\" dataset has been made.", "html": "

In this tutorial, we calculate the SOAP descriptors of an amorphous silicon dataset using rascaline, then compute the local prediction rigidity (LPR) for the atoms of a "test" set before and after modifications to the "training" dataset has been made.

\n", "thumbnail": "_images/sphx_glr_lpr_thumb.png", "ref": "examples/lpr/lpr.html"}, {"title": "Long-distance Equivariants: a tutorial", "description": "This tutorial explains how Long range equivariant descriptors can be constructed using rascaline and the resulting descriptors be used to construct a linear model with equisolve", "html": "

This tutorial explains how Long range equivariant descriptors can be constructed using rascaline and the resulting descriptors be used to construct a linear model with equisolve

\n", "thumbnail": "_images/sphx_glr_lode-linear_thumb.png", "ref": "examples/lode-linear/lode-linear.html"}, {"title": "PCA/PCovR Visualization of a training dataset for a potential", "description": "This example uses rascaline and metatensor to compute structural properties for the structures in a training dataset for a ML potential. These are then used with simple dimensionality reduction algorithms (implemented in sklearn and skmatter) to obtain a simplified description of the dataset, that is then visualized using chemiscope.", "html": "

This example uses rascaline and metatensor to compute structural properties for the structures in a training dataset for a ML potential. These are then used with simple dimensionality reduction algorithms (implemented in sklearn and skmatter) to obtain a simplified description of the dataset, that is then visualized using chemiscope.

\n", "thumbnail": "_images/sphx_glr_gaas-map_thumb.png", "ref": "examples/gaas-map/gaas-map.html"}, {"title": "Path integral metadynamics", "description": "This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions.", "html": "

This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions.

\n", "thumbnail": "_images/sphx_glr_pi-metad_thumb.png", "ref": "examples/pi-metad/pi-metad.html"}, {"title": "Path integral molecular dynamics", "description": "This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model.", "html": "

This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model.

\n", "thumbnail": "_images/sphx_glr_path-integrals_thumb.png", "ref": "examples/path-integrals/path-integrals.html"}, {"title": "Periodic Hamiltonian learning", "description": "This tutorial explains how to train a machine learning model for the electronic Hamiltonian of a periodic system. Even though we focus on periodic systems, the code and techniques presented here can be directly transferred to molecules.", "html": "

This tutorial explains how to train a machine learning model for the electronic Hamiltonian of a periodic system. Even though we focus on periodic systems, the code and techniques presented here can be directly transferred to molecules.

\n", "thumbnail": "_images/sphx_glr_periodic-hamiltonian_thumb.png", "ref": "examples/periodic-hamiltonian/periodic-hamiltonian.html"}, {"title": "Quantum heat capacity of water", "description": "This example shows how to estimate the heat capacity of liquid water from a path integral molecular dynamics simulation. The dynamics are run with i-PI, and LAMMPS is used as the driver to simulate the q-TIP4P/f water model.", "html": "

This example shows how to estimate the heat capacity of liquid water from a path integral molecular dynamics simulation. The dynamics are run with i-PI, and LAMMPS is used as the driver to simulate the q-TIP4P/f water model.

\n", "thumbnail": "_images/sphx_glr_heat-capacity_thumb.png", "ref": "examples/heat-capacity/heat-capacity.html"}, {"title": "Sample and Feature Selection with FPS and CUR", "description": "In this tutorial we generate descriptors using rascaline, then select a subset of structures using both the farthest-point sampling (FPS) and CUR algorithms implemented in scikit-matter. Finally, we also generate a selection of the most important features using the same techniques.", "html": "

In this tutorial we generate descriptors using rascaline, then select a subset of structures using both the farthest-point sampling (FPS) and CUR algorithms implemented in scikit-matter. Finally, we also generate a selection of the most important features using the same techniques.

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+ height: 100%; + flex: 1; + } + + .visualizer-info { + flex-shrink: 0; + } + + .visualizer-structure-mode, + .visualizer-map-mode { + margin: auto; + max-width: 500px; + height: 550px; + } + + .visualizer-map-mode { + display: block; + } +} diff --git a/_static/chemiscope-sphinx.html b/_static/chemiscope-sphinx.html new file mode 100644 index 00000000..fd3eaf2e --- /dev/null +++ b/_static/chemiscope-sphinx.html @@ -0,0 +1,35 @@ + + + + + + + + + + + + + +
+

+ +
+
+ + + + + +
+ +
+ + + diff --git a/_static/chemiscope-sphinx.js b/_static/chemiscope-sphinx.js new file mode 100644 index 00000000..2c93b818 --- /dev/null +++ b/_static/chemiscope-sphinx.js @@ -0,0 +1,178 @@ +/* eslint-disable */ + +/** + * Enum of the modes + */ +const VISUALISER_MODE = { + DEFAULT: 'default', + STRUCTURE: 'structure', + MAP: 'map', +}; + +/** + * Asynchronously loads the Chemiscope visualization for the dataset + */ +async function loadChemiscopeSphinx(divId, filePath, visualizerMode = VISUALISER_MODE.DEFAULT) { + // Handle warnings + Chemiscope.addWarningHandler((message) => displayWarning(divId, message)); + // Display loading + toggleLoadingVisible(divId, true); + + // Load the visualizer + try { + const dataset = await fetchDataset(filePath); + + // Setup visualizer config + const config = { + map: `${divId}-map`, + info: `${divId}-info`, + meta: `${divId}-meta`, + structure: `${divId}-structure`, + }; + + // Prepare html for the visualizer + const root = document.getElementById(divId); + root.innerHTML = generateChemiscopeHTML(config, visualizerMode); + + // Load widget + const visualiser = getVisualizer(visualizerMode); + await visualiser.load(config, dataset); + } catch (error) { + // Display errors + console.error(error); + displayWarning(divId, error); + } finally { + // Hide loading + toggleLoadingVisible(divId, false); + } +} + +/** + * Returns the appropriate Chemiscope visualizer based on the given mode + */ +function getVisualizer(mode) { + switch (mode) { + case VISUALISER_MODE.STRUCTURE: + return Chemiscope.StructureVisualizer; + case VISUALISER_MODE.MAP: + return Chemiscope.MapVisualizer; + default: + return Chemiscope.DefaultVisualizer; + } +} + +/** + * Loads the dataset and handled gzipped JSON with NaN values + */ +async function fetchDataset(filePath) { + // Get path to the file + const baseUrl = `${filePath}`; + + // Load file + const response = await fetch(baseUrl); + if (!response.ok) { + throw new Error(`Failed to fetch ${filePath}: ${response.statusText}`); + } + const buffer = await response.arrayBuffer(); + const magic = new Uint8Array(buffer.slice(0, 2)); + + let text; + // '1f 8b' is the magic constant starting gzip files + if (magic[0] == 0x1f && magic[1] == 0x8b) { + text = pako.inflate(new Uint8Array(buffer), { to: 'string' }); + } else { + const decoder = new TextDecoder('utf-8'); + text = decoder.decode(buffer); + } + return parseJsonWithNaN(text); +} + +/** + * Allow NaN in the JSON file. They are not part of the spec, but Python's json + * module output them, and they can be useful. + */ +function parseJsonWithNaN(text) { + return JSON.parse(text.replace(/\bNaN\b/g, '"***NaN***"'), (_key, value) => { + return value === '***NaN***' ? NaN : value; + }); +} + +/** + * Generates the HTML content for the Chemiscope visualizer + */ +function generateChemiscopeHTML(config, visualizerMode) { + switch (visualizerMode) { + case VISUALISER_MODE.DEFAULT: + return ` +
+
+
+
+
+
+
+
+
+
+
+
`; + case VISUALISER_MODE.STRUCTURE: + return ` +
+
+
+
+
+
+
+
+
`; + case VISUALISER_MODE.MAP: + return ` +
+
+
+
+
+
+
+
+
`; + } +} + +/** + * Toggles the visibility of the loader spinner + */ +function toggleLoadingVisible(divId, visible = true) { + const loader = document.getElementById(`${divId}-loading`); + if (loader) { + loader.style.display = visible ? 'block' : 'none'; + } +} + +/** + * Hides the specified element + */ +function hideElement(elementId) { + const element = document.getElementById(elementId); + if (element) { + element.style.display = 'none'; + } else { + console.error(`Element ${elementId} is not found`); + } +} + +/** + * Displays a warning message in the specified div + */ +function displayWarning(divId, message) { + const display = document.getElementById(`${divId}-warning-display`); + display.getElementsByTagName('p')[0].innerText = message; + display.style.display = 'flex'; + + // Automatically remove the warning after 4 seconds + setTimeout(() => { + display.style.display = 'none'; + }, 4000); +} diff --git a/_static/chemiscope.min.js b/_static/chemiscope.min.js new file mode 100644 index 00000000..221774f4 --- /dev/null +++ b/_static/chemiscope.min.js @@ -0,0 +1,2 @@ +/*! 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10;\n}\n\n.chsp-viewer-action-button {\n background-color: white;\n border: none;\n}\n\n.chsp-viewer-action-button:hover {\n background: white;\n}\n\n.chsp-viewer-action-button svg {\n opacity: 0.4;\n transition: opacity 0.15s ease-in-out;\n}\n\n.chsp-viewer-action-button:hover svg {\n opacity: 0.6;\n}\n\n.chsp-structure-viewer-grid {\n display: grid;\n position: relative;\n width: 100%;\n height: 100%;\n grid-column-gap: 2px;\n grid-row-gap: 2px;\n}\n\n.chsp-structure-viewer-cell {\n width: 99%;\n height: 99%;\n left: 0.5%;\n top: 0.5%;\n position: relative;\n border: 1px solid lightgray;\n padding: 1px;\n}\n\n.chsp-structure-viewer-cell-active {\n border-color: gray;\n}\n\n.chsp-map-options {\n display: grid;\n grid-template-columns: 1fr 0.5fr;\n align-items: center;\n justify-content: center;\n align-content: start;\n column-gap: 1em;\n}\n\n.chsp-map-options label {\n min-width: 6em;\n}\n\n.chsp-map-options > :nth-child(n + 3):not(.chsp-map-extra-options) {\n margin-top: 1.3rem;\n}\n\n.chsp-map-extra-options {\n display: grid;\n align-items: center;\n justify-items: center;\n grid-template-columns: auto 1fr 1fr;\n column-gap: 1em;\n}\n\n.chsp-map-extra-options > * {\n margin: 0.5em 0;\n}\n\n.chsp-map-extra-options label {\n min-width: auto;\n}\n\n.chsp-map-extra-options {\n grid-column: 1 / span 2;\n}\n\n.chsp-map-options .form-check-label {\n width: auto;\n}\n\n.chsp-modal-header {\n cursor: grab;\n}\n\n.chsp-play-button {\n border: 0;\n background: transparent;\n box-sizing: border-box;\n height: 1.2em;\n width: 1.2em;\n margin-left: 0.5ex;\n\n border-color: transparent transparent transparent #202020;\n transition: 100ms all ease;\n cursor: pointer;\n\n border-style: solid;\n border-width: 0.7em 0 0.7em 1em;\n}\n\n.chsp-play-button.chsp-playing {\n border-style: double;\n border-width: 0px 0 0px 1.2em;\n}\n\n.chsp-play-button:hover {\n border-color: transparent transparent transparent #404040;\n}\n\n.chsp-properties-table {\n height: 100%;\n width: 80%;\n margin: auto;\n}\n\n.chsp-properties-table td,\n.chsp-properties-table th {\n width: 50%;\n border-top: none;\n}\n\n.chsp-settings-section-title {\n font-weight: bold;\n}\n\n/* Change Plotly modebar style to match the style of the structure grid buttons */\n\n.chsp-map .modebar-group {\n padding-left: 0 !important;\n}\n\n.chsp-map .modebar-btn {\n cursor: default !important;\n font-family: apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, 'Helvetica Neue', Arial,\n 'Noto Sans', sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol',\n 'Noto Color Emoji';\n}\n\n.chsp-map .modebar-btn::after {\n opacity: 0.9;\n}\n\n.chsp-map .icon:hover + .modebar-btn::after {\n visibility: visible;\n}\n\n.chsp-map .modebar-btn::before {\n content: none !important;\n}\n\n.chsp-map .modebar-btn .icon {\n transition: opacity 0.15s ease-in-out;\n padding: 3px;\n opacity: 0.3;\n cursor: pointer;\n}\n\n.chsp-map .modebar-group svg.icon {\n width: 2em;\n height: 2em;\n border-radius: 0.2em;\n}\n\n.chsp-map .modebar-group svg.icon:active {\n color: #212529;\n background-color: #dae0e5;\n border-color: #d3d9df;\n box-shadow: 0 0 0 0.2rem rgb(216 217 219 / 50%);\n}\n\n.chsp-map .modebar-btn .icon path {\n transition:\n color 0.15s ease-in-out,\n background-color 0.15s ease-in-out,\n border-color 0.15s ease-in-out,\n box-shadow 0.15s ease-in-out;\n fill: black !important;\n}\n\n.chsp-map .modebar-btn .icon:hover {\n opacity: 0.6;\n}\n\n.chsp-map .modebar-btn.active .icon {\n opacity: 0.6;\n}\n\n.chsp-info-btns {\n display: flex;\n position: relative;\n margin-bottom: 0.5ex;\n margin-top: 0.5ex;\n justify-content: center;\n}\n\n.chsp-info-structure-btn {\n min-width: 8em;\n padding-left: 6px;\n padding-right: 4px;\n font-weight: bold;\n font-size: small;\n background-color: none;\n border-color: #66a5e8;\n border-width: 2px;\n float: left;\n}\n\n.chsp-info-structure-btn:hover {\n background-color: #5b94d0;\n}\n\n.chsp-info-atom-btn {\n margin-left: 1em;\n padding-left: 6px;\n padding-right: 4px;\n min-width: 8em;\n font-weight: bold;\n font-size: small;\n background-color: none;\n border-color: #4cb64c;\n border-width: 2px;\n}\n\n.chsp-info-atom-btn:hover {\n background-color: #44a344;\n}\n\n.chsp-info-btns-svg {\n float: left;\n padding-right: 6px;\n padding-top: 3px;\n}\n\n.chsp-info-btns-svg svg {\n display: block;\n opacity: 0.6;\n}\n\n.chsp-info-number {\n -moz-appearance: textfield;\n appearance: textfield;\n border: none;\n transition: background-color 0.15s;\n background-color: #ebedf0;\n margin-left: 2px;\n margin-right: 3px;\n font-family: inherit;\n width: 4em;\n}\n\n.chsp-info-atom-btn:hover .chsp-info-number {\n background-color: #69b569;\n}\n\n.chsp-info-structure-btn:hover .chsp-info-number {\n background-color: #7ba9d9;\n}\n\n.chsp-info-number::-webkit-outer-spin-button,\n.chsp-info-number::-webkit-inner-spin-button {\n -webkit-appearance: none;\n margin: 0;\n}\n\n.chsp-info-tables {\n position: relative;\n width: 100%;\n}\n\n.chsp-info-table {\n position: absolute;\n bottom: 0;\n left: 0;\n right: 0;\n z-index: 10;\n background-color: white;\n /* max-height is set in JavaScript */\n overflow: auto;\n}\n\n.chsp-info-table.collapsing {\n overflow: hidden;\n}\n\n.chsp-info-table table {\n margin: 0;\n}\n\n/* Change the atoms slider thumb color to green, to match structure highlight */\n.chsp-atom-slider::-webkit-slider-thumb {\n background-color: #008000;\n}\n\n.chsp-atom-slider::-moz-range-thumb {\n background-color: #008000;\n}\n\n.chsp-atom-slider::-ms-thumb {\n background-color: #008000;\n}\n\n.chsp-atom-slider::-webkit-slider-thumb:active {\n background-color: #99cc99;\n}\n\n.chsp-atom-slider::-moz-range-thumb:active {\n background-color: #99cc99;\n}\n\n.chsp-atom-slider::-ms-thumb:active {\n background-color: #99cc99;\n}\n\n.chsp-atom-slider:focus::-webkit-slider-thumb {\n box-shadow:\n 0 0 0 1px #fff,\n 0 0 0 0.2rem rgba(0, 255, 0, 0.25);\n}\n\n.chsp-atom-slider:focus::-moz-range-thumb {\n box-shadow:\n 0 0 0 1px #fff,\n 0 0 0 0.2rem rgba(0, 255, 0, 0.25);\n}\n\n.chsp-atom-slider:focus::-ms-thumb {\n box-shadow:\n 0 0 0 1px #fff,\n 0 0 0 0.2rem rgba(0, 255, 0, 0.25);\n}\n\n.chsp-settings-representation {\n display: grid;\n grid-template-columns: 1fr 1fr 1fr;\n grid-row-gap: 1ex;\n}\n\n.chsp-settings-representation label {\n cursor: help;\n}\n\n.chsp-settings-supercell {\n display: grid;\n grid-template-columns: 1fr 1fr 1fr 2fr;\n}\n\n.chsp-supercell-count {\n max-width: 3.5em;\n}\n\n.chsp-settings-camera {\n display: grid;\n gap: 1em;\n grid-template-columns: repeat(7, auto);\n justify-content: center;\n}\n\n.chsp-settings-environments {\n display: grid;\n align-items: center;\n column-gap: 1em;\n grid-template-columns: 1fr 1fr 1fr;\n}\n\n.chsp-settings-extra-options {\n display: grid;\n gap: 1em;\n grid-template-columns: 1fr 1fr 1fr;\n grid-column: 1 / span 3;\n}\n\n.chsp-settings-extra-options > :nth-child(-n + 3) {\n margin-top: 1em;\n}\n\n.chsp-settings-trajectory {\n display: grid;\n grid-template-columns: 12em 12em;\n justify-content: center;\n align-content: center;\n gap: 1em;\n margin-bottom: 1ex;\n}\n\n.chsp-cell-info {\n position: absolute;\n bottom: 5px;\n left: 5px;\n font-size: 0.8em;\n}\n\n.chsp-toggle-plot-btn {\n display: block;\n position: relative;\n margin-top: 3px;\n margin-bottom: 1px;\n}\n\n.chsp-atom-color-property {\n display: grid;\n align-items: center;\n justify-items: center;\n grid-template-columns: 1fr 1fr;\n column-gap: 1em;\n margin: 0.5em 0;\n}\n\n.chsp-atom-extra-options {\n display: grid;\n align-items: center;\n justify-items: center;\n grid-template-columns: auto 1fr 1fr;\n column-gap: 1em;\n}\n\n.chsp-atom-extra-options > * {\n margin: 0.5em 0;\n}\n\n.chsp-atom-extra-options label {\n min-width: auto;\n}\n\n.chsp-atom-extra-options {\n grid-column: 1 / span 2;\n}\n\n.chsp-target-toggle {\n padding-left: 5px;\n padding-right: 5px;\n display: flex;\n justify-content: flex-end;\n gap: 5px;\n}\n\n.chsp-target-spinner {\n width: 25px;\n height: 25px;\n margin-left: 5px;\n}\n",""]);const s=a},48654:(t,e,r)=>{"use strict";r.d(e,{A:()=>V});var n=r(78706),i=r.n(n),o=r(72859),a=r.n(o),s=r(21906),l=r.n(s),c=new URL(r(35531),r.b),u=new URL(r(45419),r.b),h=new URL(r(83385),r.b),d=new URL(r(14274),r.b),f=new URL(r(57154),r.b),p=new URL(r(35782),r.b),m=new URL(r(54718),r.b),g=new URL(r(48487),r.b),v=new URL(r(35372),r.b),b=new URL(r(17914),r.b),y=new URL(r(36366),r.b),x=new URL(r(67830),r.b),_=new URL(r(88832),r.b),w=new URL(r(57249),r.b),k=new URL(r(75932),r.b),A=new URL(r(11144),r.b),M=a()(i()),T=l()(c),S=l()(u),C=l()(h),E=l()(d),L=l()(f),z=l()(p),O=l()(m),D=l()(g),I=l()(v),F=l()(b),R=l()(y),P=l()(x),j=l()(_),N=l()(w),B=l()(k),U=l()(A);M.push([t.id,`@charset "UTF-8";/*!\n * Bootstrap v5.2.3 (https://getbootstrap.com/)\n * Copyright 2011-2022 The Bootstrap Authors\n * Copyright 2011-2022 Twitter, Inc.\n * Licensed under MIT 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var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg:transparent;--bs-alert-padding-x:1rem;--bs-alert-padding-y:1rem;--bs-alert-margin-bottom:1rem;--bs-alert-color:inherit;--bs-alert-border-color:transparent;--bs-alert-border:1px solid var(--bs-alert-border-color);--bs-alert-border-radius:0.375rem;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-primary{--bs-alert-color:#084298;--bs-alert-bg:#cfe2ff;--bs-alert-border-color:#b6d4fe}.alert-primary .alert-link{color:#06357a}.alert-secondary{--bs-alert-color:#41464b;--bs-alert-bg:#e2e3e5;--bs-alert-border-color:#d3d6d8}.alert-secondary .alert-link{color:#34383c}.alert-success{--bs-alert-color:#0f5132;--bs-alert-bg:#d1e7dd;--bs-alert-border-color:#badbcc}.alert-success .alert-link{color:#0c4128}.alert-info{--bs-alert-color:#055160;--bs-alert-bg:#cff4fc;--bs-alert-border-color:#b6effb}.alert-info .alert-link{color:#04414d}.alert-warning{--bs-alert-color:#664d03;--bs-alert-bg:#fff3cd;--bs-alert-border-color:#ffecb5}.alert-warning .alert-link{color:#523e02}.alert-danger{--bs-alert-color:#842029;--bs-alert-bg:#f8d7da;--bs-alert-border-color:#f5c2c7}.alert-danger .alert-link{color:#6a1a21}.alert-light{--bs-alert-color:#636464;--bs-alert-bg:#fefefe;--bs-alert-border-color:#fdfdfe}.alert-light 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";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:focus,.list-group-item-action:hover{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid 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var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media 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(min-width:768px){.list-group-horizontal-md{flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media 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(min-width:1200px){.list-group-horizontal-xl{flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media 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#44a344;\n}\n\n.chsp-info-btns-svg {\n float: left;\n padding-right: 6px;\n padding-top: 3px;\n}\n\n.chsp-info-btns-svg svg {\n display: block;\n opacity: 0.6;\n}\n\n.chsp-info-number {\n -moz-appearance: textfield;\n appearance: textfield;\n border: none;\n transition: background-color 0.15s;\n background-color: #ebedf0;\n margin-left: 2px;\n margin-right: 3px;\n font-family: inherit;\n width: 4em;\n}\n\n.chsp-info-atom-btn:hover .chsp-info-number {\n background-color: #69b569;\n}\n\n.chsp-info-structure-btn:hover .chsp-info-number {\n background-color: #7ba9d9;\n}\n\n.chsp-info-number::-webkit-outer-spin-button,\n.chsp-info-number::-webkit-inner-spin-button {\n -webkit-appearance: none;\n margin: 0;\n}\n\n.chsp-info-tables {\n position: relative;\n width: 100%;\n}\n\n.chsp-info-table {\n position: absolute;\n bottom: 0;\n left: 0;\n right: 0;\n z-index: 10;\n background-color: white;\n /* max-height is set in JavaScript */\n overflow: auto;\n}\n\n.chsp-info-table.collapsing {\n 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display: grid;\n grid-template-columns: 1fr 1fr 1fr;\n grid-row-gap: 1ex;\n}\n\n.chsp-settings-representation label {\n cursor: help;\n}\n\n.chsp-settings-supercell {\n display: grid;\n grid-template-columns: 1fr 1fr 1fr 2fr;\n}\n\n.chsp-supercell-count {\n max-width: 3.5em;\n}\n\n.chsp-settings-camera {\n display: grid;\n gap: 1em;\n grid-template-columns: repeat(7, auto);\n justify-content: center;\n}\n\n.chsp-settings-environments {\n display: grid;\n align-items: center;\n column-gap: 1em;\n grid-template-columns: 1fr 1fr 1fr;\n}\n\n.chsp-settings-extra-options {\n display: grid;\n gap: 1em;\n grid-template-columns: 1fr 1fr 1fr;\n grid-column: 1 / span 3;\n}\n\n.chsp-settings-extra-options > :nth-child(-n + 3) {\n margin-top: 1em;\n}\n\n.chsp-settings-trajectory {\n display: grid;\n grid-template-columns: 12em 12em;\n justify-content: center;\n align-content: center;\n gap: 1em;\n margin-bottom: 1ex;\n}\n\n.chsp-cell-info {\n position: absolute;\n bottom: 5px;\n left: 5px;\n 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TypeError(`Not a valid NetCDF v3.x file: ${e}`)}function i(t){t.offset%4!=0&&t.skip(4-t.offset%4)}function o(t){const e=t.readUint32(),r=t.readChars(e);return i(t),r}r.r(e),r.d(e,{notNetcdf:()=>n,padding:()=>i,readName:()=>o})},"./src/WebGL/shaders/lib/basic/basic.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform mat4 viewMatrix;\nuniform float opacity;\nuniform vec3 fogColor;\nuniform float fogNear;\nuniform float fogFar;\nvarying vec3 vColor;\n//DEFINEFRAGCOLOR\nvoid main() {\n gl_FragColor = vec4( vColor, opacity );\n float depth = gl_FragCoord.z / gl_FragCoord.w;\n float fogFactor = smoothstep( fogNear, fogFar, depth );\n gl_FragColor = mix( gl_FragColor, vec4( fogColor, gl_FragColor.w ), fogFactor );\n}"},"./src/WebGL/shaders/lib/basic/basic.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform mat4 viewMatrix;\nuniform mat3 normalMatrix;\n\nattribute vec3 position;\nattribute vec3 color;\n\nvarying vec3 vColor;\n\nvoid main() {\n\n vColor = color;\n vec4 mvPosition = modelViewMatrix * vec4( position, 1.0 );\n gl_Position = projectionMatrix * mvPosition;\n\n}"},"./src/WebGL/shaders/lib/instanced/instanced.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform mat4 viewMatrix;\nuniform float opacity;\n\nuniform vec3 fogColor;\nuniform float fogNear;\nuniform float fogFar;\n\nvarying vec3 vLightFront;\nvarying vec3 vColor;\n//DEFINEFRAGCOLOR\n\nvoid main() {\n\n gl_FragColor = vec4( vec3 ( 1.0 ), opacity );\n\n #ifndef WIREFRAME\n gl_FragColor.xyz *= vLightFront;\n #endif\n\n gl_FragColor = gl_FragColor * vec4( vColor, opacity );\n float depth = gl_FragCoord.z / gl_FragCoord.w;\n\n float fogFactor = smoothstep( fogNear, fogFar, depth );\n\n gl_FragColor = mix( gl_FragColor, vec4( fogColor, gl_FragColor.w ), fogFactor );\n\n}\n\n\n"},"./src/WebGL/shaders/lib/instanced/instanced.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform mat4 viewMatrix;\nuniform mat3 normalMatrix;\nuniform vec3 directionalLightColor[ 1 ];\nuniform vec3 directionalLightDirection[ 1 ];\n\nattribute vec3 offset;\nattribute vec3 position;\nattribute vec3 normal;\nattribute vec3 color;\nattribute float radius;\n\nvarying vec3 vColor;\nvarying vec3 vLightFront;\n\nvoid main() {\n\n vColor = color;\n\n vec3 objectNormal = normal;\n vec3 transformedNormal = normalMatrix * objectNormal;\n vec4 mvPosition = modelViewMatrix * vec4( position * radius + offset, 1.0 );\n\n vLightFront = vec3( 0.0 );\n\n transformedNormal = normalize( transformedNormal );\n\n vec4 lDirection = viewMatrix * vec4( directionalLightDirection[ 0 ], 0.0 );\n vec3 dirVector = normalize( lDirection.xyz );\n float dotProduct = dot( transformedNormal, dirVector );\n vec3 directionalLightWeighting = vec3( max( dotProduct, 0.0 ) );\n\n vLightFront += directionalLightColor[ 0 ] * directionalLightWeighting;\n\n gl_Position = projectionMatrix * mvPosition;\n}\n\n"},"./src/WebGL/shaders/lib/lambert/lambert.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform mat4 viewMatrix;\nuniform float opacity;\n\nuniform vec3 fogColor;\nuniform float fogNear;\nuniform float fogFar;\n\nvarying vec3 vLightFront;\nvarying vec3 vColor;\n//DEFINEFRAGCOLOR\n\nvoid main() {\n\n gl_FragColor = vec4( vec3 ( 1.0 ), opacity );\n\n #ifndef WIREFRAME\n gl_FragColor.xyz *= vLightFront;\n #endif\n\n gl_FragColor = gl_FragColor * vec4( vColor, opacity );\n float depth = gl_FragCoord.z / gl_FragCoord.w;\n\n float fogFactor = smoothstep( fogNear, fogFar, depth );\n\n gl_FragColor = mix( gl_FragColor, vec4( fogColor, gl_FragColor.w ), fogFactor );\n\n}"},"./src/WebGL/shaders/lib/lambert/lambert.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform mat4 viewMatrix;\nuniform mat3 normalMatrix;\nuniform vec3 directionalLightColor[ 1 ];\nuniform vec3 directionalLightDirection[ 1 ];\n\nattribute vec3 position;\nattribute vec3 normal;\nattribute vec3 color;\n\nvarying vec3 vColor;\nvarying vec3 vLightFront;\n\nvoid main() {\n\n vColor = color;\n\n vec3 objectNormal = normal;\n vec3 transformedNormal = normalMatrix * objectNormal;\n vec4 mvPosition = modelViewMatrix * vec4( position, 1.0 );\n\n vLightFront = vec3( 0.0 );\n\n transformedNormal = normalize( transformedNormal );\n\n vec4 lDirection = viewMatrix * vec4( directionalLightDirection[ 0 ], 0.0 );\n vec3 dirVector = normalize( lDirection.xyz );\n float dotProduct = dot( transformedNormal, dirVector );\n vec3 directionalLightWeighting = vec3( max( dotProduct, 0.0 ) );\n\n vLightFront += directionalLightColor[ 0 ] * directionalLightWeighting;\n\n gl_Position = projectionMatrix * mvPosition;\n}"},"./src/WebGL/shaders/lib/lambertdouble/lambertdouble.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform mat4 viewMatrix;\nuniform float opacity;\n\nuniform vec3 fogColor;\nuniform float fogNear;\nuniform float fogFar;\n\nvarying vec3 vLightFront;\nvarying vec3 vLightBack;\n\nvarying vec3 vColor;\n//DEFINEFRAGCOLOR\n\nvoid main() {\n\n gl_FragColor = vec4( vec3 ( 1.0 ), opacity );\n\n #ifndef WIREFRAME\n if ( gl_FrontFacing )\n gl_FragColor.xyz *= vLightFront;\n else\n gl_FragColor.xyz *= vLightBack;\n #endif\n\n gl_FragColor = gl_FragColor * vec4( vColor, opacity );\n float depth = gl_FragCoord.z / gl_FragCoord.w;\n\n float fogFactor = smoothstep( fogNear, fogFar, depth );\n\n gl_FragColor = mix( gl_FragColor, vec4( fogColor, gl_FragColor.w ), fogFactor );\n\n}\n\n\n"},"./src/WebGL/shaders/lib/lambertdouble/lambertdouble.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform mat4 viewMatrix;\nuniform mat3 normalMatrix;\nuniform vec3 directionalLightColor[ 1 ];\nuniform vec3 directionalLightDirection[ 1 ];\n\nattribute vec3 position;\nattribute vec3 normal;\nattribute vec3 color;\n\nvarying vec3 vColor;\nvarying vec3 vLightFront;\nvarying vec3 vLightBack;\n\nvoid main() {\n\n vColor = color;\n\n vec3 objectNormal = normal;\n vec3 transformedNormal = normalMatrix * objectNormal;\n vec4 mvPosition = modelViewMatrix * vec4( position, 1.0 );\n\n vLightFront = vec3( 0.0 );\n vLightBack = vec3( 0.0 );\n\n transformedNormal = normalize( transformedNormal );\n\n vec4 lDirection = viewMatrix * vec4( directionalLightDirection[ 0 ], 0.0 );\n vec3 dirVector = normalize( lDirection.xyz );\n float dotProduct = dot( transformedNormal, dirVector );\n vec3 directionalLightWeighting = vec3( max( dotProduct, 0.0 ) );\n vec3 directionalLightWeightingBack = vec3( max( -dotProduct, 0.0 ) );\n\n vLightFront += directionalLightColor[ 0 ] * directionalLightWeighting;\n vLightBack += directionalLightColor[ 0 ] * directionalLightWeightingBack;\n\n gl_Position = projectionMatrix * mvPosition;\n}\n\n"},"./src/WebGL/shaders/lib/outline/outline.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform float opacity;\nuniform vec3 outlineColor;\nuniform vec3 fogColor;\nuniform float fogNear;\nuniform float fogFar;\n//DEFINEFRAGCOLOR\n\nvoid main() {\n gl_FragColor = vec4( outlineColor, 1 );\n}\n\n\n"},"./src/WebGL/shaders/lib/outline/outline.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform float outlineWidth;\nuniform float outlinePushback;\n\nattribute vec3 position;\nattribute vec3 normal;\nattribute vec3 color;\n\nvoid main() {\n\n vec4 norm = modelViewMatrix*vec4(normalize(normal),0.0);\n vec4 mvPosition = modelViewMatrix * vec4( position, 1.0 );\n mvPosition.xy += norm.xy*outlineWidth;\n gl_Position = projectionMatrix * mvPosition;\n mvPosition.z -= outlinePushback; //go backwards in model space\n vec4 pushpos = projectionMatrix*mvPosition; //project to get z in projection space, I'm probably missing some simple math to do the same thing..\n gl_Position.z = gl_Position.w*pushpos.z/pushpos.w;\n}\n\n"},"./src/WebGL/shaders/lib/screen/screen.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform sampler2D colormap;\nvarying highp vec2 vTexCoords;\nuniform vec2 dimensions;\n//DEFINEFRAGCOLOR\nvoid main (void) {\n gl_FragColor = texture2D(colormap, vTexCoords);\n}\n "},"./src/WebGL/shaders/lib/screen/screen.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="attribute vec2 vertexPosition;\nvarying highp vec2 vTexCoords;\nconst vec2 scale = vec2(0.5, 0.5);\n\nvoid main() {\n vTexCoords = vertexPosition * scale + scale; // scale vertex attribute to [0,1] range\n gl_Position = vec4(vertexPosition, 0.0, 1.0);\n}\n "},"./src/WebGL/shaders/lib/screenaa/screenaa.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform sampler2D colormap;\nvarying highp vec2 vTexCoords;\nuniform vec2 dimensions;\n\n// Basic FXAA implementation based on the code on geeks3d.com \n#define FXAA_REDUCE_MIN (1.0/ 128.0)\n#define FXAA_REDUCE_MUL (1.0 / 8.0)\n#define FXAA_SPAN_MAX 8.0\n\nvec4 applyFXAA(vec2 fragCoord, sampler2D tex)\n{\n vec4 color;\n vec2 inverseVP = vec2(1.0 / dimensions.x, 1.0 / dimensions.y);\n vec3 rgbNW = texture2D(tex, fragCoord + vec2(-1.0, -1.0) * inverseVP).xyz;\n vec3 rgbNE = texture2D(tex, fragCoord + vec2(1.0, -1.0) * inverseVP).xyz;\n vec3 rgbSW = texture2D(tex, fragCoord + vec2(-1.0, 1.0) * inverseVP).xyz;\n vec3 rgbSE = texture2D(tex, fragCoord + vec2(1.0, 1.0) * inverseVP).xyz;\n vec3 rgbM = texture2D(tex, fragCoord * inverseVP).xyz;\n vec3 luma = vec3(0.299, 0.587, 0.114);\n float lumaNW = dot(rgbNW, luma);\n float lumaNE = dot(rgbNE, luma);\n float lumaSW = dot(rgbSW, luma);\n float lumaSE = dot(rgbSE, luma);\n float lumaM = dot(rgbM, luma);\n float lumaMin = min(lumaM, min(min(lumaNW, lumaNE), min(lumaSW, lumaSE)));\n float lumaMax = max(lumaM, max(max(lumaNW, lumaNE), max(lumaSW, lumaSE)));\n\n vec2 dir;\n dir.x = -((lumaNW + lumaNE) - (lumaSW + lumaSE));\n dir.y = ((lumaNW + lumaSW) - (lumaNE + lumaSE));\n\n float dirReduce = max((lumaNW + lumaNE + lumaSW + lumaSE) *\n (0.25 * FXAA_REDUCE_MUL), FXAA_REDUCE_MIN);\n\n float rcpDirMin = 1.0 / (min(abs(dir.x), abs(dir.y)) + dirReduce);\n dir = min(vec2(FXAA_SPAN_MAX, FXAA_SPAN_MAX),\n max(vec2(-FXAA_SPAN_MAX, -FXAA_SPAN_MAX),\n dir * rcpDirMin)) * inverseVP;\n\n vec3 rgbA = 0.5 * (\n texture2D(tex, fragCoord + dir * (1.0 / 3.0 - 0.5)).xyz +\n texture2D(tex, fragCoord + dir * (2.0 / 3.0 - 0.5)).xyz);\n vec3 rgbB = rgbA * 0.5 + 0.25 * (\n texture2D(tex, fragCoord + dir * -0.5).xyz +\n texture2D(tex, fragCoord + dir * 0.5).xyz);\n\n float lumaB = dot(rgbB, luma);\n if ((lumaB < lumaMin) || (lumaB > lumaMax))\n color = vec4(rgbA, 1.0);\n else\n color = vec4(rgbB, 1.0);\n return color;\n}\n//DEFINEFRAGCOLOR\nvoid main (void) {\n gl_FragColor = applyFXAA(vTexCoords, colormap);\n}\n "},"./src/WebGL/shaders/lib/screenaa/screenaa.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="attribute vec2 vertexPosition;\nvarying highp vec2 vTexCoords;\nconst vec2 scale = vec2(0.5, 0.5);\n\nvoid main() {\n vTexCoords = vertexPosition * scale + scale; // scale vertex attribute to [0,1] range\n gl_Position = vec4(vertexPosition, 0.0, 1.0);\n}\n "},"./src/WebGL/shaders/lib/sphereimposter/sphereimposter.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\nuniform mat4 viewMatrix;\nuniform float opacity;\nuniform mat4 projectionMatrix;\n\nuniform vec3 fogColor;\nuniform float fogNear;\nuniform float fogFar;\nuniform float uDepth;\nuniform vec3 directionalLightColor[ 1 ];\n\nvarying vec3 vColor;\nvarying vec2 mapping;\nvarying float rval;\nvarying vec3 vLight;\nvarying vec3 center;\n\n//DEFINEFRAGCOLOR\n\nvoid main() {\n float lensqr = dot(mapping,mapping);\n float rsqr = rval*rval;\n if(lensqr > rsqr)\n discard;\n float z = sqrt(rsqr-lensqr);\n vec3 cameraPos = center+ vec3(mapping.x,mapping.y,z);\n vec4 clipPos = projectionMatrix * vec4(cameraPos, 1.0);\n float ndcDepth = clipPos.z / clipPos.w;\n gl_FragDepthEXT = ((gl_DepthRange.diff * ndcDepth) + gl_DepthRange.near + gl_DepthRange.far) / 2.0;\n vec3 norm = normalize(vec3(mapping.x,mapping.y,z));\n float dotProduct = dot( norm, vLight );\n vec3 directionalLightWeighting = vec3( max( dotProduct, 0.0 ) );\n vec3 vLight = directionalLightColor[ 0 ] * directionalLightWeighting;\n gl_FragColor = vec4(vLight*vColor, opacity*opacity );\n float fogFactor = smoothstep( fogNear, fogFar, gl_FragDepthEXT/gl_FragCoord.w );\n gl_FragColor = mix( gl_FragColor, vec4( fogColor, gl_FragColor.w ), fogFactor );\n\n\n}\n\n"},"./src/WebGL/shaders/lib/sphereimposter/sphereimposter.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform mat4 viewMatrix;\nuniform mat3 normalMatrix;\nuniform vec3 directionalLightColor[ 1 ];\nuniform vec3 directionalLightDirection[ 1 ];\n\nattribute vec3 position;\nattribute vec3 normal;\nattribute vec3 color;\n\nvarying vec2 mapping;\nvarying vec3 vColor;\nvarying float rval;\nvarying vec3 vLight;\nvarying vec3 center;\n\nvoid main() {\n\n vColor = color;\n vec4 mvPosition = modelViewMatrix * vec4( position, 1.0 );\n center = mvPosition.xyz;\n vec4 projPosition = projectionMatrix * mvPosition;\n vec4 adjust = projectionMatrix* vec4(normal,0.0); adjust.z = 0.0; adjust.w = 0.0;\n vec4 lDirection = viewMatrix * vec4( directionalLightDirection[ 0 ], 0.0 );\n vLight = normalize( lDirection.xyz );\n mapping = normal.xy;\n rval = abs(normal.x);\n gl_Position = projPosition+adjust;\n\n}\n"},"./src/WebGL/shaders/lib/sphereimposteroutline/sphereimposteroutline.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform float opacity;\nuniform vec3 outlineColor;\nuniform vec3 fogColor;\nuniform float fogNear;\nuniform float fogFar;\nuniform mat4 projectionMatrix;\nvarying vec2 mapping;\nvarying float rval;\nvarying vec3 center;\n\nuniform float outlinePushback;\n\n//DEFINEFRAGCOLOR\n\nvoid main() {\n float lensqr = dot(mapping,mapping);\n float rsqr = rval*rval;\n if(lensqr > rsqr)\n discard;\n float z = sqrt(rsqr-lensqr);\n vec3 cameraPos = center+ vec3(mapping.x,mapping.y,z-outlinePushback);\n vec4 clipPos = projectionMatrix * vec4(cameraPos, 1.0);\n float ndcDepth = clipPos.z / clipPos.w;\n gl_FragDepthEXT = ((gl_DepthRange.diff * ndcDepth) + gl_DepthRange.near + gl_DepthRange.far) / 2.0;\n gl_FragColor = vec4(outlineColor, 1 );\n}\n\n\n"},"./src/WebGL/shaders/lib/sphereimposteroutline/sphereimposteroutline.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform float outlineWidth;\nuniform float outlinePushback;\n\nattribute vec3 position;\nattribute vec3 normal;\nattribute vec3 color;\n\nvarying vec2 mapping;\nvarying float rval;\nvarying vec3 center;\n\nvoid main() {\n\n vec4 mvPosition = modelViewMatrix * vec4( position, 1.0 );\n center = mvPosition.xyz;\n vec4 projPosition = projectionMatrix * mvPosition;\n vec2 norm = normal.xy + vec2(sign(normal.x)*outlineWidth,sign(normal.y)*outlineWidth);\n vec4 adjust = projectionMatrix* vec4(norm,normal.z,0.0); adjust.z = 0.0; adjust.w = 0.0;\n mapping = norm.xy;\n rval = abs(norm.x);\n gl_Position = projPosition+adjust;\n}\n\n"},"./src/WebGL/shaders/lib/sprite/sprite.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform vec3 color;\nuniform sampler2D map;\nuniform float opacity;\n\nuniform int fogType;\nuniform vec3 fogColor;\nuniform float fogDensity;\nuniform float fogNear;\nuniform float fogFar;\nuniform float alphaTest;\n\nvarying vec2 vUV;\n//DEFINEFRAGCOLOR\n\nvoid main() {\n\n vec4 texture = texture2D(map, vUV);\n\n if (texture.a < alphaTest) discard;\n\n gl_FragColor = vec4(color * texture.xyz, texture.a * opacity);\n\n if (fogType > 0) {\n\n float depth = gl_FragCoord.z / gl_FragCoord.w;\n float fogFactor = 0.0;\n\n if (fogType == 1) {\n fogFactor = smoothstep(fogNear, fogFar, depth);\n }\n\n else {\n const float LOG2 = 1.442695;\n float fogFactor = exp2(- fogDensity * fogDensity * depth * depth * LOG2);\n fogFactor = 1.0 - clamp(fogFactor, 0.0, 1.0);\n }\n\n gl_FragColor = mix(gl_FragColor, vec4(fogColor, gl_FragColor.w), fogFactor);\n\n }\n}\n\n"},"./src/WebGL/shaders/lib/sprite/sprite.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform int useScreenCoordinates;\nuniform vec3 screenPosition;\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform float rotation;\nuniform vec2 scale;\nuniform vec2 alignment;\nuniform vec2 uvOffset;\nuniform vec2 uvScale;\n\nattribute vec2 position;\nattribute vec2 uv;\n\nvarying vec2 vUV;\n\nvoid main() {\n\n vUV = uvOffset + uv * uvScale;\n\n vec2 alignedPosition = position + alignment;\n\n vec2 rotatedPosition;\n rotatedPosition.x = ( cos(rotation) * alignedPosition.x - sin(rotation) * alignedPosition.y ) * scale.x;\n rotatedPosition.y = ( sin(rotation) * alignedPosition.x + cos(rotation) * alignedPosition.y ) * scale.y;\n\n vec4 finalPosition;\n\n if(useScreenCoordinates != 0) {\n finalPosition = vec4(screenPosition.xy + rotatedPosition, screenPosition.z, 1.0);\n }\n\n else {\n finalPosition = projectionMatrix * modelViewMatrix * vec4(0.0, 0.0, 0.0, 1.0); finalPosition /= finalPosition.w;\n finalPosition.xy += rotatedPosition; \n }\n\n gl_Position = finalPosition;\n\n}\n\n"},"./src/WebGL/shaders/lib/stickimposter/stickimposter.partial.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n=" float dotProduct = dot( norm, vLight );\n vec3 light = vec3( max( dotProduct, 0.0 ) );\n gl_FragColor = vec4(light*color, opacity*opacity );\n float fogFactor = smoothstep( fogNear, fogFar, depth );\n gl_FragColor = mix( gl_FragColor, vec4( fogColor, gl_FragColor.w ), fogFactor );\n}"},"./src/WebGL/shaders/lib/stickimposter/stickimposter.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform mat4 viewMatrix;\nuniform mat3 normalMatrix;\nuniform vec3 directionalLightColor[ 1 ];\nuniform vec3 directionalLightDirection[ 1 ];\n\nattribute vec3 position;\nattribute vec3 normal;\nattribute vec3 color;\nattribute float radius;\n\nvarying vec3 vColor;\nvarying vec3 vLight;\nvarying vec3 cposition;\nvarying vec3 p1;\nvarying vec3 p2;\nvarying float r;\n\nvoid main() {\n\n vColor = color; vColor.z = abs(vColor.z); //z indicates which vertex and so would vary\n r = abs(radius);\n vec4 to = modelViewMatrix*vec4(normal, 1.0); //normal is other point of cylinder\n vec4 pt = modelViewMatrix*vec4(position, 1.0);\n vec4 mvPosition = pt;\n p1 = pt.xyz; p2 = to.xyz;\n vec3 norm = to.xyz-pt.xyz;\n float mult = 1.1; //slop to account for perspective of sphere\n if(length(p1) > length(p2)) { //billboard at level of closest point\n mvPosition = to;\n }\n vec3 n = normalize(mvPosition.xyz);\n//intersect with the plane defined by the camera looking at the billboard point\n if(color.z >= 0.0) { //p1\n if(projectionMatrix[3][3] == 0.0) { //perspective\n vec3 pnorm = normalize(p1);\n float t = dot(mvPosition.xyz-p1,n)/dot(pnorm,n);\n mvPosition.xyz = p1+t*pnorm; \n } else { //orthographic\n mvPosition.xyz = p1;\n }\n } else {\n if(projectionMatrix[3][3] == 0.0) { //perspective\n vec3 pnorm = normalize(p2);\n float t = dot(mvPosition.xyz-p2,n)/dot(pnorm,n);\n mvPosition.xyz = p2+t*pnorm;\n } else { //orthographic\n mvPosition.xyz = p2;\n } \n mult *= -1.0;\n }\n vec3 cr = normalize(cross(mvPosition.xyz,norm))*radius;\n vec3 doublecr = normalize(cross(mvPosition.xyz,cr))*radius;\n mvPosition.xyz += mult*(cr + doublecr).xyz;\n cposition = mvPosition.xyz;\n gl_Position = projectionMatrix * mvPosition;\n vec4 lDirection = viewMatrix * vec4( directionalLightDirection[ 0 ], 0.0 );\n vLight = normalize( lDirection.xyz )*directionalLightColor[0]; //not really sure this is right, but color is always white so..\n}\n\n"},"./src/WebGL/shaders/lib/stickimposteroutline/stickimposteroutline.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\n\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform mat4 viewMatrix;\nuniform mat3 normalMatrix;\nuniform vec3 directionalLightColor[ 1 ];\nuniform vec3 directionalLightDirection[ 1 ];\nuniform vec3 outlineColor;\nuniform float outlineWidth;\nuniform float outlinePushback;\n\n\nattribute vec3 position;\nattribute vec3 normal;\nattribute vec3 color;\nattribute float radius;\n\nvarying vec3 vColor;\nvarying vec3 vLight;\nvarying vec3 cposition;\nvarying vec3 p1;\nvarying vec3 p2;\nvarying float r;\n\nvoid main() {\n\n vColor = outlineColor;\n float rad = radius+sign(radius)*outlineWidth;\n r = abs(rad);\n vec4 to = modelViewMatrix*vec4(normal, 1.0); //normal is other point of cylinder\n vec4 pt = modelViewMatrix*vec4(position, 1.0);\n//pushback\n to.xyz += normalize(to.xyz)*outlinePushback;\n pt.xyz += normalize(pt.xyz)*outlinePushback;\n\n vec4 mvPosition = pt;\n p1 = pt.xyz; p2 = to.xyz;\n vec3 norm = to.xyz-pt.xyz;\n float mult = 1.1; //slop to account for perspective of sphere\n if(length(p1) > length(p2)) { //billboard at level of closest point\n mvPosition = to;\n }\n vec3 n = normalize(mvPosition.xyz);\n//intersect with the plane defined by the camera looking at the billboard point\n if(color.z >= 0.0) { //p1\n vec3 pnorm = normalize(p1);\n float t = dot(mvPosition.xyz-p1,n)/dot(pnorm,n);\n mvPosition.xyz = p1+t*pnorm;\n } else {\n vec3 pnorm = normalize(p2);\n float t = dot(mvPosition.xyz-p2,n)/dot(pnorm,n);\n mvPosition.xyz = p2+t*pnorm;\n mult *= -1.0;\n }\n vec3 cr = normalize(cross(mvPosition.xyz,norm))*rad;\n vec3 doublecr = normalize(cross(mvPosition.xyz,cr))*rad;\n mvPosition.xy += mult*(cr + doublecr).xy;\n cposition = mvPosition.xyz;\n gl_Position = projectionMatrix * mvPosition;\n vLight = vec3(1.0,1.0,1.0);\n}\n\n"},"./src/WebGL/shaders/lib/volumetric/volumetric.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="\nuniform highp sampler3D data;\nuniform highp sampler2D colormap;\nuniform highp sampler2D depthmap;\n\n\nuniform mat4 textmat;\nuniform mat4 projinv;\nuniform mat4 projectionMatrix;\n\nuniform float step;\nuniform float subsamples;\nuniform float maxdepth;\nuniform float transfermin;\nuniform float transfermax;\nin vec4 mvPosition;\nout vec4 color;\nvoid main(void) {\n\n vec4 pos = mvPosition;\n bool seengood = false;\n float i = 0.0;\n color = vec4(1,1,1,0);\n float increment = 1.0/subsamples;\n float maxsteps = (maxdepth*subsamples/step);\n//there's probably a better way to do this..\n//calculate farthest possible point in model coordinates\n vec4 maxpos = vec4(pos.x,pos.y,pos.z-maxdepth,1.0);\n// convert to projection\n maxpos = projectionMatrix*maxpos;\n vec4 startp = projectionMatrix*pos;\n// homogonize\n maxpos /= maxpos.w;\n startp /= startp.w;\n//take x,y from start and z from max\n maxpos = vec4(startp.x,startp.y,maxpos.z,1.0);\n//convert back to model space\n maxpos = projinv*maxpos;\n maxpos /= maxpos.w;\n float incr = step/subsamples;\n//get depth from depthmap\n//startp is apparently [-1,1]\n vec2 tpos = startp.xy/2.0+0.5;\n float depth = texture(depthmap, tpos).r;\n//compute vector between start and end\n vec4 direction = maxpos-pos;\n for( i = 0.0; i <= maxsteps; i++) {\n vec4 pt = (pos+(i/maxsteps)*direction);\n vec4 ppt = projectionMatrix*pt;\n float ptdepth = ppt.z/ppt.w;\n ptdepth = ((gl_DepthRange.diff * ptdepth) + gl_DepthRange.near + gl_DepthRange.far) / 2.0;\n if(ptdepth > depth) break;\n pt = textmat*pt;\n// pt /= pt.w;\n if(pt.x >= -0.01 && pt.y >= -0.01 && pt.z >= -0.01 && pt.x <= 1.01 && pt.y <= 1.01 && pt.z <= 1.01) {\n seengood = true;\n } else if(seengood) {\n break;\n }\n if( pt.x < -0.01 || pt.x > 1.01 || pt.y < -0.01 || pt.y > 1.01 || pt.z < -0.01 || pt.z > 1.01 ){\n color.a = 0.0;\n continue;\n }\n else {\n float val = texture(data, pt.zyx).r;\n if(isinf(val)) continue; //masked out\n float cval = (val-transfermin)/(transfermax-transfermin); //scale to texture 0-1 range\n vec4 val_color = texture(colormap, vec2(cval,0.5));\n color.rgb = color.rgb*color.a + (1.0-color.a)*val_color.a*val_color.rgb;\n color.a += (1.0 - color.a) * val_color.a; \n if(color.a > 0.0) color.rgb /= color.a;\n// color = vec4(pt.x, pt.y, pt.z, 1.0);\n }\n// color = vec4(pt.x, pt.y, pt.z, 0.0)\n }\n}\n\n "},"./src/WebGL/shaders/lib/volumetric/volumetric.vert":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nuniform mat4 viewMatrix;\n\nin vec3 position;\nout vec4 mvPosition;\nvoid main() {\n\n mvPosition = modelViewMatrix * vec4( position, 1.0 );\n gl_Position = projectionMatrix*mvPosition;\n}\n"},"./src/WebGL/shaders/utils/stickimposterFragmentShader.partial.frag":(t,e,r)=>{"use strict";r.r(e),r.d(e,{default:()=>n});const n="uniform float opacity;\nuniform mat4 projectionMatrix;\n\nuniform vec3 fogColor;\nuniform float fogNear;\nuniform float fogFar;\n\nvarying vec3 vLight;\nvarying vec3 vColor;\nvarying vec3 cposition;\nvarying vec3 p1;\nvarying vec3 p2;\nvarying float r;\n\n//DEFINEFRAGCOLOR\n\n//cylinder-ray intersection testing taken from http://mrl.nyu.edu/~dzorin/cg05/lecture12.pdf\n//also useful: http://stackoverflow.com/questions/9595300/cylinder-impostor-in-glsl\n//with a bit more care (caps) this could be a general cylinder imposter (see also outline)\nvoid main() {\n vec3 color = abs(vColor);\n vec3 pos = cposition;\n vec3 p = pos; //ray point\n vec3 v = vec3(0.0,0.0,-1.0); //ray normal - orthographic\n if(projectionMatrix[3][3] == 0.0) v = normalize(pos); //ray normal - perspective\n vec3 pa = p1; //cyl start\n vec3 va = normalize(p2-p1); //cyl norm\n vec3 tmp1 = v-(dot(v,va)*va);\n vec3 deltap = p-pa;\n float A = dot(tmp1,tmp1);\n if(A == 0.0) discard;\n vec3 tmp2 = deltap-(dot(deltap,va)*va);\n float B = 2.0*dot(tmp1, tmp2);\n float C = dot(tmp2,tmp2)-r*r;\n//quadratic equation!\n float det = (B*B) - (4.0*A*C);\n if(det < 0.0) discard;\n float sqrtDet = sqrt(det);\n float posT = (-B+sqrtDet)/(2.0*A);\n float negT = (-B-sqrtDet)/(2.0*A);\n float intersectionT = min(posT,negT);\n vec3 qi = p+v*intersectionT;\n float dotp1 = dot(va,qi-p1);\n float dotp2 = dot(va,qi-p2);\n vec3 norm;\n if( dotp1 < 0.0 || dotp2 > 0.0) { //(p-c)^2 + 2(p-c)vt +v^2+t^2 - r^2 = 0\n vec3 cp;\n if( dotp1 < 0.0) { \n// if(vColor.x < 0.0 ) discard; //color sign bit indicates if we should cap or not\n cp = p1;\n } else {\n// if(vColor.y < 0.0 ) discard;\n cp = p2;\n }\n vec3 diff = p-cp;\n A = dot(v,v);\n B = dot(diff,v)*2.0;\n C = dot(diff,diff)-r*r;\n det = (B*B) - (4.0*C);\n if(det < 0.0) discard;\n sqrtDet = sqrt(det);\n posT = (-B+sqrtDet)/(2.0);\n negT = (-B-sqrtDet)/(2.0);\n float t = min(posT,negT);\n qi = p+v*t; \n norm = normalize(qi-cp); \n } else {\n norm = normalize(qi-(dotp1*va + p1));\n }\n vec4 clipPos = projectionMatrix * vec4(qi, 1.0);\n float ndcDepth = clipPos.z / clipPos.w;\n float depth = ((gl_DepthRange.diff * ndcDepth) + gl_DepthRange.near + gl_DepthRange.far) / 2.0;\n gl_FragDepthEXT = depth;"},"./src/GLDraw.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{CAP:()=>n,GLDraw:()=>i});var n,i,o=r("./src/WebGL/math/index.ts");!function(t){t[t.NONE=0]="NONE",t[t.FLAT=1]="FLAT",t[t.ROUND=2]="ROUND"}(n||(n={})),function(t){function e(t,e,r){var n,i,o,a,s,l=Math.hypot(t,e);l<1e-4?(i=0,o=1):(i=-t/l,o=e/l),e=-i*t+o*e,(n=Math.hypot(e,r))<1e-4?(a=0,s=1):(a=r/n,s=e/n);var c=new Float32Array(9);return c[0]=o,c[1]=i,c[2]=0,c[3]=-i*s,c[4]=o*s,c[5]=a,c[6]=i*a,c[7]=-o*a,c[8]=s,c}var r=new class{constructor(){this.cache={};let t,e=[],r=Math.pow(2,4),n=2,i=Math.pow(2,n),a=r/i;for(e[0]=new o.Vector3(-1,0,0),e[a]=new o.Vector3(0,0,1),e[2*a]=new o.Vector3(1,0,0),e[3*a]=new o.Vector3(0,0,-1),n=3;n<=4;n++){for(i=Math.pow(2,n-1),a=r/i,t=0;t{"use strict";r.r(e),r.d(e,{GLModel:()=>p});var n=r("./src/WebGL/index.ts"),i=r("./src/WebGL/shapes/index.ts"),o=r("./src/WebGL/math/index.ts"),a=r("./src/colors.ts"),s=r("./src/GLDraw.ts"),l=r("./src/glcartoon.ts"),c=r("./src/utilities.ts"),u=r("./src/Gradient.ts"),h=r("./src/parsers/index.ts"),d=r("./node_modules/netcdfjs/lib-esm/index.js"),f=r("./src/parsers/utils/assignBonds.ts");class p{static sameObj(t,e){return t&&e?JSON.stringify(t)==JSON.stringify(e):t==e}constructor(t,e){this.atoms=[],this.frames=[],this.box=null,this.atomdfs=null,this.id=0,this.hidden=!1,this.molObj=null,this.renderedMolObj=null,this.lastColors=null,this.modelData={},this.modelDatas=null,this.idMatrix=new o.Matrix4,this.dontDuplicateAtoms=!0,this.defaultColor=a.elementColors.defaultColor,this.defaultStickRadius=.25,this.options=e||{},this.ElementColors=this.options.defaultcolors?this.options.defaultcolors:a.elementColors.defaultColors,this.defaultSphereRadius=this.options.defaultSphereRadius?this.options.defaultSphereRadius:1.5,this.defaultCartoonQuality=this.options.cartoonQuality?this.options.cartoonQuality:10,this.id=t}getRadiusFromStyle(t,e){var r=this.defaultSphereRadius;if(void 0!==e.radius)r=e.radius;else if(p.vdwRadii[t.elem])r=p.vdwRadii[t.elem];else if(t.elem.length>1){let e=t.elem;e=e[0].toUpperCase()+e[1].toLowerCase(),p.vdwRadii[e]&&(r=p.vdwRadii[e])}return void 0!==e.scale&&(r*=e.scale),r}drawAtomCross(t,e){if(t.style.cross){var r=t.style.cross;if(!r.hidden){var i=r.linewidth||p.defaultlineWidth;e[i]||(e[i]=new n.Geometry);var a=e[i].updateGeoGroup(6),s=this.getRadiusFromStyle(t,r),l=[[s,0,0],[-s,0,0],[0,s,0],[0,-s,0],[0,0,s],[0,0,-s]],u=t.clickable||t.hoverable;u&&void 0===t.intersectionShape&&(t.intersectionShape={sphere:[],cylinder:[],line:[]});for(var h=(0,c.getColorFromStyle)(t,r),d=a.vertexArray,f=a.colorArray,m=0;m<6;m++){var g=3*a.vertices;if(a.vertices++,d[g]=t.x+l[m][0],d[g+1]=t.y+l[m][1],d[g+2]=t.z+l[m][2],f[g]=h.r,f[g+1]=h.g,f[g+2]=h.b,u){var v=new o.Vector3(l[m][0],l[m][1],l[m][2]);v.multiplyScalar(.1),v.set(v.x+t.x,v.y+t.y,v.z+t.z),t.intersectionShape.line.push(v)}}}}}getGoodCross(t,e,r,n){for(var i=null,a=-1,s=0,l=t.bonds.length;sa&&(i=h,(a=c)>.1))return i}return i}getSideBondV(t,e,r){var n,i,a,s,l=new o.Vector3(t.x,t.y,t.z),c=new o.Vector3(e.x,e.y,e.z).clone(),u=null;if(c.sub(l),1===t.bonds.length)1===e.bonds.length?(u=c.clone(),Math.abs(u.x)>1e-4?u.y+=1:u.x+=1):(n=(r+1)%e.bonds.length,i=e.bonds[n],(a=this.atoms[i]).index==t.index&&(n=(n+1)%e.bonds.length,i=e.bonds[n],a=this.atoms[i]),(s=new o.Vector3(a.x,a.y,a.z).clone()).sub(l),(u=s.clone()).cross(c));else if((u=this.getGoodCross(t,e,l,c)).lengthSq()<.01){var h=this.getGoodCross(e,t,l,c);null!=h&&(u=h)}return u.lengthSq()<.01&&(u=c.clone(),Math.abs(u.x)>1e-4?u.y+=1:u.x+=1),u.cross(c),u.normalize(),u}addLine(t,e,r,n,i,o){t[r]=n.x,t[r+1]=n.y,t[r+2]=n.z,e[r]=o.r,e[r+1]=o.g,e[r+2]=o.b,t[r+3]=i.x,t[r+4]=i.y,t[r+5]=i.z,e[r+3]=o.r,e[r+4]=o.g,e[r+5]=o.b}drawBondLines(t,e,r){if(t.style.line){var i=t.style.line;if(!i.hidden){var s,l,u,h,d=i.linewidth||p.defaultlineWidth;r[d]||(r[d]=new n.Geometry);for(var f=r[d].updateGeoGroup(6*t.bonds.length),m=f.vertexArray,g=f.colorArray,v=0;v=b.index)){var y=new o.Vector3(t.x,t.y,t.z),x=new o.Vector3(b.x,b.y,b.z),_=y.clone().add(x).multiplyScalar(.5),w=!1,k=t.clickable||t.hoverable,A=b.clickable||b.hoverable;(k||A)&&(k&&(void 0===t.intersectionShape&&(t.intersectionShape={sphere:[],cylinder:[],line:[],triangle:[]}),t.intersectionShape.line.push(y),t.intersectionShape.line.push(_)),A&&(void 0===b.intersectionShape&&(b.intersectionShape={sphere:[],cylinder:[],line:[],triangle:[]}),b.intersectionShape.line.push(_),b.intersectionShape.line.push(x)));var M=(0,c.getColorFromStyle)(t,t.style.line),T=(0,c.getColorFromStyle)(b,b.style.line);if(t.bondStyles&&t.bondStyles[v]){var S=t.bondStyles[v];if(!S.iswire)continue;S.singleBond&&(w=!0),void 0!==S.color1&&(M=a.CC.color(S.color1)),void 0!==S.color2&&(T=a.CC.color(S.color2))}var C,E,L=3*f.vertices;if(t.bondOrder[v]>1&&t.bondOrder[v]<4&&!w){var z=this.getSideBondV(t,b,v),O=x.clone();O.sub(y),2==t.bondOrder[v]?(z.multiplyScalar(.1),(s=y.clone()).add(z),(l=y.clone()).sub(z),(u=s.clone()).add(O),(h=l.clone()).add(O),M==T?(f.vertices+=4,this.addLine(m,g,L,s,u,M),this.addLine(m,g,L+6,l,h,M)):(f.vertices+=8,O.multiplyScalar(.5),(C=s.clone()).add(O),(E=l.clone()).add(O),this.addLine(m,g,L,s,C,M),this.addLine(m,g,L+6,C,u,T),this.addLine(m,g,L+12,l,E,M),this.addLine(m,g,L+18,E,h,T))):3==t.bondOrder[v]&&(z.multiplyScalar(.1),(s=y.clone()).add(z),(l=y.clone()).sub(z),(u=s.clone()).add(O),(h=l.clone()).add(O),M==T?(f.vertices+=6,this.addLine(m,g,L,y,x,M),this.addLine(m,g,L+6,s,u,M),this.addLine(m,g,L+12,l,h,M)):(f.vertices+=12,O.multiplyScalar(.5),(C=s.clone()).add(O),(E=l.clone()).add(O),this.addLine(m,g,L,y,_,M),this.addLine(m,g,L+6,_,x,T),this.addLine(m,g,L+12,s,C,M),this.addLine(m,g,L+18,C,u,T),this.addLine(m,g,L+24,l,E,M),this.addLine(m,g,L+30,E,h,T)))}else M==T?(f.vertices+=2,this.addLine(m,g,L,y,x,M)):(f.vertices+=4,this.addLine(m,g,L,y,_,M),this.addLine(m,g,L+6,_,x,T))}}}}}drawAtomSphere(t,e){if(t.style.sphere){var r=t.style.sphere;if(!r.hidden){var n=(0,c.getColorFromStyle)(t,r),a=this.getRadiusFromStyle(t,r);if((!0===t.clickable||t.hoverable)&&void 0!==t.intersectionShape){var l=new o.Vector3(t.x,t.y,t.z);t.intersectionShape.sphere.push(new i.Sphere(l,a))}s.GLDraw.drawSphere(e,t,a,n)}}}drawAtomClickSphere(t){if(t.style.clicksphere){var e=t.style.clicksphere;if(!e.hidden){var r=this.getRadiusFromStyle(t,e);if((!0===t.clickable||t.hoverable)&&void 0!==t.intersectionShape){var n=new o.Vector3(t.x,t.y,t.z);t.intersectionShape.sphere.push(new i.Sphere(n,r))}}}}drawAtomInstanced(t,e){if(t.style.sphere){var r=t.style.sphere;if(!r.hidden){var n=this.getRadiusFromStyle(t,r),a=(0,c.getColorFromStyle)(t,r),s=e.updateGeoGroup(1),l=s.vertices,u=3*l,h=s.vertexArray,d=s.colorArray,f=s.radiusArray;if(h[u]=t.x,h[u+1]=t.y,h[u+2]=t.z,d[u]=a.r,d[u+1]=a.g,d[u+2]=a.b,f[l]=n,(!0===t.clickable||t.hoverable)&&void 0!==t.intersectionShape){var p=new o.Vector3(t.x,t.y,t.z);t.intersectionShape.sphere.push(new i.Sphere(p,n))}s.vertices+=1}}}drawSphereImposter(t,e,r,n){var i,o=t.updateGeoGroup(4),a=o.vertices,s=3*a,l=o.vertexArray,c=o.colorArray;for(i=0;i<4;i++)l[s+3*i]=e.x,l[s+3*i+1]=e.y,l[s+3*i+2]=e.z;var u=o.normalArray;for(i=0;i<4;i++)c[s+3*i]=n.r,c[s+3*i+1]=n.g,c[s+3*i+2]=n.b;u[s+0]=-r,u[s+1]=r,u[s+2]=0,u[s+3]=-r,u[s+4]=-r,u[s+5]=0,u[s+6]=r,u[s+7]=-r,u[s+8]=0,u[s+9]=r,u[s+10]=r,u[s+11]=0,o.vertices+=4;var h=o.faceArray,d=o.faceidx;h[d+0]=a,h[d+1]=a+1,h[d+2]=a+2,h[d+3]=a+2,h[d+4]=a+3,h[d+5]=a,o.faceidx+=6}drawAtomImposter(t,e){if(t.style.sphere){var r=t.style.sphere;if(!r.hidden){var n=this.getRadiusFromStyle(t,r),a=(0,c.getColorFromStyle)(t,r);if((!0===t.clickable||t.hoverable)&&void 0!==t.intersectionShape){var s=new o.Vector3(t.x,t.y,t.z);t.intersectionShape.sphere.push(new i.Sphere(s,n))}this.drawSphereImposter(e,t,n,a)}}}calculateDashes(t,e,r,n,i){var a=Math.sqrt(Math.pow(t.x-e.x,2)+Math.pow(t.y-e.y,2)+Math.pow(t.z-e.z,2));r=Math.max(r,0),i=Math.max(i,0)+2*r,(n=Math.max(n,.001))+i>a&&(n=a,i=0);var s,l=Math.floor((a-n)/(n+i))+1;i=(a-l*n)/l;for(var c=new o.Vector3(t.x,t.y,t.z),u=new o.Vector3((e.x-t.x)/(a/i),(e.y-t.y)/(a/i),(e.z-t.z)/(a/i)),h=new o.Vector3((e.x-t.x)/(a/n),(e.y-t.y)/(a/n),(e.z-t.z)/(a/n)),d=[],f=0;f{var e=r.imposter?p.drawStickImposter:s.GLDraw.drawCylinder;return!D&&t>=1?e:(t,r,n,i,o,a=0,s=0,l=.1,c=.25)=>{this.calculateDashes(r,n,i,l,c).forEach((r=>{e(t,r.from,r.to,i,o,a,s)}))}};for(f=0;f3){if(t.bondOrder[f]<1&&(z*=t.bondOrder[f]),!N.capDrawn&&N.bonds.length<4&&(F=2),R!=U?(k=(new o.Vector3).addVectors(G,V).multiplyScalar(.5),j(r,G,k,z,R,I,0,E,L),j(r,k,V,z,U,0,F,E,L)):j(r,G,V,z,R,I,F,E,L),h=t.clickable||t.hoverable,d=N.clickable||N.hoverable,h||d){if(k||(k=(new o.Vector3).addVectors(G,V).multiplyScalar(.5)),h){var H=new i.Cylinder(G,k,z),W=new i.Sphere(G,z);t.intersectionShape.cylinder.push(H),t.intersectionShape.sphere.push(W)}if(d){var q=new i.Cylinder(V,k,z),Y=new i.Sphere(V,z);N.intersectionShape.cylinder.push(q),N.intersectionShape.sphere.push(Y)}}}else if(t.bondOrder[f]>1){var Z=0,X=0;z!=T&&(Z=2,X=2);var $,J,K,Q,tt,et=V.clone(),rt=null;et.sub(G),rt=this.getSideBondV(t,N,f),2==t.bondOrder[f]?($=z*S,rt.multiplyScalar(1.5*$),(J=G.clone()).add(rt),(K=G.clone()).sub(rt),(Q=J.clone()).add(et),(tt=K.clone()).add(et),R!=U?(k=(new o.Vector3).addVectors(J,Q).multiplyScalar(.5),A=(new o.Vector3).addVectors(K,tt).multiplyScalar(.5),j(r,J,k,$,R,Z,0),j(r,k,Q,$,U,0,X),j(r,K,A,$,R,Z,0),j(r,A,tt,$,U,0,X)):(j(r,J,Q,$,R,Z,X),j(r,K,tt,$,R,Z,X)),h=t.clickable||t.hoverable,d=N.clickable||N.hoverable,(h||d)&&(k||(k=(new o.Vector3).addVectors(J,Q).multiplyScalar(.5)),A||(A=(new o.Vector3).addVectors(K,tt).multiplyScalar(.5)),h&&(v=new i.Cylinder(J,k,$),b=new i.Cylinder(K,A,$),t.intersectionShape.cylinder.push(v),t.intersectionShape.cylinder.push(b)),d&&(x=new i.Cylinder(Q,k,$),_=new i.Cylinder(tt,A,$),N.intersectionShape.cylinder.push(x),N.intersectionShape.cylinder.push(_)))):3==t.bondOrder[f]&&($=z*C,rt.cross(et),rt.normalize(),rt.multiplyScalar(3*$),(J=G.clone()).add(rt),(K=G.clone()).sub(rt),(Q=J.clone()).add(et),(tt=K.clone()).add(et),R!=U?(k=(new o.Vector3).addVectors(J,Q).multiplyScalar(.5),A=(new o.Vector3).addVectors(K,tt).multiplyScalar(.5),M=(new o.Vector3).addVectors(G,V).multiplyScalar(.5),j(r,J,k,$,R,Z,0),j(r,k,Q,$,U,0,X),j(r,G,M,$,R,I,0),j(r,M,V,$,U,0,F),j(r,K,A,$,R,Z,0),j(r,A,tt,$,U,0,X)):(j(r,J,Q,$,R,Z,X),j(r,G,V,$,R,I,F),j(r,K,tt,$,R,Z,X)),h=t.clickable||t.hoverable,d=N.clickable||N.hoverable,(h||d)&&(k||(k=(new o.Vector3).addVectors(J,Q).multiplyScalar(.5)),A||(A=(new o.Vector3).addVectors(K,tt).multiplyScalar(.5)),M||(M=(new o.Vector3).addVectors(G,V).multiplyScalar(.5)),h&&(v=new i.Cylinder(J.clone(),k.clone(),$),b=new i.Cylinder(K.clone(),A.clone(),$),y=new i.Cylinder(G.clone(),M.clone(),$),t.intersectionShape.cylinder.push(v),t.intersectionShape.cylinder.push(b),t.intersectionShape.cylinder.push(y)),d&&(x=new i.Cylinder(Q.clone(),k.clone(),$),_=new i.Cylinder(tt.clone(),A.clone(),$),w=new i.Cylinder(V.clone(),M.clone(),$),N.intersectionShape.cylinder.push(x),N.intersectionShape.cylinder.push(_),N.intersectionShape.cylinder.push(w))))}}}var nt=!1,it=0,ot=!1;for(f=0;f0&&(nt=!0):0==it&&(t.bonds.length>0||u.showNonBonded)&&(nt=!0),nt&&(z=T,r.imposter?this.drawSphereImposter(r.sphereGeometry,t,z,R):s.GLDraw.drawSphere(r,t,z,R))}}}createMolObj(t,e){e=e||{};var r,i,o,c,u=new n.Object3D,h=[],d={},f={},p=this.drawAtomSphere,m=null,g=null;e.supportsImposters?(p=this.drawAtomImposter,(m=new n.Geometry(!0)).imposter=!0,(g=new n.Geometry(!0,!0)).imposter=!0,g.sphereGeometry=new n.Geometry(!0),g.sphereGeometry.imposter=!0,g.drawnCaps={}):e.supportsAIA?(p=this.drawAtomInstanced,(m=new n.Geometry(!1,!0,!0)).instanced=!0,g=new n.Geometry(!0)):(m=new n.Geometry(!0),g=new n.Geometry(!0));var v,b={},y=[Number.POSITIVE_INFINITY,Number.NEGATIVE_INFINITY];for(r=0,o=t.length;ry[1]&&(y[1]=x.resi)),h.push(x))}}if(h.length>0&&(0,l.drawCartoon)(u,h,y,this.defaultCartoonQuality),m&&m.vertices>0){m.initTypedArrays();var _=null,w=null;m.imposter?_=new n.SphereImposterMaterial({ambient:0,vertexColors:!0,reflectivity:0}):m.instanced?(w=new n.Geometry(!0),s.GLDraw.drawSphere(w,{x:0,y:0,z:0},1,new a.Color(.5,.5,.5)),w.initTypedArrays(),_=new n.InstancedMaterial({sphereMaterial:new n.MeshLambertMaterial({ambient:0,vertexColors:!0,reflectivity:0}),sphere:w})):_=new n.MeshLambertMaterial({ambient:0,vertexColors:!0,reflectivity:0}),b.sphere<1&&b.sphere>=0&&(_.transparent=!0,_.opacity=b.sphere),w=new n.Mesh(m,_),u.add(w)}if(g.vertices>0){var k=null,A=null,M=g.sphereGeometry;M&&void 0!==M.vertices&&0!=M.vertices||(M=null),g.initTypedArrays(),M&&M.initTypedArrays();var T={ambient:0,vertexColors:!0,reflectivity:0};g.imposter?(k=new n.StickImposterMaterial(T),A=new n.SphereImposterMaterial(T)):(k=new n.MeshLambertMaterial(T),A=new n.MeshLambertMaterial(T),k.wireframe&&(g.setUpWireframe(),M&&M.setUpWireframe())),b.stick<1&&b.stick>=0&&(k.transparent=!0,k.opacity=b.stick,A.transparent=!0,A.opacity=b.stick);var S=new n.Mesh(g,k);if(u.add(S),M){var C=new n.Mesh(M,A);u.add(C)}}for(r in d)if(d.hasOwnProperty(r)){v=r;var E=new n.LineBasicMaterial({linewidth:v,vertexColors:!0});b.line<1&&b.line>=0&&(E.transparent=!0,E.opacity=b.line),d[r].initTypedArrays();var L=new n.Line(d[r],E,n.LineStyle.LinePieces);u.add(L)}for(r in f)if(f.hasOwnProperty(r)){v=r;var z=new n.LineBasicMaterial({linewidth:v,vertexColors:!0});b.cross<1&&b.cross>=0&&(z.transparent=!0,z.opacity=b.cross),f[r].initTypedArrays();var O=new n.Line(f[r],z,n.LineStyle.LinePieces);u.add(O)}if(this.dontDuplicateAtoms&&this.modelData.symmetries&&this.modelData.symmetries.length>0){var D,I=new n.Object3D;for(D=0;Dr?e-n:e}adjustCoordinatesToBox(){if(this.box&&this.atomdfs)for(var t=this.box[0],e=this.box[1],r=this.box[2],n=.9*t,i=.9*e,o=.9*r,a=0;a=r)&&(t=r-1),null!=n.frames.url){var a=n.frames.url;(0,c.getbin)(a+"/traj/frame/"+t+"/"+n.frames.path,void 0,"POST",void 0).then((function(t){for(var e=new Float32Array(t,44),r=0,o=0;o=n&&t<=i)return!0}}return!1}static deepCopyAndCache(t,e){if("object"!=typeof t||null==t)return t;if(t.__cache_created)return t;const r={};for(const n in t){const i=t[n];if(Array.isArray(i)){r[n]=[];for(let t=0;t=n[0][0]&&a<=n[1][0]&&s>=n[0][1]&&s<=n[1][1]&&l>=n[0][2]&&l<=n[1][2]&&(a>=r[0][0]&&a<=r[1][0]&&s>=r[0][1]&&s<=r[1][1]&&l>=r[0][2]&&l<=r[1][2]||o.push(this.atoms[t]))}return o}static getFloat(t){return"number"==typeof t?t:parseFloat(t)}selectedAtoms(t,e){var r=[];t=p.deepCopyAndCache(t||{},this),e||(e=this.atoms);for(var n=e.length,i=0;i0&&r.push(n[t])}}if(t.hasOwnProperty("within")&&t.within.hasOwnProperty("sel")&&t.within.hasOwnProperty("distance")){var s=this.selectedAtoms(t.within.sel,this.atoms),l={};const e=p.getFloat(t.within.distance),n=e*e;for(let t=0;t0&&(l[e]=1)}var c=[];if(t.within.invert)for(let t=0;t0;)if(e=d.pop(),f=e.chain,m=e.resi,void 0===h[e.index]){h[e.index]=!0;for(var g=0;g0&&(this.molObj=null)}else console.log("Callback is not a function")}setHoverable(t,e,r,n){if(e=!!e,r=(0,c.makeFunction)(r),n=(0,c.makeFunction)(n),null!==r)if(null!==n){var i=this.selectedAtoms(t,this.atoms),o=i.length;for(let t=0;t0&&(this.molObj=null)}else console.log("Unhover_callback is not a function");else console.log("Hover_callback is not a function")}enableContextMenu(t,e){var r;e=!!e;var n=this.selectedAtoms(t,this.atoms),i=n.length;for(r=0;r0&&(this.molObj=null)}setColorByElement(t,e){if(null===this.molObj||!p.sameObj(e,this.lastColors)){this.lastColors=e;var r=this.selectedAtoms(t,r);r.length>0&&(this.molObj=null);for(var n=0;n0&&(this.molObj=null),"string"==typeof r&&void 0!==u.Gradient.builtinGradients[r]&&(r=new u.Gradient.builtinGradients[r]),n||(n=r.range()),n||(n=(0,c.getPropertyRange)(a,e)),i=0;i0&&(this.molObj=null);for(let t=0;t=i)continue;let a={b:r,e:i},s=o.bondOrder[t];1!=s&&(a.o=s),e.b.push(a)}}return e}globj(t,e){(null===this.molObj||e.regen)&&(this.molObj=this.createMolObj(this.atoms,e),this.renderedMolObj&&(t.remove(this.renderedMolObj),this.renderedMolObj=null),this.renderedMolObj=this.molObj.clone(),this.hidden&&(this.renderedMolObj.setVisible(!1),this.molObj.setVisible(!1)),t.add(this.renderedMolObj))}exportVRML(){return this.createMolObj(this.atoms,{supportsImposters:!1,supportsAIA:!1}).vrml()}removegl(t){this.renderedMolObj&&(void 0!==this.renderedMolObj.geometry&&this.renderedMolObj.geometry.dispose(),void 0!==this.renderedMolObj.material&&this.renderedMolObj.material.dispose(),t.remove(this.renderedMolObj),this.renderedMolObj=null),this.molObj=null}hide(){this.hidden=!0,this.renderedMolObj&&this.renderedMolObj.setVisible(!1),this.molObj&&this.molObj.setVisible(!1)}show(){this.hidden=!1,this.renderedMolObj&&this.renderedMolObj.setVisible(!0),this.molObj&&this.molObj.setVisible(!0)}addPropertyLabels(t,e,r,n){for(var i=this.selectedAtoms(e,i),o=(0,c.deepCopy)(n),a=0;aMOLECULE/gm)?"mol2":t.match(/^data_/gm)&&t.match(/^loop_/gm)?"cif":t.match(/^HETATM/gm)||t.match(/^ATOM/gm)?"pdb":t.match(/ITEM: TIMESTEP/gm)?"lammpstrj":t.match(/^.*\n.*\n.\s*(\d+)\s+(\d+)/gm)?"sdf":t.match(/^%VERSION\s+VERSION_STAMP/gm)?"prmtop":"xyz",console.log("Best guess: "+e))),(0,h.Parsers[e])(t,r)}}p.defaultAtomStyle={line:{}},p.defaultlineWidth=1,p.vdwRadii={H:1.2,He:1.4,Li:1.82,Be:1.53,B:1.92,C:1.7,N:1.55,O:1.52,F:1.47,Ne:1.54,Na:2.27,Mg:1.73,Al:1.84,Si:2.1,P:1.8,S:1.8,Cl:1.75,Ar:1.88,K:2.75,Ca:2.31,Ni:1.63,Cu:1.4,Zn:1.39,Ga:1.87,Ge:2.11,As:1.85,Se:1.9,Br:1.85,Kr:2.02,Rb:3.03,Sr:2.49,Pd:1.63,Ag:1.72,Cd:1.58,In:1.93,Sn:2.17,Sb:2.06,Te:2.06,I:1.98,Xe:2.16,Cs:3.43,Ba:2.68,Pt:1.75,Au:1.66,Hg:1.55,Tl:1.96,Pb:2.02,Bi:2.07,Po:1.97,At:2.02,Rn:2.2,Fr:3.48,Ra:2.83,U:1.86},p.ignoredKeys=new Set(["props","invert","model","frame","byres","expand","within","and","or","not"])},"./src/GLShape.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{GLShape:()=>d,splitMesh:()=>f});var n=r("./src/WebGL/index.ts"),i=r("./src/WebGL/shapes/index.ts"),o=r("./src/WebGL/math/index.ts"),a=r("./src/colors.ts"),s=r("./src/ProteinSurface4.ts"),l=r("./src/VolumeData.ts"),c=r("./src/GLDraw.ts"),u=r("./src/glcartoon.ts"),h=r("./src/utilities.ts");class d{static finalizeGeo(t){var e=t.updateGeoGroup(0);e.vertices>0&&e.truncateArrayBuffers(!0,!0)}static updateColor(t,e){var r,n,i;e=e||a.CC.color(e),t.colorsNeedUpdate=!0,e.constructor!==Array&&(r=e.r,n=e.g,i=e.b);for(let o in t.geometryGroups){let a=t.geometryGroups[o],s=a.colorArray;for(let t=0,o=a.vertices;t0?u/t:(t+u)/t}d.multiplyScalar(c);var f=new o.Vector3(n.x,n.y,n.z).add(d),p=d.clone().negate();let m=new o.Vector3(n.x,n.y,n.z);t.intersectionShape.cylinder.push(new i.Cylinder(m,f.clone(),s)),t.intersectionShape.sphere.push(new i.Sphere(m,s));var g=[];g[0]=d.clone(),Math.abs(g[0].x)>1e-4?g[0].y+=1:g[0].x+=1,g[0].cross(d),g[0].normalize(),g[4]=g[0].clone(),g[4].crossVectors(g[0],d),g[4].normalize(),g[8]=g[0].clone().negate(),g[12]=g[4].clone().negate(),g[2]=g[0].clone().add(g[4]).normalize(),g[6]=g[4].clone().add(g[8]).normalize(),g[10]=g[8].clone().add(g[12]).normalize(),g[14]=g[12].clone().add(g[0]).normalize(),g[1]=g[0].clone().add(g[2]).normalize(),g[3]=g[2].clone().add(g[4]).normalize(),g[5]=g[4].clone().add(g[6]).normalize(),g[7]=g[6].clone().add(g[8]).normalize(),g[9]=g[8].clone().add(g[10]).normalize(),g[11]=g[10].clone().add(g[12]).normalize(),g[13]=g[12].clone().add(g[14]).normalize(),g[15]=g[14].clone().add(g[0]).normalize();var v,b,y,x,_,w,k,A,M,T,S,C,E,L,z,O,D,I,F,R,P,j,N=h.vertices,B=h.vertexArray,U=h.faceArray,G=h.normalArray,V=h.lineArray;for(b=0,y=g.length;b0){var Y=B[v-3],Z=B[v-2],X=B[v-1],$=new o.Vector3(Y,Z,X),J=new o.Vector3(a.x,a.y,a.z),K=f.clone(),Q=new o.Vector3(q.x,q.y,q.z);t.intersectionShape.triangle.push(new i.Triangle(Q,J,$)),t.intersectionShape.triangle.push(new i.Triangle($.clone(),K,Q.clone()))}}h.vertices+=48,B[v=3*h.vertices]=n.x,B[v+1]=n.y,B[v+2]=n.z,B[v+3]=f.x,B[v+4]=f.y,B[v+5]=f.z,B[v+6]=a.x,B[v+7]=a.y,B[v+8]=a.z,h.vertices+=3;var tt=h.vertices-3,et=h.vertices-2,rt=h.vertices-1,nt=3*tt,it=3*et,ot=3*rt;for(b=0,y=g.length-1;bs&&(s=u),h>l&&(l=h),d>c&&(c=d)}t.center.set((s+i)/2,(l+o)/2,(c+a)/2),t.radius=t.center.distanceTo({x:s,y:l,z:c}),t.box={min:{x:i,y:o,z:a},max:{x:s,y:l,z:c}}}static addCustomGeo(t,e,r,n,a){var s,l,c,u,h,f,p,m,g,v=e.addGeoGroup(),b=r.vertexArr,y=r.normalArr,x=r.faceArr;v.vertices=b.length,v.faceidx=x.length;var _=v.vertexArray,w=v.colorArray;for(n.constructor!==Array&&(m=n.r,g=n.g,u=n.b),f=0,p=v.vertices;fc?(h.fromCap=0,h.toCap=2):(h.fromCap=2,h.toCap=2),this.addCylinder(h)}}addLine(t){var e,r;e=t.start?new o.Vector3(t.start.x||0,t.start.y||0,t.start.z||0):new o.Vector3(0,0,0),t.end?void 0===(r=new o.Vector3(t.end.x,t.end.y||0,t.end.z||0)).x&&(r.x=3):r=new o.Vector3(3,0,0);var n=this.geo.updateGeoGroup(2),i=n.vertices,a=3*i,s=n.vertexArray;s[a]=e.x,s[a+1]=e.y,s[a+2]=e.z,s[a+3]=r.x,s[a+4]=r.y,s[a+5]=r.z,n.vertices+=2;var l=n.lineArray,c=n.lineidx;l[c]=i,l[c+1]=i+1,n.lineidx+=2;var u=new o.Vector3;this.components.push({centroid:u.addVectors(e,r).multiplyScalar(.5)}),n=this.geo.updateGeoGroup(0),d.updateBoundingFromPoints(this.boundingSphere,this.components,n.vertexArray,n.vertices)}addArrow(t){if(t.start?t.start=new o.Vector3(t.start.x||0,t.start.y||0,t.start.z||0):t.start=new o.Vector3(0,0,0),t.dir instanceof o.Vector3&&"number"==typeof t.length){var e=t.dir.clone().multiplyScalar(t.length).add(t.start);t.end=e}else t.end?(t.end=new o.Vector3(t.end.x,t.end.y||0,t.end.z||0),void 0===t.end.x&&(t.end.x=3)):t.end=new o.Vector3(3,0,0);t.radius=t.radius||.1,t.radiusRatio=t.radiusRatio||1.618034,t.mid=0=0?g[i]-l:l-g[i])>0&&(v[i]|=d.ISDONE);var b=[],y=[];s.MarchingCube.march(v,b,y,{fulltable:!0,voxel:c,unitCube:t.unit,origin:t.origin,matrix:t.matrix,nX:h,nY:f,nZ:p}),!c&&u>0&&s.MarchingCube.laplacianSmooth(u,b,y);var x=[],_=[],w=[];if(e.selectedRegion&&void 0===e.coords&&(e.coords=e.selectedRegion),void 0===e.coords&&void 0!==e.selection&&(n?e.coords=n.selectedAtoms(e.selection):console.log("addIsosurface needs viewer is selection provided.")),void 0!==e.coords){var k=e.coords[0].x,A=e.coords[0].y,M=e.coords[0].z,T=e.coords[0].x,S=e.coords[0].y,C=e.coords[0].z;for(let t=0;tk?k=e.coords[t].x:e.coords[t].xA?A=e.coords[t].y:e.coords[t].yM?M=e.coords[t].z:e.coords[t].zT&&b[t].xS&&b[t].yC&&b[t].z=64e3&&(e.push({vertexArr:[],normalArr:[],faceArr:[]}),t.colorArr&&(e.colorArr=[]),i++)}return e}d.ISDONE=2,d.drawCustom=function(t,e,r){var n=r,i=n.vertexArr,o=n.faceArr;0!==i.length&&0!==o.length||console.warn("Error adding custom shape component: No vertices and/or face indices supplied!");var s=r.color;void 0===s&&(s=t.color),s=a.CC.color(s);for(var l=f(n),c=0,u=l.length;c{"use strict";r.r(e),r.d(e,{GLViewer:()=>m,createStereoViewer:()=>b,createViewer:()=>g,createViewerGrid:()=>v});var n=r("./src/WebGL/index.ts"),i=r("./src/WebGL/math/index.ts"),o=r("./src/colors.ts"),a=r("./src/utilities.ts"),s=r("./src/Gradient.ts"),l=r("./src/GLModel.ts"),c=r("./src/Label.ts"),u=r("./src/GLShape.ts"),h=r("./src/VolumeData.ts"),d=r("./src/ProteinSurface4.ts"),f=r("./src/VolumetricRender.ts"),p=r("./node_modules/upng-js/UPNG.js");class m{getWidth(){let t=this.container,e=t.offsetWidth;if(0==e&&"none"===t.style.display){let r=t.style.position,n=t.style.visibility;t.style.display="block",t.style.visibility="hidden",t.style.position="absolute",e=t.offsetWidth,t.style.display="none",t.style.visibility=n,t.style.position=r}return e}getHeight(){let t=this.container,e=t.offsetHeight;if(0==e&&"none"===t.style.display){let r=t.style.position,n=t.style.visibility;t.style.display="block",t.style.visibility="hidden",t.style.position="absolute",e=t.offsetHeight,t.style.display="none",t.style.visibility=n,t.style.position=r}return e}setupRenderer(){this.renderer=new n.Renderer({antialias:this.config.antialias,preserveDrawingBuffer:!0,premultipliedAlpha:!1,id:this.config.id,row:this.config.row,col:this.config.col,rows:this.config.rows,cols:this.config.cols,canvas:this.config.canvas,containerWidth:this.WIDTH,containerHeight:this.HEIGHT}),this.renderer.domElement.style.width="100%",this.renderer.domElement.style.height="100%",this.renderer.domElement.style.padding="0",this.renderer.domElement.style.position="absolute",this.renderer.domElement.style.top="0px",this.renderer.domElement.style.left="0px",this.renderer.domElement.style.zIndex="0"}initializeScene(){this.scene=new n.Scene,this.scene.fog=new n.Fog(this.bgColor,100,200),this.modelGroup=new n.Object3D,this.rotationGroup=new n.Object3D,this.rotationGroup.useQuaternion=!0,this.rotationGroup.quaternion=new i.Quaternion(0,0,0,1),this.rotationGroup.add(this.modelGroup),this.scene.add(this.rotationGroup);var t=new n.Light(16777215);t.position=new i.Vector3(.2,.2,1).normalize(),t.intensity=1,this.scene.add(t)}initContainer(t){this.container=t,this.WIDTH=this.getWidth(),this.HEIGHT=this.getHeight(),this.ASPECT=this.renderer.getAspect(this.WIDTH,this.HEIGHT),this.renderer.setSize(this.WIDTH,this.HEIGHT),this.container.append(this.renderer.domElement),this.glDOM=this.renderer.domElement,this.nomouse||(this.glDOM.addEventListener("mousedown",this._handleMouseDown.bind(this),{passive:!1}),this.glDOM.addEventListener("touchstart",this._handleMouseDown.bind(this),{passive:!1}),this.glDOM.addEventListener("wheel",this._handleMouseScroll.bind(this),{passive:!1}),this.glDOM.addEventListener("mousemove",this._handleMouseMove.bind(this),{passive:!1}),this.glDOM.addEventListener("touchmove",this._handleMouseMove.bind(this),{passive:!1}),this.glDOM.addEventListener("contextmenu",this._handleContextMenu.bind(this),{passive:!1}))}decAnim(){this.animated--,this.animated<0&&(this.animated=0)}incAnim(){this.animated++}nextSurfID(){var t=0;for(let r in this.surfaces)if(this.surfaces.hasOwnProperty(r)){var e=parseInt(r);isNaN(e)||e>t&&(t=e)}return t+1}setSlabAndFog(){let t=this.camera.position.z-this.rotationGroup.position.z;t<1&&(t=1),this.camera.near=t+this.slabNear,this.camera.near<1&&(this.camera.near=1),this.camera.far=t+this.slabFar,this.camera.near+1>this.camera.far&&(this.camera.far=this.camera.near+1),this.camera.fov=this.fov,this.camera.right=t*Math.tan(Math.PI/180*this.fov),this.camera.left=-this.camera.right,this.camera.top=this.camera.right/this.ASPECT,this.camera.bottom=-this.camera.top,this.camera.updateProjectionMatrix(),this.scene.fog.near=this.camera.near+this.fogStart*(this.camera.far-this.camera.near),this.scene.fog.far=this.camera.far,this.config.disableFog&&(this.scene.fog.near=this.scene.fog.far)}show(t){if(this.renderer.setViewport(),this.scene&&(this.setSlabAndFog(),this.renderer.render(this.scene,this.camera),this.viewChangeCallback&&this.viewChangeCallback(this._viewer.getView()),!t&&this.linkedViewers.length>0))for(var e=this._viewer.getView(),r=0;r0){let e=this.CAMERA_Z-this.config.lowerZoomLimit;t>e&&(t=e)}if(this.config.upperZoomLimit&&this.config.upperZoomLimit>0){let e=this.CAMERA_Z-this.config.upperZoomLimit;tthis.CAMERA_Z-1&&(t=this.CAMERA_Z-1),t}static slerp(t,e,r){if(1==r)return e.clone();if(0==r)return t.clone();let n=t.x*e.x+t.y*e.y+t.z*e.z+t.w*e.w;if(n>.9995){let n=new i.Quaternion(t.x+r*(e.x-t.x),t.y+r*(e.y-t.y),t.z+r*(e.z-t.z),t.w+r*(e.w-t.w));return n.normalize(),n}n<0&&(e=e.clone().multiplyScalar(-1),n=-n),n>1?n=1:n<-1&&(n=-1);var o=Math.acos(n)*r,a=e.clone();a.sub(t.clone().multiplyScalar(n)),a.normalize();var s=Math.cos(o),l=Math.sin(o),c=new i.Quaternion(t.x*s+a.x*l,t.y*s+a.y*l,t.z*s+a.z*l,t.w*s+a.w*l);return c.normalize(),c}constructor(t,e={}){if(this.nomouse=!1,this.glDOM=null,this.models=[],this.surfaces={},this.shapes=[],this.labels=[],this.clickables=[],this.hoverables=[],this.contextMenuEnabledObjects=[],this.current_hover=null,this.hoverDuration=500,this.longTouchDuration=1e3,this.viewer_frame=0,this.viewChangeCallback=null,this.stateChangeCallback=null,this.NEAR=1,this.FAR=800,this.CAMERA_Z=150,this.fov=20,this.linkedViewers=[],this.renderer=null,this.control_all=!1,this.scene=null,this.rotationGroup=null,this.modelGroup=null,this.fogStart=.4,this.slabNear=-50,this.slabFar=50,this.cq=new i.Quaternion(0,0,0,1),this.dq=new i.Quaternion(0,0,0,1),this.animated=0,this.animationTimers=new Set,this.isDragging=!1,this.mouseStartX=0,this.mouseStartY=0,this.touchDistanceStart=0,this.touchHold=!1,this.currentModelPos=0,this.cz=0,this.cslabNear=0,this.cslabFar=0,this.userContextMenuHandler=null,this.config=e,this.callback=this.config.callback,this.defaultcolors=this.config.defaultcolors,this.defaultcolors||(this.defaultcolors=o.elementColors.defaultColors),this.nomouse=this.config.nomouse,this.bgColor=0,this.config.backgroundColor=this.config.backgroundColor||"#ffffff",void 0!==this.config.backgroundColor&&(this.bgColor=o.CC.color(this.config.backgroundColor).getHex()),this.config.backgroundAlpha=null==this.config.backgroundAlpha?1:this.config.backgroundAlpha,this.camerax=0,void 0!==this.config.camerax&&(this.camerax=parseFloat(this.config.camerax)),this._viewer=this,this.container=t,null!=this.config.hoverDuration&&(this.hoverDuration=this.config.hoverDuration),void 0===this.config.antialias&&(this.config.antialias=!0),void 0===this.config.cartoonQuality&&(this.config.cartoonQuality=10),this.WIDTH=this.getWidth(),this.HEIGHT=this.getHeight(),this.setupRenderer(),this.row=null==this.config.row?0:this.config.row,this.col=null==this.config.col?0:this.config.col,this.cols=this.config.cols,this.rows=this.config.rows,this.viewers=this.config.viewers,this.control_all=this.config.control_all,this.ASPECT=this.renderer.getAspect(this.WIDTH,this.HEIGHT),this.camera=new n.Camera(this.fov,this.ASPECT,this.NEAR,this.FAR,this.config.orthographic),this.camera.position=new i.Vector3(this.camerax,0,this.CAMERA_Z),this.lookingAt=new i.Vector3,this.camera.lookAt(this.lookingAt),this.raycaster=new n.Raycaster(new i.Vector3(0,0,0),new i.Vector3(0,0,0)),this.projector=new n.Projector,this.initializeScene(),this.renderer.setClearColorHex(this.bgColor,this.config.backgroundAlpha),this.scene.fog.color=o.CC.color(this.bgColor),document.body.addEventListener("mouseup",this._handleMouseUp.bind(this)),document.body.addEventListener("touchend",this._handleMouseUp.bind(this)),this.initContainer(this.container),this.config.style&&this.setViewStyle(this.config),window.addEventListener("resize",this.resize.bind(this)),void 0!==window.ResizeObserver&&(this.divwatcher=new window.ResizeObserver(this.resize.bind(this)),this.divwatcher.observe(this.container)),void 0!==window.IntersectionObserver){let t=(t,e)=>{t.forEach((t=>{t.isIntersecting&&this.resize()}))};this.intwatcher=new window.IntersectionObserver(t),this.intwatcher.observe(this.container)}try{"function"==typeof this.callback&&this.callback(this)}catch(t){console.log("error with glviewer callback: "+t)}}targetedObjects(t,e,r){var n={x:t,y:e,z:-1};return Array.isArray(r)||(r=this.selectedAtoms(r)),0==r.length?[]:(this.raycaster.setFromCamera(n,this.camera),this.raycaster.intersectObjects(this.modelGroup,r))}modelToScreen(t){let e=!1;Array.isArray(t)||(t=[t],e=!0);let r=this.renderer.getXRatio(),n=this.renderer.getYRatio(),o=this.col,a=this.row,s=o*(this.WIDTH/r),l=(n-a-1)*(this.HEIGHT/n),c=[],u=this.canvasOffset();return t.forEach((t=>{let e=new i.Vector3(t.x,t.y,t.z);e.applyMatrix4(this.modelGroup.matrixWorld),this.projector.projectVector(e,this.camera);let o=this.WIDTH/r*(e.x+1)/2+u.left+s,a=-this.HEIGHT/n*(e.y-1)/2+u.top+l;c.push({x:o,y:a})})),e&&(c=c[0]),c}screenOffsetToModel(t,e,r){var n=t/this.WIDTH,o=e/this.HEIGHT,a=void 0===r?this.rotationGroup.position.z:r,s=this.rotationGroup.quaternion,l=new i.Vector3(0,0,a);return this.projector.projectVector(l,this.camera),l.x+=2*n,l.y-=2*o,this.projector.unprojectVector(l,this.camera),l.z=0,l.applyQuaternion(s),l}screenToModelDistance(t,e){let r=this.canvasOffset(),n=new i.Vector3(e.x,e.y,e.z);n.applyMatrix4(this.modelGroup.matrixWorld);let o=n.clone();this.projector.projectVector(n,this.camera);let a=new i.Vector3(2*(t.x-r.left)/this.WIDTH-1,2*(t.y-r.top)/-this.HEIGHT+1,n.z);return this.projector.unprojectVector(a,this.camera),a.distanceTo(o)}setViewChangeCallback(t){"function"!=typeof t&&null!=t||(this.viewChangeCallback=t)}setStateChangeCallback(t){"function"!=typeof t&&null!=t||(this.stateChangeCallback=t)}getConfig(){return this.config}setConfig(t){this.config=t}getInternalState(){var t={models:[],surfaces:[],shapes:[],labels:[]};for(let e=0;e{e.getCanvas().toBlob((function(e){e.arrayBuffer().then(t)}),"image/png")}))),n+=1,n==t&&(e.viewChangeCallback=i,Promise.all(o).then((t=>{let n=[];for(let e=0;e0&&(this.hoverTimeout=setTimeout((function(){a.handleHoverSelection(o.x,o.y,t)}),this.hoverDuration)),this.isDragging)){t.targetTouches&&(t.targetTouches.length>1||1===t.targetTouches.length&&!this.closeEnoughForClick(t))&&clearTimeout(this.longTouchTimeout);var l=(e-this.mouseStartX)/this.WIDTH,c=(r-this.mouseStartY)/this.HEIGHT;0!=this.touchDistanceStart&&t.targetTouches&&2==t.targetTouches.length?(s=2,c=2*(this.calcTouchDistance(t)-this.touchDistanceStart)/(this.WIDTH+this.HEIGHT)):t.targetTouches&&3==t.targetTouches.length&&(s=1),l*=n,c*=i;var u,h=Math.hypot(l,c);if(3==s||3==this.mouseButton&&t.ctrlKey)this.slabNear=this.cslabNear+100*l,this.slabFar=this.cslabFar-100*c;else if(2==s||3==this.mouseButton||t.shiftKey)(u=.85*(this.CAMERA_Z-this.rotationGroup.position.z))<80&&(u=80),this.rotationGroup.position.z=this.cz+c*u,this.rotationGroup.position.z=this.adjustZoomToLimits(this.rotationGroup.position.z);else if(1==s||2==this.mouseButton||t.ctrlKey){var d=this.screenOffsetToModel(n*(e-this.mouseStartX),i*(r-this.mouseStartY));this.modelGroup.position.addVectors(this.currentModelPos,d)}else if((0===s||1==this.mouseButton)&&0!==h){var f=Math.sin(h*Math.PI)/h;this.dq.x=Math.cos(h*Math.PI),this.dq.y=0,this.dq.z=f*l,this.dq.w=-f*c,this.rotationGroup.quaternion.set(1,0,0,0),this.rotationGroup.quaternion.multiply(this.dq),this.rotationGroup.quaternion.multiply(this.cq)}this.show()}}_handleContextMenu(t){if(t.preventDefault(),this.closeEnoughForClick(t)){var e=this.mouseStartX,r=this.mouseStartY,n=this.canvasOffset();let o=this.mouseXY(e,r),a=o.x,s=o.y,l=this.targetedObjects(a,s,this.contextMenuEnabledObjects);var i=null;l.length&&(i=l[0].clickable),n=this.canvasOffset(),e=this.mouseStartX-n.left,r=this.mouseStartY-n.top,this.userContextMenuHandler&&(this.userContextMenuHandler(i,e,r,l,t),this.isDragging=!1)}}setContainer(t){let e=(0,a.getElement)(t)||this.container;return this.initContainer(e),this}setBackgroundColor(t,e){(void 0===e||e<0||e>1)&&(e=1);var r=o.CC.color(t);return this.scene.fog.color=r,this.bgColor=r.getHex(),this.renderer.setClearColorHex(r.getHex(),e),this.show(),this}setProjection(t){this.camera.ortho="orthographic"===t,this.setSlabAndFog()}setViewStyle(t){if("outline"===t.style){var e={};t.color&&(e.color=o.CC.color(t.color)),t.width&&(e.width=t.width),this.renderer.enableOutline(e)}else this.renderer.disableOutline();return this}updateSize(){this.renderer.setSize(this.WIDTH,this.HEIGHT),this.ASPECT=this.renderer.getAspect(this.WIDTH,this.HEIGHT),this.renderer.setSize(this.WIDTH,this.HEIGHT),this.camera.aspect=this.ASPECT,this.camera.updateProjectionMatrix()}setWidth(t){return this.WIDTH=t||this.WIDTH,this.updateSize(),this}setHeight(t){return this.HEIGHT=t||this.HEIGHT,this.updateSize(),this}resize(){this.WIDTH=this.getWidth(),this.HEIGHT=this.getHeight();let t=!1;if(console.log("resize "+this.container.id),console.log("lost "+this.renderer.isLost()+" w"+this.WIDTH+" h"+this.HEIGHT),this.renderer.isLost()&&this.WIDTH>0&&this.HEIGHT>0){let e=!1,r=this.container.querySelector("canvas");r&&r!=this.renderer.getCanvas()?this.config.canvas=r:(r.remove(),this.config&&null!=this.config.canvas&&(delete this.config.canvas,e=!0)),this.setupRenderer(),this.initContainer(this.container),this.renderer.setClearColorHex(this.bgColor,this.config.backgroundAlpha),t=!0,e&&(this.config.canvas=this.renderer.getCanvas()),console.log("regen "+t+" resetcanvas "+e)}if(0==this.WIDTH||0==this.HEIGHT?this.animated&&this._viewer.pauseAnimate():this.animated&&this._viewer.resumeAnimate(),this.updateSize(),t){let t=this.renderer.supportedExtensions();if(t.regen=!0,this.viewers)for(let e=0,r=this.viewers.length;e=0&&(this.modelGroup.remove(this.labels[r].sprite),(this.viewer_frame<0||this.labels[r].frame==this.viewer_frame)&&this.modelGroup.add(this.labels[r].sprite));for(r in this.surfaces)if(this.surfaces.hasOwnProperty(r)){var a=this.surfaces[r];for(i=0;i1||1==a[i].symmetries.length&&!a[i].symmetries[i].isIdentity()){var c,u=new n.Object3D;for(c=0;c0?this.animateMotion(e,r,this.modelGroup.position,this.adjustZoomToLimits(i),this.rotationGroup.quaternion,this.lookingAt):(this.rotationGroup.position.z=this.adjustZoomToLimits(i),this.show()),this}translate(t,e,r=0,n=!1){var o=t/this.WIDTH,a=e/this.HEIGHT,s=new i.Vector3(0,0,-this.CAMERA_Z);this.projector.projectVector(s,this.camera),s.x-=o,s.y-=a,this.projector.unprojectVector(s,this.camera),s.z=0;var l=this.lookingAt.clone().add(s);return r>0?this.animateMotion(r,n,this.modelGroup.position,this.rotationGroup.position.z,this.rotationGroup.quaternion,l):(this.lookingAt=l,this.camera.lookAt(this.lookingAt),this.show()),this}translateScene(t,e,r=0,n=!1){var i=this.screenOffsetToModel(t,e),o=this.modelGroup.position.clone().add(i);return r>0?this.animateMotion(r,n,this.modelGroup.position,this.rotationGroup.position.z,this.rotationGroup.quaternion,this.lookingAt):(this.modelGroup.position=o,this.show()),this}fitSlab(t){t=t||{};var e=this.getAtomsFromSel(t),r=(0,a.getExtent)(e),n=r[1][0]-r[0][0],i=r[1][1]-r[0][1],o=r[1][2]-r[0][2],s=Math.hypot(n,i,o);return s<5&&(s=5),this.slabNear=-s/1.9,this.slabFar=s/2,this}center(t={},e=0,r=!1){var n,o,s=this.getAtomsFromSel(t),l=(0,a.getExtent)(s);(0,a.isEmptyObject)(t)?(this.shapes.forEach((t=>{if(t&&t.boundingSphere&&t.boundingSphere.center){var e=t.boundingSphere.center,r=t.boundingSphere.radius;r>0?(s.push(new i.Vector3(e.x+r,e.y,e.z)),s.push(new i.Vector3(e.x-r,e.y,e.z)),s.push(new i.Vector3(e.x,e.y+r,e.z)),s.push(new i.Vector3(e.x,e.y-r,e.z)),s.push(new i.Vector3(e.x,e.y,e.z+r)),s.push(new i.Vector3(e.x,e.y,e.z-r))):s.push(e)}})),l=(0,a.getExtent)(s),n=s,o=l):(n=this.getAtomsFromSel({}),o=(0,a.getExtent)(n));var c=new i.Vector3(l[2][0],l[2][1],l[2][2]),u=o[1][0]-o[0][0],h=o[1][1]-o[0][1],d=o[1][2]-o[0][2],f=Math.hypot(u,h,d);f<5&&(f=5),this.slabNear=-f/1.9,this.slabFar=f/2,u=l[1][0]-l[0][0],h=l[1][1]-l[0][1],d=l[1][2]-l[0][2],(f=Math.hypot(u,h,d))<5&&(f=5);for(var p=25,m=0;mp&&(p=g)}f=2*Math.sqrt(p);var v=c.clone().multiplyScalar(-1);return e>0?this.animateMotion(e,r,v,this.rotationGroup.position.z,this.rotationGroup.quaternion,this.lookingAt):(this.modelGroup.position=v,this.show()),this}zoomTo(t={},e=0,r=!1){let n=this.getAtomsFromSel(t),o=(0,a.getExtent)(n),s=o;if((0,a.isEmptyObject)(t)){let t=n&&n.length;if(this.shapes.forEach((t=>{if(t&&t.boundingSphere)if(t.boundingSphere.box){let e=t.boundingSphere.box;n.push(new i.Vector3(e.min.x,e.min.y,e.min.z)),n.push(new i.Vector3(e.max.x,e.max.y,e.max.z))}else if(t.boundingSphere.center){var e=t.boundingSphere.center,r=t.boundingSphere.radius;r>0?(n.push(new i.Vector3(e.x+r,e.y,e.z)),n.push(new i.Vector3(e.x-r,e.y,e.z)),n.push(new i.Vector3(e.x,e.y+r,e.z)),n.push(new i.Vector3(e.x,e.y-r,e.z)),n.push(new i.Vector3(e.x,e.y,e.z+r)),n.push(new i.Vector3(e.x,e.y,e.z-r))):n.push(e)}})),s=(0,a.getExtent)(n),!t)for(let t=0;t<3;t++)o[2][t]=(s[0][t]+s[1][t])/2}else{let t=this.getAtomsFromSel({});s=(0,a.getExtent)(t)}var l=new i.Vector3(o[2][0],o[2][1],o[2][2]),c=s[1][0]-s[0][0],u=s[1][1]-s[0][1],h=s[1][2]-s[0][2],d=Math.hypot(c,u,h);d<5&&(d=5),this.slabNear=-d/1.9,this.slabFar=d/2,0===Object.keys(t).length&&(this.slabNear=Math.min(2*-d,-50),this.slabFar=Math.max(2*d,50));var f=this.config.minimumZoomToDistance||5;c=o[1][0]-o[0][0],u=o[1][1]-o[0][1],h=o[1][2]-o[0][2],(d=Math.hypot(c,u,h))p&&(p=g)}d=2*Math.sqrt(p);var v=l.clone().multiplyScalar(-1),b=-(.5*d/Math.tan(Math.PI/180*this.camera.fov/2)-this.CAMERA_Z);return b=this.adjustZoomToLimits(b),e>0?this.animateMotion(e,r,v,b,this.rotationGroup.quaternion,this.lookingAt):(this.modelGroup.position=v,this.rotationGroup.position.z=b,this.show()),this}setSlab(t,e){this.slabNear=t,this.slabFar=e}getSlab(){return{near:this.slabNear,far:this.slabFar}}addLabel(t,e={},r,n=!1){if(r){var i=(0,a.getExtent)(this.getAtomsFromSel(r));e.position={x:i[2][0],y:i[2][1],z:i[2][2]}}var o=new c.Label(t,e);return o.setContext(),this.modelGroup.add(o.sprite),this.labels.push(o),n||this.show(),o}addResLabels(t,e,r=!1){let n=this.labels.length;return this.applyToModels("addResLabels",t,this,e,r),this.show(),this.labels.slice(n)}addPropertyLabels(t,e,r){return this.applyToModels("addPropertyLabels",t,e,this,r),this.show(),this}removeLabel(t){for(var e=0;e0&&void 0===this.shapes[this.shapes.length-1];)this.shapes.pop();return this}removeAllShapes(){for(var t=0;t-1e-4&&o.x<1.0001&&o.y>-1e-4&&o.y<1.0001&&o.z>-1e-4&&o.z<1.0001)}}for(let o=0;oo){t.start=r,t.end=n,e.addLine(t);break}h.addVectors(r,c),t.start=r,t.end=h,e.addLine(t),r=h.clone(),d+=a,h.addVectors(r,u),r=h.clone(),d+=s}return e.finalize(),e}addCustom(t){t=t||{};var e=new u.GLShape(t);return e.shapePosition=this.shapes.length,e.addCustom(t),this.shapes.push(e),e.finalize(),e}addVolumetricData(t,e,r={}){var n=new h.VolumeData(t,e);return r.hasOwnProperty("transferfn")?this.addVolumetricRender(n,r):this.addIsosurface(n,r)}addIsosurface(t,e={},r){var n=new u.GLShape(e);return n.shapePosition=this.shapes.length,n.addIsosurface(t,e,r,this),this.shapes.push(n),n}addVolumetricRender(t,e){e=e||{};var r=new f.GLVolumetricRender(t,e,this);return r.shapePosition=this.shapes.length,this.shapes.push(r),r}hasVolumetricRender(){return this.renderer.supportsVolumetric()}enableFog(t){t?this.scene.fog=new n.Fog(this.bgColor,100,200):(this.config.disableFog=!0,this.show())}setFrame(t){this.viewer_frame=t;let e=this;return new Promise((function(r){var n=e.models.map((function(r){return r.setFrame(t,e)}));Promise.all(n).then((function(){r()}))}))}getFrame(){return this.viewer_frame}getNumFrames(){var t=0;for(let e=0;et&&(t=this.models[e].getNumFrames());for(let e=0;e=t&&(t=this.shapes[e].frame+1);for(let e=0;e=t&&(t=this.labels[e].frame+1);return t}animate(t){this.incAnim();var e=100,r="forward",n=1/0;(t=t||{}).interval&&(e=t.interval),t.loop&&(r=t.loop),t.reps&&(n=t.reps);var i=this.getNumFrames(),o=this,s=0;t.startFrame&&(s=t.startFrame%i);var l=1;t.step&&(n/=l=t.step);var c,u,h=0,d=i*n,f=new Date,p=function(t){f=new Date,"forward"==t?o.setFrame(s).then((function(){s=(s+l)%i,c()})):"backward"==t?o.setFrame(i-1-s).then((function(){s=(s+l)%i,c()})):o.setFrame(s).then((function(){l*=(s+=l)%(i-1)==0?-1:1,c()}))};return c=function(){if(o.render(),o.getCanvas().isConnected)if(++h>=d||!o.isAnimated())u.cancel(),o.animationTimers.delete(u),o.decAnim();else{var t=e-((new Date).getTime()-f.getTime());t=t>0?t:0,o.animationTimers.delete(u),u=new a.PausableTimer(p,t,r),o.animationTimers.add(u)}else o.stopAnimate()},u=new a.PausableTimer(p,0,r),this.animationTimers.add(u),this}stopAnimate(){return this.animated=0,this.animationTimers.forEach((function(t){t.cancel()})),this.animationTimers=new Set,this}pauseAnimate(){return this.animationTimers.forEach((function(t){t.pause()})),this}resumeAnimate(){return this.animationTimers.forEach((function(t){t.resume()})),this}isAnimated(){return this.animated>0}getModelOpt(t){return t&&!t.defaultcolors?(t.defaultcolors=this.defaultcolors,t.cartoonQuality=t.cartoonQuality||this.config.cartoonQuality):void 0===t&&(t={defaultcolors:this.defaultcolors,cartoonQuality:this.config.cartoonQuality}),t}addModel(t,e="",r){r=this.getModelOpt(r);var n=new l.GLModel(this.models.length,r);return n.addMolData(t,e,r),this.models.push(n),n}addModels(t,e,r){(r=this.getModelOpt(r)).multimodel=!0,r.frames=!0;for(var n=l.GLModel.parseMolData(t,e,r),i=0;i0&&void 0===this.models[this.models.length-1];)this.models.pop();return this}}removeAllModels(){for(var t=0;te[1][0]||n.ye[1][1]||n.ze[1][2]||r.push(n))}return r}static volume(t){return(t[1][0]-t[0][0])*(t[1][1]-t[0][1])*(t[1][2]-t[0][2])}carveUpExtent(t,e,r){let n=[],i={};for(let t=0,r=e.length;tn&&r>i?0:n>r&&n>i?1:2;var o=a(t),l=a(t),c=(t[1][e]-t[0][e])/2+t[0][e];o[1][e]=c,l[0][e]=c;var u=s(o),h=s(l);return u.concat(h)},l=s(t);for(let t=0,i=l.length;t0)for(let t=0,e=h.length;t1||1==w.length&&!w[0].isIdentity()){_=!0;break}}var k=function(t,r,n){var i;b=l?m.shallowCopy(p.getAtomsFromSel(l)):n;var o=(0,a.getExtent)(n,!0);if(e.map&&e.map.prop){var c=e.map.prop;let t=(0,s.getGradient)(e.map.scheme||e.map.gradient||new s.Gradient.RWB),r=t.range();r||(r=(0,a.getPropertyRange)(n,c)),e.colorscheme={prop:c,gradient:t}}for(let t=0,n=r.length;t0){var x=(0,a.getExtent)(b,!0);y.sort((function(t,e){var r=function(t,e){var r=t.extent,n=r[1][0]-r[0][0],i=r[1][1]-r[0][1],o=r[1][2]-r[0][2],a=n-e[2][0];a*=a;var s=i-e[2][1];s*=s;var l=o-e[2][2];return a+s+l*l};return r(t,x)-r(e,x)}))}var _=[];for(let t=0,e=r.length;t0&&(A.push({geo:new n.Geometry(!0),mat:f,done:!1,finished:!1,symmetries:this.models[x].getSymmetries()}),C.push(k(A[A.length-1],T[x],S[x])));M=Promise.all(C)}else A.push({geo:new n.Geometry(!0),mat:f,done:!1,finished:!1,symmetries:[new i.Matrix4]}),M=k(A[A.length-1],v,y);return this.surfaces[h]=A,M.surfid=h,c&&"function"==typeof c?(M.then((function(t){c(t)})),h):M}setSurfaceMaterialStyle(t,e){if((0,a.adjustVolumeStyle)(e),this.surfaces[t]){var r=this.surfaces[t];r.style=e;for(var i=0;i0?this.camera.position.x=r*Math.tan(Math.PI/180*e):this.camera.position.x=-r*Math.tan(Math.PI/180*e),this.camera.lookAt(new i.Vector3(0,0,this.rotationGroup.position.z)),this.camera.position.x}setDefaultCartoonQuality(t){this.config.cartoonQuality=t}}function g(t,e){if(t=(0,a.getElement)(t)){e=e||{};try{return new m(t,e)}catch(t){throw"error creating viewer: "+t}}}function v(t,e={},r={}){if(t=(0,a.getElement)(t)){var n=[],i=document.createElement("canvas");r.rows=e.rows,r.cols=e.cols,r.control_all=null!=e.control_all&&e.control_all,t.appendChild(i);try{for(var o=0;o{"use strict";r.r(e),r.d(e,{CustomLinear:()=>u,Gradient:()=>d,GradientType:()=>i,ROYGB:()=>l,RWB:()=>s,Sinebow:()=>c,builtinGradients:()=>h,getGradient:()=>a,normalizeValue:()=>o});var n=r("./src/colors.ts");class i{}function o(t,e,r){return e>=t?(re&&(r=e),{lo:t,hi:e,val:r}):(r>t&&(r=t),r=2?(this.max=t[1],this.min=t[0]):t&&e&&!Array.isArray(t)&&(this.min=t,this.max=e)}range(){return void 0!==this.min&&void 0!==this.max?[this.min,this.max]:null}valueToHex(t,e){var r,n;if(t=this.mult*t,e?(r=e[0],n=e[1]):(r=this.min,n=this.max),void 0===t)return 16777215;var i=o(r,n,t);r=i.lo;var a,s=n=i.hi;return(t=i.val)<(s=e&&void 0!==e[2]?e[2]:void 0!==this.mid?this.mid:(r+n)/2)?16711680+256*(a=Math.floor(255*Math.sqrt((t-r)/(s-r))))+a:t>s?65536*(a=Math.floor(255*Math.sqrt(1-(t-s)/(n-s))))+256*a+255:16777215}}class l extends i{constructor(t,e){super(),this.gradient="ROYGB",this.mult=1,this.min=t,this.max=e,void 0===e&&Array.isArray(t)&&t.length>=2?(this.max=t[1],this.min=t[0]):t&&e&&!Array.isArray(t)&&(this.min=t,this.max=e)}valueToHex(t,e){var r,n;if(t=this.mult*t,e?(r=e[0],n=e[1]):(r=this.min,n=this.max),void 0===t)return 16777215;var i=o(r,n,t),a=((r=i.lo)+(n=i.hi))/2,s=(r+a)/2,l=(a+n)/2;return(t=i.val)=2&&(this.max=t[1],this.min=t[0]),e=2?(this.max=t[1],this.min=t[0],i=e):(this.min=t,this.max=e,i=r),i)for(let t of i)this.colors.push(n.CC.color(t));else this.colors.push(n.CC.color(0))}range(){return void 0!==this.min&&void 0!==this.max?[this.min,this.max]:null}valueToHex(t,e){var r,i;if(e?(r=e[0],i=e[1]):(r=this.min,i=this.max),void 0===t)return 16777215;var a=o(r,i,t);r=a.lo,i=a.hi,t=a.val;let s=this.colors.length,l=(i-r)/s,c=Math.min(Math.floor((t-r)/l),s-1),u=Math.min(c+1,s-1),h=(t-r-c*l)/l,d=this.colors[c],f=this.colors[u];return new n.Color(d.r+h*(f.r-d.r),d.g+h*(f.g-d.g),d.b+h*(f.b-d.b)).getHex()}}const h={rwb:s,RWB:s,roygb:l,ROYGB:l,sinebow:c,linear:u};class d extends i{valueToHex(t,e){return 0}range(){return null}}d.RWB=s,d.ROYGB=l,d.Sinebow=c,d.CustomLinear=u,d.builtinGradients=h,d.normalizeValue=o,d.getGradient=a},"./src/Label.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Label:()=>l,LabelCount:()=>a});var n=r("./src/WebGL/index.ts"),i=r("./src/Gradient.ts"),o=r("./src/colors.ts");let a=0;function s(t,e,r){var n=r;return void 0!==t&&(t instanceof o.Color?n=t.scaled():void 0!==(n=o.CC.color(t)).scaled&&(n=n.scaled())),void 0!==e&&(n.a=parseFloat(e)),n}class l{constructor(t,e){this.id=a++,this.stylespec=e||{},this.canvas=document.createElement("canvas"),this.canvas.width=134,this.canvas.height=35,this.context=this.canvas.getContext("2d"),this.sprite=new n.Sprite,this.text=t,this.frame=this.stylespec.frame}getStyle(){return this.stylespec}setContext(){var t=this.stylespec,e=void 0!==t.useScreen&&t.useScreen,r=t.showBackground;"0"!==r&&"false"!==r||(r=!1),void 0===r&&(r=!0);var o=t.font?t.font:"sans-serif",a=parseInt(t.fontSize)?parseInt(t.fontSize):18,l=s(t.fontColor,t.fontOpacity,{r:255,g:255,b:255,a:1}),c=t.padding?t.padding:4,u=t.borderThickness?t.borderThickness:0,h=s(t.backgroundColor,t.backgroundOpacity,{r:0,g:0,b:0,a:1}),d=s(t.borderColor,t.borderOpacity,h),f=t.position?t.position:{x:-10,y:1,z:1},p=void 0===t.inFront||t.inFront;"false"!==p&&"0"!==p||(p=!1);var m=t.alignment||n.SpriteAlignment.topLeft;"string"==typeof m&&m in n.SpriteAlignment&&(m=n.SpriteAlignment[m]);var g="";t.bold&&(g="bold "),this.context.font=g+a+"px "+o;var v=this.context.measureText(this.text).width;r||(u=0);var b=v+2.5*u+2*c,y=1.25*a+2*u+2*c;if(t.backgroundImage){var x=t.backgroundImage,_=t.backgroundWidth?t.backgroundWidth:x.width,w=t.backgroundHeight?t.backgroundHeight:x.height;_>b&&(b=_),w>y&&(y=w)}if(this.canvas.width=b,this.canvas.height=y,this.context.clearRect(0,0,this.canvas.width,this.canvas.height),g="",t.bold&&(g="bold "),this.context.font=g+a+"px "+o,this.context.fillStyle="rgba("+h.r+","+h.g+","+h.b+","+h.a+")",this.context.strokeStyle="rgba("+d.r+","+d.g+","+d.b+","+d.a+")",t.backgroundGradient){let e=this.context.createLinearGradient(0,y/2,b,y/2),r=i.Gradient.getGradient(t.backgroundGradient),n=r.range(),o=-1,a=1;n&&(o=n[0],a=n[1]);let l=a-o;for(let t=0;t<1.01;t+=.1){let n=s(r.valueToHex(o+l*t)),i="rgba("+n.r+","+n.g+","+n.b+","+n.a+")";e.addColorStop(t,i)}this.context.fillStyle=e}this.context.lineWidth=u,r&&function(t,e,r,n,i,o,a){t.beginPath(),t.moveTo(e+6,r),t.lineTo(e+n-6,r),t.quadraticCurveTo(e+n,r,e+n,r+6),t.lineTo(e+n,r+i-6),t.quadraticCurveTo(e+n,r+i,e+n-6,r+i),t.lineTo(e+6,r+i),t.quadraticCurveTo(e,r+i,e,r+i-6),t.lineTo(e,r+6),t.quadraticCurveTo(e,r,e+6,r),t.closePath(),t.fill(),a&&t.stroke()}(this.context,u,u,b-2*u,y-2*u,0,u>0),t.backgroundImage&&this.context.drawImage(x,0,0,b,y),this.context.fillStyle="rgba("+l.r+","+l.g+","+l.b+","+l.a+")",this.context.fillText(this.text,u+c,a+u+c,v);var k=new n.Texture(this.canvas);k.needsUpdate=!0,this.sprite.material=new n.SpriteMaterial({map:k,useScreenCoordinates:e,alignment:m,depthTest:!p,screenOffset:t.screenOffset||null}),this.sprite.scale.set(1,1,1),this.sprite.position.set(f.x,f.y,f.z)}dispose(){void 0!==this.sprite.material.map&&this.sprite.material.map.dispose(),void 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60,3728,3993,3219,3482,1692,1941,1183,1430,2710,2975,2197,2460,666,915,153,400,3840,3593,3331,3082,1804,1541,1295,1030,2822,2575,2309,2060,778,515,265,0],this.triTable2=[[],[8,3,0],[9,0,1],[8,3,1,8,1,9],[11,2,3],[11,2,0,11,0,8],[11,2,3,0,1,9],[2,1,11,1,9,11,11,9,8],[10,1,2],[8,3,0,1,2,10],[9,0,2,9,2,10],[3,2,8,2,10,8,8,10,9],[10,1,3,10,3,11],[1,0,10,0,8,10,10,8,11],[0,3,9,3,11,9,9,11,10],[8,10,9,8,11,10],[8,4,7],[3,0,4,3,4,7],[1,9,0,8,4,7],[9,4,1,4,7,1,1,7,3],[2,3,11,7,8,4],[7,11,4,11,2,4,4,2,0],[3,11,2,4,7,8,9,0,1],[2,7,11,2,1,7,1,4,7,1,9,4],[10,1,2,8,4,7],[2,10,1,0,4,7,0,7,3],[4,7,8,0,2,10,0,10,9],[2,7,3,2,9,7,7,9,4,2,10,9],[8,4,7,11,10,1,11,1,3],[11,4,7,1,4,11,1,11,10,1,0,4],[3,8,0,7,11,4,11,9,4,11,10,9],[7,11,4,4,11,9,11,10,9],[9,5,4],[3,0,8,4,9,5],[5,4,0,5,0,1],[4,8,5,8,3,5,5,3,1],[11,2,3,9,5,4],[9,5,4,8,11,2,8,2,0],[3,11,2,1,5,4,1,4,0],[8,5,4,2,5,8,2,8,11,2,1,5],[2,10,1,9,5,4],[0,8,3,5,4,9,10,1,2],[10,5,2,5,4,2,2,4,0],[3,4,8,3,2,4,2,5,4,2,10,5],[5,4,9,1,3,11,1,11,10],[0,9,1,4,8,5,8,10,5,8,11,10],[3,4,0,3,10,4,4,10,5,3,11,10],[4,8,5,5,8,10,8,11,10],[9,5,7,9,7,8],[0,9,3,9,5,3,3,5,7],[8,0,7,0,1,7,7,1,5],[1,7,3,1,5,7],[11,2,3,8,9,5,8,5,7],[9,2,0,9,7,2,2,7,11,9,5,7],[0,3,8,2,1,11,1,7,11,1,5,7],[2,1,11,11,1,7,1,5,7],[1,2,10,5,7,8,5,8,9],[9,1,0,10,5,2,5,3,2,5,7,3],[5,2,10,8,2,5,8,5,7,8,0,2],[10,5,2,2,5,3,5,7,3],[3,9,1,3,8,9,7,11,10,7,10,5],[9,1,0,10,7,11,10,5,7],[3,8,0,7,10,5,7,11,10],[11,5,7,11,10,5],[11,7,6],[0,8,3,11,7,6],[9,0,1,11,7,6],[7,6,11,3,1,9,3,9,8],[2,3,7,2,7,6],[8,7,0,7,6,0,0,6,2],[1,9,0,3,7,6,3,6,2],[7,6,2,7,2,9,2,1,9,7,9,8],[1,2,10,6,11,7],[2,10,1,7,6,11,8,3,0],[11,7,6,10,9,0,10,0,2],[7,6,11,3,2,8,8,2,10,8,10,9],[6,10,7,10,1,7,7,1,3],[6,10,1,6,1,7,7,1,0,7,0,8],[9,0,3,6,9,3,6,10,9,6,3,7],[6,10,7,7,10,8,10,9,8],[8,4,6,8,6,11],[11,3,6,3,0,6,6,0,4],[0,1,9,4,6,11,4,11,8],[1,9,4,11,1,4,11,3,1,11,4,6],[3,8,2,8,4,2,2,4,6],[2,0,4,2,4,6],[1,9,0,3,8,2,2,8,4,2,4,6],[9,4,1,1,4,2,4,6,2],[10,1,2,11,8,4,11,4,6],[10,1,2,11,3,6,6,3,0,6,0,4],[0,2,10,0,10,9,4,11,8,4,6,11],[2,11,3,6,9,4,6,10,9],[8,4,6,8,6,1,6,10,1,8,1,3],[1,0,10,10,0,6,0,4,6],[8,0,3,9,6,10,9,4,6],[10,4,6,10,9,4],[9,5,4,7,6,11],[4,9,5,3,0,8,11,7,6],[6,11,7,4,0,1,4,1,5],[6,11,7,4,8,5,5,8,3,5,3,1],[4,9,5,6,2,3,6,3,7],[9,5,4,8,7,0,0,7,6,0,6,2],[4,0,1,4,1,5,6,3,7,6,2,3],[7,4,8,5,2,1,5,6,2],[6,11,7,1,2,10,9,5,4],[11,7,6,8,3,0,1,2,10,9,5,4],[11,7,6,10,5,2,2,5,4,2,4,0],[7,4,8,2,11,3,10,5,6],[4,9,5,6,10,7,7,10,1,7,1,3],[5,6,10,0,9,1,8,7,4],[5,6,10,7,0,3,7,4,0],[10,5,6,4,8,7],[5,6,9,6,11,9,9,11,8],[0,9,5,0,5,3,3,5,6,3,6,11],[0,1,5,0,5,11,5,6,11,0,11,8],[11,3,6,6,3,5,3,1,5],[9,5,6,3,9,6,3,8,9,3,6,2],[5,6,9,9,6,0,6,2,0],[0,3,8,2,5,6,2,1,5],[1,6,2,1,5,6],[1,2,10,5,6,9,9,6,11,9,11,8],[1,0,9,6,10,5,11,3,2],[6,10,5,2,8,0,2,11,8],[3,2,11,10,5,6],[10,5,6,9,3,8,9,1,3],[0,9,1,5,6,10],[8,0,3,10,5,6],[10,5,6],[10,6,5],[8,3,0,10,6,5],[0,1,9,5,10,6],[10,6,5,9,8,3,9,3,1],[3,11,2,10,6,5],[6,5,10,2,0,8,2,8,11],[1,9,0,6,5,10,11,2,3],[1,10,2,5,9,6,9,11,6,9,8,11],[1,2,6,1,6,5],[0,8,3,2,6,5,2,5,1],[5,9,6,9,0,6,6,0,2],[9,6,5,3,6,9,3,9,8,3,2,6],[11,6,3,6,5,3,3,5,1],[0,5,1,0,11,5,5,11,6,0,8,11],[0,5,9,0,3,5,3,6,5,3,11,6],[5,9,6,6,9,11,9,8,11],[10,6,5,4,7,8],[5,10,6,7,3,0,7,0,4],[5,10,6,0,1,9,8,4,7],[4,5,9,6,7,10,7,1,10,7,3,1],[7,8,4,2,3,11,10,6,5],[11,6,7,10,2,5,2,4,5,2,0,4],[11,6,7,8,0,3,1,10,2,9,4,5],[6,7,11,1,10,2,9,4,5],[7,8,4,5,1,2,5,2,6],[4,1,0,4,5,1,6,7,3,6,3,2],[9,4,5,8,0,7,0,6,7,0,2,6],[4,5,9,6,3,2,6,7,3],[6,7,11,4,5,8,5,3,8,5,1,3],[6,7,11,4,1,0,4,5,1],[4,5,9,3,8,0,11,6,7],[9,4,5,7,11,6],[10,6,4,10,4,9],[8,3,0,9,10,6,9,6,4],[1,10,0,10,6,0,0,6,4],[8,6,4,8,1,6,6,1,10,8,3,1],[2,3,11,6,4,9,6,9,10],[0,10,2,0,9,10,4,8,11,4,11,6],[10,2,1,11,6,3,6,0,3,6,4,0],[10,2,1,11,4,8,11,6,4],[9,1,4,1,2,4,4,2,6],[1,0,9,3,2,8,2,4,8,2,6,4],[2,4,0,2,6,4],[3,2,8,8,2,4,2,6,4],[1,4,9,11,4,1,11,1,3,11,6,4],[0,9,1,4,11,6,4,8,11],[11,6,3,3,6,0,6,4,0],[8,6,4,8,11,6],[6,7,10,7,8,10,10,8,9],[9,3,0,6,3,9,6,9,10,6,7,3],[6,1,10,6,7,1,7,0,1,7,8,0],[6,7,10,10,7,1,7,3,1],[7,11,6,3,8,2,8,10,2,8,9,10],[11,6,7,10,0,9,10,2,0],[2,1,10,7,11,6,8,0,3],[1,10,2,6,7,11],[7,2,6,7,9,2,2,9,1,7,8,9],[1,0,9,3,6,7,3,2,6],[8,0,7,7,0,6,0,2,6],[2,7,3,2,6,7],[7,11,6,3,9,1,3,8,9],[9,1,0,11,6,7],[0,3,8,11,6,7],[11,6,7],[11,7,5,11,5,10],[3,0,8,7,5,10,7,10,11],[9,0,1,10,11,7,10,7,5],[3,1,9,3,9,8,7,10,11,7,5,10],[10,2,5,2,3,5,5,3,7],[5,10,2,8,5,2,8,7,5,8,2,0],[9,0,1,10,2,5,5,2,3,5,3,7],[1,10,2,5,8,7,5,9,8],[2,11,1,11,7,1,1,7,5],[0,8,3,2,11,1,1,11,7,1,7,5],[9,0,2,9,2,7,2,11,7,9,7,5],[11,3,2,8,5,9,8,7,5],[1,3,7,1,7,5],[8,7,0,0,7,1,7,5,1],[0,3,9,9,3,5,3,7,5],[9,7,5,9,8,7],[4,5,8,5,10,8,8,10,11],[3,0,4,3,4,10,4,5,10,3,10,11],[0,1,9,4,5,8,8,5,10,8,10,11],[5,9,4,1,11,3,1,10,11],[3,8,4,3,4,2,2,4,5,2,5,10],[10,2,5,5,2,4,2,0,4],[0,3,8,5,9,4,10,2,1],[2,1,10,9,4,5],[8,4,5,2,8,5,2,11,8,2,5,1],[3,2,11,1,4,5,1,0,4],[9,4,5,8,2,11,8,0,2],[11,3,2,9,4,5],[4,5,8,8,5,3,5,1,3],[5,0,4,5,1,0],[3,8,0,4,5,9],[9,4,5],[7,4,11,4,9,11,11,9,10],[3,0,8,7,4,11,11,4,9,11,9,10],[11,7,4,1,11,4,1,10,11,1,4,0],[8,7,4,11,1,10,11,3,1],[2,3,7,2,7,9,7,4,9,2,9,10],[4,8,7,0,10,2,0,9,10],[2,1,10,0,7,4,0,3,7],[10,2,1,8,7,4],[2,11,7,2,7,1,1,7,4,1,4,9],[3,2,11,4,8,7,9,1,0],[7,4,11,11,4,2,4,0,2],[2,11,3,7,4,8],[9,1,4,4,1,7,1,3,7],[1,0,9,8,7,4],[3,4,0,3,7,4],[8,7,4],[8,9,10,8,10,11],[0,9,3,3,9,11,9,10,11],[1,10,0,0,10,8,10,11,8],[10,3,1,10,11,3],[3,8,2,2,8,10,8,9,10],[9,2,0,9,10,2],[8,0,3,1,10,2],[10,2,1],[2,11,1,1,11,9,11,8,9],[11,3,2,0,9,1],[11,0,2,11,8,0],[11,3,2],[8,1,3,8,9,1],[9,1,0],[8,0,3],[]]}march(t,e,r,n){let o=!!n.fulltable,a=n.hasOwnProperty("origin")&&n.origin.hasOwnProperty("x")?n.origin:{x:0,y:0,z:0},s=!!n.voxel,l=n.matrix,c=n.nX||0,u=n.nY||0,h=n.nZ||0,d=n.scale||1,f=null;f=n.unitCube?n.unitCube:{x:d,y:d,z:d};let p,m,g=new Int32Array(c*u*h);for(p=0,m=g.length;p>2))+n+((2&e)>>1))*h+i+(1&e)]&this.ISDONE)<=3&&(e.push(e[n]),n=e.length-1,e.push(e[i]),i=e.length-1,e.push(e[o]),o=e.length-1),r.push(n),r.push(i),r.push(o)}}}laplacianSmooth(t,e,r){let n,i,o,a,s,l=new Array(e.length);for(n=0,i=e.length;n1e6&&(this.scaleFactor=this.defaultScaleFactor/2);let n=1/this.scaleFactor*5.5;this.pminx=t[0][0],this.pmaxx=t[1][0],this.pminy=t[0][1],this.pmaxy=t[1][1],this.pminz=t[0][2],this.pmaxz=t[1][2],e?(this.pminx-=this.probeRadius+n,this.pminy-=this.probeRadius+n,this.pminz-=this.probeRadius+n,this.pmaxx+=this.probeRadius+n,this.pmaxy+=this.probeRadius+n,this.pmaxz+=this.probeRadius+n):(this.pminx-=n,this.pminy-=n,this.pminz-=n,this.pmaxx+=n,this.pmaxy+=n,this.pmaxz+=n),this.pminx=Math.floor(this.pminx*this.scaleFactor)/this.scaleFactor,this.pminy=Math.floor(this.pminy*this.scaleFactor)/this.scaleFactor,this.pminz=Math.floor(this.pminz*this.scaleFactor)/this.scaleFactor,this.pmaxx=Math.ceil(this.pmaxx*this.scaleFactor)/this.scaleFactor,this.pmaxy=Math.ceil(this.pmaxy*this.scaleFactor)/this.scaleFactor,this.pmaxz=Math.ceil(this.pmaxz*this.scaleFactor)/this.scaleFactor,this.ptranx=-this.pminx,this.ptrany=-this.pminy,this.ptranz=-this.pminz,this.pLength=Math.ceil(this.scaleFactor*(this.pmaxx-this.pminx))+1,this.pWidth=Math.ceil(this.scaleFactor*(this.pmaxy-this.pminy))+1,this.pHeight=Math.ceil(this.scaleFactor*(this.pmaxz-this.pminz))+1,this.boundingatom(e),this.cutRadius=this.probeRadius*this.scaleFactor,this.vpBits=new Uint8Array(this.pLength*this.pWidth*this.pHeight),this.vpDistance=new Float64Array(this.pLength*this.pWidth*this.pHeight),this.vpAtomID=new Int32Array(this.pLength*this.pWidth*this.pHeight)}boundingatom(t){let e={};for(const r in this.vdwRadii){let n=this.vdwRadii[r];e[r]=t?(n+this.probeRadius)*this.scaleFactor+.5:n*this.scaleFactor+.5;let i=e[r]*e[r];this.widxz[r]=Math.floor(e[r])+1,this.depty[r]=new Int32Array(this.widxz[r]*this.widxz[r]);let o=0;for(let t=0;ti)this.depty[r][o]=-1;else{let t=Math.sqrt(i-n);this.depty[r][o]=Math.floor(t)}o++}}}fillvoxels(t,e){for(let t=0,e=this.vpBits.length;t=this.pLength||c>=this.pWidth||u>=this.pHeight)continue;let d=a*s+c*this.pHeight+u;if(this.vpBits[d]&this.INOUT){let a=e[this.vpAtomID[d]];if(a.serial!=t.serial){let e=r+f-Math.floor(.5+this.scaleFactor*(a.x+this.ptranx)),s=n+o-Math.floor(.5+this.scaleFactor*(a.y+this.ptrany)),l=i+p-Math.floor(.5+this.scaleFactor*(a.z+this.ptranz));f*f+o*o+p*p=this.pLength||c>=this.pWidth||u>=this.pHeight)continue;let d=a*s+c*this.pHeight+u;if(this.vpBits[d]&this.ISDONE){let a=e[this.vpAtomID[d]];if(a.serial!=t.serial){let e=n+f-Math.floor(.5+this.scaleFactor*(a.x+this.ptranx)),s=i+r-Math.floor(.5+this.scaleFactor*(a.y+this.ptrany)),l=o+p-Math.floor(.5+this.scaleFactor*(a.z+this.ptranz));f*f+r*r+p*p-1&&a-1&&l-1&&s=s)||(this.vpBits[t]|=this.ISBOUND))}fastoneshell(t,e){let r,n,i,o,a,s,l,c,u,h=[];if(0===t.length)return h;let d={ix:-1,iy:-1,iz:-1},f=this.pWidth*this.pHeight;for(let p=0,m=t.length;p-1&&d.iy-1&&d.iz-1&&(u=d.ix*f+this.pHeight*d.iy+d.iz,this.vpBits[u]&this.INOUT&&!(this.vpBits[u]&this.ISDONE)?(e.set(d.ix,d.iy,i+this.nb[t][2],c),o=d.ix-c.ix,a=d.iy-c.iy,s=d.iz-c.iz,l=o*o+a*a+s*s,this.vpDistance[u]=l,this.vpBits[u]|=this.ISDONE,this.vpBits[u]|=this.ISBOUND,h.push({ix:d.ix,iy:d.iy,iz:d.iz})):this.vpBits[u]&this.INOUT&&this.vpBits[u]&this.ISDONE&&(o=d.ix-c.ix,a=d.iy-c.iy,s=d.iz-c.iz,l=o*o+a*a+s*s,l-1&&d.iy-1&&d.iz-1&&(u=d.ix*f+this.pHeight*d.iy+d.iz,this.vpBits[u]&this.INOUT&&!(this.vpBits[u]&this.ISDONE)?(e.set(d.ix,d.iy,i+this.nb[t][2],c),o=d.ix-c.ix,a=d.iy-c.iy,s=d.iz-c.iz,l=o*o+a*a+s*s,this.vpDistance[u]=l,this.vpBits[u]|=this.ISDONE,this.vpBits[u]|=this.ISBOUND,h.push({ix:d.ix,iy:d.iy,iz:d.iz})):this.vpBits[u]&this.INOUT&&this.vpBits[u]&this.ISDONE&&(o=d.ix-c.ix,a=d.iy-c.iy,s=d.iz-c.iz,l=o*o+a*a+s*s,l-1&&d.iy-1&&d.iz-1&&(u=d.ix*f+this.pHeight*d.iy+d.iz,this.vpBits[u]&this.INOUT&&!(this.vpBits[u]&this.ISDONE)?(e.set(d.ix,d.iy,i+this.nb[t][2],c),o=d.ix-c.ix,a=d.iy-c.iy,s=d.iz-c.iz,l=o*o+a*a+s*s,this.vpDistance[u]=l,this.vpBits[u]|=this.ISDONE,this.vpBits[u]|=this.ISBOUND,h.push({ix:d.ix,iy:d.iy,iz:d.iz})):this.vpBits[u]&this.INOUT&&this.vpBits[u]&this.ISDONE&&(o=d.ix-c.ix,a=d.iy-c.iy,s=d.iz-c.iz,l=o*o+a*a+s*s,l{"use strict";r.r(e),r.d(e,{VolumeData:()=>l});var n=r("./src/utilities.ts"),i=r("./src/WebGL/math/index.ts"),o=r("./src/parsers/VASP.ts"),a=r("./src/parsers/CUBE.ts"),s=r("./node_modules/pako/dist/pako.esm.mjs");class l{constructor(t,e,r){if(this.unit={x:1,y:1,z:1},this.origin={x:0,y:0,z:0},this.size={x:0,y:0,z:0},this.data=new Float32Array([]),this.matrix=null,this.inversematrix=null,this.isbinary=new Set(["ccp4","CCP4"]),this.getCoordinates=function(t){var e=t/(this.size.y*this.size.z),r=t%(this.size.y*this.size.z),n=t%this.size.z;return e*=this.unit.x,r*=this.unit.y,n*=this.unit.z,{x:e+=this.origin.x,y:r+=this.origin.y,z:n+=this.origin.z}},this.vasp=function(t){var e=t.replace(/^\s+/,"").split(/[\n\r]/),r=(0,o.VASP)(t)[0].length;if(0==r)return console.log("No good formating of CHG or CHGCAR file, not atomic information provided in the file."),void(this.data=[]);var n,a=1.889725992,s=parseFloat(e[1]);n=e[2].replace(/^\s+/,"").split(/\s+/);var l=new i.Vector3(parseFloat(n[0]),parseFloat(n[1]),parseFloat(n[2])).multiplyScalar(s*a);n=e[3].replace(/^\s+/,"").split(/\s+/);var c=new i.Vector3(parseFloat(n[0]),parseFloat(n[1]),parseFloat(n[2])).multiplyScalar(s*a);n=e[4].replace(/^\s+/,"").split(/\s+/);var u=new i.Vector3(parseFloat(n[0]),parseFloat(n[1]),parseFloat(n[2])).multiplyScalar(s*a),h=l.x*(c.y*u.z-u.y*c.z)-c.x*(l.y*u.z-u.y*l.z)+u.x*(l.y*c.z-c.y*l.z),d=1/(h=Math.abs(h)/Math.pow(a,3));e.splice(0,8+r+1);var f=e[0].replace(/^\s+/,"").replace(/\s+/g," ").split(" "),p=Math.abs(parseFloat(f[0])),m=Math.abs(parseFloat(f[1])),g=Math.abs(parseFloat(f[2])),v=this.origin=new i.Vector3(0,0,0);this.size={x:p,y:m,z:g},this.unit=new i.Vector3(l.x,c.y,u.z),l=l.multiplyScalar(1/(a*p)),c=c.multiplyScalar(1/(a*m)),u=u.multiplyScalar(1/(a*g)),0==l.y&&0==l.z&&0==c.x&&0==c.z&&0==u.x&&0==u.y||(this.matrix=new i.Matrix4(l.x,c.x,u.x,0,l.y,c.y,u.y,0,l.z,c.z,u.z,0,0,0,0,1),this.matrix=this.matrix.multiplyMatrices(this.matrix,(new i.Matrix4).makeTranslation(v.x,v.y,v.z)),this.origin=new i.Vector3(0,0,0),this.unit=new i.Vector3(1,1,1)),e.splice(0,1);var b=e.join(" "),y=(b=b.replace(/^\s+/,"")).split(/[\s\r]+/);y.splice(p*m*g+1);for(var x=Float32Array.from(y,parseFloat),_=0;_=this.size.x||e<0||e>=this.size.y||r<0||r>=this.size.z?-1:t*this.size.y*this.size.z+e*this.size.z+r}getVal(t,e,r){let n=this.getIndex(t,e,r);return n<0?0:this.data[n]}cube(t){var e=t.split(/\r?\n/);if(!(e.length<6)){var r=(0,a.CUBE)(t,{}).modelData[0].cryst,n=e[2].replace(/^\s+/,"").replace(/\s+/g," ").split(" "),i=parseFloat(n[0]),o=Math.abs(i);this.origin=r.origin,this.size=r.size,this.unit=r.unit,this.matrix=r.matrix4;var s=6;i<0&&s++;var l=e.splice(o+s).join(" "),c=(l=l.replace(/^\s+/,"")).split(/[\s\r]+/);this.data=Float32Array.from(c,parseFloat)}}ccp4(t){var e={};t=new Int8Array(t);var r=new Int32Array(t.buffer,0,56),n=new Float32Array(t.buffer,0,56),o=new DataView(t.buffer);if(e.MAP=String.fromCharCode(o.getUint8(208),o.getUint8(209),o.getUint8(210),o.getUint8(211)),e.MACHST=[o.getUint8(212),o.getUint8(213)],17===e.MACHST[0]&&17===e.MACHST[1])for(var a=t.byteLength,s=0;s{"use strict";r.r(e),r.d(e,{GLVolumetricRender:()=>l});var n=r("./src/WebGL/shapes/index.ts"),i=r("./src/WebGL/math/index.ts"),o=r("./src/WebGL/index.ts"),a=r("./src/colors.ts"),s=r("./src/GLShape.ts");class l{static interpolateArray(t,e){function r(t,e,r){return t+(e-t)*r}var n=[],i=(t.length-1)/(e-1);n[0]=t[0];for(var o=1;o=0||t.getIndex(u,h,d)>=0)for(let e=s;e=0&&!r[s]&&(e-a.x)*(e-a.x)+(n-a.y)*(n-a.y)+(o-a.z)*(o-a.z){"use strict";r.r(e),r.d(e,{Camera:()=>o});var n=r("./src/WebGL/core/index.ts"),i=r("./src/WebGL/math/index.ts");class o extends n.Object3D{constructor(t=50,e=1,r=.1,n=2e3,o=!1){super(),this.projectionMatrix=new i.Matrix4,this.projectionMatrixInverse=new i.Matrix4,this.matrixWorldInverse=new i.Matrix4,this.fov=t,this.aspect=e,this.near=r,this.far=n;var a=this.position.z;this.right=a*Math.tan(Math.PI/180*t),this.left=-this.right,this.top=this.right/this.aspect,this.bottom=-this.top,this.ortho=!!o,this.updateProjectionMatrix()}lookAt(t){this.matrix.lookAt(this.position,t,this.up),this.rotationAutoUpdate&&(!1===this.useQuaternion&&this.rotation instanceof i.Vector3?this.rotation.setEulerFromRotationMatrix(this.matrix,this.eulerOrder):console.error("Unimplemented math operation."))}updateProjectionMatrix(){this.ortho?this.projectionMatrix.makeOrthographic(this.left,this.right,this.top,this.bottom,this.near,this.far):this.projectionMatrix.makePerspective(this.fov,this.aspect,this.near,this.far),this.projectionMatrixInverse.getInverse(this.projectionMatrix)}}},"./src/WebGL/Fog.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Fog:()=>i});var n=r("./src/colors.ts");class i{constructor(t,e=1,r=1e3){this.name="",this.color=new n.Color(t),this.near=e,this.far=r}clone(){return new i(this.color.getHex(),this.near,this.far)}}},"./src/WebGL/Renderer.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Renderer:()=>f});var n=r("./src/WebGL/Camera.ts"),i=r("./src/WebGL/constants/Sides.ts"),o=r("./src/WebGL/constants/TextureConstants.ts"),a=r("./src/WebGL/core/index.ts"),s=r("./src/colors.ts"),l=r("./src/WebGL/materials/index.ts"),c=r("./src/WebGL/math/index.ts"),u=r("./src/WebGL/objects/index.ts"),h=r("./src/WebGL/shaders/index.ts"),d=r("./src/WebGL/SpritePlugin.ts");class f{constructor(t){this.context=null,this.devicePixelRatio=1,this.autoClear=!0,this.autoClearColor=!0,this.autoClearDepth=!0,this.autoClearStencil=!0,this.sortObjects=!0,this.autoUpdateObjects=!0,this.autoUpdateScene=!0,this.info={memory:{programs:0,geometries:0,textures:0},render:{calls:0,vertices:0,faces:0,points:0}},this._programs=[],this._programs_counter=0,this._webglversion=1,this._currentProgram=null,this._currentMaterialId=-1,this._currentGeometryGroupHash=null,this._currentCamera=null,this._geometryGroupCounter=0,this._oldDoubleSided=-1,this._oldFlipSided=-1,this._oldDepthTest=-1,this._oldDepthWrite=-1,this._oldPolygonOffset=null,this._oldLineWidth=null,this._viewportWidth=0,this._viewportHeight=0,this._currentWidth=0,this._currentHeight=0,this._enabledAttributes={},this._projScreenMatrix=new c.Matrix4,this._vector3=new c.Vector3,this._worldInverse=new c.Matrix4,this._projInverse=new c.Matrix4,this._textureMatrix=new c.Matrix4,this._direction=new c.Vector3,this._lightsNeedUpdate=!0,this._lights={ambient:[0,0,0],directional:{length:0,colors:[],positions:[]},point:{length:0,colors:[],positions:[],distances:[]},spot:{length:0,colors:[],positions:[],distances:[],directions:[],anglesCos:[],exponents:[]},hemi:{length:0,skyColors:[],groundColors:[],positions:[]}},this.sprites=new d.SpritePlugin,this._screenshader=null,this._vertexattribpos=null,this._screenQuadVBO=null,this._fb=null,this._targetTexture=null,this._depthTexture=null,t=t||{},this.row=t.row,this.col=t.col,this.rows=t.rows,this.cols=t.cols,this._canvas=void 0!==t.canvas?t.canvas:document.createElement("canvas"),this._precision=void 0!==t.precision?t.precision:"highp",this._alpha=void 0===t.alpha||t.alpha,this._premultipliedAlpha=void 0===t.premultipliedAlpha||t.premultipliedAlpha,this._antialias=void 0!==t.antialias&&t.antialias,this._stencil=void 0===t.stencil||t.stencil,this._preserveDrawingBuffer=void 0!==t.preserveDrawingBuffer&&t.preserveDrawingBuffer,this._clearColor=void 0!==t.clearColor?new s.Color(t.clearColor):new s.Color(0),this._clearAlpha=void 0!==t.clearAlpha?t.clearAlpha:0,this._outlineMaterial=new l.MeshOutlineMaterial(t.outline),this._outlineSphereImposterMaterial=new l.SphereImposterOutlineMaterial(t.outline),this._outlineStickImposterMaterial=new l.StickImposterOutlineMaterial(t.outline),this._outlineEnabled=!!t.outline,this.domElement=this._canvas,this._canvas.id=t.id,0!=t.containerWidth&&0!=t.containerHeight&&(this.initGL(),this.setDefaultGLState(),this.context=this._gl,this.isWebGL1()?this._extInstanced=this._gl.getExtension("ANGLE_instanced_arrays"):this._extInstanced={vertexAttribDivisorANGLE:this._gl.vertexAttribDivisor.bind(this._gl),drawElementsInstancedANGLE:this._gl.drawElementsInstanced.bind(this._gl)},this._extFragDepth=this._gl.getExtension("EXT_frag_depth"),this._extFloatLinear=this._gl.getExtension("OES_texture_float_linear"),this._extColorBufferFloat=this._gl.getExtension("EXT_color_buffer_float"),this.sprites.init(this))}supportedExtensions(){return{supportsAIA:Boolean(this._extInstanced),supportsImposters:Boolean(this._extFragDepth)||!this.isWebGL1(),regen:!1}}getContext(){return this._gl}getCanvas(){return this._canvas}isLost(){return null==this._gl||this._gl.isContextLost()}getPrecision(){return this._precision}setClearColorHex(t,e){this._clearColor.setHex(t),this._clearAlpha=e,this.isLost()||this._gl.clearColor(this._clearColor.r,this._clearColor.g,this._clearColor.b,this._clearAlpha)}enableOutline(t){this._outlineMaterial=new l.MeshOutlineMaterial(t),this._outlineSphereImposterMaterial=new l.SphereImposterOutlineMaterial(t),this._outlineStickImposterMaterial=new l.StickImposterOutlineMaterial(t),this._outlineEnabled=!0}disableOutline(){this._outlineEnabled=!1}setViewport(){if(null!=this.rows&&null!=this.cols&&null!=this.row&&null!=this.col){var t=this._canvas.width/this.cols,e=this._canvas.height/this.rows;this._viewportWidth=t,this._viewportHeight=e,this.isLost()||(this._gl.enable(this._gl.SCISSOR_TEST),this._gl.scissor(t*this.col,e*this.row,t,e),this._gl.viewport(t*this.col,e*this.row,t,e))}}setSize(t,e){if(this.devicePixelRatio=void 0!==window.devicePixelRatio?window.devicePixelRatio:1,this._antialias&&this.devicePixelRatio<2&&(this.devicePixelRatio*=2),null!=this.rows&&null!=this.cols&&null!=this.row&&null!=this.col){var r=t/this.cols,n=e/this.rows;this._canvas.width=t*this.devicePixelRatio,this._canvas.height=e*this.devicePixelRatio,this._viewportWidth=r*this.devicePixelRatio,this._viewportHeight=n*this.devicePixelRatio,this._canvas.style.width=t+"px",this._canvas.style.height=e+"px",this.setViewport()}else this._viewportWidth=this._canvas.width=t*this.devicePixelRatio,this._viewportHeight=this._canvas.height=e*this.devicePixelRatio,this._canvas.style.width=t+"px",this._canvas.style.height=e+"px",this.isLost()||this._gl.viewport(0,0,this._gl.drawingBufferWidth,this._gl.drawingBufferHeight);this.initFrameBuffer()}clear(t,e,r){var n=0;(void 0===t||t)&&(n|=this._gl.COLOR_BUFFER_BIT),(void 0===e||e)&&(n|=this._gl.DEPTH_BUFFER_BIT),(void 0===r||r)&&(n|=this._gl.STENCIL_BUFFER_BIT),this._gl.clear(n)}clearTarget(t,e,r){this.clear(t,e,r)}setMaterialFaces(t,e){var r=t.side===i.DoubleSide,n=t.side===i.BackSide;t.imposter||(n=e?!n:n),this._oldDoubleSided!==r&&(r?this._gl.disable(this._gl.CULL_FACE):this._gl.enable(this._gl.CULL_FACE),this._oldDoubleSided=r),this._oldFlipSided!==n&&(n?this._gl.frontFace(this._gl.CW):this._gl.frontFace(this._gl.CCW),this._oldFlipSided=n),this._gl.cullFace(this._gl.BACK)}setDepthTest(t){this._oldDepthTest!==t&&(t?this._gl.enable(this._gl.DEPTH_TEST):this._gl.disable(this._gl.DEPTH_TEST),this._oldDepthTest=t)}setDepthWrite(t){this._oldDepthWrite!==t&&(this._gl.depthMask(t),this._oldDepthWrite=t)}setBlending(t){t?(this._gl.enable(this._gl.BLEND),this._gl.blendEquationSeparate(this._gl.FUNC_ADD,this._gl.FUNC_ADD),this._gl.blendFuncSeparate(this._gl.SRC_ALPHA,this._gl.ONE_MINUS_SRC_ALPHA,this._gl.ONE,this._gl.ONE_MINUS_SRC_ALPHA)):this._gl.disable(this._gl.BLEND)}initMaterial(t,e,r,n){var i,o;if(t.addEventListener("dispose",this.onMaterialDispose.bind(this)),o=t.shaderID){var a=h.ShaderLib[o];t.vertexShader=a.vertexShader,t.fragmentShader=a.fragmentShader,t.uniforms=h.ShaderUtils.clone(a.uniforms)}i={wireframe:t.wireframe,fragdepth:t.imposter,volumetric:t.volumetric},t.program=this.buildProgram(t.fragmentShader,t.vertexShader,t.uniforms,i)}renderBuffer(t,e,r,n,i,o){var a,s;if(n.visible&&(a=this.setProgram(t,e,r,n,o,this))){s=a.attributes;var l,c,h=!1,d=n.wireframe?1:0,f=16777215*i.id+2*a.id+d;if(f!==this._currentGeometryGroupHash&&(this._currentGeometryGroupHash=f,h=!0),h&&(this.disableAttributes(),s.position>=0&&(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,i.__webglVertexBuffer),this.enableAttribute(s.position),this._gl.vertexAttribPointer(s.position,3,this._gl.FLOAT,!1,0,0)),s.color>=0&&(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,i.__webglColorBuffer),this.enableAttribute(s.color),this._gl.vertexAttribPointer(s.color,3,this._gl.FLOAT,!1,0,0)),s.normal>=0&&(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,i.__webglNormalBuffer),this.enableAttribute(s.normal),this._gl.vertexAttribPointer(s.normal,3,this._gl.FLOAT,!1,0,0)),s.offset>=0&&(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,i.__webglOffsetBuffer),this.enableAttribute(s.offset),this._gl.vertexAttribPointer(s.offset,3,this._gl.FLOAT,!1,0,0)),s.radius>=0&&(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,i.__webglRadiusBuffer),this.enableAttribute(s.radius),this._gl.vertexAttribPointer(s.radius,1,this._gl.FLOAT,!1,0,0))),o instanceof u.Mesh){if("instanced"===n.shaderID){var p=n.sphere.geometryGroups[0];h&&(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,i.__webglVertexBuffer),this._gl.bufferData(this._gl.ARRAY_BUFFER,p.vertexArray,this._gl.STATIC_DRAW),this._gl.bindBuffer(this._gl.ARRAY_BUFFER,i.__webglNormalBuffer),this._gl.bufferData(this._gl.ARRAY_BUFFER,p.normalArray,this._gl.STATIC_DRAW),this._gl.bindBuffer(this._gl.ELEMENT_ARRAY_BUFFER,i.__webglFaceBuffer),this._gl.bufferData(this._gl.ELEMENT_ARRAY_BUFFER,p.faceArray,this._gl.STATIC_DRAW)),l=p.faceidx,this._extInstanced.vertexAttribDivisorANGLE(s.offset,1),this._extInstanced.vertexAttribDivisorANGLE(s.radius,1),this._extInstanced.vertexAttribDivisorANGLE(s.color,1),this._extInstanced.drawElementsInstancedANGLE(this._gl.TRIANGLES,l,this._gl.UNSIGNED_SHORT,0,i.radiusArray.length),this._extInstanced.vertexAttribDivisorANGLE(s.offset,0),this._extInstanced.vertexAttribDivisorANGLE(s.radius,0),this._extInstanced.vertexAttribDivisorANGLE(s.color,0)}else n.wireframe?(c=i.lineidx,this.setLineWidth(n.wireframeLinewidth),h&&this._gl.bindBuffer(this._gl.ELEMENT_ARRAY_BUFFER,i.__webglLineBuffer),this._gl.drawElements(this._gl.LINES,c,this._gl.UNSIGNED_SHORT,0)):(l=i.faceidx,h&&this._gl.bindBuffer(this._gl.ELEMENT_ARRAY_BUFFER,i.__webglFaceBuffer),this._gl.drawElements(this._gl.TRIANGLES,l,this._gl.UNSIGNED_SHORT,0));this.info.render.calls++,this.info.render.vertices+=l,this.info.render.faces+=l/3}else o instanceof u.Line&&(c=i.vertices,this.setLineWidth(n.linewidth),this._gl.drawArrays(this._gl.LINES,0,c),this.info.render.calls++)}}render(t,e,r){if(e instanceof n.Camera!=0){var i,o,a,s,l,c=t.__lights,u=t.fog;if(this._currentMaterialId=-1,this._lightsNeedUpdate=!0,this.autoUpdateScene&&t.updateMatrixWorld(),void 0===e.parent&&e.updateMatrixWorld(),e.matrixWorldInverse.getInverse(e.matrixWorld),this._projScreenMatrix.multiplyMatrices(e.projectionMatrix,e.matrixWorldInverse),!this.isLost()){this.autoUpdateObjects&&this.initWebGLObjects(t),this.info.render.calls=0,this.info.render.vertices=0,this.info.render.faces=0,this.info.render.points=0,this._currentWidth=this._viewportWidth,this._currentHeight=this._viewportHeight,this.setViewport(),this.setFrameBuffer(),(this.autoClear||r)&&(this._gl.clearColor(this._clearColor.r,this._clearColor.g,this._clearColor.b,this._clearAlpha),this.clear(this.autoClearColor,this.autoClearDepth,this.autoClearStencil));var h=!1;for(i=0,o=(l=t.__webglObjects).length;i=0;--r)t[r].object===e&&t.splice(r,1)}removeInstancesDirect(t,e){for(var r=t.length-1;r>=0;--r)t[r]===e&&t.splice(r,1)}unrollBufferMaterial(t){var e=t.object.material;if(e.volumetric)t.opaque=null,t.transparent=null,t.volumetric=e;else if(e.transparent){if(t.opaque=null,t.volumetric=null,t.transparent=e,!e.wireframe){var r=e.clone();r.opacity=0,t.blank=r}}else t.opaque=e,t.transparent=null,t.volumetric=null}setBuffers(t,e){var r=t.vertexArray,n=t.colorArray;if(void 0!==t.__webglOffsetBuffer?(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,t.__webglOffsetBuffer),this._gl.bufferData(this._gl.ARRAY_BUFFER,r,e)):(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,t.__webglVertexBuffer),this._gl.bufferData(this._gl.ARRAY_BUFFER,r,e)),this._gl.bindBuffer(this._gl.ARRAY_BUFFER,t.__webglColorBuffer),this._gl.bufferData(this._gl.ARRAY_BUFFER,n,e),t.normalArray&&void 0!==t.__webglNormalBuffer){var i=t.normalArray;this._gl.bindBuffer(this._gl.ARRAY_BUFFER,t.__webglNormalBuffer),this._gl.bufferData(this._gl.ARRAY_BUFFER,i,e)}if(t.radiusArray&&void 0!==t.__webglRadiusBuffer&&(this._gl.bindBuffer(this._gl.ARRAY_BUFFER,t.__webglRadiusBuffer),this._gl.bufferData(this._gl.ARRAY_BUFFER,t.radiusArray,e)),t.faceArray&&void 0!==t.__webglFaceBuffer){var o=t.faceArray;this._gl.bindBuffer(this._gl.ELEMENT_ARRAY_BUFFER,t.__webglFaceBuffer),this._gl.bufferData(this._gl.ELEMENT_ARRAY_BUFFER,o,e)}if(t.lineArray&&void 0!==t.__webglLineBuffer){var a=t.lineArray;this._gl.bindBuffer(this._gl.ELEMENT_ARRAY_BUFFER,t.__webglLineBuffer),this._gl.bufferData(this._gl.ELEMENT_ARRAY_BUFFER,a,e)}}createMeshBuffers(t){t.radiusArray&&(t.__webglRadiusBuffer=this._gl.createBuffer()),t.useOffset&&(t.__webglOffsetBuffer=this._gl.createBuffer()),t.__webglVertexBuffer=this._gl.createBuffer(),t.__webglNormalBuffer=this._gl.createBuffer(),t.__webglColorBuffer=this._gl.createBuffer(),t.__webglFaceBuffer=this._gl.createBuffer(),t.__webglLineBuffer=this._gl.createBuffer(),this.info.memory.geometries++}createLineBuffers(t){t.__webglVertexBuffer=this._gl.createBuffer(),t.__webglColorBuffer=this._gl.createBuffer(),this.info.memory.geometries++}addBuffer(t,e,r){t.push({buffer:e,object:r,opaque:null,transparent:null})}setupMatrices(t,e){t._modelViewMatrix.multiplyMatrices(e.matrixWorldInverse,t.matrixWorld),t._normalMatrix.getInverse(t._modelViewMatrix),t._normalMatrix.transpose()}filterFallback(t){return this._gl.LINEAR}setTextureParameters(t,e){t==this._gl.TEXTURE_2D?(this._gl.texParameteri(t,this._gl.TEXTURE_WRAP_S,this._gl.CLAMP_TO_EDGE),this._gl.texParameteri(t,this._gl.TEXTURE_WRAP_T,this._gl.CLAMP_TO_EDGE),this._gl.texParameteri(t,this._gl.TEXTURE_MAG_FILTER,this.filterFallback(e.magFilter)),this._gl.texParameteri(t,this._gl.TEXTURE_MIN_FILTER,this.filterFallback(e.minFilter))):(this._gl.texParameteri(t,this._gl.TEXTURE_WRAP_S,this._gl.CLAMP_TO_EDGE),this._gl.texParameteri(t,this._gl.TEXTURE_WRAP_T,this._gl.CLAMP_TO_EDGE),this._gl.texParameteri(t,this._gl.TEXTURE_WRAP_R,this._gl.CLAMP_TO_EDGE),this._extColorBufferFloat&&this._extFloatLinear?(this._gl.texParameteri(t,this._gl.TEXTURE_MAG_FILTER,this._gl.LINEAR),this._gl.texParameteri(t,this._gl.TEXTURE_MIN_FILTER,this._gl.LINEAR)):(this._gl.texParameteri(t,this._gl.TEXTURE_MAG_FILTER,this._gl.NEAREST),this._gl.texParameteri(t,this._gl.TEXTURE_MIN_FILTER,this._gl.NEAREST)))}paramToGL(t){return t===o.UnsignedByteType?this._gl.UNSIGNED_BYTE:t===o.RGBAFormat?this._gl.RGBA:t===o.NearestFilter?this._gl.NEAREST:0}setupLights(t,e){var r,n,i,o,s,l=this._lights,c=l.directional.colors,u=l.directional.positions,h=0,d=0;for(r=0,n=e.length;r{"use strict";r.r(e),r.d(e,{SpritePlugin:()=>i});var n=r("./src/WebGL/shaders/index.ts");class i{constructor(){this.sprite={vertices:null,faces:null,vertexBuffer:null,elementBuffer:null,program:null,attributes:{},uniforms:null}}init(t){this.gl=t.context,this.renderer=t,this.precision=t.getPrecision(),this.sprite.vertices=new Float32Array(16),this.sprite.faces=new Uint16Array(6);var e=0;this.sprite.vertices[e++]=-1,this.sprite.vertices[e++]=-1,this.sprite.vertices[e++]=0,this.sprite.vertices[e++]=0,this.sprite.vertices[e++]=1,this.sprite.vertices[e++]=-1,this.sprite.vertices[e++]=1,this.sprite.vertices[e++]=0,this.sprite.vertices[e++]=1,this.sprite.vertices[e++]=1,this.sprite.vertices[e++]=1,this.sprite.vertices[e++]=1,this.sprite.vertices[e++]=-1,this.sprite.vertices[e++]=1,this.sprite.vertices[e++]=0,this.sprite.vertices[e++]=1,e=0,this.sprite.faces[e++]=0,this.sprite.faces[e++]=1,this.sprite.faces[e++]=2,this.sprite.faces[e++]=0,this.sprite.faces[e++]=2,this.sprite.faces[e++]=3,this.sprite.vertexBuffer=this.gl.createBuffer(),this.sprite.elementBuffer=this.gl.createBuffer(),this.gl.bindBuffer(this.gl.ARRAY_BUFFER,this.sprite.vertexBuffer),this.gl.bufferData(this.gl.ARRAY_BUFFER,this.sprite.vertices,this.gl.STATIC_DRAW),this.gl.bindBuffer(this.gl.ELEMENT_ARRAY_BUFFER,this.sprite.elementBuffer),this.gl.bufferData(this.gl.ELEMENT_ARRAY_BUFFER,this.sprite.faces,this.gl.STATIC_DRAW),this.sprite.program=this.createProgram(n.ShaderLib.sprite,this.precision||1),this.sprite.attributes={};const r={};this.sprite.attributes.position=this.gl.getAttribLocation(this.sprite.program,"position"),this.sprite.attributes.uv=this.gl.getAttribLocation(this.sprite.program,"uv"),r.uvOffset=this.gl.getUniformLocation(this.sprite.program,"uvOffset"),r.uvScale=this.gl.getUniformLocation(this.sprite.program,"uvScale"),r.rotation=this.gl.getUniformLocation(this.sprite.program,"rotation"),r.scale=this.gl.getUniformLocation(this.sprite.program,"scale"),r.alignment=this.gl.getUniformLocation(this.sprite.program,"alignment"),r.color=this.gl.getUniformLocation(this.sprite.program,"color"),r.map=this.gl.getUniformLocation(this.sprite.program,"map"),r.opacity=this.gl.getUniformLocation(this.sprite.program,"opacity"),r.useScreenCoordinates=this.gl.getUniformLocation(this.sprite.program,"useScreenCoordinates"),r.screenPosition=this.gl.getUniformLocation(this.sprite.program,"screenPosition"),r.modelViewMatrix=this.gl.getUniformLocation(this.sprite.program,"modelViewMatrix"),r.projectionMatrix=this.gl.getUniformLocation(this.sprite.program,"projectionMatrix"),r.fogType=this.gl.getUniformLocation(this.sprite.program,"fogType"),r.fogDensity=this.gl.getUniformLocation(this.sprite.program,"fogDensity"),r.fogNear=this.gl.getUniformLocation(this.sprite.program,"fogNear"),r.fogFar=this.gl.getUniformLocation(this.sprite.program,"fogFar"),r.fogColor=this.gl.getUniformLocation(this.sprite.program,"fogColor"),r.alphaTest=this.gl.getUniformLocation(this.sprite.program,"alphaTest"),this.sprite.uniforms=r}render(t,e,r,n,i){var a,s,l,c,u,h,d,f,p,m;if(!this.gl)throw new Error("WebGLRenderer not initialized");let g=[];null===(a=null==t?void 0:t.__webglSprites)||void 0===a||a.forEach((t=>{(i&&0==t.material.depthTest||!i&&t.material.depthTest)&&g.push(t)}));let v=g.length;if(!v)return;const b=this.sprite.attributes,y=this.sprite.uniforms;if(!y)throw new Error("Uniforms not defined");var x=.5*r,_=.5*n;this.gl.useProgram(this.sprite.program),this.gl.enableVertexAttribArray(b.position),this.gl.enableVertexAttribArray(b.uv),this.gl.disable(this.gl.CULL_FACE),this.gl.enable(this.gl.BLEND),this.gl.bindBuffer(this.gl.ARRAY_BUFFER,this.sprite.vertexBuffer),this.gl.vertexAttribPointer(b.position,2,this.gl.FLOAT,!1,16,0),this.gl.vertexAttribPointer(b.uv,2,this.gl.FLOAT,!1,16,8),this.gl.bindBuffer(this.gl.ELEMENT_ARRAY_BUFFER,this.sprite.elementBuffer),this.gl.uniformMatrix4fv(y.projectionMatrix,!1,e.projectionMatrix.elements),this.gl.activeTexture(this.gl.TEXTURE0),this.gl.uniform1i(y.map,0);var w,k=0,A=0,M=t.fog;let T,S,C,E;M?(this.gl.uniform3f(y.fogColor,M.color.r,M.color.g,M.color.b),this.gl.uniform1f(y.fogNear,M.near),this.gl.uniform1f(y.fogFar,M.far),this.gl.uniform1i(y.fogType,1),k=1,A=1):(this.gl.uniform1i(y.fogType,0),k=0,A=0);let L=[];for(w=0;w{"use strict";var n;r.r(e),r.d(e,{Coloring:()=>n}),function(t){t[t.NoColors=0]="NoColors",t[t.FaceColors=1]="FaceColors",t[t.VertexColors=2]="VertexColors"}(n||(n={}))},"./src/WebGL/constants/Shading.ts":(t,e,r)=>{"use strict";var n;r.r(e),r.d(e,{Shading:()=>n}),function(t){t[t.NoShading=0]="NoShading",t[t.FlatShading=1]="FlatShading",t[t.SmoothShading=2]="SmoothShading"}(n||(n={}))},"./src/WebGL/constants/Sides.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{BackSide:()=>i,DoubleSide:()=>o,FrontSide:()=>n});const n=0,i=1,o=2},"./src/WebGL/constants/SpriteAlignment.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{SpriteAlignment:()=>i});var n=r("./src/WebGL/math/index.ts");const i={topLeft:new n.Vector2(1,-1),topCenter:new n.Vector2(0,-1),topRight:new n.Vector2(-1,-1),centerLeft:new n.Vector2(1,0),center:new n.Vector2(0,0),centerRight:new n.Vector2(-1,0),bottomLeft:new n.Vector2(1,1),bottomCenter:new n.Vector2(0,1),bottomRight:new n.Vector2(-1,1)}},"./src/WebGL/constants/TextureConstants.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{ClampToEdgeWrapping:()=>n,FloatType:()=>l,LinearFilter:()=>i,LinearMipMapLinearFilter:()=>a,NearestFilter:()=>o,R32Format:()=>h,RFormat:()=>u,RGBAFormat:()=>c,UnsignedByteType:()=>s});const n=1001,i=1006,o=1007,a=1008,s=1009,l=1010,c=1021,u=1022,h=1023},"./src/WebGL/constants/TextureOperations.ts":(t,e,r)=>{"use strict";var n;r.r(e),r.d(e,{TextureOperations:()=>n}),function(t){t[t.MultiplyOperation=0]="MultiplyOperation",t[t.MixOperation=1]="MixOperation",t[t.AddOperation=2]="AddOperation"}(n||(n={}))},"./src/WebGL/constants/index.ts":(t,e,r)=>{"use 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e=this.listeners[t.type];if(void 0!==e){t.target=this;for(var r=0,n=e.length;r{"use strict";r.r(e),r.d(e,{Geometry:()=>l,GeometryGroup:()=>s,GeometryIDCount:()=>c});var n=r("./src/WebGL/materials/LineBasicMaterial.ts"),i=r("./src/WebGL/core/EventDispatcher.ts"),o=r("./src/WebGL/math/index.ts"),a=r("./src/colors.ts");class s{constructor(t=0){this.vertexArray=null,this.colorArray=null,this.normalArray=null,this.radiusArray=null,this.faceArray=null,this.lineArray=null,this.vertices=0,this.faceidx=0,this.lineidx=0,this.__inittedArrays=!1,this.id=t}setColors(t){var e=this.vertexArray,r=this.colorArray;if(!e)throw new Error("vertex array not initialized");if(!r)throw new Error("color array not initialized");if(e.length==r.length)for(var n=0;n0?this.lineArray=(null==a?void 0:a.subarray(0,this.lineidx))||null:this.lineArray=new Uint16Array(0)):(this.normalArray=new Float32Array(0),this.faceArray=new Uint16Array(0),this.lineArray=new 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e,r=this.groups>0?this.geometryGroups[this.groups-1]:null;return(!r||r.vertices+t>((null===(e=null==r?void 0:r.vertexArray)||void 0===e?void 0:e.length)||0)/3)&&(r=this.addGeoGroup()),r}vrml(t,e){for(var r="",n=this.geometryGroups.length,i=0;i{"use strict";r.r(e),r.d(e,{Light:()=>l,Object3D:()=>a,Object3DIDCount:()=>o,Scene:()=>s});var n=r("./src/WebGL/math/index.ts"),i=r("./src/colors.ts");let o=0;class a{constructor(){this.id=o++,this.name="",this.children=[],this.position=new n.Vector3,this.rotation=new n.Vector3,this.matrix=new n.Matrix4,this.matrixWorld=new n.Matrix4,this.quaternion=new n.Quaternion,this.eulerOrder="XYZ",this.up=new n.Vector3(0,1,0),this.scale=new n.Vector3(1,1,1),this.matrixAutoUpdate=!0,this.matrixWorldNeedsUpdate=!0,this.rotationAutoUpdate=!0,this.useQuaternion=!1,this.visible=!0}lookAt(t){this.matrix.lookAt(t,this.position,this.up),this.rotationAutoUpdate&&(!0===this.useQuaternion?console.error("Unimplemented math operation."):this.rotation instanceof n.Vector3&&this.rotation.setEulerFromRotationMatrix(this.matrix,this.eulerOrder))}add(t){if(t!==this){t.parent=this,this.children.push(t);for(var e=this;void 0!==e.parent;)e=e.parent;void 0!==e&&e instanceof s&&e.__addObject(t)}else console.error("Can't add $3Dmol.Object3D to itself")}remove(t){var e=this.children.indexOf(t);if(-1!==e){t.parent=void 0,this.children.splice(e,1);for(var r=this;void 0!==r.parent;)r=r.parent;void 0!==r&&r instanceof s&&r.__removeObject(t)}}vrml(t){t||(t=" ");var e=2*Math.atan2(this.quaternion.lengthxyz(),this.quaternion.w),r=0,n=0,i=0;if(0!=e){let t=Math.sin(e/2);r=this.quaternion.x/t,n=this.quaternion.y/t,i=this.quaternion.z/t}var o=t+"Transform {\n"+t+" center "+this.position.x+" "+this.position.y+" "+this.position.z+"\n"+t+" rotation "+r+" "+n+" "+i+" "+e+"\n"+t+" children [\n";this.geometry&&(o+=this.geometry.vrml(t,this.material));for(var a=0;a{"use strict";r.r(e),r.d(e,{Projector:()=>i});const n=new(r("./src/WebGL/math/index.ts").Matrix4);class i{static unprojectVector(t,e){return e.projectionMatrixInverse.getInverse(e.projectionMatrix),n.multiplyMatrices(e.matrixWorld,e.projectionMatrixInverse),t.applyProjection(n)}static projectVector(t,e){return e.matrixWorldInverse.getInverse(e.matrixWorld),n.multiplyMatrices(e.projectionMatrix,e.matrixWorldInverse),t.applyProjection(n)}projectVector(t,e){return i.projectVector(t,e)}unprojectVector(t,e){return i.unprojectVector(t,e)}}},"./src/WebGL/core/Raycaster.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Raycaster:()=>s,intersectObject:()=>v});var n=r("./src/WebGL/math/index.ts"),i=r("./src/WebGL/shapes/index.ts");const o=(t,e)=>t.distance-e.distance,a=new n.Matrix4;class s{constructor(t,e,r,i){this.precision=1e-4,this.linePrecision=.2,this.ray=new n.Ray(t,e),this.ray.direction.lengthSq()>0&&this.ray.direction.normalize(),this.near=i||0,this.far=r||1/0}set(t,e){this.ray.set(t,e)}setFromCamera(t,e){e.ortho?(this.ray.origin.set(t.x,t.y,(e.near+e.far)/(e.near-e.far)).unproject(e),this.ray.direction.set(0,0,-1).transformDirection(e.matrixWorld)):(this.ray.origin.setFromMatrixPosition(e.matrixWorld),this.ray.direction.set(t.x,t.y,t.z),e.projectionMatrixInverse.getInverse(e.projectionMatrix),a.multiplyMatrices(e.matrixWorld,e.projectionMatrixInverse),this.ray.direction.applyProjection(a),this.ray.direction.sub(this.ray.origin).normalize())}intersectObjects(t,e){for(var r=[],n=0,i=e.length;nMath.min(Math.max(t,-1),1);var c=new i.Sphere,u=new i.Cylinder,h=new i.Triangle,d=new n.Vector3,f=new n.Vector3,p=new n.Vector3,m=new n.Vector3,g=new n.Vector3;function v(t,e,r,n){if(g.getPositionFromMatrix(t.matrixWorld),void 0===e.intersectionShape)return n;var o,a,s,v,b,y,x,_,w,k,A,M,T,S,C=e.intersectionShape,E=r.linePrecision,L=(E*=t.matrixWorld.getMaxScaleOnAxis())*E;if(void 0!==e.boundingSphere&&e.boundingSphere instanceof i.Sphere&&(c.copy(e.boundingSphere),c.applyMatrix4(t.matrixWorld),!r.ray.isIntersectionSphere(c)))return n;for(o=0,a=C.triangle.length;o=0)continue;if(d.subVectors(h.a,r.ray.origin),(x=s.dot(d)/v)<0)continue;f.copy(r.ray.direction).multiplyScalar(x).add(r.ray.origin),f.sub(h.a),p.copy(h.b).sub(h.a),m.copy(h.c).sub(h.a);var z=p.dot(m),O=p.lengthSq(),D=m.lengthSq();if((M=(O*f.dot(m)-z*f.dot(p))/(O*D-z*z))<0||M>1)continue;if((A=(f.dot(p)-M*z)/O)<0||A>1||A+M>1)continue;n.push({clickable:e,distance:x})}for(o=0,a=C.cylinder.length;ou.lengthSq()||M<0)continue;n.push({clickable:e,distance:x})}}for(o=0,a=C.line.length;o{"use strict";r.r(e),r.d(e,{Texture:()=>s,TextureIdCount:()=>l});var n=r("./src/WebGL/constants/TextureConstants.ts"),i=r("./src/WebGL/math/index.ts"),o=r("./src/WebGL/core/EventDispatcher.ts"),a=r("./src/WebGL/core/UVMapping.ts");class s extends o.EventDispatcher{constructor(t,e){super(),this.id=l++,this.name="",this.image=t,this.mapping=new a.UVMapping,this.wrapS=n.ClampToEdgeWrapping,this.wrapT=n.ClampToEdgeWrapping,this.anisotropy=1,e?(this.format=n.RFormat,this.type=n.FloatType,this.premultiplyAlpha=!1,this.flipY=!1,this.unpackAlignment=1,this.magFilter=n.NearestFilter,this.minFilter=n.NearestFilter):(this.format=n.RGBAFormat,this.type=n.UnsignedByteType,this.offset=new i.Vector2(0,0),this.repeat=new i.Vector2(1,1),this.premultiplyAlpha=!1,this.flipY=!0,this.unpackAlignment=4,this.magFilter=n.LinearFilter,this.minFilter=n.LinearMipMapLinearFilter),this.needsUpdate=!1,this.onUpdate=null}clone(t=new s){return t.image=this.image,t.mapping=this.mapping,t.wrapS=this.wrapS,t.wrapT=this.wrapT,t.magFilter=this.magFilter,t.minFilter=this.minFilter,t.anisotropy=this.anisotropy,t.format=this.format,t.type=this.type,t.offset.copy(this.offset),t.repeat.copy(this.repeat),t.premultiplyAlpha=this.premultiplyAlpha,t.flipY=this.flipY,t.unpackAlignment=this.unpackAlignment,t}dispose(){this.dispatchEvent({type:"dispose"})}}let l=0},"./src/WebGL/core/UVMapping.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{UVMapping:()=>n});class n{}},"./src/WebGL/core/index.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{EventDispatcher:()=>n.EventDispatcher,Geometry:()=>i.Geometry,GeometryGroup:()=>i.GeometryGroup,GeometryIDCount:()=>i.GeometryIDCount,Light:()=>o.Light,Object3D:()=>o.Object3D,Object3DIDCount:()=>o.Object3DIDCount,Projector:()=>a.Projector,Raycaster:()=>s.Raycaster,Scene:()=>o.Scene,Texture:()=>l.Texture,TextureIdCount:()=>l.TextureIdCount,UVMapping:()=>c.UVMapping,intersectObject:()=>s.intersectObject});var n=r("./src/WebGL/core/EventDispatcher.ts"),i=r("./src/WebGL/core/Geometry.ts"),o=r("./src/WebGL/core/Object3D.ts"),a=r("./src/WebGL/core/Projector.ts"),s=r("./src/WebGL/core/Raycaster.ts"),l=r("./src/WebGL/core/Texture.ts"),c=r("./src/WebGL/core/UVMapping.ts")},"./src/WebGL/index.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{BackSide:()=>n.BackSide,Camera:()=>u.Camera,ClampToEdgeWrapping:()=>n.ClampToEdgeWrapping,Coloring:()=>n.Coloring,Cylinder:()=>c.Cylinder,DoubleSide:()=>n.DoubleSide,EventDispatcher:()=>i.EventDispatcher,FloatType:()=>n.FloatType,Fog:()=>h.Fog,FrontSide:()=>n.FrontSide,Geometry:()=>i.Geometry,GeometryGroup:()=>i.GeometryGroup,GeometryIDCount:()=>i.GeometryIDCount,ImposterMaterial:()=>o.ImposterMaterial,InstancedMaterial:()=>o.InstancedMaterial,Light:()=>i.Light,Line:()=>s.Line,LineBasicMaterial:()=>o.LineBasicMaterial,LineStyle:()=>s.LineStyle,LinearFilter:()=>n.LinearFilter,LinearMipMapLinearFilter:()=>n.LinearMipMapLinearFilter,Material:()=>o.Material,MaterialIdCount:()=>o.MaterialIdCount,Matrix3:()=>a.Matrix3,Matrix4:()=>a.Matrix4,Mesh:()=>s.Mesh,MeshDoubleLambertMaterial:()=>o.MeshDoubleLambertMaterial,MeshLambertMaterial:()=>o.MeshLambertMaterial,MeshOutlineMaterial:()=>o.MeshOutlineMaterial,NearestFilter:()=>n.NearestFilter,Object3D:()=>i.Object3D,Object3DIDCount:()=>i.Object3DIDCount,Projector:()=>i.Projector,Quaternion:()=>a.Quaternion,R32Format:()=>n.R32Format,RFormat:()=>n.RFormat,RGBAFormat:()=>n.RGBAFormat,Ray:()=>a.Ray,Raycaster:()=>i.Raycaster,Renderer:()=>d.Renderer,Scene:()=>i.Scene,ShaderLib:()=>l.ShaderLib,ShaderUtils:()=>l.ShaderUtils,Shading:()=>n.Shading,Sphere:()=>c.Sphere,SphereImposterMaterial:()=>o.SphereImposterMaterial,SphereImposterOutlineMaterial:()=>o.SphereImposterOutlineMaterial,Sprite:()=>s.Sprite,SpriteAlignment:()=>n.SpriteAlignment,SpriteMaterial:()=>o.SpriteMaterial,SpritePlugin:()=>f.SpritePlugin,StickImposterMaterial:()=>o.StickImposterMaterial,StickImposterOutlineMaterial:()=>o.StickImposterOutlineMaterial,Texture:()=>i.Texture,TextureIdCount:()=>i.TextureIdCount,TextureOperations:()=>n.TextureOperations,Triangle:()=>c.Triangle,UVMapping:()=>i.UVMapping,UnsignedByteType:()=>n.UnsignedByteType,Vector2:()=>a.Vector2,Vector3:()=>a.Vector3,VolumetricMaterial:()=>o.VolumetricMaterial,basic:()=>l.basic,clamp:()=>a.clamp,clone:()=>l.clone,conversionMatrix3:()=>a.conversionMatrix3,degToRad:()=>a.degToRad,instanced:()=>l.instanced,intersectObject:()=>i.intersectObject,lambert:()=>l.lambert,lambertdouble:()=>l.lambertdouble,outline:()=>l.outline,screen:()=>l.screen,screenaa:()=>l.screenaa,sphereimposter:()=>l.sphereimposter,sphereimposteroutline:()=>l.sphereimposteroutline,sprite:()=>l.sprite,stickimposter:()=>l.stickimposter,stickimposteroutline:()=>l.stickimposteroutline,volumetric:()=>l.volumetric});var n=r("./src/WebGL/constants/index.ts"),i=r("./src/WebGL/core/index.ts"),o=r("./src/WebGL/materials/index.ts"),a=r("./src/WebGL/math/index.ts"),s=r("./src/WebGL/objects/index.ts"),l=r("./src/WebGL/shaders/index.ts"),c=r("./src/WebGL/shapes/index.ts"),u=r("./src/WebGL/Camera.ts"),h=r("./src/WebGL/Fog.ts"),d=r("./src/WebGL/Renderer.ts"),f=r("./src/WebGL/SpritePlugin.ts")},"./src/WebGL/materials/ImposterMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{ImposterMaterial:()=>l});var n=r("./src/WebGL/constants/Coloring.ts"),i=r("./src/WebGL/constants/Shading.ts"),o=r("./src/colors.ts"),a=r("./src/WebGL/math/index.ts"),s=r("./src/WebGL/materials/Material.ts");class l extends s.Material{constructor(t){super(),this.color=new o.Color(16777215),this.ambient=new o.Color(1048575),this.emissive=new o.Color(0),this.imposter=!0,this.wrapAround=!1,this.wrapRGB=new a.Vector3(1,1,1),this.map=void 0,this.lightMap=null,this.specularMap=null,this.envMap=null,this.reflectivity=1,this.refractionRatio=.98,this.fog=!0,this.wireframe=!1,this.wireframeLinewidth=1,this.wireframeLinecap="round",this.wireframeLinejoin="round",this.shading=i.Shading.SmoothShading,this.shaderID=null,this.vertexColors=n.Coloring.NoColors,this.skinning=!1,this.setValues(t)}clone(t=new l){return super.clone.call(this,t),t.color.copy(this.color),t.ambient.copy(this.ambient),t.emissive.copy(this.emissive),t.wrapAround=this.wrapAround,t.wrapRGB.copy(this.wrapRGB),t.map=this.map,t.lightMap=this.lightMap,t.specularMap=this.specularMap,t.envMap=this.envMap,t.combine=this.combine,t.reflectivity=this.reflectivity,t.refractionRatio=this.refractionRatio,t.fog=this.fog,t.shading=this.shading,t.shaderID=this.shaderID,t.vertexColors=this.vertexColors,t.skinning=this.skinning,t.morphTargets=this.morphTargets,t.morphNormals=this.morphNormals,t}}},"./src/WebGL/materials/InstancedMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{InstancedMaterial:()=>l});var n=r("./src/WebGL/constants/Coloring.ts"),i=r("./src/WebGL/constants/Shading.ts"),o=r("./src/colors.ts"),a=r("./src/WebGL/math/index.ts"),s=r("./src/WebGL/materials/Material.ts");class l extends s.Material{constructor(t){super(),this.color=new o.Color(16777215),this.ambient=new o.Color(1048575),this.emissive=new o.Color(0),this.wrapAround=!1,this.wrapRGB=new a.Vector3(1,1,1),this.map=void 0,this.lightMap=null,this.specularMap=null,this.envMap=null,this.reflectivity=1,this.refractionRatio=.98,this.fog=!0,this.wireframe=!1,this.wireframeLinewidth=1,this.wireframeLinecap="round",this.wireframeLinejoin="round",this.shading=i.Shading.SmoothShading,this.shaderID="instanced",this.vertexColors=n.Coloring.NoColors,this.skinning=!1,this.sphere=null,this.setValues(t)}clone(t=new l){return super.clone.call(this,t),t.color.copy(this.color),t.ambient.copy(this.ambient),t.emissive.copy(this.emissive),t.wrapAround=this.wrapAround,t.wrapRGB.copy(this.wrapRGB),t.map=this.map,t.lightMap=this.lightMap,t.specularMap=this.specularMap,t.envMap=this.envMap,t.combine=this.combine,t.reflectivity=this.reflectivity,t.refractionRatio=this.refractionRatio,t.fog=this.fog,t.shading=this.shading,t.shaderID=this.shaderID,t.vertexColors=this.vertexColors,t.skinning=this.skinning,t.morphTargets=this.morphTargets,t.morphNormals=this.morphNormals,t.sphere=this.sphere,t}}},"./src/WebGL/materials/LineBasicMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{LineBasicMaterial:()=>o});var n=r("./src/colors.ts"),i=r("./src/WebGL/materials/Material.ts");class o extends i.Material{constructor(t){super(),this.color=new n.Color(16777215),this.linewidth=1,this.linecap="round",this.linejoin="round",this.vertexColors=!1,this.fog=!0,this.shaderID="basic",this.setValues(t)}clone(t=new o){return super.clone.call(this,t),t.color.copy(this.color),t}}},"./src/WebGL/materials/Material.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Material:()=>s,MaterialIdCount:()=>l});var n=r("./src/WebGL/constants/Sides.ts"),i=r("./src/WebGL/core/index.ts"),o=r("./src/WebGL/math/index.ts"),a=r("./src/colors.ts");class s extends i.EventDispatcher{constructor(){super(...arguments),this.id=l++,this.name="",this.side=n.FrontSide,this.opacity=1,this.transparent=!1,this.depthTest=!0,this.depthWrite=!0,this.stencilTest=!0,this.polygonOffset=!1,this.polygonOffsetFactor=0,this.polygonOffsetUnits=0,this.alphaTest=0,this.visible=!0,this.needsUpdate=!0,this.outline=!1,this.wireframe=!1}setValues(t={}){if(void 0!==t)for(var e in t){var r=t[e];if(void 0!==r){if(e in this){var n=this[e];n instanceof a.Color&&r instanceof a.Color?n.copy(r):n instanceof a.Color?n.set(r):n instanceof o.Vector3&&r instanceof o.Vector3?n.copy(r):this[e]=r}}else console.warn("$3Dmol.Material: '"+e+"' parameter is undefined.")}}clone(t=new s){return t.name=this.name,t.side=this.side,t.opacity=this.opacity,t.transparent=this.transparent,t.depthTest=this.depthTest,t.depthWrite=this.depthWrite,t.stencilTest=this.stencilTest,t.polygonOffset=this.polygonOffset,t.polygonOffsetFactor=this.polygonOffsetFactor,t.polygonOffsetUnits=this.polygonOffsetUnits,t.alphaTest=this.alphaTest,t.overdraw=this.overdraw,t.visible=this.visible,t}dispose(){this.dispatchEvent({type:"dispose"})}}let l=0},"./src/WebGL/materials/MeshDoubleLambertMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{MeshDoubleLambertMaterial:()=>o});var n=r("./src/WebGL/constants/Sides.ts"),i=r("./src/WebGL/materials/MeshLambertMaterial.ts");class o extends i.MeshLambertMaterial{constructor(t){super(t),this.shaderID="lambertdouble",this.side=n.DoubleSide,this.outline=!1}clone(t=new o){return super.clone.call(this,t),t}}},"./src/WebGL/materials/MeshLambertMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{MeshLambertMaterial:()=>l});var n=r("./src/WebGL/constants/Coloring.ts"),i=r("./src/WebGL/constants/Shading.ts"),o=r("./src/WebGL/materials/Material.ts"),a=r("./src/colors.ts"),s=r("./src/WebGL/math/index.ts");class l extends o.Material{constructor(t){super(),this.color=new a.Color(16777215),this.ambient=new a.Color(1048575),this.emissive=new a.Color(0),this.wrapAround=!1,this.wrapRGB=new s.Vector3(1,1,1),this.map=void 0,this.lightMap=null,this.specularMap=null,this.envMap=null,this.reflectivity=1,this.refractionRatio=.98,this.fog=!0,this.wireframe=!1,this.wireframeLinewidth=1,this.wireframeLinecap="round",this.wireframeLinejoin="round",this.shading=i.Shading.SmoothShading,this.shaderID="lambert",this.vertexColors=n.Coloring.NoColors,this.skinning=!1,this.setValues(t)}clone(t=new l){return super.clone.call(this,t),t.color.copy(this.color),t.ambient.copy(this.ambient),t.emissive.copy(this.emissive),t.wrapAround=this.wrapAround,t.wrapRGB.copy(this.wrapRGB),t.map=this.map,t.lightMap=this.lightMap,t.specularMap=this.specularMap,t.envMap=this.envMap,t.combine=this.combine,t.reflectivity=this.reflectivity,t.refractionRatio=this.refractionRatio,t.fog=this.fog,t.shading=this.shading,t.shaderID=this.shaderID,t.vertexColors=this.vertexColors,t.skinning=this.skinning,t.morphTargets=this.morphTargets,t.morphNormals=this.morphNormals,t}}},"./src/WebGL/materials/MeshOutlineMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{MeshOutlineMaterial:()=>o});var n=r("./src/colors.ts"),i=r("./src/WebGL/materials/Material.ts");class o extends i.Material{constructor(t){super(),t=t||{},this.fog=!0,this.shaderID="outline",this.wireframe=!1,this.outlineColor=t.color||new n.Color(0,0,0),this.outlineWidth=t.width||.1,this.outlinePushback=t.pushback||1}clone(t=new o){return super.clone.call(this,t),t.fog=this.fog,t.shaderID=this.shaderID,t.wireframe=this.wireframe,t}}},"./src/WebGL/materials/SphereImposterMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{SphereImposterMaterial:()=>i});var n=r("./src/WebGL/materials/ImposterMaterial.ts");class i extends n.ImposterMaterial{constructor(t){super(t),this.shaderID="sphereimposter",this.setValues(t)}clone(t=new i){return super.clone.call(this,t),t}}},"./src/WebGL/materials/SphereImposterOutlineMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{SphereImposterOutlineMaterial:()=>o});var n=r("./src/colors.ts"),i=r("./src/WebGL/materials/ImposterMaterial.ts");class o extends i.ImposterMaterial{constructor(t){super(t),t=t||{},this.shaderID="sphereimposteroutline",this.outlineColor=t.color||new n.Color(0,0,0),this.outlineWidth=t.width||.1,this.outlinePushback=t.pushback||1,this.setValues(t)}clone(t=new o){return super.clone.call(this,t),t.outlineColor=this.outlineColor,t.outlineWidth=this.outlineWidth,t.outlinePushback=this.outlinePushback,t}}},"./src/WebGL/materials/SpriteMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{SpriteMaterial:()=>l});var n=r("./src/WebGL/constants/SpriteAlignment.ts"),i=r("./src/WebGL/core/Texture.ts"),o=r("./src/colors.ts"),a=r("./src/WebGL/math/index.ts"),s=r("./src/WebGL/materials/Material.ts");class l extends s.Material{constructor(t){super(),this.color=new o.Color(16777215),this.map=new i.Texture,this.useScreenCoordinates=!0,this.fog=!1,this.uvOffset=new a.Vector2(0,0),this.uvScale=new a.Vector2(1,1),this.depthTest=!this.useScreenCoordinates,this.sizeAttenuation=!this.useScreenCoordinates,this.screenOffset=this.screenOffset,this.scaleByViewPort=!this.sizeAttenuation,this.alignment=n.SpriteAlignment.center.clone(),this.setValues(t),void 0===(t=t||{}).depthTest&&(this.depthTest=!this.useScreenCoordinates),void 0===t.sizeAttenuation&&(this.sizeAttenuation=!this.useScreenCoordinates),void 0===t.scaleByViewPort&&(this.scaleByViewPort=!this.sizeAttenuation)}clone(t=new l){return super.clone.call(this,t),t.color.copy(this.color),t.map=this.map,t.useScreenCoordinates=this.useScreenCoordinates,t.screenOffset=this.screenOffset,t.sizeAttenuation=this.sizeAttenuation,t.scaleByViewport=this.scaleByViewPort,t.alignment.copy(this.alignment),t.uvOffset.copy(this.uvOffset),t}}},"./src/WebGL/materials/StickImposterMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{StickImposterMaterial:()=>i});var n=r("./src/WebGL/materials/ImposterMaterial.ts");class i extends n.ImposterMaterial{constructor(t){super(t),this.shaderID="stickimposter",this.setValues(t)}clone(t=new i){return super.clone.call(this,t),t}}},"./src/WebGL/materials/StickImposterOutlineMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{StickImposterOutlineMaterial:()=>o});var n=r("./src/colors.ts"),i=r("./src/WebGL/materials/ImposterMaterial.ts");class o extends i.ImposterMaterial{constructor(t={}){super(t),this.shaderID="stickimposteroutline",this.outlineColor=new n.Color(0,0,0),this.outlineWidth=.1,this.outlinePushback=1,t.color&&(this.outlineColor=t.color),t.width&&(this.outlineWidth=t.width),t.pushback&&(this.outlinePushback=t.pushback),this.setValues(t)}clone(t=new o){return super.clone.call(this,t),t.outlineColor=this.outlineColor,t.outlineWidth=this.outlineWidth,t.outlinePushback=this.outlinePushback,t}}},"./src/WebGL/materials/VolumetricMaterial.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{VolumetricMaterial:()=>a});var n=r("./src/WebGL/constants/Sides.ts"),i=r("./src/colors.ts"),o=r("./src/WebGL/materials/Material.ts");class a extends o.Material{constructor(t){super(),this.transparent=!1,this.volumetric=!0,this.color=new i.Color(16777215),this.transferfn=null,this.map=void 0,this.extent=[],this.maxdepth=100,this.unit=0,this.texmatrix=null,this.transfermin=-1,this.transfermax=1,this.subsamples=5,this.shaderID="volumetric",this.side=n.FrontSide,this.setValues(t)}clone(t=new a){return super.clone.call(this,t),t.transparent=this.transparent,t.volumetric=this.volumetric,t.color=this.color,t.transferfn=this.transferfn,t.map=this.map,t.extent=this.extent,t.maxdepth=this.maxdepth,t.unit=this.unit,t.texmatrix=this.texmatrix,t.transfermin=this.transfermin,t.transfermax=this.transfermax,t.subsamples=this.subsamples,t.shaderID=this.shaderID,t.side=this.side,t}}},"./src/WebGL/materials/index.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{ImposterMaterial:()=>n.ImposterMaterial,InstancedMaterial:()=>i.InstancedMaterial,LineBasicMaterial:()=>o.LineBasicMaterial,Material:()=>a.Material,MaterialIdCount:()=>a.MaterialIdCount,MeshDoubleLambertMaterial:()=>s.MeshDoubleLambertMaterial,MeshLambertMaterial:()=>l.MeshLambertMaterial,MeshOutlineMaterial:()=>c.MeshOutlineMaterial,SphereImposterMaterial:()=>u.SphereImposterMaterial,SphereImposterOutlineMaterial:()=>h.SphereImposterOutlineMaterial,SpriteMaterial:()=>d.SpriteMaterial,StickImposterMaterial:()=>f.StickImposterMaterial,StickImposterOutlineMaterial:()=>p.StickImposterOutlineMaterial,VolumetricMaterial:()=>m.VolumetricMaterial});var n=r("./src/WebGL/materials/ImposterMaterial.ts"),i=r("./src/WebGL/materials/InstancedMaterial.ts"),o=r("./src/WebGL/materials/LineBasicMaterial.ts"),a=r("./src/WebGL/materials/Material.ts"),s=r("./src/WebGL/materials/MeshDoubleLambertMaterial.ts"),l=r("./src/WebGL/materials/MeshLambertMaterial.ts"),c=r("./src/WebGL/materials/MeshOutlineMaterial.ts"),u=r("./src/WebGL/materials/SphereImposterMaterial.ts"),h=r("./src/WebGL/materials/SphereImposterOutlineMaterial.ts"),d=r("./src/WebGL/materials/SpriteMaterial.ts"),f=r("./src/WebGL/materials/StickImposterMaterial.ts"),p=r("./src/WebGL/materials/StickImposterOutlineMaterial.ts"),m=r("./src/WebGL/materials/VolumetricMaterial.ts")},"./src/WebGL/math/Quaternion.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Quaternion:()=>n});class n{constructor(t,e,r,n){this.x=t||0,this.y=e||0,this.z=r||0,this.w=void 0!==n?n:1}set(t,e,r,n){return this.x=t,this.y=e,this.z=r,this.w=n,this}copy(t){return this.x=t.x,this.y=t.y,this.z=t.z,this.w=t.w,this}conjugate(){return this.x*=-1,this.y*=-1,this.z*=-1,this}inverse(){return this.conjugate().normalize()}length(){return Math.sqrt(this.x*this.x+this.y*this.y+this.z*this.z+this.w*this.w)}lengthxyz(){return Math.sqrt(this.x*this.x+this.y*this.y+this.z*this.z)}normalize(){let t=this.length();return 0===t?(this.x=0,this.y=0,this.z=0,this.w=1):(t=1/t,this.x*=t,this.y*=t,this.z*=t,this.w*=t),this}multiply(t){return this.multiplyQuaternions(this,t)}multiplyScalar(t){return this.x*=t,this.y*=t,this.z*=t,this.w*=t,this}multiplyQuaternions(t,e){const r=t.x,n=t.y,i=t.z,o=t.w,a=e.x,s=e.y,l=e.z,c=e.w;return this.x=r*c+o*a+n*l-i*s,this.y=n*c+o*s+i*a-r*l,this.z=i*c+o*l+r*s-n*a,this.w=o*c-r*a-n*s-i*l,this}sub(t){return this.x-=t.x,this.y-=t.y,this.z-=t.z,this.w-=t.w,this}clone(){return new n(this.x,this.y,this.z,this.w)}setFromEuler(t){const e=Math.cos(t.x/2),r=Math.cos(t.y/2),n=Math.cos(t.z/2),i=Math.sin(t.x/2),o=Math.sin(t.y/2),a=Math.sin(t.z/2);return this.x=i*r*n+e*o*a,this.y=e*o*n-i*r*a,this.z=e*r*a+i*o*n,this.w=e*r*n-i*o*a,this}}},"./src/WebGL/math/Vector2.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Vector2:()=>n});class n{constructor(t,e){this.x=t||0,this.y=e||0}set(t,e){return this.x=t,this.y=e,this}subVectors(t,e){return this.x=t.x-e.x,this.y=t.y-e.y,this}copy(t){return this.x=t.x,this.y=t.y,this}clone(){return new n(this.x,this.y)}}},"./src/WebGL/math/index.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Matrix3:()=>l.Matrix3,Matrix4:()=>l.Matrix4,Quaternion:()=>n.Quaternion,Ray:()=>l.Ray,Vector2:()=>i.Vector2,Vector3:()=>l.Vector3,clamp:()=>o.clamp,conversionMatrix3:()=>a.conversionMatrix3,degToRad:()=>s.degToRad});var n=r("./src/WebGL/math/Quaternion.ts"),i=r("./src/WebGL/math/Vector2.ts"),o=r("./src/WebGL/math/utils/clamp.ts"),a=r("./src/WebGL/math/utils/conversionMatrix3.ts"),s=r("./src/WebGL/math/utils/degToRad.ts"),l=r("./src/WebGL/math/math.ts")},"./src/WebGL/math/math.ts":(t,e,r)=>{"use strict";r.r(e),r.d(e,{Matrix3:()=>d,Matrix4:()=>u,Ray:()=>f,Vector3:()=>h});var n,i,o,a,s,l=r("./src/WebGL/math/utils/degToRad.ts"),c=r("./src/WebGL/math/utils/clamp.ts");class u{constructor(t=1,e=0,r=0,n=0,i=0,o=1,a=0,s=0,l=0,c=0,u=1,h=0,d=0,f=0,p=0,m=1){void 0!==t&&"number"!=typeof t?this.elements=new Float32Array(t):(this.elements=new Float32Array(16),this.elements[0]=t,this.elements[4]=e,this.elements[8]=r,this.elements[12]=n,this.elements[1]=i,this.elements[5]=o,this.elements[9]=a,this.elements[13]=s,this.elements[2]=l,this.elements[6]=c,this.elements[10]=u,this.elements[14]=h,this.elements[3]=d,this.elements[7]=f,this.elements[11]=p,this.elements[15]=m)}makeScale(t,e,r){throw new Error("Method not implemented.")}set(t,e,r,n,i,o,a,s,l,c,u,h,d,f,p,m){const g=this.elements;return g[0]=t,g[4]=e,g[8]=r,g[12]=n,g[1]=i,g[5]=o,g[9]=a,g[13]=s,g[2]=l,g[6]=c,g[10]=u,g[14]=h,g[3]=d,g[7]=f,g[11]=p,g[15]=m,this}identity(){return this.set(1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1),this}copy(t){const e=t.elements;return this.set(e[0],e[4],e[8],e[12],e[1],e[5],e[9],e[13],e[2],e[6],e[10],e[14],e[3],e[7],e[11],e[15]),this}matrix3FromTopLeft(){const t=this.elements;return new d(t[0],t[4],t[8],t[1],t[5],t[9],t[2],t[6],t[10])}setRotationFromEuler(t,e){const r=this.elements,{x:n,y:i,z:o}=t,a=Math.cos(n),s=Math.sin(n),l=Math.cos(i),c=Math.sin(i),u=Math.cos(o),h=Math.sin(o);if(void 0===e||"XYZ"===e){const t=a*u,e=a*h,n=s*u,i=s*h;r[0]=l*u,r[4]=-l*h,r[8]=c,r[1]=e+n*c,r[5]=t-i*c,r[9]=-s*l,r[2]=i-t*c,r[6]=n+e*c,r[10]=a*l}else console.error(`Error with matrix4 setRotationFromEuler. Order: ${e}`);return this}setRotationFromQuaternion(t){const e=this.elements,{x:r,y:n,z:i,w:o}=t,a=r+r,s=n+n,l=i+i,c=r*a,u=r*s,h=r*l,d=n*s,f=n*l,p=i*l,m=o*a,g=o*s,v=o*l;return e[0]=1-(d+p),e[4]=u-v,e[8]=h+g,e[1]=u+v,e[5]=1-(c+p),e[9]=f-m,e[2]=h-g,e[6]=f+m,e[10]=1-(c+d),this}multiplyMatrices(t,e){const r=t.elements,n=e.elements,i=this.elements,o=r[0],a=r[4],s=r[8],l=r[12],c=r[1],u=r[5],h=r[9],d=r[13],f=r[2],p=r[6],m=r[10],g=r[14],v=r[3],b=r[7],y=r[11],x=r[15],_=n[0],w=n[4],k=n[8],A=n[12],M=n[1],T=n[5],S=n[9],C=n[13],E=n[2],L=n[6],z=n[10],O=n[14],D=n[3],I=n[7],F=n[11],R=n[15];return i[0]=o*_+a*M+s*E+l*D,i[4]=o*w+a*T+s*L+l*I,i[8]=o*k+a*S+s*z+l*F,i[12]=o*A+a*C+s*O+l*R,i[1]=c*_+u*M+h*E+d*D,i[5]=c*w+u*T+h*L+d*I,i[9]=c*k+u*S+h*z+d*F,i[13]=c*A+u*C+h*O+d*R,i[2]=f*_+p*M+m*E+g*D,i[6]=f*w+p*T+m*L+g*I,i[10]=f*k+p*S+m*z+g*F,i[14]=f*A+p*C+m*O+g*R,i[3]=v*_+b*M+y*E+x*D,i[7]=v*w+b*T+y*L+x*I,i[11]=v*k+b*S+y*z+x*F,i[15]=v*A+b*C+y*O+x*R,this}multiplyScalar(t){const e=this.elements;return e[0]*=t,e[4]*=t,e[8]*=t,e[12]*=t,e[1]*=t,e[5]*=t,e[9]*=t,e[13]*=t,e[2]*=t,e[6]*=t,e[10]*=t,e[14]*=t,e[3]*=t,e[7]*=t,e[11]*=t,e[15]*=t,this}makeTranslation(t,e,r){return this.set(1,0,0,t,0,1,0,e,0,0,1,r,0,0,0,1),this}snap(t){t||(t=4);const e=Math.pow(10,4),r=this.elements;for(let t=0;t<16;t++){const n=Math.round(r[t]);n===Math.round(r[t]*e)/e&&(r[t]=n)}return this}transpose(){const t=this.elements;let e;return e=t[1],t[1]=t[4],t[4]=e,e=t[2],t[2]=t[8],t[8]=e,e=t[6],t[6]=t[9],t[9]=e,e=t[3],t[3]=t[12],t[12]=e,e=t[7],t[7]=t[13],t[13]=e,e=t[11],t[11]=t[14],t[14]=e,this}setPosition(t){const e=this.elements;return e[12]=t.x,e[13]=t.y,e[14]=t.z,this}translate(t){const e=this.elements;return e[12]+=t.x,e[13]+=t.y,e[14]+=t.z,this}getInverse(t,e){const r=this.elements,n=t.elements,i=n[0],o=n[4],a=n[8],s=n[12],l=n[1],c=n[5],u=n[9],h=n[13],d=n[2],f=n[6],p=n[10],m=n[14],g=n[3],v=n[7],b=n[11],y=n[15];r[0]=u*m*v-h*p*v+h*f*b-c*m*b-u*f*y+c*p*y,r[4]=s*p*v-a*m*v-s*f*b+o*m*b+a*f*y-o*p*y,r[8]=a*h*v-s*u*v+s*c*b-o*h*b-a*c*y+o*u*y,r[12]=s*u*f-a*h*f-s*c*p+o*h*p+a*c*m-o*u*m,r[1]=h*p*g-u*m*g-h*d*b+l*m*b+u*d*y-l*p*y,r[5]=a*m*g-s*p*g+s*d*b-i*m*b-a*d*y+i*p*y,r[9]=s*u*g-a*h*g-s*l*b+i*h*b+a*l*y-i*u*y,r[13]=a*h*d-s*u*d+s*l*p-i*h*p-a*l*m+i*u*m,r[2]=c*m*g-h*f*g+h*d*v-l*m*v-c*d*y+l*f*y,r[6]=s*f*g-o*m*g-s*d*v+i*m*v+o*d*y-i*f*y,r[10]=o*h*g-s*c*g+s*l*v-i*h*v-o*l*y+i*c*y,r[14]=s*c*d-o*h*d-s*l*f+i*h*f+o*l*m-i*c*m,r[3]=u*f*g-c*p*g-u*d*v+l*p*v+c*d*b-l*f*b,r[7]=o*p*g-a*f*g+a*d*v-i*p*v-o*d*b+i*f*b,r[11]=a*c*g-o*u*g-a*l*v+i*u*v+o*l*b-i*c*b,r[15]=o*u*d-a*c*d+a*l*f-i*u*f-o*l*p+i*c*p;const x=i*r[0]+l*r[4]+d*r[8]+g*r[12];if(0===x){const t="Matrix4.getInverse(): can't invert matrix, determinant is 0";if(e)throw new Error(t);return console.warn(t),this.identity(),this}return this.multiplyScalar(1/x),this}isReflected(){const t=this.elements,e=t[0],r=t[4],n=t[8],i=t[1],o=t[5],a=t[9],s=t[2],l=t[6],c=t[10];return e*o*c+i*l*n+s*r*a-s*o*n-i*r*c-e*l*a<0}scale(t){const e=this.elements,{x:r}=t,{y:n}=t,{z:i}=t;return e[0]*=r,e[4]*=n,e[8]*=i,e[1]*=r,e[5]*=n,e[9]*=i,e[2]*=r,e[6]*=n,e[10]*=i,e[3]*=r,e[7]*=n,e[11]*=i,this}getMaxScaleOnAxis(){const t=this.elements,e=t[0]*t[0]+t[1]*t[1]+t[2]*t[2],r=t[4]*t[4]+t[5]*t[5]+t[6]*t[6],n=t[8]*t[8]+t[9]*t[9]+t[10]*t[10];return Math.sqrt(Math.max(e,Math.max(r,n)))}makeFrustum(t,e,r,n,i,o){const a=this.elements,s=2*i/(e-t),l=2*i/(n-r),c=(e+t)/(e-t),u=(n+r)/(n-r),h=-(o+i)/(o-i),d=-2*o*i/(o-i);return a[0]=s,a[4]=0,a[8]=c,a[12]=0,a[1]=0,a[5]=l,a[9]=u,a[13]=0,a[2]=0,a[6]=0,a[10]=h,a[14]=d,a[3]=0,a[7]=0,a[11]=-1,a[15]=0,this}makePerspective(t,e,r,n){const i=r*Math.tan((0,l.degToRad)(.5*t)),o=-i,a=o*e,s=i*e;return this.makeFrustum(a,s,o,i,r,n)}makeOrthographic(t,e,r,n,i,o){const a=this.elements,s=1/(e-t),l=1/(r-n),c=1/(o-i),u=(e+t)*s,h=(r+n)*l,d=(o+i)*c;return a[0]=2*s,a[4]=0,a[8]=0,a[12]=-u,a[1]=0,a[5]=2*l,a[9]=0,a[13]=-h,a[2]=0,a[6]=0,a[10]=-2*c,a[14]=-d,a[3]=0,a[7]=0,a[11]=0,a[15]=1,this}isEqual(t){const e=t.elements,r=this.elements;return r[0]===e[0]&&r[4]===e[4]&&r[8]===e[8]&&r[12]===e[12]&&r[1]===e[1]&&r[5]===e[5]&&r[9]===e[9]&&r[13]===e[13]&&r[2]===e[2]&&r[6]===e[6]&&r[10]===e[10]&&r[14]===e[14]&&r[3]===e[3]&&r[7]===e[7]&&r[11]===e[11]&&r[15]===e[15]}clone(){const t=this.elements;return new u(t[0],t[4],t[8],t[12],t[1],t[5],t[9],t[13],t[2],t[6],t[10],t[14],t[3],t[7],t[11],t[15])}isIdentity(){const t=this.elements;return 1===t[0]&&0===t[4]&&0===t[8]&&0===t[12]&&0===t[1]&&1===t[5]&&0===t[9]&&0===t[13]&&0===t[2]&&0===t[6]&&1===t[10]&&0===t[14]&&0===t[3]&&0===t[7]&&0===t[11]&&1===t[15]}isNearlyIdentity(t){return this.clone().snap(t).isIdentity()}getScale(t){const e=this.elements;return t=t||new h,o.set(e[0],e[1],e[2]),a.set(e[4],e[5],e[6]),s.set(e[8],e[9],e[10]),t.x=o.length(),t.y=a.length(),t.z=s.length(),t}lookAt(t,e,r){const n=this.elements;return s.subVectors(t,e).normalize(),0===s.length()&&(s.z=1),o.crossVectors(r,s).normalize(),0===o.length()&&(s.x+=1e-4,o.crossVectors(r,s).normalize()),a.crossVectors(s,o),n[0]=o.x,n[4]=a.x,n[8]=s.x,n[1]=o.y,n[5]=a.y,n[9]=s.y,n[2]=o.z,n[6]=a.z,n[10]=s.z,this}compose(t,e,r){const o=this.elements;return n.identity(),n.setRotationFromQuaternion(e),i.makeScale(r.x,r.y,r.z),this.multiplyMatrices(n,i),o[12]=t.x,o[13]=t.y,o[14]=t.z,this}}n=new u,i=new u;class h{constructor(t,e,r){this.x=t||0,this.y=e||0,this.z=r||0,this.atomid=void 0}set(t,e,r){return this.x=t,this.y=e,this.z=r,this}copy(t){return this.x=t.x,this.y=t.y,this.z=t.z,this}add(t){return this.x+=t.x,this.y+=t.y,this.z+=t.z,this}addVectors(t,e){return this.x=t.x+e.x,this.y=t.y+e.y,this.z=t.z+e.z,this}multiplyVectors(t,e){return this.x=t.x*e.x,this.y=t.y*e.y,this.z=t.z*e.z,this}sub(t){return this.x-=t.x,this.y-=t.y,this.z-=t.z,this}subVectors(t,e){return this.x=t.x-e.x,this.y=t.y-e.y,this.z=t.z-e.z,this}multiplyScalar(t){return this.x*=t,this.y*=t,this.z*=t,this}divideScalar(t){return 0!==t?(this.x/=t,this.y/=t,this.z/=t):(this.x=0,this.y=0,this.z=0),this}max(t){return this.x=Math.max(this.x,t.x),this.y=Math.max(this.y,t.y),this.z=Math.max(this.z,t.z),this}min(t){return this.x=Math.min(this.x,t.x),this.y=Math.min(this.y,t.y),this.z=Math.min(this.z,t.z),this}distanceTo(t){return Math.sqrt(this.distanceToSquared(t))}distanceToSquared(t){const e=this.x-t.x,r=this.y-t.y,n=this.z-t.z;return e*e+r*r+n*n}applyMatrix3(t){const{x:e}=this,{y:r}=this,{z:n}=this,i=t.elements;return this.x=i[0]*e+i[3]*r+i[6]*n,this.y=i[1]*e+i[4]*r+i[7]*n,this.z=i[2]*e+i[5]*r+i[8]*n,this}applyMatrix4(t){const{x:e}=this,{y:r}=this,{z:n}=this,i=t.elements;return this.x=i[0]*e+i[4]*r+i[8]*n+i[12],this.y=i[1]*e+i[5]*r+i[9]*n+i[13],this.z=i[2]*e+i[6]*r+i[10]*n+i[14],this}applyProjection(t){const{x:e}=this,{y:r}=this,{z:n}=this,i=t.elements,o=i[3]*e+i[7]*r+i[11]*n+i[15];return this.x=(i[0]*e+i[4]*r+i[8]*n+i[12])/o,this.y=(i[1]*e+i[5]*r+i[9]*n+i[13])/o,this.z=(i[2]*e+i[6]*r+i[10]*n+i[14])/o,this}applyQuaternion(t){const{x:e}=this,{y:r}=this,{z:n}=this,i=t.x,o=t.y,a=t.z,s=t.w,l={};l.x=2*(r*a-n*o),l.y=2*(n*i-e*a),l.z=2*(e*o-r*i);const c={};return c.x=l.y*a-l.z*o,c.y=l.z*i-l.x*a,c.z=l.x*o-l.y*i,this.x=e+s*l.x+c.x,this.y=r+s*l.y+c.y,this.z=n+s*l.z+c.z,this}negate(){return this.multiplyScalar(-1)}dot(t){return this.x*t.x+this.y*t.y+this.z*t.z}length(){return Math.sqrt(this.x*this.x+this.y*this.y+this.z*this.z)}lengthSq(){return this.x*this.x+this.y*this.y+this.z*this.z}normalize(){return this.divideScalar(this.length())}cross(t){const{x:e}=this,{y:r}=this,{z:n}=this;return this.x=r*t.z-n*t.y,this.y=n*t.x-e*t.z,this.z=e*t.y-r*t.x,this}crossVectors(t,e){return this.x=t.y*e.z-t.z*e.y,this.y=t.z*e.x-t.x*e.z,this.z=t.x*e.y-t.y*e.x,this}equals(t){return this.x==t.x&&this.y==t.y&&this.z==t.z}getPositionFromMatrix(t){return this.x=t.elements[12],this.y=t.elements[13],this.z=t.elements[14],this}setEulerFromRotationMatrix(t,e){const r=t.elements,n=r[0],i=r[4],o=r[8],a=r[5],s=r[9],l=r[6],u=r[10];return void 0===e||"XYZ"===e?(this.y=Math.asin((0,c.clamp)(o,-1,1)),Math.abs(o)<.99999?(this.x=Math.atan2(-s,u),this.z=Math.atan2(-i,n)):(this.x=Math.atan2(l,a),this.z=0)):console.error(`Error with vector's setEulerFromRotationMatrix: Unknown order: ${e}`),this}rotateAboutVector(t,e){t.normalize();const r=Math.cos(e),n=Math.sin(e),i=this.clone().multiplyScalar(r),o=t.clone().cross(this).multiplyScalar(n),a=t.clone().multiplyScalar(t.clone().dot(this)).multiplyScalar(1-r),s=i.add(o).add(a);return this.x=s.x,this.y=s.y,this.z=s.z,this}setFromMatrixPosition(t){const e=t.elements;return this.x=e[12],this.y=e[13],this.z=e[14],this}transformDirection(t){const{x:e}=this,{y:r}=this,{z:n}=this,i=t.elements;return this.x=i[0]*e+i[4]*r+i[8]*n,this.y=i[1]*e+i[5]*r+i[9]*n,this.z=i[2]*e+i[6]*r+i[10]*n,this.normalize()}clone(){return new h(this.x,this.y,this.z)}unproject(t){const e=n;return e.multiplyMatrices(t.matrixWorld,e.getInverse(t.projectionMatrix)),this.applyMatrix4(e)}}o=new h,a=new h,s=new h;class d{constructor(t=1,e=0,r=0,n=0,i=1,o=0,a=0,s=0,l=1){this.elements=new Float32Array(9),this.set(t,e,r,n,i,o,a,s,l)}set(t,e,r,n,i,o,a,s,l){const c=this.elements;return c[0]=t,c[3]=e,c[6]=r,c[1]=n,c[4]=i,c[7]=o,c[2]=a,c[5]=s,c[8]=l,this}identity(){return this.set(1,0,0,0,1,0,0,0,1),this}copy(t){const e=t.elements;this.set(e[0],e[3],e[6],e[1],e[4],e[7],e[2],e[5],e[8])}multiplyScalar(t){const e=this.elements;return e[0]*=t,e[3]*=t,e[6]*=t,e[1]*=t,e[4]*=t,e[7]*=t,e[2]*=t,e[5]*=t,e[8]*=t,this}getInverse3(t){const e=t.elements,r=this.elements;r[0]=e[4]*e[8]-e[5]*e[7],r[3]=e[6]*e[5]-e[3]*e[8],r[6]=e[3]*e[7]-e[6]*e[4],r[1]=e[7]*e[2]-e[1]*e[8],r[4]=e[0]*e[8]-e[6]*e[2],r[7]=e[1]*e[6]-e[0]*e[7],r[2]=e[1]*e[5]-e[2]*e[4],r[5]=e[2]*e[3]-e[0]*e[5],r[8]=e[0]*e[4]-e[1]*e[3];const n=e[0]*r[0]+e[3]*r[1]+e[6]*r[2];return this.multiplyScalar(1/n),this}getInverse(t,e){const r=t.elements,n=this.elements;n[0]=r[10]*r[5]-r[6]*r[9],n[1]=-r[10]*r[1]+r[2]*r[9],n[2]=r[6]*r[1]-r[2]*r[5],n[3]=-r[10]*r[4]+r[6]*r[8],n[4]=r[10]*r[0]-r[2]*r[8],n[5]=-r[6]*r[0]+r[2]*r[4],n[6]=r[9]*r[4]-r[5]*r[8],n[7]=-r[9]*r[0]+r[1]*r[8],n[8]=r[5]*r[0]-r[1]*r[4];const i=r[0]*n[0]+r[1]*n[3]+r[2]*n[6];if(0===i){const t="Matrix3.getInverse(): can't invert matrix, determinant is 0";if(e)throw new Error(t);return console.warn(t),this.identity(),this}return this.multiplyScalar(1/i),this}getDeterminant(){const t=this.elements;return t[0]*t[4]*t[8]+t[1]*t[5]*t[6]+t[2]*t[3]*t[7]-t[2]*t[4]*t[6]-t[1]*t[3]*t[8]-t[0]*t[5]*t[7]}transpose(){let t;const e=this.elements;return t=e[1],e[1]=e[3],e[3]=t,t=e[2],e[2]=e[6],e[6]=t,t=e[5],e[5]=e[7],e[7]=t,this}clone(){const t=this.elements;return new d(t[0],t[3],t[6],t[1],t[4],t[7],t[2],t[5],t[8])}getMatrix4(){const t=this.elements;return new u(t[0],t[3],t[6],0,t[1],t[4],t[7],0,t[2],t[5],t[8],0)}}class f{constructor(t,e){this.origin=void 0!==t?t:new h,this.direction=void 0!==e?e:new h}set(t,e){return this.origin.copy(t),this.direction.copy(e),this}copy(t){return this.origin.copy(t.origin),this.direction.copy(t.direction),this}at(t,e){return(e||new h).copy(this.direction).multiplyScalar(t).add(this.origin)}recast(t){const e=o;return this.origin.copy(this.at(t,e)),this}closestPointToPoint(t,e){const r=e||new h;r.subVectors(t,this.origin);const n=r.dot(this.direction);return r.copy(this.direction).multiplyScalar(n).add(this.origin)}distanceToPoint(t){const e=o,r=e.subVectors(t,this.origin).dot(this.direction);return 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n=r("./src/WebGL/shaders/lib/basic/index.ts"),i=r("./src/WebGL/shaders/lib/instanced/index.ts"),o=r("./src/WebGL/shaders/lib/lambert/index.ts"),a=r("./src/WebGL/shaders/lib/lambertdouble/index.ts"),s=r("./src/WebGL/shaders/lib/outline/index.ts"),l=r("./src/WebGL/shaders/lib/screen/index.ts"),c=r("./src/WebGL/shaders/lib/screenaa/index.ts"),u=r("./src/WebGL/shaders/lib/sphereimposter/index.ts"),h=r("./src/WebGL/shaders/lib/sphereimposteroutline/index.ts"),d=r("./src/WebGL/shaders/lib/sprite/index.ts"),f=r("./src/WebGL/shaders/lib/stickimposter/index.ts"),p=r("./src/WebGL/shaders/lib/stickimposteroutline/index.ts"),m=r("./src/WebGL/shaders/lib/volumetric/index.ts");const 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_(t,e,r,i){var o,a=t.state;return null===a.window&&(a.wsize=1<=a.wsize?(n.arraySet(a.window,e,r-a.wsize,a.wsize,0),a.wnext=0,a.whave=a.wsize):((o=a.wsize-a.wnext)>i&&(o=i),n.arraySet(a.window,e,r-i,o,a.wnext),(i-=o)?(n.arraySet(a.window,e,r-i,i,0),a.wnext=i,a.whave=a.wsize):(a.wnext+=o,a.wnext===a.wsize&&(a.wnext=0),a.whave>>8&255,r.check=o(r.check,j,2,0),b=0,y=0,r.mode=2;break}if(r.flags=0,r.head&&(r.head.done=!1),!(1&r.wrap)||(((255&b)<<8)+(b>>8))%31){t.msg="incorrect header check",r.mode=u;break}if(8!=(15&b)){t.msg="unknown compression method",r.mode=u;break}if(y-=4,D=8+(15&(b>>>=4)),0===r.wbits)r.wbits=D;else if(D>r.wbits){t.msg="invalid window size",r.mode=u;break}r.dmax=1<>8&1),512&r.flags&&(j[0]=255&b,j[1]=b>>>8&255,r.check=o(r.check,j,2,0)),b=0,y=0,r.mode=3;case 3:for(;y<32;){if(0===g)break t;g--,b+=d[p++]<>>8&255,j[2]=b>>>16&255,j[3]=b>>>24&255,r.check=o(r.check,j,4,0)),b=0,y=0,r.mode=4;case 4:for(;y<16;){if(0===g)break t;g--,b+=d[p++]<>8),512&r.flags&&(j[0]=255&b,j[1]=b>>>8&255,r.check=o(r.check,j,2,0)),b=0,y=0,r.mode=5;case 5:if(1024&r.flags){for(;y<16;){if(0===g)break t;g--,b+=d[p++]<>>8&255,r.check=o(r.check,j,2,0)),b=0,y=0}else r.head&&(r.head.extra=null);r.mode=6;case 6:if(1024&r.flags&&((A=r.length)>g&&(A=g),A&&(r.head&&(D=r.head.extra_len-r.length,r.head.extra||(r.head.extra=new Array(r.head.extra_len)),n.arraySet(r.head.extra,d,p,A,D)),512&r.flags&&(r.check=o(r.check,d,A,p)),g-=A,p+=A,r.length-=A),r.length))break t;r.length=0,r.mode=7;case 7:if(2048&r.flags){if(0===g)break t;A=0;do{D=d[p+A++],r.head&&D&&r.length<65536&&(r.head.name+=String.fromCharCode(D))}while(D&&A>9&1,r.head.done=!0),t.adler=r.check=0,r.mode=c;break;case 10:for(;y<32;){if(0===g)break t;g--,b+=d[p++]<>>=7&y,y-=7&y,r.mode=27;break}for(;y<3;){if(0===g)break t;g--,b+=d[p++]<>>=1)){case 0:r.mode=14;break;case 1:if(x(r),r.mode=20,6===e){b>>>=2,y-=2;break t}break;case 2:r.mode=17;break;case 3:t.msg="invalid block type",r.mode=u}b>>>=2,y-=2;break;case 14:for(b>>>=7&y,y-=7&y;y<32;){if(0===g)break t;g--,b+=d[p++]<>>16^65535)){t.msg="invalid stored block lengths",r.mode=u;break}if(r.length=65535&b,b=0,y=0,r.mode=15,6===e)break t;case 15:r.mode=16;case 16:if(A=r.length){if(A>g&&(A=g),A>v&&(A=v),0===A)break t;n.arraySet(f,d,p,A,m),g-=A,p+=A,v-=A,m+=A,r.length-=A;break}r.mode=c;break;case 17:for(;y<14;){if(0===g)break t;g--,b+=d[p++]<>>=5,y-=5,r.ndist=1+(31&b),b>>>=5,y-=5,r.ncode=4+(15&b),b>>>=4,y-=4,r.nlen>286||r.ndist>30){t.msg="too many length or distance symbols",r.mode=u;break}r.have=0,r.mode=18;case 18:for(;r.have>>=3,y-=3}for(;r.have<19;)r.lens[N[r.have++]]=0;if(r.lencode=r.lendyn,r.lenbits=7,F={bits:r.lenbits},I=s(0,r.lens,0,19,r.lencode,0,r.work,F),r.lenbits=F.bits,I){t.msg="invalid code lengths set",r.mode=u;break}r.have=0,r.mode=19;case 19:for(;r.have>>16&255,E=65535&P,!((S=P>>>24)<=y);){if(0===g)break t;g--,b+=d[p++]<>>=S,y-=S,r.lens[r.have++]=E;else{if(16===E){for(R=S+2;y>>=S,y-=S,0===r.have){t.msg="invalid bit length repeat",r.mode=u;break}D=r.lens[r.have-1],A=3+(3&b),b>>>=2,y-=2}else if(17===E){for(R=S+3;y>>=S)),b>>>=3,y-=3}else{for(R=S+7;y>>=S)),b>>>=7,y-=7}if(r.have+A>r.nlen+r.ndist){t.msg="invalid bit length repeat",r.mode=u;break}for(;A--;)r.lens[r.have++]=D}}if(r.mode===u)break;if(0===r.lens[256]){t.msg="invalid code -- missing end-of-block",r.mode=u;break}if(r.lenbits=9,F={bits:r.lenbits},I=s(1,r.lens,0,r.nlen,r.lencode,0,r.work,F),r.lenbits=F.bits,I){t.msg="invalid literal/lengths set",r.mode=u;break}if(r.distbits=6,r.distcode=r.distdyn,F={bits:r.distbits},I=s(2,r.lens,r.nlen,r.ndist,r.distcode,0,r.work,F),r.distbits=F.bits,I){t.msg="invalid distances set",r.mode=u;break}if(r.mode=20,6===e)break t;case 20:r.mode=21;case 21:if(g>=6&&v>=258){t.next_out=m,t.avail_out=v,t.next_in=p,t.avail_in=g,r.hold=b,r.bits=y,a(t,k),m=t.next_out,f=t.output,v=t.avail_out,p=t.next_in,d=t.input,g=t.avail_in,b=r.hold,y=r.bits,r.mode===c&&(r.back=-1);break}for(r.back=0;C=(P=r.lencode[b&(1<>>16&255,E=65535&P,!((S=P>>>24)<=y);){if(0===g)break t;g--,b+=d[p++]<>L)])>>>16&255,E=65535&P,!(L+(S=P>>>24)<=y);){if(0===g)break t;g--,b+=d[p++]<>>=L,y-=L,r.back+=L}if(b>>>=S,y-=S,r.back+=S,r.length=E,0===C){r.mode=26;break}if(32&C){r.back=-1,r.mode=c;break}if(64&C){t.msg="invalid literal/length code",r.mode=u;break}r.extra=15&C,r.mode=22;case 22:if(r.extra){for(R=r.extra;y>>=r.extra,y-=r.extra,r.back+=r.extra}r.was=r.length,r.mode=23;case 23:for(;C=(P=r.distcode[b&(1<>>16&255,E=65535&P,!((S=P>>>24)<=y);){if(0===g)break t;g--,b+=d[p++]<>L)])>>>16&255,E=65535&P,!(L+(S=P>>>24)<=y);){if(0===g)break t;g--,b+=d[p++]<>>=L,y-=L,r.back+=L}if(b>>>=S,y-=S,r.back+=S,64&C){t.msg="invalid distance code",r.mode=u;break}r.offset=E,r.extra=15&C,r.mode=24;case 24:if(r.extra){for(R=r.extra;y>>=r.extra,y-=r.extra,r.back+=r.extra}if(r.offset>r.dmax){t.msg="invalid distance too far back",r.mode=u;break}r.mode=25;case 25:if(0===v)break t;if(A=k-v,r.offset>A){if((A=r.offset-A)>r.whave&&r.sane){t.msg="invalid distance too far back",r.mode=u;break}A>r.wnext?(A-=r.wnext,M=r.wsize-A):M=r.wnext-A,A>r.length&&(A=r.length),T=r.window}else T=f,M=m-r.offset,A=r.length;A>v&&(A=v),v-=A,r.length-=A;do{f[m++]=T[M++]}while(--A);0===r.length&&(r.mode=21);break;case 26:if(0===v)break t;f[m++]=r.length,v--,r.mode=21;break;case 27:if(r.wrap){for(;y<32;){if(0===g)break t;g--,b|=d[p++]<{"use strict";var n=r("./node_modules/upng-js/node_modules/pako/lib/utils/common.js"),i=[3,4,5,6,7,8,9,10,11,13,15,17,19,23,27,31,35,43,51,59,67,83,99,115,131,163,195,227,258,0,0],o=[16,16,16,16,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19,20,20,20,20,21,21,21,21,16,72,78],a=[1,2,3,4,5,7,9,13,17,25,33,49,65,97,129,193,257,385,513,769,1025,1537,2049,3073,4097,6145,8193,12289,16385,24577,0,0],s=[16,16,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,64,64];t.exports=function(t,e,r,l,c,u,h,d){var f,p,m,g,v,b,y,x,_,w=d.bits,k=0,A=0,M=0,T=0,S=0,C=0,E=0,L=0,z=0,O=0,D=null,I=0,F=new n.Buf16(16),R=new n.Buf16(16),P=null,j=0;for(k=0;k<=15;k++)F[k]=0;for(A=0;A=1&&0===F[T];T--);if(S>T&&(S=T),0===T)return c[u++]=20971520,c[u++]=20971520,d.bits=1,0;for(M=1;M0&&(0===t||1!==T))return-1;for(R[1]=0,k=1;k<15;k++)R[k+1]=R[k]+F[k];for(A=0;A852||2===t&&z>592)return 1;for(;;){y=k-E,h[A]b?(x=P[j+h[A]],_=D[I+h[A]]):(x=96,_=0),f=1<>E)+(p-=f)]=y<<24|x<<16|_}while(0!==p);for(f=1<>=1;if(0!==f?(O&=f-1,O+=f):O=0,A++,0==--F[k]){if(k===T)break;k=e[r+h[A]]}if(k>S&&(O&g)!==m){for(0===E&&(E=S),v+=M,L=1<<(C=k-E);C+E852||2===t&&z>592)return 1;c[m=O&g]=S<<24|C<<16|v-u}}return 0!==O&&(c[v+O]=k-E<<24|64<<16),d.bits=S,0}},"./node_modules/upng-js/node_modules/pako/lib/zlib/messages.js":t=>{"use strict";t.exports={2:"need dictionary",1:"stream end",0:"","-1":"file error","-2":"stream error","-3":"data error","-4":"insufficient memory","-5":"buffer error","-6":"incompatible version"}},"./node_modules/upng-js/node_modules/pako/lib/zlib/trees.js":(t,e,r)=>{"use strict";var n=r("./node_modules/upng-js/node_modules/pako/lib/utils/common.js");function i(t){for(var e=t.length;--e>=0;)t[e]=0}var o=[0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,0],a=[0,0,0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13],s=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,3,7],l=[16,17,18,0,8,7,9,6,10,5,11,4,12,3,13,2,14,1,15],c=new Array(576);i(c);var u=new Array(60);i(u);var h=new Array(512);i(h);var d=new Array(256);i(d);var f=new Array(29);i(f);var p,m,g,v=new Array(30);function b(t,e,r,n,i){this.static_tree=t,this.extra_bits=e,this.extra_base=r,this.elems=n,this.max_length=i,this.has_stree=t&&t.length}function y(t,e){this.dyn_tree=t,this.max_code=0,this.stat_desc=e}function x(t){return t<256?h[t]:h[256+(t>>>7)]}function _(t,e){t.pending_buf[t.pending++]=255&e,t.pending_buf[t.pending++]=e>>>8&255}function w(t,e,r){t.bi_valid>16-r?(t.bi_buf|=e<>16-t.bi_valid,t.bi_valid+=r-16):(t.bi_buf|=e<>>=1,r<<=1}while(--e>0);return r>>>1}function M(t,e,r){var n,i,o=new Array(16),a=0;for(n=1;n<=15;n++)o[n]=a=a+r[n-1]<<1;for(i=0;i<=e;i++){var s=t[2*i+1];0!==s&&(t[2*i]=A(o[s]++,s))}}function T(t){var e;for(e=0;e<286;e++)t.dyn_ltree[2*e]=0;for(e=0;e<30;e++)t.dyn_dtree[2*e]=0;for(e=0;e<19;e++)t.bl_tree[2*e]=0;t.dyn_ltree[512]=1,t.opt_len=t.static_len=0,t.last_lit=t.matches=0}function S(t){t.bi_valid>8?_(t,t.bi_buf):t.bi_valid>0&&(t.pending_buf[t.pending++]=t.bi_buf),t.bi_buf=0,t.bi_valid=0}function C(t,e,r,n){var i=2*e,o=2*r;return t[i]>1;r>=1;r--)E(t,o,r);i=l;do{r=t.heap[1],t.heap[1]=t.heap[t.heap_len--],E(t,o,1),n=t.heap[1],t.heap[--t.heap_max]=r,t.heap[--t.heap_max]=n,o[2*i]=o[2*r]+o[2*n],t.depth[i]=(t.depth[r]>=t.depth[n]?t.depth[r]:t.depth[n])+1,o[2*r+1]=o[2*n+1]=i,t.heap[1]=i++,E(t,o,1)}while(t.heap_len>=2);t.heap[--t.heap_max]=t.heap[1],function(t,e){var r,n,i,o,a,s,l=e.dyn_tree,c=e.max_code,u=e.stat_desc.static_tree,h=e.stat_desc.has_stree,d=e.stat_desc.extra_bits,f=e.stat_desc.extra_base,p=e.stat_desc.max_length,m=0;for(o=0;o<=15;o++)t.bl_count[o]=0;for(l[2*t.heap[t.heap_max]+1]=0,r=t.heap_max+1;r<573;r++)(o=l[2*l[2*(n=t.heap[r])+1]+1]+1)>p&&(o=p,m++),l[2*n+1]=o,n>c||(t.bl_count[o]++,a=0,n>=f&&(a=d[n-f]),s=l[2*n],t.opt_len+=s*(o+a),h&&(t.static_len+=s*(u[2*n+1]+a)));if(0!==m){do{for(o=p-1;0===t.bl_count[o];)o--;t.bl_count[o]--,t.bl_count[o+1]+=2,t.bl_count[p]--,m-=2}while(m>0);for(o=p;0!==o;o--)for(n=t.bl_count[o];0!==n;)(i=t.heap[--r])>c||(l[2*i+1]!==o&&(t.opt_len+=(o-l[2*i+1])*l[2*i],l[2*i+1]=o),n--)}}(t,e),M(o,c,t.bl_count)}function O(t,e,r){var n,i,o=-1,a=e[1],s=0,l=7,c=4;for(0===a&&(l=138,c=3),e[2*(r+1)+1]=65535,n=0;n<=r;n++)i=a,a=e[2*(n+1)+1],++s>=7;n<30;n++)for(v[n]=i<<7,t=0;t<1<0?(2===t.strm.data_type&&(t.strm.data_type=function(t){var e,r=4093624447;for(e=0;e<=31;e++,r>>>=1)if(1&r&&0!==t.dyn_ltree[2*e])return 0;if(0!==t.dyn_ltree[18]||0!==t.dyn_ltree[20]||0!==t.dyn_ltree[26])return 1;for(e=32;e<256;e++)if(0!==t.dyn_ltree[2*e])return 1;return 0}(t)),z(t,t.l_desc),z(t,t.d_desc),a=function(t){var e;for(O(t,t.dyn_ltree,t.l_desc.max_code),O(t,t.dyn_dtree,t.d_desc.max_code),z(t,t.bl_desc),e=18;e>=3&&0===t.bl_tree[2*l[e]+1];e--);return t.opt_len+=3*(e+1)+5+5+4,e}(t),i=t.opt_len+3+7>>>3,(o=t.static_len+3+7>>>3)<=i&&(i=o)):i=o=r+5,r+4<=i&&-1!==e?F(t,e,r,n):4===t.strategy||o===i?(w(t,2+(n?1:0),3),L(t,c,u)):(w(t,4+(n?1:0),3),function(t,e,r,n){var 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e;for(e=0;e<286;e++)t.dyn_ltree[2*e]=0;for(e=0;e<30;e++)t.dyn_dtree[2*e]=0;for(e=0;e<19;e++)t.bl_tree[2*e]=0;t.dyn_ltree[512]=1,t.opt_len=t.static_len=0,t.sym_next=t.matches=0},T=t=>{t.bi_valid>8?x(t,t.bi_buf):t.bi_valid>0&&(t.pending_buf[t.pending++]=t.bi_buf),t.bi_buf=0,t.bi_valid=0},S=(t,e,r,n)=>{const i=2*e,o=2*r;return t[i]{const n=t.heap[r];let i=r<<1;for(;i<=t.heap_len&&(i{let n,a,s,l,c=0;if(0!==t.sym_next)do{n=255&t.pending_buf[t.sym_buf+c++],n+=(255&t.pending_buf[t.sym_buf+c++])<<8,a=t.pending_buf[t.sym_buf+c++],0===n?w(t,a,e):(s=h[a],w(t,s+256+1,e),l=i[s],0!==l&&(a-=d[s],_(t,a,l)),n--,s=y(n),w(t,s,r),l=o[s],0!==l&&(n-=f[s],_(t,n,l)))}while(c{const r=e.dyn_tree,n=e.stat_desc.static_tree,i=e.stat_desc.has_stree,o=e.stat_desc.elems;let 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Array(16);for(r=0,n=0;n<28;n++)for(d[n]=r,t=0;t<1<>=7;n<30;n++)for(f[n]=s<<7,t=0;t<1<{let i,o,a=0;t.level>0?(2===t.strm.data_type&&(t.strm.data_type=(t=>{let e,r=4093624447;for(e=0;e<=31;e++,r>>>=1)if(1&r&&0!==t.dyn_ltree[2*e])return 0;if(0!==t.dyn_ltree[18]||0!==t.dyn_ltree[20]||0!==t.dyn_ltree[26])return 1;for(e=32;e<256;e++)if(0!==t.dyn_ltree[2*e])return 1;return 0})(t)),L(t,t.l_desc),L(t,t.d_desc),a=(t=>{let e;for(z(t,t.dyn_ltree,t.l_desc.max_code),z(t,t.dyn_dtree,t.d_desc.max_code),L(t,t.bl_desc),e=18;e>=3&&0===t.bl_tree[2*s[e]+1];e--);return t.opt_len+=3*(e+1)+5+5+4,e})(t),i=t.opt_len+3+7>>>3,o=t.static_len+3+7>>>3,o<=i&&(i=o)):i=o=r+5,r+4<=i&&-1!==e?I(t,e,r,n):4===t.strategy||o===i?(_(t,2+(n?1:0),3),E(t,l,c)):(_(t,4+(n?1:0),3),((t,e,r,n)=>{let i;for(_(t,e-257,5),_(t,r-1,5),_(t,n-4,4),i=0;i(t.pending_buf[t.sym_buf+t.sym_next++]=e,t.pending_buf[t.sym_buf+t.sym_next++]=e>>8,t.pending_buf[t.sym_buf+t.sym_next++]=r,0===e?t.dyn_ltree[2*r]++:(t.matches++,e--,t.dyn_ltree[2*(h[r]+256+1)]++,t.dyn_dtree[2*y(e)]++),t.sym_next===t.sym_end),_tr_align:t=>{_(t,2,3),w(t,256,l),(t=>{16===t.bi_valid?(x(t,t.bi_buf),t.bi_buf=0,t.bi_valid=0):t.bi_valid>=8&&(t.pending_buf[t.pending++]=255&t.bi_buf,t.bi_buf>>=8,t.bi_valid-=8)})(t)}},R=(t,e,r,n)=>{let i=65535&t,o=t>>>16&65535,a=0;for(;0!==r;){a=r>2e3?2e3:r,r-=a;do{i=i+e[n++]|0,o=o+i|0}while(--a);i%=65521,o%=65521}return i|o<<16};const P=new Uint32Array((()=>{let t,e=[];for(var r=0;r<256;r++){t=r;for(var n=0;n<8;n++)t=1&t?3988292384^t>>>1:t>>>1;e[r]=t}return e})());var j=(t,e,r,n)=>{const i=P,o=n+r;t^=-1;for(let r=n;r>>8^i[255&(t^e[r])];return~t},N={2:"need dictionary",1:"stream end",0:"","-1":"file error","-2":"stream error","-3":"data error","-4":"insufficient memory","-5":"buffer error","-6":"incompatible version"},B={Z_NO_FLUSH:0,Z_PARTIAL_FLUSH:1,Z_SYNC_FLUSH:2,Z_FULL_FLUSH:3,Z_FINISH:4,Z_BLOCK:5,Z_TREES:6,Z_OK:0,Z_STREAM_END:1,Z_NEED_DICT:2,Z_ERRNO:-1,Z_STREAM_ERROR:-2,Z_DATA_ERROR:-3,Z_MEM_ERROR:-4,Z_BUF_ERROR:-5,Z_NO_COMPRESSION:0,Z_BEST_SPEED:1,Z_BEST_COMPRESSION:9,Z_DEFAULT_COMPRESSION:-1,Z_FILTERED:1,Z_HUFFMAN_ONLY:2,Z_RLE:3,Z_FIXED:4,Z_DEFAULT_STRATEGY:0,Z_BINARY:0,Z_TEXT:1,Z_UNKNOWN:2,Z_DEFLATED:8};const{_tr_init:U,_tr_stored_block:G,_tr_flush_block:V,_tr_tally:H,_tr_align:W}=F,{Z_NO_FLUSH:q,Z_PARTIAL_FLUSH:Y,Z_FULL_FLUSH:Z,Z_FINISH:X,Z_BLOCK:$,Z_OK:J,Z_STREAM_END:K,Z_STREAM_ERROR:Q,Z_DATA_ERROR:tt,Z_BUF_ERROR:et,Z_DEFAULT_COMPRESSION:rt,Z_FILTERED:nt,Z_HUFFMAN_ONLY:it,Z_RLE:ot,Z_FIXED:at,Z_DEFAULT_STRATEGY:st,Z_UNKNOWN:lt,Z_DEFLATED:ct}=B,ut=258,ht=262,dt=42,ft=113,pt=666,mt=(t,e)=>(t.msg=N[e],e),gt=t=>2*t-(t>4?9:0),vt=t=>{let e=t.length;for(;--e>=0;)t[e]=0},bt=t=>{let e,r,n,i=t.w_size;e=t.hash_size,n=e;do{r=t.head[--n],t.head[n]=r>=i?r-i:0}while(--e);e=i,n=e;do{r=t.prev[--n],t.prev[n]=r>=i?r-i:0}while(--e)};let yt=(t,e,r)=>(e<{const e=t.state;let r=e.pending;r>t.avail_out&&(r=t.avail_out),0!==r&&(t.output.set(e.pending_buf.subarray(e.pending_out,e.pending_out+r),t.next_out),t.next_out+=r,e.pending_out+=r,t.total_out+=r,t.avail_out-=r,e.pending-=r,0===e.pending&&(e.pending_out=0))},_t=(t,e)=>{V(t,t.block_start>=0?t.block_start:-1,t.strstart-t.block_start,e),t.block_start=t.strstart,xt(t.strm)},wt=(t,e)=>{t.pending_buf[t.pending++]=e},kt=(t,e)=>{t.pending_buf[t.pending++]=e>>>8&255,t.pending_buf[t.pending++]=255&e},At=(t,e,r,n)=>{let i=t.avail_in;return i>n&&(i=n),0===i?0:(t.avail_in-=i,e.set(t.input.subarray(t.next_in,t.next_in+i),r),1===t.state.wrap?t.adler=R(t.adler,e,i,r):2===t.state.wrap&&(t.adler=j(t.adler,e,i,r)),t.next_in+=i,t.total_in+=i,i)},Mt=(t,e)=>{let r,n,i=t.max_chain_length,o=t.strstart,a=t.prev_length,s=t.nice_match;const l=t.strstart>t.w_size-ht?t.strstart-(t.w_size-ht):0,c=t.window,u=t.w_mask,h=t.prev,d=t.strstart+ut;let f=c[o+a-1],p=c[o+a];t.prev_length>=t.good_match&&(i>>=2),s>t.lookahead&&(s=t.lookahead);do{if(r=e,c[r+a]===p&&c[r+a-1]===f&&c[r]===c[o]&&c[++r]===c[o+1]){o+=2,r++;do{}while(c[++o]===c[++r]&&c[++o]===c[++r]&&c[++o]===c[++r]&&c[++o]===c[++r]&&c[++o]===c[++r]&&c[++o]===c[++r]&&c[++o]===c[++r]&&c[++o]===c[++r]&&oa){if(t.match_start=e,a=n,n>=s)break;f=c[o+a-1],p=c[o+a]}}}while((e=h[e&u])>l&&0!=--i);return a<=t.lookahead?a:t.lookahead},Tt=t=>{const e=t.w_size;let r,n,i;do{if(n=t.window_size-t.lookahead-t.strstart,t.strstart>=e+(e-ht)&&(t.window.set(t.window.subarray(e,e+e-n),0),t.match_start-=e,t.strstart-=e,t.block_start-=e,t.insert>t.strstart&&(t.insert=t.strstart),bt(t),n+=e),0===t.strm.avail_in)break;if(r=At(t.strm,t.window,t.strstart+t.lookahead,n),t.lookahead+=r,t.lookahead+t.insert>=3)for(i=t.strstart-t.insert,t.ins_h=t.window[i],t.ins_h=yt(t,t.ins_h,t.window[i+1]);t.insert&&(t.ins_h=yt(t,t.ins_h,t.window[i+3-1]),t.prev[i&t.w_mask]=t.head[t.ins_h],t.head[t.ins_h]=i,i++,t.insert--,!(t.lookahead+t.insert<3)););}while(t.lookahead{let r,n,i,o=t.pending_buf_size-5>t.w_size?t.w_size:t.pending_buf_size-5,a=0,s=t.strm.avail_in;do{if(r=65535,i=t.bi_valid+42>>3,t.strm.avail_outn+t.strm.avail_in&&(r=n+t.strm.avail_in),r>i&&(r=i),r>8,t.pending_buf[t.pending-2]=~r,t.pending_buf[t.pending-1]=~r>>8,xt(t.strm),n&&(n>r&&(n=r),t.strm.output.set(t.window.subarray(t.block_start,t.block_start+n),t.strm.next_out),t.strm.next_out+=n,t.strm.avail_out-=n,t.strm.total_out+=n,t.block_start+=n,r-=n),r&&(At(t.strm,t.strm.output,t.strm.next_out,r),t.strm.next_out+=r,t.strm.avail_out-=r,t.strm.total_out+=r)}while(0===a);return s-=t.strm.avail_in,s&&(s>=t.w_size?(t.matches=2,t.window.set(t.strm.input.subarray(t.strm.next_in-t.w_size,t.strm.next_in),0),t.strstart=t.w_size,t.insert=t.strstart):(t.window_size-t.strstart<=s&&(t.strstart-=t.w_size,t.window.set(t.window.subarray(t.w_size,t.w_size+t.strstart),0),t.matches<2&&t.matches++,t.insert>t.strstart&&(t.insert=t.strstart)),t.window.set(t.strm.input.subarray(t.strm.next_in-s,t.strm.next_in),t.strstart),t.strstart+=s,t.insert+=s>t.w_size-t.insert?t.w_size-t.insert:s),t.block_start=t.strstart),t.high_wateri&&t.block_start>=t.w_size&&(t.block_start-=t.w_size,t.strstart-=t.w_size,t.window.set(t.window.subarray(t.w_size,t.w_size+t.strstart),0),t.matches<2&&t.matches++,i+=t.w_size,t.insert>t.strstart&&(t.insert=t.strstart)),i>t.strm.avail_in&&(i=t.strm.avail_in),i&&(At(t.strm,t.window,t.strstart,i),t.strstart+=i,t.insert+=i>t.w_size-t.insert?t.w_size-t.insert:i),t.high_water>3,i=t.pending_buf_size-i>65535?65535:t.pending_buf_size-i,o=i>t.w_size?t.w_size:i,n=t.strstart-t.block_start,(n>=o||(n||e===X)&&e!==q&&0===t.strm.avail_in&&n<=i)&&(r=n>i?i:n,a=e===X&&0===t.strm.avail_in&&r===n?1:0,G(t,t.block_start,r,a),t.block_start+=r,xt(t.strm)),a?3:1)},Ct=(t,e)=>{let r,n;for(;;){if(t.lookahead=3&&(t.ins_h=yt(t,t.ins_h,t.window[t.strstart+3-1]),r=t.prev[t.strstart&t.w_mask]=t.head[t.ins_h],t.head[t.ins_h]=t.strstart),0!==r&&t.strstart-r<=t.w_size-ht&&(t.match_length=Mt(t,r)),t.match_length>=3)if(n=H(t,t.strstart-t.match_start,t.match_length-3),t.lookahead-=t.match_length,t.match_length<=t.max_lazy_match&&t.lookahead>=3){t.match_length--;do{t.strstart++,t.ins_h=yt(t,t.ins_h,t.window[t.strstart+3-1]),r=t.prev[t.strstart&t.w_mask]=t.head[t.ins_h],t.head[t.ins_h]=t.strstart}while(0!=--t.match_length);t.strstart++}else t.strstart+=t.match_length,t.match_length=0,t.ins_h=t.window[t.strstart],t.ins_h=yt(t,t.ins_h,t.window[t.strstart+1]);else n=H(t,0,t.window[t.strstart]),t.lookahead--,t.strstart++;if(n&&(_t(t,!1),0===t.strm.avail_out))return 1}return t.insert=t.strstart<2?t.strstart:2,e===X?(_t(t,!0),0===t.strm.avail_out?3:4):t.sym_next&&(_t(t,!1),0===t.strm.avail_out)?1:2},Et=(t,e)=>{let r,n,i;for(;;){if(t.lookahead=3&&(t.ins_h=yt(t,t.ins_h,t.window[t.strstart+3-1]),r=t.prev[t.strstart&t.w_mask]=t.head[t.ins_h],t.head[t.ins_h]=t.strstart),t.prev_length=t.match_length,t.prev_match=t.match_start,t.match_length=2,0!==r&&t.prev_length4096)&&(t.match_length=2)),t.prev_length>=3&&t.match_length<=t.prev_length){i=t.strstart+t.lookahead-3,n=H(t,t.strstart-1-t.prev_match,t.prev_length-3),t.lookahead-=t.prev_length-1,t.prev_length-=2;do{++t.strstart<=i&&(t.ins_h=yt(t,t.ins_h,t.window[t.strstart+3-1]),r=t.prev[t.strstart&t.w_mask]=t.head[t.ins_h],t.head[t.ins_h]=t.strstart)}while(0!=--t.prev_length);if(t.match_available=0,t.match_length=2,t.strstart++,n&&(_t(t,!1),0===t.strm.avail_out))return 1}else if(t.match_available){if(n=H(t,0,t.window[t.strstart-1]),n&&_t(t,!1),t.strstart++,t.lookahead--,0===t.strm.avail_out)return 1}else t.match_available=1,t.strstart++,t.lookahead--}return t.match_available&&(n=H(t,0,t.window[t.strstart-1]),t.match_available=0),t.insert=t.strstart<2?t.strstart:2,e===X?(_t(t,!0),0===t.strm.avail_out?3:4):t.sym_next&&(_t(t,!1),0===t.strm.avail_out)?1:2};function Lt(t,e,r,n,i){this.good_length=t,this.max_lazy=e,this.nice_length=r,this.max_chain=n,this.func=i}const zt=[new Lt(0,0,0,0,St),new Lt(4,4,8,4,Ct),new Lt(4,5,16,8,Ct),new Lt(4,6,32,32,Ct),new Lt(4,4,16,16,Et),new Lt(8,16,32,32,Et),new Lt(8,16,128,128,Et),new Lt(8,32,128,256,Et),new Lt(32,128,258,1024,Et),new Lt(32,258,258,4096,Et)];function Ot(){this.strm=null,this.status=0,this.pending_buf=null,this.pending_buf_size=0,this.pending_out=0,this.pending=0,this.wrap=0,this.gzhead=null,this.gzindex=0,this.method=ct,this.last_flush=-1,this.w_size=0,this.w_bits=0,this.w_mask=0,this.window=null,this.window_size=0,this.prev=null,this.head=null,this.ins_h=0,this.hash_size=0,this.hash_bits=0,this.hash_mask=0,this.hash_shift=0,this.block_start=0,this.match_length=0,this.prev_match=0,this.match_available=0,this.strstart=0,this.match_start=0,this.lookahead=0,this.prev_length=0,this.max_chain_length=0,this.max_lazy_match=0,this.level=0,this.strategy=0,this.good_match=0,this.nice_match=0,this.dyn_ltree=new Uint16Array(1146),this.dyn_dtree=new Uint16Array(122),this.bl_tree=new Uint16Array(78),vt(this.dyn_ltree),vt(this.dyn_dtree),vt(this.bl_tree),this.l_desc=null,this.d_desc=null,this.bl_desc=null,this.bl_count=new Uint16Array(16),this.heap=new Uint16Array(573),vt(this.heap),this.heap_len=0,this.heap_max=0,this.depth=new Uint16Array(573),vt(this.depth),this.sym_buf=0,this.lit_bufsize=0,this.sym_next=0,this.sym_end=0,this.opt_len=0,this.static_len=0,this.matches=0,this.insert=0,this.bi_buf=0,this.bi_valid=0}const Dt=t=>{if(!t)return 1;const e=t.state;return!e||e.strm!==t||e.status!==dt&&57!==e.status&&69!==e.status&&73!==e.status&&91!==e.status&&103!==e.status&&e.status!==ft&&e.status!==pt?1:0},It=t=>{if(Dt(t))return mt(t,Q);t.total_in=t.total_out=0,t.data_type=lt;const e=t.state;return e.pending=0,e.pending_out=0,e.wrap<0&&(e.wrap=-e.wrap),e.status=2===e.wrap?57:e.wrap?dt:ft,t.adler=2===e.wrap?0:1,e.last_flush=-2,U(e),J},Ft=t=>{const e=It(t);var r;return e===J&&((r=t.state).window_size=2*r.w_size,vt(r.head),r.max_lazy_match=zt[r.level].max_lazy,r.good_match=zt[r.level].good_length,r.nice_match=zt[r.level].nice_length,r.max_chain_length=zt[r.level].max_chain,r.strstart=0,r.block_start=0,r.lookahead=0,r.insert=0,r.match_length=r.prev_length=2,r.match_available=0,r.ins_h=0),e},Rt=(t,e,r,n,i,o)=>{if(!t)return Q;let a=1;if(e===rt&&(e=6),n<0?(a=0,n=-n):n>15&&(a=2,n-=16),i<1||i>9||r!==ct||n<8||n>15||e<0||e>9||o<0||o>at||8===n&&1!==a)return mt(t,Q);8===n&&(n=9);const s=new Ot;return t.state=s,s.strm=t,s.status=dt,s.wrap=a,s.gzhead=null,s.w_bits=n,s.w_size=1<Dt(t)||2!==t.state.wrap?Q:(t.state.gzhead=e,J),Nt=(t,e)=>{if(Dt(t)||e>$||e<0)return t?mt(t,Q):Q;const r=t.state;if(!t.output||0!==t.avail_in&&!t.input||r.status===pt&&e!==X)return mt(t,0===t.avail_out?et:Q);const n=r.last_flush;if(r.last_flush=e,0!==r.pending){if(xt(t),0===t.avail_out)return r.last_flush=-1,J}else if(0===t.avail_in&>(e)<=gt(n)&&e!==X)return mt(t,et);if(r.status===pt&&0!==t.avail_in)return mt(t,et);if(r.status===dt&&0===r.wrap&&(r.status=ft),r.status===dt){let e=ct+(r.w_bits-8<<4)<<8,n=-1;if(n=r.strategy>=it||r.level<2?0:r.level<6?1:6===r.level?2:3,e|=n<<6,0!==r.strstart&&(e|=32),e+=31-e%31,kt(r,e),0!==r.strstart&&(kt(r,t.adler>>>16),kt(r,65535&t.adler)),t.adler=1,r.status=ft,xt(t),0!==r.pending)return r.last_flush=-1,J}if(57===r.status)if(t.adler=0,wt(r,31),wt(r,139),wt(r,8),r.gzhead)wt(r,(r.gzhead.text?1:0)+(r.gzhead.hcrc?2:0)+(r.gzhead.extra?4:0)+(r.gzhead.name?8:0)+(r.gzhead.comment?16:0)),wt(r,255&r.gzhead.time),wt(r,r.gzhead.time>>8&255),wt(r,r.gzhead.time>>16&255),wt(r,r.gzhead.time>>24&255),wt(r,9===r.level?2:r.strategy>=it||r.level<2?4:0),wt(r,255&r.gzhead.os),r.gzhead.extra&&r.gzhead.extra.length&&(wt(r,255&r.gzhead.extra.length),wt(r,r.gzhead.extra.length>>8&255)),r.gzhead.hcrc&&(t.adler=j(t.adler,r.pending_buf,r.pending,0)),r.gzindex=0,r.status=69;else if(wt(r,0),wt(r,0),wt(r,0),wt(r,0),wt(r,0),wt(r,9===r.level?2:r.strategy>=it||r.level<2?4:0),wt(r,3),r.status=ft,xt(t),0!==r.pending)return r.last_flush=-1,J;if(69===r.status){if(r.gzhead.extra){let e=r.pending,n=(65535&r.gzhead.extra.length)-r.gzindex;for(;r.pending+n>r.pending_buf_size;){let i=r.pending_buf_size-r.pending;if(r.pending_buf.set(r.gzhead.extra.subarray(r.gzindex,r.gzindex+i),r.pending),r.pending=r.pending_buf_size,r.gzhead.hcrc&&r.pending>e&&(t.adler=j(t.adler,r.pending_buf,r.pending-e,e)),r.gzindex+=i,xt(t),0!==r.pending)return r.last_flush=-1,J;e=0,n-=i}let i=new Uint8Array(r.gzhead.extra);r.pending_buf.set(i.subarray(r.gzindex,r.gzindex+n),r.pending),r.pending+=n,r.gzhead.hcrc&&r.pending>e&&(t.adler=j(t.adler,r.pending_buf,r.pending-e,e)),r.gzindex=0}r.status=73}if(73===r.status){if(r.gzhead.name){let e,n=r.pending;do{if(r.pending===r.pending_buf_size){if(r.gzhead.hcrc&&r.pending>n&&(t.adler=j(t.adler,r.pending_buf,r.pending-n,n)),xt(t),0!==r.pending)return r.last_flush=-1,J;n=0}e=r.gzindexn&&(t.adler=j(t.adler,r.pending_buf,r.pending-n,n)),r.gzindex=0}r.status=91}if(91===r.status){if(r.gzhead.comment){let e,n=r.pending;do{if(r.pending===r.pending_buf_size){if(r.gzhead.hcrc&&r.pending>n&&(t.adler=j(t.adler,r.pending_buf,r.pending-n,n)),xt(t),0!==r.pending)return r.last_flush=-1,J;n=0}e=r.gzindexn&&(t.adler=j(t.adler,r.pending_buf,r.pending-n,n))}r.status=103}if(103===r.status){if(r.gzhead.hcrc){if(r.pending+2>r.pending_buf_size&&(xt(t),0!==r.pending))return r.last_flush=-1,J;wt(r,255&t.adler),wt(r,t.adler>>8&255),t.adler=0}if(r.status=ft,xt(t),0!==r.pending)return r.last_flush=-1,J}if(0!==t.avail_in||0!==r.lookahead||e!==q&&r.status!==pt){let n=0===r.level?St(r,e):r.strategy===it?((t,e)=>{let r;for(;;){if(0===t.lookahead&&(Tt(t),0===t.lookahead)){if(e===q)return 1;break}if(t.match_length=0,r=H(t,0,t.window[t.strstart]),t.lookahead--,t.strstart++,r&&(_t(t,!1),0===t.strm.avail_out))return 1}return t.insert=0,e===X?(_t(t,!0),0===t.strm.avail_out?3:4):t.sym_next&&(_t(t,!1),0===t.strm.avail_out)?1:2})(r,e):r.strategy===ot?((t,e)=>{let r,n,i,o;const a=t.window;for(;;){if(t.lookahead<=ut){if(Tt(t),t.lookahead<=ut&&e===q)return 1;if(0===t.lookahead)break}if(t.match_length=0,t.lookahead>=3&&t.strstart>0&&(i=t.strstart-1,n=a[i],n===a[++i]&&n===a[++i]&&n===a[++i])){o=t.strstart+ut;do{}while(n===a[++i]&&n===a[++i]&&n===a[++i]&&n===a[++i]&&n===a[++i]&&n===a[++i]&&n===a[++i]&&n===a[++i]&&it.lookahead&&(t.match_length=t.lookahead)}if(t.match_length>=3?(r=H(t,1,t.match_length-3),t.lookahead-=t.match_length,t.strstart+=t.match_length,t.match_length=0):(r=H(t,0,t.window[t.strstart]),t.lookahead--,t.strstart++),r&&(_t(t,!1),0===t.strm.avail_out))return 1}return t.insert=0,e===X?(_t(t,!0),0===t.strm.avail_out?3:4):t.sym_next&&(_t(t,!1),0===t.strm.avail_out)?1:2})(r,e):zt[r.level].func(r,e);if(3!==n&&4!==n||(r.status=pt),1===n||3===n)return 0===t.avail_out&&(r.last_flush=-1),J;if(2===n&&(e===Y?W(r):e!==$&&(G(r,0,0,!1),e===Z&&(vt(r.head),0===r.lookahead&&(r.strstart=0,r.block_start=0,r.insert=0))),xt(t),0===t.avail_out))return r.last_flush=-1,J}return e!==X?J:r.wrap<=0?K:(2===r.wrap?(wt(r,255&t.adler),wt(r,t.adler>>8&255),wt(r,t.adler>>16&255),wt(r,t.adler>>24&255),wt(r,255&t.total_in),wt(r,t.total_in>>8&255),wt(r,t.total_in>>16&255),wt(r,t.total_in>>24&255)):(kt(r,t.adler>>>16),kt(r,65535&t.adler)),xt(t),r.wrap>0&&(r.wrap=-r.wrap),0!==r.pending?J:K)},Bt=t=>{if(Dt(t))return Q;const e=t.state.status;return t.state=null,e===ft?mt(t,tt):J},Ut=(t,e)=>{let r=e.length;if(Dt(t))return Q;const n=t.state,i=n.wrap;if(2===i||1===i&&n.status!==dt||n.lookahead)return Q;if(1===i&&(t.adler=R(t.adler,e,r,0)),n.wrap=0,r>=n.w_size){0===i&&(vt(n.head),n.strstart=0,n.block_start=0,n.insert=0);let t=new Uint8Array(n.w_size);t.set(e.subarray(r-n.w_size,r),0),e=t,r=n.w_size}const o=t.avail_in,a=t.next_in,s=t.input;for(t.avail_in=r,t.next_in=0,t.input=e,Tt(n);n.lookahead>=3;){let t=n.strstart,e=n.lookahead-2;do{n.ins_h=yt(n,n.ins_h,n.window[t+3-1]),n.prev[t&n.w_mask]=n.head[n.ins_h],n.head[n.ins_h]=t,t++}while(--e);n.strstart=t,n.lookahead=2,Tt(n)}return n.strstart+=n.lookahead,n.block_start=n.strstart,n.insert=n.lookahead,n.lookahead=0,n.match_length=n.prev_length=2,n.match_available=0,t.next_in=a,t.input=s,t.avail_in=o,n.wrap=i,J};const Gt=(t,e)=>Object.prototype.hasOwnProperty.call(t,e);var Vt=function(t){const e=Array.prototype.slice.call(arguments,1);for(;e.length;){const r=e.shift();if(r){if("object"!=typeof r)throw new TypeError(r+"must be non-object");for(const e in r)Gt(r,e)&&(t[e]=r[e])}}return t},Ht=t=>{let e=0;for(let r=0,n=t.length;r=252?6:t>=248?5:t>=240?4:t>=224?3:t>=192?2:1;qt[254]=qt[254]=1;var Yt=t=>{if("function"==typeof TextEncoder&&TextEncoder.prototype.encode)return(new TextEncoder).encode(t);let e,r,n,i,o,a=t.length,s=0;for(i=0;i>>6,e[o++]=128|63&r):r<65536?(e[o++]=224|r>>>12,e[o++]=128|r>>>6&63,e[o++]=128|63&r):(e[o++]=240|r>>>18,e[o++]=128|r>>>12&63,e[o++]=128|r>>>6&63,e[o++]=128|63&r);return e},Zt=(t,e)=>{const r=e||t.length;if("function"==typeof TextDecoder&&TextDecoder.prototype.decode)return(new TextDecoder).decode(t.subarray(0,e));let n,i;const o=new Array(2*r);for(i=0,n=0;n4)o[i++]=65533,n+=a-1;else{for(e&=2===a?31:3===a?15:7;a>1&&n1?o[i++]=65533:e<65536?o[i++]=e:(e-=65536,o[i++]=55296|e>>10&1023,o[i++]=56320|1023&e)}}return((t,e)=>{if(e<65534&&t.subarray&&Wt)return String.fromCharCode.apply(null,t.length===e?t:t.subarray(0,e));let r="";for(let n=0;n{(e=e||t.length)>t.length&&(e=t.length);let r=e-1;for(;r>=0&&128==(192&t[r]);)r--;return 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strict";t.exports=[{path:"",backoff:0},{path:"M-2.4,-3V3L0.6,0Z",backoff:.6},{path:"M-3.7,-2.5V2.5L1.3,0Z",backoff:1.3},{path:"M-4.45,-3L-1.65,-0.2V0.2L-4.45,3L1.55,0Z",backoff:1.55},{path:"M-2.2,-2.2L-0.2,-0.2V0.2L-2.2,2.2L-1.4,3L1.6,0L-1.4,-3Z",backoff:1.6},{path:"M-4.4,-2.1L-0.6,-0.2V0.2L-4.4,2.1L-4,3L2,0L-4,-3Z",backoff:2},{path:"M2,0A2,2 0 1,1 0,-2A2,2 0 0,1 2,0Z",backoff:0,noRotate:!0},{path:"M2,2V-2H-2V2Z",backoff:0,noRotate:!0}]},77061:(t,e,r)=>{"use strict";var n=r(91208),i=r(75058),o=r(21197),a=r(46121).templatedArray,s=r(53644);function l(t){return["In order for absolute positioning of the arrow to work, *a"+t+"ref* must be exactly the same as *"+t+"ref*, otherwise *a"+t+"ref* will revert to *pixel* (explained next).","For relative positioning, *a"+t+"ref* can be set to *pixel*,","in which case the *a"+t+"* value is specified in pixels","relative to *"+t+"*.","Absolute positioning is useful","for trendline annotations which should continue to indicate","the correct trend when zoomed. Relative positioning is useful","for specifying the text offset for an annotated point."].join(" ")}function c(t,e,r){return["Sets the",t,"component of the arrow tail about the arrow head.","If `a"+t+"ref` is `pixel`, a positive (negative)","component corresponds to an arrow pointing","from",r,"to",e,"("+e,"to",r+").","If `a"+t+"ref` is not `pixel` and is exactly the same as `"+t+"ref`,","this is an absolute value on that axis,","like `"+t+"`, specified in the same coordinates as `"+t+"ref`."].join(" ")}t.exports=a("annotation",{visible:{valType:"boolean",dflt:!0,editType:"calc+arraydraw",description:["Determines whether or not this annotation is visible."].join(" ")},text:{valType:"string",editType:"calc+arraydraw",description:["Sets the text associated with this annotation.","Plotly uses a subset of HTML tags to do things like","newline (
), bold (), italics (),","hyperlinks (). Tags , , , , "," are also supported."].join(" ")},textangle:{valType:"angle",dflt:0,editType:"calc+arraydraw",description:["Sets the angle at which the `text` is drawn","with respect to the horizontal."].join(" ")},font:i({editType:"calc+arraydraw",colorEditType:"arraydraw",description:"Sets the annotation text font."}),width:{valType:"number",min:1,dflt:null,editType:"calc+arraydraw",description:["Sets an explicit width for the text box. null (default) lets the","text set the box width. Wider text will be clipped.","There is no automatic wrapping; use
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HTML tags) or if an","explicit width is set to override the text width."].join(" ")},valign:{valType:"enumerated",values:["top","middle","bottom"],dflt:"middle",editType:"arraydraw",description:["Sets the vertical alignment of the `text` within the box.","Has an effect only if an explicit height is set to override","the text height."].join(" ")},bgcolor:{valType:"color",dflt:"rgba(0,0,0,0)",editType:"arraydraw",description:"Sets the background color of the annotation."},bordercolor:{valType:"color",dflt:"rgba(0,0,0,0)",editType:"arraydraw",description:["Sets the color of the border enclosing the annotation `text`."].join(" ")},borderpad:{valType:"number",min:0,dflt:1,editType:"calc+arraydraw",description:["Sets the padding (in px) between the `text`","and the enclosing border."].join(" ")},borderwidth:{valType:"number",min:0,dflt:1,editType:"calc+arraydraw",description:["Sets the width (in px) of the border enclosing","the annotation `text`."].join(" ")},showarrow:{valType:"boolean",dflt:!0,editType:"calc+arraydraw",description:["Determines whether or not the annotation is drawn with an arrow.","If *true*, `text` is placed near the arrow's tail.","If *false*, `text` lines up with the `x` and `y` provided."].join(" ")},arrowcolor:{valType:"color",editType:"arraydraw",description:"Sets the color of the annotation arrow."},arrowhead:{valType:"integer",min:0,max:n.length,dflt:1,editType:"arraydraw",description:"Sets the end annotation arrow head style."},startarrowhead:{valType:"integer",min:0,max:n.length,dflt:1,editType:"arraydraw",description:"Sets the start annotation arrow head style."},arrowside:{valType:"flaglist",flags:["end","start"],extras:["none"],dflt:"end",editType:"arraydraw",description:"Sets the annotation arrow head position."},arrowsize:{valType:"number",min:.3,dflt:1,editType:"calc+arraydraw",description:["Sets the size of the end annotation arrow head, relative to `arrowwidth`.","A value of 1 (default) gives a head about 3x as wide as the line."].join(" ")},startarrowsize:{valType:"number",min:.3,dflt:1,editType:"calc+arraydraw",description:["Sets the size of the start annotation arrow head, relative to `arrowwidth`.","A value of 1 (default) gives a head about 3x as wide as the line."].join(" ")},arrowwidth:{valType:"number",min:.1,editType:"calc+arraydraw",description:"Sets the width (in px) of annotation arrow line."},standoff:{valType:"number",min:0,dflt:0,editType:"calc+arraydraw",description:["Sets a distance, in pixels, to move the end arrowhead away from the","position it is pointing at, for example to point at the edge of","a marker independent of zoom. Note that this shortens the arrow","from the `ax` / `ay` vector, in contrast to `xshift` / `yshift`","which moves everything by this amount."].join(" ")},startstandoff:{valType:"number",min:0,dflt:0,editType:"calc+arraydraw",description:["Sets a distance, in pixels, to move the start arrowhead away from the","position it is pointing at, for example to point at the edge of","a marker independent of zoom. Note that this shortens the arrow","from the `ax` / `ay` vector, in contrast to `xshift` / `yshift`","which moves everything by this amount."].join(" ")},ax:{valType:"any",editType:"calc+arraydraw",description:[c("x","left","right")].join(" ")},ay:{valType:"any",editType:"calc+arraydraw",description:[c("y","top","bottom")].join(" ")},axref:{valType:"enumerated",dflt:"pixel",values:["pixel",o.idRegex.x.toString()],editType:"calc",description:["Indicates in what coordinates the tail of the","annotation (ax,ay) is specified.",s.axisRefDescription("x","left","right"),l("x")].join(" ")},ayref:{valType:"enumerated",dflt:"pixel",values:["pixel",o.idRegex.y.toString()],editType:"calc",description:["Indicates in what coordinates the tail of the","annotation (ax,ay) is specified.",s.axisRefDescription("y","bottom","top"),l("y")].join(" ")},xref:{valType:"enumerated",values:["paper",o.idRegex.x.toString()],editType:"calc",description:["Sets the annotation's x coordinate axis.",s.axisRefDescription("x","left","right")].join(" ")},x:{valType:"any",editType:"calc+arraydraw",description:["Sets the annotation's x position.","If the axis `type` is *log*, then you must take the","log of your desired range.","If the axis `type` is *date*, it should be date strings,","like date data, though Date objects and unix milliseconds","will be accepted and converted to strings.","If the axis `type` is *category*, it should be numbers,","using the scale where each category is assigned a serial","number from zero in the order it appears."].join(" ")},xanchor:{valType:"enumerated",values:["auto","left","center","right"],dflt:"auto",editType:"calc+arraydraw",description:["Sets the text box's horizontal position anchor","This anchor binds the `x` position to the *left*, *center*","or *right* of the annotation.","For example, if `x` is set to 1, `xref` to *paper* and","`xanchor` to *right* then the right-most portion of the","annotation lines up with the right-most edge of the","plotting area.","If *auto*, the anchor is equivalent to *center* for","data-referenced annotations or if there is an arrow,","whereas for paper-referenced with no arrow, the anchor picked","corresponds to the closest side."].join(" ")},xshift:{valType:"number",dflt:0,editType:"calc+arraydraw",description:["Shifts the position of the whole annotation and arrow to the","right (positive) or left (negative) by this many pixels."].join(" ")},yref:{valType:"enumerated",values:["paper",o.idRegex.y.toString()],editType:"calc",description:["Sets the annotation's y coordinate axis.",s.axisRefDescription("y","bottom","top")].join(" ")},y:{valType:"any",editType:"calc+arraydraw",description:["Sets the annotation's y position.","If the axis `type` is *log*, then you must take the","log of your desired range.","If the axis `type` is *date*, it should be date strings,","like date data, though Date objects and unix milliseconds","will be accepted and converted to strings.","If the axis `type` is *category*, it should be numbers,","using the scale where each category is assigned a serial","number from zero in the order it appears."].join(" ")},yanchor:{valType:"enumerated",values:["auto","top","middle","bottom"],dflt:"auto",editType:"calc+arraydraw",description:["Sets the text box's vertical position anchor","This anchor binds the `y` position to the *top*, *middle*","or *bottom* of the annotation.","For example, if `y` is set to 1, `yref` to *paper* and","`yanchor` to *top* then the top-most portion of the","annotation lines up with the top-most edge of the","plotting area.","If *auto*, the anchor is equivalent to *middle* for","data-referenced annotations or if there is an arrow,","whereas for paper-referenced with no arrow, the anchor picked","corresponds to the closest side."].join(" ")},yshift:{valType:"number",dflt:0,editType:"calc+arraydraw",description:["Shifts the position of the whole annotation and arrow up","(positive) or down (negative) by this many pixels."].join(" ")},clicktoshow:{valType:"enumerated",values:[!1,"onoff","onout"],dflt:!1,editType:"arraydraw",description:["Makes this annotation respond to clicks on the plot.","If you click a data point that exactly matches the `x` and `y`","values of this annotation, and it is hidden (visible: false),","it will appear. In *onoff* mode, you must click the same point","again to make it disappear, so if you click multiple points,","you can show multiple annotations. In *onout* mode, a click","anywhere else in the plot (on another data point or not) will","hide this annotation.","If you need to show/hide this annotation in response to different","`x` or `y` values, you can set `xclick` and/or `yclick`. This is","useful for example to label the side of a bar. To label markers","though, `standoff` is preferred over `xclick` and `yclick`."].join(" ")},xclick:{valType:"any",editType:"arraydraw",description:["Toggle this annotation when clicking a data point whose `x` value","is `xclick` rather than the annotation's `x` value."].join(" ")},yclick:{valType:"any",editType:"arraydraw",description:["Toggle this annotation when clicking a data point whose `y` value","is `yclick` rather than the annotation's `y` value."].join(" ")},hovertext:{valType:"string",editType:"arraydraw",description:["Sets text to appear when hovering over this annotation.","If omitted or blank, no hover label will appear."].join(" ")},hoverlabel:{bgcolor:{valType:"color",editType:"arraydraw",description:["Sets the background color of the hover label.","By default uses the annotation's `bgcolor` made opaque,","or white if it was transparent."].join(" ")},bordercolor:{valType:"color",editType:"arraydraw",description:["Sets the border color of the hover label.","By default uses either dark grey or white, for maximum","contrast with `hoverlabel.bgcolor`."].join(" ")},font:i({editType:"arraydraw",description:["Sets the hover label text font.","By default uses the global hover font and size,","with color from `hoverlabel.bordercolor`."].join(" ")}),editType:"arraydraw"},captureevents:{valType:"boolean",editType:"arraydraw",description:["Determines whether the annotation text box captures mouse move","and click events, or allows those events to pass through to data","points in the plot that may be behind the annotation. By default","`captureevents` is *false* unless `hovertext` is provided.","If you use the event `plotly_clickannotation` without `hovertext`","you must explicitly enable `captureevents`."].join(" ")},editType:"calc",_deprecated:{ref:{valType:"string",editType:"calc",description:["Obsolete. Set `xref` and `yref` separately instead."].join(" ")}}})},37830:(t,e,r)=>{"use strict";var n=r(12822),i=r(75815),o=r(8214).draw;function a(t){var e=t._fullLayout;n.filterVisible(e.annotations).forEach((function(e){var r=i.getFromId(t,e.xref),n=i.getFromId(t,e.yref),o=i.getRefType(e.xref),a=i.getRefType(e.yref);e._extremes={},"range"===o&&s(e,r),"range"===a&&s(e,n)}))}function s(t,e){var r,n=e._id,o=n.charAt(0),a=t[o],s=t["a"+o],l=t[o+"ref"],c=t["a"+o+"ref"],u=t["_"+o+"padplus"],h=t["_"+o+"padminus"],d={x:1,y:-1}[o]*t[o+"shift"],f=3*t.arrowsize*t.arrowwidth||0,p=f+d,m=f-d,g=3*t.startarrowsize*t.arrowwidth||0,v=g+d,b=g-d;if(c===l){var y=i.findExtremes(e,[e.r2c(a)],{ppadplus:p,ppadminus:m}),x=i.findExtremes(e,[e.r2c(s)],{ppadplus:Math.max(u,v),ppadminus:Math.max(h,b)});r={min:[y.min[0],x.min[0]],max:[y.max[0],x.max[0]]}}else v=s?v+s:v,b=s?b-s:b,r=i.findExtremes(e,[e.r2c(a)],{ppadplus:Math.max(u,p,v),ppadminus:Math.max(h,m,b)});t._extremes[n]=r}t.exports=function(t){var e=t._fullLayout;if(n.filterVisible(e.annotations).length&&t._fullData.length)return n.syncOrAsync([o,a],t)}},74434:(t,e,r)=>{"use strict";var n=r(12822),i=r(25059),o=r(46121).arrayEditor;function a(t,e){var r,n,i,o,a,l,c,u=t._fullLayout.annotations,h=[],d=[],f=[],p=(e||[]).length;for(r=0;r0||r.explicitOff.length>0},onClick:function(t,e){var r,s,l=a(t,e),c=l.on,u=l.off.concat(l.explicitOff),h={},d=t._fullLayout.annotations;if(c.length||u.length){for(r=0;r{"use strict";var n=r(12822),i=r(17499);t.exports=function(t,e,r,o){o("opacity");var a=o("bgcolor"),s=o("bordercolor"),l=i.opacity(s);o("borderpad");var c=o("borderwidth"),u=o("showarrow");if(o("text",u?" 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v(t,e){var r=t._fullLayout.annotations[e]||{},n=l.getFromId(t,r.xref),i=l.getFromId(t,r.yref);n&&n.setScale(),i&&i.setScale(),y(t,r,e,!1,n,i)}function b(t,e,r,n,i){var o=i[r],a=i[r+"ref"],s=-1!==r.indexOf("y"),c="domain"===l.getRefType(a),u=s?n.h:n.w;return t?c?o+(s?-e:e)/t._length:t.p2r(t.r2p(o)+e):o+(s?-e:e)/u}function y(t,e,r,o,v,y){var x,_,w=t._fullLayout,k=t._fullLayout._size,A=t._context.edits;o?(x="annotation-"+o,_=o+".annotations"):(x="annotation",_="annotations");var M=m(t.layout,_,e),T=M.modifyBase,S=M.modifyItem,C=M.getUpdateObj;w._infolayer.selectAll("."+x+'[data-index="'+r+'"]').remove();var E="clip"+w._uid+"_ann"+r;if(e._input&&!1!==e.visible){var L={x:{},y:{}},z=+e.textangle||0,O=w._infolayer.append("g").classed(x,!0).attr("data-index",String(r)).style("opacity",e.opacity),D=O.append("g").classed("annotation-text-g",!0),I=A[e.showarrow?"annotationTail":"annotationPosition"],F=e.captureevents||A.annotationText||I,R=D.append("g").style("pointer-events",F?"all":null).call(f,"pointer").on("click",(function(){t._dragging=!1,t.emit("plotly_clickannotation",q(n.event))}));e.hovertext&&R.on("mouseover",(function(){var r=e.hoverlabel,n=r.font,i=this.getBoundingClientRect(),o=t.getBoundingClientRect();h.loneHover({x0:i.left-o.left,x1:i.right-o.left,y:(i.top+i.bottom)/2-o.top,text:e.hovertext,color:r.bgcolor,borderColor:r.bordercolor,fontFamily:n.family,fontSize:n.size,fontColor:n.color,fontWeight:n.weight,fontStyle:n.style,fontVariant:n.variant,fontShadow:n.fontShadow,fontLineposition:n.fontLineposition,fontTextcase:n.fontTextcase},{container:w._hoverlayer.node(),outerContainer:w._paper.node(),gd:t})})).on("mouseout",(function(){h.loneUnhover(w._hoverlayer.node())}));var P=e.borderwidth,j=e.borderpad,N=P+j,B=R.append("rect").attr("class","bg").style("stroke-width",P+"px").call(c.stroke,e.bordercolor).call(c.fill,e.bgcolor),U=e.width||e.height,G=w._topclips.selectAll("#"+E).data(U?[0]:[]);G.enter().append("clipPath").classed("annclip",!0).attr("id",E).append("rect"),G.exit().remove();var V=e.font,H=w._meta?a.templateString(e.text,w._meta):e.text,W=R.append("text").classed("annotation-text",!0).text(H);A.annotationText?W.call(d.makeEditable,{delegate:R,gd:t}).call(Y).on("edit",(function(r){e.text=r,this.call(Y),S("text",r),v&&v.autorange&&T(v._name+".autorange",!0),y&&y.autorange&&T(y._name+".autorange",!0),i.call("_guiRelayout",t,C())})):W.call(Y)}else n.selectAll("#"+E).remove();function q(t){var n={index:r,annotation:e._input,fullAnnotation:e,event:t};return o&&(n.subplotId=o),n}function Y(r){return r.call(u.font,V).attr({"text-anchor":{left:"start",right:"end"}[e.align]||"middle"}),d.convertToTspans(r,t,Z),r}function Z(){var r=W.selectAll("a");1===r.size()&&r.text()===W.text()&&R.insert("a",":first-child").attr({"xlink:xlink:href":r.attr("xlink:href"),"xlink:xlink:show":r.attr("xlink:show")}).style({cursor:"pointer"}).node().appendChild(B.node());var n=R.select(".annotation-text-math-group"),h=!n.empty(),m=u.bBox((h?n:W).node()),x=m.width,_=m.height,M=e.width||x,F=e.height||_,j=Math.round(M+2*N),V=Math.round(F+2*N);function H(t,e){return"auto"===e&&(e=t<1/3?"left":t>2/3?"right":"center"),{center:0,middle:0,left:.5,bottom:-.5,right:-.5,top:.5}[e]}for(var Y=!1,Z=["x","y"],X=0;X1)&&(nt===rt?((ft=it.r2fraction(e["a"+et]))<0||ft>1)&&(Y=!0):Y=!0),$=it._offset+it.r2p(e[et]),Q=.5}else{var pt="domain"===dt;"x"===et?(K=e[et],$=pt?it._offset+it._length*K:$=k.l+k.w*K):(K=1-e[et],$=pt?it._offset+it._length*K:$=k.t+k.h*K),Q=e.showarrow?.5:K}if(e.showarrow){ht.head=$;var mt=e["a"+et];if(tt=at*H(.5,e.xanchor)-st*H(.5,e.yanchor),nt===rt){var gt=l.getRefType(nt);"domain"===gt?("y"===et&&(mt=1-mt),ht.tail=it._offset+it._length*mt):"paper"===gt?"y"===et?(mt=1-mt,ht.tail=k.t+k.h*mt):ht.tail=k.l+k.w*mt:ht.tail=it._offset+it.r2p(mt),J=tt}else ht.tail=$+mt,J=tt+mt;ht.text=ht.tail+tt;var vt=w["x"===et?"width":"height"];if("paper"===rt&&(ht.head=a.constrain(ht.head,1,vt-1)),"pixel"===nt){var bt=-Math.max(ht.tail-3,ht.text),yt=Math.min(ht.tail+3,ht.text)-vt;bt>0?(ht.tail+=bt,ht.text+=bt):yt>0&&(ht.tail-=yt,ht.text-=yt)}ht.tail+=ut,ht.head+=ut}else J=tt=lt*H(Q,ct),ht.text=$+tt;ht.text+=ut,tt+=ut,J+=ut,e["_"+et+"padplus"]=lt/2+J,e["_"+et+"padminus"]=lt/2-J,e["_"+et+"size"]=lt,e["_"+et+"shift"]=tt}if(Y)R.remove();else{var xt=0,_t=0;if("left"!==e.align&&(xt=(M-x)*("center"===e.align?.5:1)),"top"!==e.valign&&(_t=(F-_)*("middle"===e.valign?.5:1)),h)n.select("svg").attr({x:N+xt-1,y:N+_t}).call(u.setClipUrl,U?E:null,t);else{var wt=N+_t-m.top,kt=N+xt-m.left;W.call(d.positionText,kt,wt).call(u.setClipUrl,U?E:null,t)}G.select("rect").call(u.setRect,N,N,M,F),B.call(u.setRect,P/2,P/2,j-P,V-P),R.call(u.setTranslate,Math.round(L.x.text-j/2),Math.round(L.y.text-V/2)),D.attr({transform:"rotate("+z+","+L.x.text+","+L.y.text+")"});var At,Mt=function(r,n){O.selectAll(".annotation-arrow-g").remove();var l=L.x.head,h=L.y.head,d=L.x.tail+r,f=L.y.tail+n,m=L.x.text+r,x=L.y.text+n,_=a.rotationXYMatrix(z,m,x),w=a.apply2DTransform(_),M=a.apply2DTransform2(_),E=+B.attr("width"),I=+B.attr("height"),F=m-.5*E,P=F+E,j=x-.5*I,N=j+I,U=[[F,j,F,N],[F,N,P,N],[P,N,P,j],[P,j,F,j]].map(M);if(!U.reduce((function(t,e){return t^!!a.segmentsIntersect(l,h,l+1e6,h+1e6,e[0],e[1],e[2],e[3])}),!1)){U.forEach((function(t){var e=a.segmentsIntersect(d,f,l,h,t[0],t[1],t[2],t[3]);e&&(d=e.x,f=e.y)}));var G=e.arrowwidth,V=e.arrowcolor,H=e.arrowside,W=O.append("g").style({opacity:c.opacity(V)}).classed("annotation-arrow-g",!0),q=W.append("path").attr("d","M"+d+","+f+"L"+l+","+h).style("stroke-width",G+"px").call(c.stroke,c.rgb(V));if(g(q,H,e),A.annotationPosition&&q.node().parentNode&&!o){var Y=l,Z=h;if(e.standoff){var X=Math.sqrt(Math.pow(l-d,2)+Math.pow(h-f,2));Y+=e.standoff*(d-l)/X,Z+=e.standoff*(f-h)/X}var $,J,K=W.append("path").classed("annotation-arrow",!0).classed("anndrag",!0).classed("cursor-move",!0).attr({d:"M3,3H-3V-3H3ZM0,0L"+(d-Y)+","+(f-Z),transform:s(Y,Z)}).style("stroke-width",G+6+"px").call(c.stroke,"rgba(0,0,0,0)").call(c.fill,"rgba(0,0,0,0)");p.init({element:K.node(),gd:t,prepFn:function(){var t=u.getTranslate(R);$=t.x,J=t.y,v&&v.autorange&&T(v._name+".autorange",!0),y&&y.autorange&&T(y._name+".autorange",!0)},moveFn:function(t,r){var n=w($,J),i=n[0]+t,o=n[1]+r;R.call(u.setTranslate,i,o),S("x",b(v,t,"x",k,e)),S("y",b(y,r,"y",k,e)),e.axref===e.xref&&S("ax",b(v,t,"ax",k,e)),e.ayref===e.yref&&S("ay",b(y,r,"ay",k,e)),W.attr("transform",s(t,r)),D.attr({transform:"rotate("+z+","+i+","+o+")"})},doneFn:function(){i.call("_guiRelayout",t,C());var e=document.querySelector(".js-notes-box-panel");e&&e.redraw(e.selectedObj)}})}}};e.showarrow&&Mt(0,0),I&&p.init({element:R.node(),gd:t,prepFn:function(){At=D.attr("transform")},moveFn:function(t,r){var n="pointer";if(e.showarrow)e.axref===e.xref?S("ax",b(v,t,"ax",k,e)):S("ax",e.ax+t),e.ayref===e.yref?S("ay",b(y,r,"ay",k.w,e)):S("ay",e.ay+r),Mt(t,r);else{if(o)return;var i,a;if(v)i=b(v,t,"x",k,e);else{var l=e._xsize/k.w,c=e.x+(e._xshift-e.xshift)/k.w-l/2;i=p.align(c+t/k.w,l,0,1,e.xanchor)}if(y)a=b(y,r,"y",k,e);else{var u=e._ysize/k.h,h=e.y-(e._yshift+e.yshift)/k.h-u/2;a=p.align(h-r/k.h,u,0,1,e.yanchor)}S("x",i),S("y",a),v&&y||(n=p.getCursor(v?.5:i,y?.5:a,e.xanchor,e.yanchor))}D.attr({transform:s(t,r)+At}),f(R,n)},clickFn:function(r,n){e.captureevents&&t.emit("plotly_clickannotation",q(n))},doneFn:function(){f(R),i.call("_guiRelayout",t,C());var e=document.querySelector(".js-notes-box-panel");e&&e.redraw(e.selectedObj)}})}}}t.exports={draw:function(t){var e=t._fullLayout;e._infolayer.selectAll(".annotation").remove();for(var r=0;r{"use strict";var n=r(27941),i=r(17499),o=r(91208),a=r(12822),s=a.strScale,l=a.strRotate,c=a.strTranslate;t.exports=function(t,e,r){var a,u,h,d,f=t.node(),p=o[r.arrowhead||0],m=o[r.startarrowhead||0],g=(r.arrowwidth||1)*(r.arrowsize||1),v=(r.arrowwidth||1)*(r.startarrowsize||1),b=e.indexOf("start")>=0,y=e.indexOf("end")>=0,x=p.backoff*g+r.standoff,_=m.backoff*v+r.startstandoff;if("line"===f.nodeName){a={x:+t.attr("x1"),y:+t.attr("y1")},u={x:+t.attr("x2"),y:+t.attr("y2")};var w=a.x-u.x,k=a.y-u.y;if(d=(h=Math.atan2(k,w))+Math.PI,x&&_&&x+_>Math.sqrt(w*w+k*k))return void I();if(x){if(x*x>w*w+k*k)return void I();var A=x*Math.cos(h),M=x*Math.sin(h);u.x+=A,u.y+=M,t.attr({x2:u.x,y2:u.y})}if(_){if(_*_>w*w+k*k)return void I();var T=_*Math.cos(h),S=_*Math.sin(h);a.x-=T,a.y-=S,t.attr({x1:a.x,y1:a.y})}}else if("path"===f.nodeName){var C=f.getTotalLength(),E="";if(C{"use strict";var n=r(8214),i=r(74434);t.exports={moduleType:"component",name:"annotations",layoutAttributes:r(77061),supplyLayoutDefaults:r(26194),includeBasePlot:r(39859)("annotations"),calcAutorange:r(37830),draw:n.draw,drawOne:n.drawOne,drawRaw:n.drawRaw,hasClickToShow:i.hasClickToShow,onClick:i.onClick,convertCoords:r(44102)}},98368:(t,e,r)=>{"use strict";var n=r(77061),i=r(62309).overrideAll,o=r(46121).templatedArray;t.exports=i(o("annotation",{visible:n.visible,x:{valType:"any",description:["Sets the annotation's x position."].join(" ")},y:{valType:"any",description:["Sets the annotation's y position."].join(" ")},z:{valType:"any",description:["Sets the annotation's z position."].join(" ")},ax:{valType:"number",description:["Sets the x component of the arrow tail about the arrow head (in pixels)."].join(" ")},ay:{valType:"number",description:["Sets the y component of the arrow tail about the arrow head (in pixels)."].join(" ")},xanchor:n.xanchor,xshift:n.xshift,yanchor:n.yanchor,yshift:n.yshift,text:n.text,textangle:n.textangle,font:n.font,width:n.width,height:n.height,opacity:n.opacity,align:n.align,valign:n.valign,bgcolor:n.bgcolor,bordercolor:n.bordercolor,borderpad:n.borderpad,borderwidth:n.borderwidth,showarrow:n.showarrow,arrowcolor:n.arrowcolor,arrowhead:n.arrowhead,startarrowhead:n.startarrowhead,arrowside:n.arrowside,arrowsize:n.arrowsize,startarrowsize:n.startarrowsize,arrowwidth:n.arrowwidth,standoff:n.standoff,startstandoff:n.startstandoff,hovertext:n.hovertext,hoverlabel:n.hoverlabel,captureevents:n.captureevents}),"calc","from-root")},81030:(t,e,r)=>{"use strict";var n=r(12822),i=r(75815);function o(t,e){var r=e.fullSceneLayout.domain,o=e.fullLayout._size,a={pdata:null,type:"linear",autorange:!1,range:[-1/0,1/0]};t._xa={},n.extendFlat(t._xa,a),i.setConvert(t._xa),t._xa._offset=o.l+r.x[0]*o.w,t._xa.l2p=function(){return.5*(1+t._pdata[0]/t._pdata[3])*o.w*(r.x[1]-r.x[0])},t._ya={},n.extendFlat(t._ya,a),i.setConvert(t._ya),t._ya._offset=o.t+(1-r.y[1])*o.h,t._ya.l2p=function(){return.5*(1-t._pdata[1]/t._pdata[3])*o.h*(r.y[1]-r.y[0])}}t.exports=function(t){for(var e=t.fullSceneLayout.annotations,r=0;r{"use strict";var n=r(12822),i=r(75815),o=r(35677),a=r(35486),s=r(98368);function l(t,e,r,o){function l(r,i){return n.coerce(t,e,s,r,i)}function c(t){var n=t+"axis",o={_fullLayout:{}};return o._fullLayout[n]=r[n],i.coercePosition(e,o,l,t,t,.5)}l("visible")&&(a(t,e,o.fullLayout,l),c("x"),c("y"),c("z"),n.noneOrAll(t,e,["x","y","z"]),e.xref="x",e.yref="y",e.zref="z",l("xanchor"),l("yanchor"),l("xshift"),l("yshift"),e.showarrow&&(e.axref="pixel",e.ayref="pixel",l("ax",-10),l("ay",-30),n.noneOrAll(t,e,["ax","ay"])))}t.exports=function(t,e,r){o(t,e,{name:"annotations",handleItemDefaults:l,fullLayout:r.fullLayout})}},86191:(t,e,r)=>{"use strict";var n=r(8214).drawRaw,i=r(40747),o=["x","y","z"];t.exports=function(t){for(var e=t.fullSceneLayout,r=t.dataScale,a=e.annotations,s=0;s1){c=!0;break}}c?t.fullLayout._infolayer.select(".annotation-"+t.id+'[data-index="'+s+'"]').remove():(l._pdata=i(t.glplot.cameraParams,[e.xaxis.r2l(l.x)*r[0],e.yaxis.r2l(l.y)*r[1],e.zaxis.r2l(l.z)*r[2]]),n(t.graphDiv,l,s,t.id,l._xa,l._ya))}}},95997:(t,e,r)=>{"use strict";var n=r(25059),i=r(12822);t.exports={moduleType:"component",name:"annotations3d",schema:{subplots:{scene:{annotations:r(98368)}}},layoutAttributes:r(98368),handleDefaults:r(76023),includeBasePlot:function(t,e){var r=n.subplotsRegistry.gl3d;if(r)for(var o=r.attrRegex,a=Object.keys(t),s=0;s{"use strict";e.defaults=["#1f77b4","#ff7f0e","#2ca02c","#d62728","#9467bd","#8c564b","#e377c2","#7f7f7f","#bcbd22","#17becf"],e.defaultLine="#444",e.lightLine="#eee",e.background="#fff",e.borderLine="#BEC8D9",e.lightFraction=1e3/11},17499:(t,e,r)=>{"use strict";var n=r(18106),i=r(7370),o=r(98507).isTypedArray,a=t.exports={},s=r(84226);a.defaults=s.defaults;var l=a.defaultLine=s.defaultLine;a.lightLine=s.lightLine;var c=a.background=s.background;function u(t){if(i(t)||"string"!=typeof t)return t;var e=t.trim();if("rgb"!==e.substr(0,3))return t;var r=e.match(/^rgba?\s*\(([^()]*)\)$/);if(!r)return t;var n=r[1].trim().split(/\s*[\s,]\s*/),o="a"===e.charAt(3)&&4===n.length;if(!o&&3!==n.length)return t;for(var a=0;a=0))return t;if(3===a)n[a]>1&&(n[a]=1);else if(n[a]>=1)return t}var s=Math.round(255*n[0])+", "+Math.round(255*n[1])+", "+Math.round(255*n[2]);return o?"rgba("+s+", "+n[3]+")":"rgb("+s+")"}a.tinyRGB=function(t){var e=t.toRgb();return"rgb("+Math.round(e.r)+", "+Math.round(e.g)+", "+Math.round(e.b)+")"},a.rgb=function(t){return a.tinyRGB(n(t))},a.opacity=function(t){return t?n(t).getAlpha():0},a.addOpacity=function(t,e){var r=n(t).toRgb();return"rgba("+Math.round(r.r)+", "+Math.round(r.g)+", "+Math.round(r.b)+", "+e+")"},a.combine=function(t,e){var r=n(t).toRgb();if(1===r.a)return n(t).toRgbString();var i=n(e||c).toRgb(),o=1===i.a?i:{r:255*(1-i.a)+i.r*i.a,g:255*(1-i.a)+i.g*i.a,b:255*(1-i.a)+i.b*i.a},a={r:o.r*(1-r.a)+r.r*r.a,g:o.g*(1-r.a)+r.g*r.a,b:o.b*(1-r.a)+r.b*r.a};return n(a).toRgbString()},a.interpolate=function(t,e,r){var i=n(t).toRgb(),o=n(e).toRgb(),a={r:r*i.r+(1-r)*o.r,g:r*i.g+(1-r)*o.g,b:r*i.b+(1-r)*o.b};return n(a).toRgbString()},a.contrast=function(t,e,r){var i=n(t);return 1!==i.getAlpha()&&(i=n(a.combine(t,c))),(i.isDark()?e?i.lighten(e):c:r?i.darken(r):l).toString()},a.stroke=function(t,e){var r=n(e);t.style({stroke:a.tinyRGB(r),"stroke-opacity":r.getAlpha()})},a.fill=function(t,e){var r=n(e);t.style({fill:a.tinyRGB(r),"fill-opacity":r.getAlpha()})},a.clean=function(t){if(t&&"object"==typeof t){var e,r,n,i,s=Object.keys(t);for(e=0;e{"use strict";var n=r(86130),i=r(75058),o=r(98260).extendFlat,a=r(62309).overrideAll;t.exports=a({orientation:{valType:"enumerated",values:["h","v"],dflt:"v",description:"Sets the orientation of the colorbar."},thicknessmode:{valType:"enumerated",values:["fraction","pixels"],dflt:"pixels",description:["Determines whether this color bar's thickness","(i.e. the measure in the constant color direction)","is set in units of plot *fraction* or in *pixels*.","Use `thickness` to set the value."].join(" ")},thickness:{valType:"number",min:0,dflt:30,description:["Sets the thickness of the color bar","This measure excludes the size of the padding, ticks and labels."].join(" ")},lenmode:{valType:"enumerated",values:["fraction","pixels"],dflt:"fraction",description:["Determines whether this color bar's length","(i.e. the measure in the color variation direction)","is set in units of plot *fraction* or in *pixels.","Use `len` to set the value."].join(" ")},len:{valType:"number",min:0,dflt:1,description:["Sets the length of the color bar","This measure excludes the padding of both ends.","That is, the color bar length is this length minus the","padding on both ends."].join(" ")},x:{valType:"number",description:["Sets the x position with respect to `xref` of the color bar (in plot fraction).","When `xref` is *paper*, defaults to 1.02 when `orientation` is *v* and","0.5 when `orientation` is *h*.","When `xref` is *container*, defaults to *1* when `orientation` is *v* and","0.5 when `orientation` is *h*.","Must be between *0* and *1* if `xref` is *container*","and between *-2* and *3* if `xref` is *paper*."].join(" ")},xref:{valType:"enumerated",dflt:"paper",values:["container","paper"],editType:"layoutstyle",description:["Sets the container `x` refers to.","*container* spans the entire `width` of the plot.","*paper* refers to the width of the plotting area only."].join(" ")},xanchor:{valType:"enumerated",values:["left","center","right"],description:["Sets this color bar's horizontal position anchor.","This anchor binds the `x` position to the *left*, *center*","or *right* of the color bar.","Defaults to *left* when `orientation` is *v* and","*center* when `orientation` is *h*."].join(" ")},xpad:{valType:"number",min:0,dflt:10,description:"Sets the amount of padding (in px) along the x direction."},y:{valType:"number",description:["Sets the y position with respect to `yref` of the color bar (in plot fraction).","When `yref` is *paper*, defaults to 0.5 when `orientation` is *v* and","1.02 when `orientation` is *h*.","When `yref` is *container*, defaults to 0.5 when `orientation` is *v* and","1 when `orientation` is *h*.","Must be between *0* and *1* if `yref` is *container*","and between *-2* and *3* if `yref` is *paper*."].join(" ")},yref:{valType:"enumerated",dflt:"paper",values:["container","paper"],editType:"layoutstyle",description:["Sets the container `y` refers to.","*container* spans the entire `height` of the plot.","*paper* refers to the height of the plotting area only."].join(" ")},yanchor:{valType:"enumerated",values:["top","middle","bottom"],description:["Sets this color bar's vertical position anchor","This anchor binds the `y` position to the *top*, *middle*","or *bottom* of the color bar.","Defaults to *middle* when `orientation` is *v* and","*bottom* when `orientation` is *h*."].join(" ")},ypad:{valType:"number",min:0,dflt:10,description:"Sets the amount of padding (in px) along the y direction."},outlinecolor:n.linecolor,outlinewidth:n.linewidth,bordercolor:n.linecolor,borderwidth:{valType:"number",min:0,dflt:0,description:["Sets the width (in px) or the border enclosing this color bar."].join(" ")},bgcolor:{valType:"color",dflt:"rgba(0,0,0,0)",description:"Sets the color of padded area."},tickmode:n.minor.tickmode,nticks:n.nticks,tick0:n.tick0,dtick:n.dtick,tickvals:n.tickvals,ticktext:n.ticktext,ticks:o({},n.ticks,{dflt:""}),ticklabeloverflow:o({},n.ticklabeloverflow,{description:["Determines how we handle tick labels that would overflow either the graph div or the domain of the axis.","The default value for inside tick labels is *hide past domain*.","In other cases the default is *hide past div*."].join(" ")}),ticklabelposition:{valType:"enumerated",values:["outside","inside","outside top","inside top","outside left","inside left","outside right","inside right","outside bottom","inside bottom"],dflt:"outside",description:["Determines where tick labels are drawn relative to the ticks.","Left and right options are used when `orientation` is *h*,","top and bottom when `orientation` is *v*."].join(" ")},ticklen:n.ticklen,tickwidth:n.tickwidth,tickcolor:n.tickcolor,ticklabelstep:n.ticklabelstep,showticklabels:n.showticklabels,labelalias:n.labelalias,tickfont:i({description:"Sets the color bar's tick label font"}),tickangle:n.tickangle,tickformat:n.tickformat,tickformatstops:n.tickformatstops,tickprefix:n.tickprefix,showtickprefix:n.showtickprefix,ticksuffix:n.ticksuffix,showticksuffix:n.showticksuffix,separatethousands:n.separatethousands,exponentformat:n.exponentformat,minexponent:n.minexponent,showexponent:n.showexponent,title:{text:{valType:"string",description:["Sets the title of the color bar.","Note that before the existence of `title.text`, the title's","contents used to be defined as the `title` attribute itself.","This behavior has been deprecated."].join(" ")},font:i({description:["Sets this color bar's title font.","Note that the title's font used to be set","by the now deprecated `titlefont` attribute."].join(" ")}),side:{valType:"enumerated",values:["right","top","bottom"],description:["Determines the location of color bar's title","with respect to the color bar.","Defaults to *top* when `orientation` if *v* and ","defaults to *right* when `orientation` if *h*.","Note that the title's location used to be set","by the now deprecated `titleside` attribute."].join(" ")}},_deprecated:{title:{valType:"string",description:["Deprecated in favor of color bar's `title.text`.","Note that value of color bar's `title` is no longer a simple","*string* but a set of sub-attributes."].join(" ")},titlefont:i({description:"Deprecated in favor of color bar's `title.font`."}),titleside:{valType:"enumerated",values:["right","top","bottom"],dflt:"top",description:"Deprecated in favor of color bar's `title.side`."}}},"colorbars","from-root")},30733:t=>{"use strict";t.exports={cn:{colorbar:"colorbar",cbbg:"cbbg",cbfill:"cbfill",cbfills:"cbfills",cbline:"cbline",cblines:"cblines",cbaxis:"cbaxis",cbtitleunshift:"cbtitleunshift",cbtitle:"cbtitle",cboutline:"cboutline",crisp:"crisp",jsPlaceholder:"js-placeholder"}}},81692:(t,e,r)=>{"use strict";var n=r(12822),i=r(46121),o=r(49342),a=r(8736),s=r(84411),l=r(12213),c=r(76699);t.exports=function(t,e,r){var u=i.newContainer(e,"colorbar"),h=t.colorbar||{};function d(t,e){return n.coerce(h,u,c,t,e)}var f=r.margin||{t:0,b:0,l:0,r:0},p=r.width-f.l-f.r,m=r.height-f.t-f.b,g="v"===d("orientation"),v=d("thicknessmode");d("thickness","fraction"===v?30/(g?p:m):30);var b=d("lenmode");d("len","fraction"===b?1:g?m:p);var y,x,_,w="paper"===d("yref"),k="paper"===d("xref"),A="left";g?(_="middle",A=k?"left":"right",y=k?1.02:1,x=.5):(_=w?"bottom":"top",A="center",y=.5,x=w?1.02:1),n.coerce(h,u,{x:{valType:"number",min:k?-2:0,max:k?3:1,dflt:y}},"x"),n.coerce(h,u,{y:{valType:"number",min:w?-2:0,max:w?3:1,dflt:x}},"y"),d("xanchor",A),d("xpad"),d("yanchor",_),d("ypad"),n.noneOrAll(h,u,["x","y"]),d("outlinecolor"),d("outlinewidth"),d("bordercolor"),d("borderwidth"),d("bgcolor");var M=n.coerce(h,u,{ticklabelposition:{valType:"enumerated",dflt:"outside",values:g?["outside","inside","outside top","inside top","outside bottom","inside bottom"]:["outside","inside","outside left","inside left","outside right","inside right"]}},"ticklabelposition");d("ticklabeloverflow",-1!==M.indexOf("inside")?"hide past domain":"hide past div"),o(h,u,d,"linear");var T=r.font,S={noAutotickangles:!0,noTicklabelshift:!0,noTicklabelstandoff:!0,outerTicks:!1,font:T};-1!==M.indexOf("inside")&&(S.bgColor="black"),l(h,u,d,"linear",S),s(h,u,d,"linear",S),a(h,u,d,"linear",S),d("title.text",r._dfltTitle.colorbar);var C=u.showticklabels?u.tickfont:T,E=n.extendFlat({},T,{family:C.family,size:n.bigFont(C.size)});n.coerceFont(d,"title.font",E),d("title.side",g?"top":"right")}},29648:(t,e,r)=>{"use strict";var n=r(27941),i=r(18106),o=r(51137),a=r(25059),s=r(75815),l=r(19846),c=r(12822),u=c.strTranslate,h=r(98260).extendFlat,d=r(76292),f=r(40666),p=r(17499),m=r(6883),g=r(80394),v=r(42226).flipScale,b=r(91200),y=r(52869),x=r(86130),_=r(89701),w=_.LINE_SPACING,k=_.FROM_TL,A=_.FROM_BR,M=r(30733).cn;t.exports={draw:function(t){var e=t._fullLayout._infolayer.selectAll("g."+M.colorbar).data(function(t){var e,r,n,i,o=t._fullLayout,a=t.calcdata,s=[];function l(t){return h(t,{_fillcolor:null,_line:{color:null,width:null,dash:null},_levels:{start:null,end:null,size:null},_filllevels:null,_fillgradient:null,_zrange:null})}function c(){"function"==typeof i.calc?i.calc(t,n,e):(e._fillgradient=r.reversescale?v(r.colorscale):r.colorscale,e._zrange=[r[i.min],r[i.max]])}for(var u=0;u0?n>=l:n<=l));i++)n>u&&n0?n>=l:n<=l));i++)n>r[0]&&n1){var ft=Math.pow(10,Math.floor(Math.log(dt)/Math.LN10));ut*=ft*c.roundUp(dt/ft,[2,5,10]),(Math.abs(q.start)/q.size+1e-6)%1<2e-6&&(lt.tick0=0)}lt.dtick=ut}lt.domain=a?[at+O/j.h,at+Q-O/j.h]:[at+z/j.w,at+Q-z/j.w],lt.setScale(),t.attr("transform",u(Math.round(j.l),Math.round(j.t)));var pt,mt=t.select("."+M.cbtitleunshift).attr("transform",u(-Math.round(j.l),-Math.round(j.t))),gt=lt.ticklabelposition,vt=lt.title.font.size,bt=t.select("."+M.cbaxis),yt=0,xt=0;function _t(n,i){var o={propContainer:lt,propName:e._propPrefix+"title",traceIndex:e._traceIndex,_meta:e._meta,placeholder:P._dfltTitle.colorbar,containerGroup:t.select("."+M.cbtitle)},a="h"===n.charAt(0)?n.substr(1):"h"+n;t.selectAll("."+a+",."+a+"-math-group").remove(),m.draw(r,n,h(o,i||{}))}return c.syncOrAsync([o.previousPromises,function(){var t,e;(a&&ct||!a&&!ct)&&("top"===G&&(t=z+j.l+tt*D,e=O+j.t+et*(1-at-Q)+3+.75*vt),"bottom"===G&&(t=z+j.l+tt*D,e=O+j.t+et*(1-at)-3-.25*vt),"right"===G&&(e=O+j.t+et*I+3+.75*vt,t=z+j.l+tt*at),_t(lt._id+"title",{attributes:{x:t,y:e,"text-anchor":a?"start":"middle"}}))},function(){if(!a&&!ct||a&&ct){var o,l=t.select("."+M.cbtitle),h=l.select("text"),d=[-T/2,T/2],p=l.select(".h"+lt._id+"title-math-group").node(),m=15.6;if(h.node()&&(m=parseInt(h.node().style.fontSize,10)*w),p?(o=f.bBox(p),xt=o.width,(yt=o.height)>m&&(d[1]-=(yt-m)/2)):h.node()&&!h.classed(M.jsPlaceholder)&&(o=f.bBox(h.node()),xt=o.width,yt=o.height),a){if(yt){if(yt+=5,"top"===G)lt.domain[1]-=yt/j.h,d[1]*=-1;else{lt.domain[0]+=yt/j.h;var v=g.lineCount(h);d[1]+=(1-v)*m}l.attr("transform",u(d[0],d[1])),lt.setScale()}}else xt&&("right"===G&&(lt.domain[0]+=(xt+vt/2)/j.w),l.attr("transform",u(d[0],d[1])),lt.setScale())}t.selectAll("."+M.cbfills+",."+M.cblines).attr("transform",a?u(0,Math.round(j.h*(1-lt.domain[1]))):u(Math.round(j.w*lt.domain[0]),0)),bt.attr("transform",a?u(0,Math.round(-j.t)):u(Math.round(-j.l),0));var b=t.select("."+M.cbfills).selectAll("rect."+M.cbfill).attr("style","").data(Z);b.enter().append("rect").classed(M.cbfill,!0).attr("style",""),b.exit().remove();var y=V.map(lt.c2p).map(Math.round).sort((function(t,e){return t-e}));b.each((function(t,o){var s=[0===o?V[0]:(Z[o]+Z[o-1])/2,o===Z.length-1?V[1]:(Z[o]+Z[o+1])/2].map(lt.c2p).map(Math.round);a&&(s[1]=c.constrain(s[1]+(s[1]>s[0])?1:-1,y[0],y[1]));var l=n.select(this).attr(a?"x":"y",rt).attr(a?"y":"x",n.min(s)).attr(a?"width":"height",Math.max($,2)).attr(a?"height":"width",Math.max(n.max(s)-n.min(s),2));if(e._fillgradient)f.gradient(l,r,e._id,a?"vertical":"horizontalreversed",e._fillgradient,"fill");else{var u=W(t).replace("e-","");l.attr("fill",i(u).toHexString())}}));var x=t.select("."+M.cblines).selectAll("path."+M.cbline).data(B.color&&B.width?X:[]);x.enter().append("path").classed(M.cbline,!0),x.exit().remove(),x.each((function(t){var e=rt,r=Math.round(lt.c2p(t))+B.width/2%1;n.select(this).attr("d","M"+(a?e+","+r:r+","+e)+(a?"h":"v")+$).call(f.lineGroupStyle,B.width,H(t),B.dash)})),bt.selectAll("g."+lt._id+"tick,path").remove();var _=rt+$+(T||0)/2-("outside"===e.ticks?1:0),k=s.calcTicks(lt),A=s.getTickSigns(lt)[2];return s.drawTicks(r,lt,{vals:"inside"===lt.ticks?s.clipEnds(lt,k):k,layer:bt,path:s.makeTickPath(lt,_,A),transFn:s.makeTransTickFn(lt)}),s.drawLabels(r,lt,{vals:k,layer:bt,transFn:s.makeTransTickLabelFn(lt),labelFns:s.makeLabelFns(lt,_)})},function(){if(a&&!ct||!a&&ct){var t,i,o=lt.position||0,s=lt._offset+lt._length/2;if("right"===G)i=s,t=j.l+tt*o+10+vt*(lt.showticklabels?1:.5);else if(t=s,"bottom"===G&&(i=j.t+et*o+10+(-1===gt.indexOf("inside")?lt.tickfont.size:0)+("intside"!==lt.ticks&&e.ticklen||0)),"top"===G){var l=U.text.split("
").length;i=j.t+et*o+10-$-w*vt*l}_t((a?"h":"v")+lt._id+"title",{avoid:{selection:n.select(r).selectAll("g."+lt._id+"tick"),side:G,offsetTop:a?0:j.t,offsetLeft:a?j.l:0,maxShift:a?P.width:P.height},attributes:{x:t,y:i,"text-anchor":"middle"},transform:{rotate:a?-90:0,offset:0}})}},o.previousPromises,function(){var n,s=$+T/2;-1===gt.indexOf("inside")&&(n=f.bBox(bt.node()),s+=a?n.width:n.height),pt=mt.select("text");var c=0,h=a&&"top"===G,m=!a&&"right"===G,g=0;if(pt.node()&&!pt.classed(M.jsPlaceholder)){var b,y=mt.select(".h"+lt._id+"title-math-group").node();y&&(a&&ct||!a&&!ct)?(c=(n=f.bBox(y)).width,b=n.height):(c=(n=f.bBox(mt.node())).right-j.l-(a?rt:st),b=n.bottom-j.t-(a?st:rt),a||"top"!==G||(s+=n.height,g=n.height)),m&&(pt.attr("transform",u(c/2+vt/2,0)),c*=2),s=Math.max(s,a?c:b)}var x=2*(a?z:O)+s+S+T/2,w=0;!a&&U.text&&"bottom"===L&&I<=0&&(x+=w=x/2,g+=w),P._hColorbarMoveTitle=w,P._hColorbarMoveCBTitle=g;var N=S+T,B=(a?rt:st)-N/2-(a?z:0),V=(a?st:rt)-(a?K:O+g-w);t.select("."+M.cbbg).attr("x",B).attr("y",V).attr(a?"width":"height",Math.max(x-w,2)).attr(a?"height":"width",Math.max(K+N,2)).call(p.fill,C).call(p.stroke,e.bordercolor).style("stroke-width",S);var H=m?Math.max(c-10,0):0;t.selectAll("."+M.cboutline).attr("x",(a?rt:st+z)+H).attr("y",(a?st+O-K:rt)+(h?yt:0)).attr(a?"width":"height",Math.max($,2)).attr(a?"height":"width",Math.max(K-(a?2*O+yt:2*z+H),2)).call(p.stroke,e.outlinecolor).style({fill:"none","stroke-width":T});var W=a?nt*x:0,q=a?0:(1-it)*x-g;if(W=R?j.l-W:-W,q=F?j.t-q:-q,t.attr("transform",u(W,q)),!a&&(S||i(C).getAlpha()&&!i.equals(P.paper_bgcolor,C))){var Y=bt.selectAll("text"),Z=Y[0].length,X=t.select("."+M.cbbg).node(),J=f.bBox(X),Q=f.getTranslate(t);Y.each((function(t,e){var r=Z-1;if(0===e||e===r){var n,i=f.bBox(this),o=f.getTranslate(this);if(e===r){var a=i.right+o.x;(n=J.right+Q.x+st-S-2+D-a)>0&&(n=0)}else if(0===e){var s=i.left+o.x;(n=J.left+Q.x+st+S+2-s)<0&&(n=0)}n&&(Z<3?this.setAttribute("transform","translate("+n+",0) "+this.getAttribute("transform")):this.setAttribute("visibility","hidden"))}}))}var tt={},et=k[E],ot=A[E],at=k[L],ut=A[L],ht=x-$;a?("pixels"===d?(tt.y=I,tt.t=K*at,tt.b=K*ut):(tt.t=tt.b=0,tt.yt=I+l*at,tt.yb=I-l*ut),"pixels"===_?(tt.x=D,tt.l=x*et,tt.r=x*ot):(tt.l=ht*et,tt.r=ht*ot,tt.xl=D-v*et,tt.xr=D+v*ot)):("pixels"===d?(tt.x=D,tt.l=K*et,tt.r=K*ot):(tt.l=tt.r=0,tt.xl=D+l*et,tt.xr=D-l*ot),"pixels"===_?(tt.y=1-I,tt.t=x*at,tt.b=x*ut):(tt.t=ht*at,tt.b=ht*ut,tt.yt=I-v*at,tt.yb=I+v*ut));var dt=e.y<.5?"b":"t",ft=e.x<.5?"l":"r";r._fullLayout._reservedMargin[e._id]={};var xt={r:P.width-B-W,l:B+tt.r,b:P.height-V-q,t:V+tt.b};R&&F?o.autoMargin(r,e._id,tt):R?r._fullLayout._reservedMargin[e._id][dt]=xt[dt]:F||a?r._fullLayout._reservedMargin[e._id][ft]=xt[ft]:r._fullLayout._reservedMargin[e._id][dt]=xt[dt]}],r)}(r,e,t);v&&v.then&&(t._promises||[]).push(v),t._context.edits.colorbarPosition&&function(t,e,r){var n,i,o,s="v"===e.orientation,c=r._fullLayout._size;l.init({element:t.node(),gd:r,prepFn:function(){n=t.attr("transform"),d(t)},moveFn:function(r,a){t.attr("transform",n+u(r,a)),i=l.align((s?e._uFrac:e._vFrac)+r/c.w,s?e._thickFrac:e._lenFrac,0,1,e.xanchor),o=l.align((s?e._vFrac:1-e._uFrac)-a/c.h,s?e._lenFrac:e._thickFrac,0,1,e.yanchor);var h=l.getCursor(i,o,e.xanchor,e.yanchor);d(t,h)},doneFn:function(){if(d(t),void 0!==i&&void 0!==o){var n={};n[e._propPrefix+"x"]=i,n[e._propPrefix+"y"]=o,void 0!==e._traceIndex?a.call("_guiRestyle",r,n,e._traceIndex):a.call("_guiRelayout",r,n)}}})}(r,e,t)})),e.exit().each((function(e){o.autoMargin(t,e._id)})).remove(),e.order()}}},52467:(t,e,r)=>{"use strict";var n=r(12822);t.exports=function(t){return n.isPlainObject(t.colorbar)}},10552:(t,e,r)=>{"use strict";t.exports={moduleType:"component",name:"colorbar",attributes:r(76699),supplyDefaults:r(81692),draw:r(29648).draw,hasColorbar:r(52467)}},89322:(t,e,r)=>{"use strict";var n=r(76699),i=r(46233).counter,o=r(54747),a=r(78920).scales,s=o(a);function l(t){return"`"+t+"`"}t.exports=function(t,e){t=t||"";var r,o,c=(e=e||{}).cLetter||"c",u="onlyIfNumerical"in e?e.onlyIfNumerical:Boolean(t),h="noScale"in e?e.noScale:"marker.line"===t,d="showScaleDflt"in e?e.showScaleDflt:"z"===c,f="string"==typeof e.colorscaleDflt?a[e.colorscaleDflt]:null,p=e.editTypeOverride||"",m=t?t+".":"";"colorAttr"in e?(r=e.colorAttr,o=e.colorAttr):o="in "+l(m+(r={z:"z",c:"color"}[c]));var g=u?" Has an effect only if "+o+" is set to a numerical array.":"",v=c+"auto",b=c+"min",y=c+"max",x=c+"mid",_=l(m+v),w=l(m+b),k=l(m+y),A=w+" and "+k,M={};M[b]=M[y]=void 0;var T={};T[v]=!1;var S={};return"color"===r&&(S.color={valType:"color",arrayOk:!0,editType:p||"style",description:["Sets the",t,"color.","It accepts either a specific color","or an array of numbers that are mapped to the colorscale","relative to the max and min values of the array or relative to",A,"if set."].join(" ")},e.anim&&(S.color.anim=!0)),S[v]={valType:"boolean",dflt:!0,editType:"calc",impliedEdits:M,description:["Determines whether or not the color domain is computed","with respect to the input data (here "+o+") or the bounds set in",A+g,"Defaults to `false` when",A,"are set by the user."].join(" ")},S[b]={valType:"number",dflt:null,editType:p||"plot",impliedEdits:T,description:["Sets the lower bound of the color domain."+g,"Value should have the same units as",o,"and if set,",k,"must be set as well."].join(" ")},S[y]={valType:"number",dflt:null,editType:p||"plot",impliedEdits:T,description:["Sets the upper bound of the color domain."+g,"Value should have the same units as",o,"and if set,",w,"must be set as well."].join(" ")},S[x]={valType:"number",dflt:null,editType:"calc",impliedEdits:M,description:["Sets the mid-point of the color domain by scaling",w,"and/or",k,"to be equidistant to this point."+g,"Value should have the same units as",o+".","Has no effect when",_,"is `false`."].join(" ")},S.colorscale={valType:"colorscale",editType:"calc",dflt:f,impliedEdits:{autocolorscale:!1},description:["Sets the colorscale."+g,"The colorscale must be an array containing","arrays mapping a normalized value to an","rgb, rgba, hex, hsl, hsv, or named color string.","At minimum, a mapping for the lowest (0) and highest (1)","values are required. 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e=t[0].trace,r=e.error_y||{},o=e.error_x||{},a=n.select(this);a.selectAll("path.yerror").style("stroke-width",r.thickness+"px").call(i.stroke,r.color),o.copy_ystyle&&(o=r),a.selectAll("path.xerror").style("stroke-width",o.thickness+"px").call(i.stroke,o.color)}))}},60713:(t,e,r)=>{"use strict";var n=r(75058),i=r(53572).hoverlabel,o=r(98260).extendFlat;t.exports={hoverlabel:{bgcolor:o({},i.bgcolor,{arrayOk:!0,description:"Sets the background color of the hover labels for this trace"}),bordercolor:o({},i.bordercolor,{arrayOk:!0,description:"Sets the border color of the hover labels for this trace."}),font:n({arrayOk:!0,editType:"none",description:"Sets the font used in hover labels."}),align:o({},i.align,{arrayOk:!0}),namelength:o({},i.namelength,{arrayOk:!0}),editType:"none"}}},56173:(t,e,r)=>{"use strict";var n=r(12822),i=r(25059);function o(t,e,r,i){i=i||n.identity,Array.isArray(t)&&(e[0][r]=i(t))}t.exports=function(t){var e=t.calcdata,r=t._fullLayout;function a(t){return 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n=t.xaxes||[],i=t.yaxes||[],o=0;o=0&&r.index{"use strict";var n=r(27941),i=r(7370),o=r(18106),a=r(12822),s=a.pushUnique,l=a.strTranslate,c=a.strRotate,u=r(16677),h=r(80394),d=r(27517),f=r(40666),p=r(17499),m=r(19846),g=r(75815),v=r(21197).zindexSeparator,b=r(25059),y=r(66811),x=r(99259),_=r(64083),w=r(67739),k=x.YANGLE,A=Math.PI*k/180,M=1/Math.sin(A),T=Math.cos(A),S=Math.sin(A),C=x.HOVERARROWSIZE,E=x.HOVERTEXTPAD,L={box:!0,ohlc:!0,violin:!0,candlestick:!0},z={scatter:!0,scattergl:!0,splom:!0};function O(t,e){return t.distance-e.distance}function D(t){return[t.trace.index,t.index,t.x0,t.y0,t.name,t.attr,t.xa?t.xa._id:"",t.ya?t.ya._id:""].join(",")}e.hover=function(t,e,r,o){t=a.getGraphDiv(t);var l=e.target;a.throttle(t._fullLayout._uid+x.HOVERID,x.HOVERMINTIME,(function(){!function(t,e,r,o,l){r||(r="xy"),"string"==typeof r&&(r=r.split(v)[0]);var 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0!==_&&Math.min(u,_)-Math.max(c,x)>1&&("left"===i.side?(s=i._mainLinePosition,l=r.width):l=i._mainLinePosition):void 0!==b&&void 0!==y&&Math.min(u,y)-Math.max(c,b)>1&&("top"===i.side?(s=i._mainLinePosition,l=r.height):l=i._mainLinePosition)}g[v++]=[{datum:t,traceIndex:t.trace.index,dp:0,pos:t.pos,posref:t.posref,size:t.by*(o?M:1)/2,pmin:s,pmax:l}]})),g.sort((function(t,e){return t[0].posref-e[0].posref||p*(e[0].traceIndex-t[0].traceIndex)}));!i&&f<=m;){for(f++,i=!0,s=0;s.01){for(l=S.length-1;l>=0;l--)S[l].dp+=o;for(T.push.apply(T,S),g.splice(s+1,1),u=0,l=T.length-1;l>=0;l--)u+=T[l].dp;for(a=u/T.length,l=T.length-1;l>=0;l--)T[l].dp-=a;i=!1}else s++}g.forEach(A)}for(s=g.length-1;s>=0;s--){var z=g[s];for(l=z.length-1;l>=0;l--){var O=z[l],D=O.datum;D.offset=O.dp,D.del=O.del}}}(ce,ae,_,le.commonLabelBoundingBox),j(ce,ae,_._invScaleX,_._invScaleY)),l&&l.tagName){var ue=b.getComponentMethod("annotations","hasClickToShow")(t,qt);d(n.select(l),ue?"pointer":"")}l&&!o&&function(t,e,r){if(!r||r.length!==t._hoverdata.length)return!0;for(var n=r.length-1;n>=0;n--){var i=r[n],o=t._hoverdata[n];if(i.curveNumber!==o.curveNumber||String(i.pointNumber)!==String(o.pointNumber)||String(i.pointNumbers)!==String(o.pointNumbers))return!0}return!1}(t,0,Wt)&&(Wt&&t.emit("plotly_unhover",{event:e,points:Wt}),t.emit("plotly_hover",{event:e,points:t._hoverdata,xaxes:$,yaxes:J,xvals:nt,yvals:it}))}(t,e,r,o,l)}))},e.loneHover=function(t,e){var r=!0;Array.isArray(t)||(r=!1,t=[t]);var i=e.gd,o=H(i),a=W(i),s=!1,l=F(t.map((function(t){var r=t._x0||t.x0||t.x||0,n=t._x1||t.x1||t.x||0,s=t._y0||t.y0||t.y||0,l=t._y1||t.y1||t.y||0,c=t.eventData;if(c){var u=Math.min(r,n),h=Math.max(r,n),d=Math.min(s,l),f=Math.max(s,l),m=t.trace;if(b.traceIs(m,"gl3d")){var g=i._fullLayout[m.scene]._scene.container,v=g.offsetLeft,y=g.offsetTop;u+=v,h+=v,d+=y,f+=y}c.bbox={x0:u+a,x1:h+a,y0:d+o,y1:f+o},e.inOut_bbox&&e.inOut_bbox.push(c.bbox)}else c=!1;return{color:t.color||p.defaultLine,x0:t.x0||t.x||0,x1:t.x1||t.x||0,y0:t.y0||t.y||0,y1:t.y1||t.y||0,xLabel:t.xLabel,yLabel:t.yLabel,zLabel:t.zLabel,text:t.text,name:t.name,idealAlign:t.idealAlign,borderColor:t.borderColor,fontFamily:t.fontFamily,fontSize:t.fontSize,fontColor:t.fontColor,fontWeight:t.fontWeight,fontStyle:t.fontStyle,fontVariant:t.fontVariant,nameLength:t.nameLength,textAlign:t.textAlign,trace:t.trace||{index:0,hoverinfo:""},xa:{_offset:0},ya:{_offset:0},index:0,hovertemplate:t.hovertemplate||!1,hovertemplateLabels:t.hovertemplateLabels||!1,eventData:c}})),{gd:i,hovermode:"closest",rotateLabels:s,bgColor:e.bgColor||p.background,container:n.select(e.container),outerContainer:e.outerContainer||e.container}).hoverLabels,c=0,u=0;return l.sort((function(t,e){return t.y0-e.y0})).each((function(t,r){var n=t.y0-t.by/2;t.offset=n-5([\s\S]*)<\/extra>/;function F(t,e){var r=e.gd,i=r._fullLayout,o=e.hovermode,s=e.rotateLabels,u=e.bgColor,d=e.container,m=e.outerContainer,g=e.commonLabelOpts||{};if(0===t.length)return[[]];var v=e.fontFamily||x.HOVERFONT,A=e.fontSize||x.HOVERFONTSIZE,M=e.fontWeight||i.font.weight,T=e.fontStyle||i.font.style,S=e.fontVariant||i.font.variant,L=e.fontTextcase||i.font.textcase,z=e.fontLineposition||i.font.lineposition,O=e.fontShadow||i.font.shadow,I=t[0],F=I.xa,P=I.ya,j=o.charAt(0),N=j+"Label",B=I[N];if(void 0===B&&"multicategory"===F.type)for(var U=0;Ui.width-k&&(D=i.width-k),e.attr("d","M"+(y-D)+",0L"+(y-D+C)+","+w+C+"H"+k+"v"+w+(2*E+_.height)+"H"+-k+"V"+w+C+"H"+(y-D-C)+"Z"),y=D,Q.minX=y-k,Q.maxX=y+k,"top"===F.side?(Q.minY=x-(2*E+_.height),Q.maxY=x-E):(Q.minY=x+E,Q.maxY=x+(2*E+_.height))}else{var R,j,N;"right"===P.side?(R="start",j=1,N="",y=F._offset+F._length):(R="end",j=-1,N="-",y=F._offset),x=P._offset+(I.y0+I.y1)/2,s.attr("text-anchor",R),e.attr("d","M0,0L"+N+C+","+C+"V"+(E+_.height/2)+"h"+N+(2*E+_.width)+"V-"+(E+_.height/2)+"H"+N+C+"V-"+C+"Z"),Q.minY=x-(E+_.height/2),Q.maxY=x+(E+_.height/2),"right"===P.side?(Q.minX=y+C,Q.maxX=y+C+(2*E+_.width)):(Q.minX=y-C-(2*E+_.width),Q.maxX=y-C);var U,G=_.height/2,H=V-_.top-G,W="clip"+i._uid+"commonlabel"+P._id;if(y<_.width+2*E+C){U="M-"+(C+E)+"-"+G+"h-"+(_.width-E)+"V"+G+"h"+(_.width-E)+"Z";var Y=_.width-y+E;h.positionText(s,Y,H),"end"===R&&s.selectAll("tspan").each((function(){var t=n.select(this),e=f.tester.append("text").text(t.text()).call(f.font,b),i=q(r,e.node());Math.round(i.width)=0?pt:mt+bt=0?mt:Tt+bt=0?dt:ft+yt=0?ft:St+yt=0,"top"!==t.idealAlign&&J||!K?J?(N+=G/2,t.anchor="start"):t.anchor="middle":(N-=G/2,t.anchor="end"),t.crossPos=N;else{if(t.pos=N,J=j+U/2+Q<=H,K=j-U/2-Q>=0,"left"!==t.idealAlign&&J||!K)if(J)j+=U/2,t.anchor="start";else{t.anchor="middle";var tt=Q/2,et=j+tt-H,rt=j-tt;et>0&&(j-=et),rt<0&&(j+=-rt)}else j-=U/2,t.anchor="end";t.crossPos=j}w.attr("text-anchor",t.anchor),I&&D.attr("text-anchor",t.anchor),e.attr("transform",l(j,N)+(s?c(k):""))})),{hoverLabels:Ct,commonLabelBoundingBox:Q}}function R(t,e,r,n,i,o){var s="",l="";void 0!==t.nameOverride&&(t.name=t.nameOverride),t.name&&(t.trace._meta&&(t.name=a.templateString(t.name,t.trace._meta)),s=G(t.name,t.nameLength));var c=r.charAt(0),u="x"===c?"y":"x";void 0!==t.zLabel?(void 0!==t.xLabel&&(l+="x: "+t.xLabel+"
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l(t){a.font[t]||(a.font[t]=s?e.legend.font[t]:e.font[t])}e&&o(e.hovermode)&&(a.font||(a.font={}),l("size"),l("family"),l("color"),l("weight"),l("style"),l("variant"),s?(a.bgcolor||(a.bgcolor=i.combine(e.legend.bgcolor,e.paper_bgcolor)),a.bordercolor||(a.bordercolor=e.legend.bordercolor)):a.bgcolor||(a.bgcolor=e.paper_bgcolor)),r("hoverlabel.bgcolor",a.bgcolor),r("hoverlabel.bordercolor",a.bordercolor),r("hoverlabel.namelength",a.namelength),n.coerceFont(r,"hoverlabel.font",a.font),r("hoverlabel.align",a.align)}},85400:(t,e,r)=>{"use strict";var n=r(12822),i=r(53572);t.exports=function(t,e){function r(r,o){return void 0!==e[r]?e[r]:n.coerce(t,e,i,r,o)}return r("clickmode"),r("hoversubplots"),r("hovermode")}},70410:(t,e,r)=>{"use strict";var n=r(27941),i=r(12822),o=r(19846),a=r(66811),s=r(53572),l=r(87408);t.exports={moduleType:"component",name:"fx",constants:r(99259),schema:{layout:s},attributes:r(60713),layoutAttributes:s,supplyLayoutGlobalDefaults:r(26271),supplyDefaults:r(55470),supplyLayoutDefaults:r(3315),calc:r(56173),getDistanceFunction:a.getDistanceFunction,getClosest:a.getClosest,inbox:a.inbox,quadrature:a.quadrature,appendArrayPointValue:a.appendArrayPointValue,castHoverOption:function(t,e,r){return i.castOption(t,e,"hoverlabel."+r)},castHoverinfo:function(t,e,r){return i.castOption(t,r,"hoverinfo",(function(r){return i.coerceHoverinfo({hoverinfo:r},{_module:t._module},e)}))},hover:l.hover,unhover:o.unhover,loneHover:l.loneHover,loneUnhover:function(t){var e=i.isD3Selection(t)?t:n.select(t);e.selectAll("g.hovertext").remove(),e.selectAll(".spikeline").remove()},click:r(43006)}},53572:(t,e,r)=>{"use strict";var n=r(99259),i=r(75058),o=i({editType:"none",description:"Sets the default hover label font used by all traces on the graph."});o.family.dflt=n.HOVERFONT,o.size.dflt=n.HOVERFONTSIZE,t.exports={clickmode:{valType:"flaglist",flags:["event","select"],dflt:"event",editType:"plot",extras:["none"],description:["Determines the mode of single click interactions.","*event* is the default value and emits the `plotly_click`","event. 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This mode also supports persistent selections,","meaning that pressing Shift while clicking, adds to / subtracts from an","existing selection. *select* with `hovermode`: *x* can be confusing, consider","explicitly setting `hovermode`: *closest* when using this feature.","Selection events are sent accordingly as long as *event* flag is set as well.","When the *event* flag is missing, `plotly_click` and `plotly_selected`","events are not fired."].join(" ")},dragmode:{valType:"enumerated",values:["zoom","pan","select","lasso","drawclosedpath","drawopenpath","drawline","drawrect","drawcircle","orbit","turntable",!1],dflt:"zoom",editType:"modebar",description:["Determines the mode of drag interactions.","*select* and *lasso* apply only to scatter traces with","markers or text. *orbit* and *turntable* apply only to","3D scenes."].join(" ")},hovermode:{valType:"enumerated",values:["x","y","closest",!1,"x unified","y unified"],dflt:"closest",editType:"modebar",description:["Determines the mode of hover interactions.","If *closest*, a single hoverlabel will appear","for the *closest* point within the `hoverdistance`.","If *x* (or *y*), multiple hoverlabels will appear for multiple points","at the *closest* x- (or y-) coordinate within the `hoverdistance`,","with the caveat that no more than one hoverlabel will appear per trace.","If *x unified* (or *y unified*), a single hoverlabel will appear","multiple points at the closest x- (or y-) coordinate within the `hoverdistance`","with the caveat that no more than one hoverlabel will appear per trace.","In this mode, spikelines are enabled by default perpendicular to the specified axis.","If false, hover interactions are disabled."].join(" ")},hoversubplots:{valType:"enumerated",values:["single","overlaying","axis"],dflt:"overlaying",editType:"none",description:["Determines expansion of hover effects to other subplots","If *single* just the axis pair of the primary point is included without overlaying subplots.","If *overlaying* all subplots using the main axis and occupying the same space are included.","If *axis*, also include stacked subplots using the same axis","when `hovermode` is set to *x*, *x unified*, *y* or *y unified*."].join(" ")},hoverdistance:{valType:"integer",min:-1,dflt:20,editType:"none",description:["Sets the default distance (in pixels) to look for data","to add hover labels (-1 means no cutoff, 0 means no looking for data).","This is only a real distance for hovering on point-like objects,","like scatter points. 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You may reuse x axes","within the same column, and y axes within the same row.","Non-cartesian subplots and traces that support `domain` can place themselves","in this grid separately using the `gridcell` attribute."].join(" ")},xaxes:{valType:"info_array",freeLength:!0,items:{valType:"enumerated",values:[a.x.toString(),""],editType:"plot"},editType:"plot",description:["Used with `yaxes` when the x and y axes are shared across columns and rows.","Each entry should be an x axis id like *x*, *x2*, etc., or ** to","not put an x axis in that column. Entries other than ** must be unique.","Ignored if `subplots` is present. If missing but `yaxes` is present,","will generate consecutive IDs."].join(" ")},yaxes:{valType:"info_array",freeLength:!0,items:{valType:"enumerated",values:[a.y.toString(),""],editType:"plot"},editType:"plot",description:["Used with `yaxes` when the x and y axes are shared across columns and rows.","Each entry should be an y axis id like *y*, *y2*, etc., or ** to","not put a y axis in that row. Entries other than ** must be unique.","Ignored if `subplots` is present. If missing but `xaxes` is present,","will generate consecutive IDs."].join(" ")},pattern:{valType:"enumerated",values:["independent","coupled"],dflt:"coupled",editType:"plot",description:["If no `subplots`, `xaxes`, or `yaxes` are given but we do have `rows` and `columns`,","we can generate defaults using consecutive axis IDs, in two ways:","*coupled* gives one x axis per column and one y axis per row.","*independent* uses a new xy pair for each cell, left-to-right across each row","then iterating rows according to `roworder`."].join(" ")},xgap:{valType:"number",min:0,max:1,editType:"plot",description:["Horizontal space between grid cells, expressed as a fraction","of the total width available to one cell. Defaults to 0.1","for coupled-axes grids and 0.2 for independent grids."].join(" ")},ygap:{valType:"number",min:0,max:1,editType:"plot",description:["Vertical space between grid cells, expressed as a fraction","of the total height available to one cell. Defaults to 0.1","for coupled-axes grids and 0.3 for independent grids."].join(" ")},domain:o({name:"grid",editType:"plot",noGridCell:!0},{description:["The first and last cells end exactly at the domain","edges, with no grout around the edges."].join(" ")}),xside:{valType:"enumerated",values:["bottom","bottom plot","top plot","top"],dflt:"bottom plot",editType:"plot",description:["Sets where the x axis labels and titles go. *bottom* means","the very bottom of the grid. *bottom plot* is the lowest plot","that each x axis is used in. *top* and *top plot* are similar."].join(" ")},yside:{valType:"enumerated",values:["left","left plot","right plot","right"],dflt:"left plot",editType:"plot",description:["Sets where the y axis labels and titles go. *left* means","the very left edge of the grid. *left plot* is the leftmost plot","that each y axis is used in. *right* and *right plot* are similar."].join(" ")},editType:"plot"};function c(t,e,r){var n=e[r+"axes"],i=Object.keys((t._splomAxes||{})[r]||{});return Array.isArray(n)?n:i.length?i:void 0}function u(t,e,r,n,i,o){var a=e(t+"gap",r),s=e("domain."+t);e(t+"side",n);for(var l=new Array(i),c=s[0],u=(s[1]-c)/(i-a),h=u*(1-a),d=0;d1){d||f||p||"independent"===A("pattern")&&(d=!0),g._hasSubplotGrid=d;var y,x,_="top to bottom"===A("roworder"),w=d?.2:.1,k=d?.3:.1;m&&e._splomGridDflt&&(y=e._splomGridDflt.xside,x=e._splomGridDflt.yside),g._domains={x:u("x",A,w,y,b),y:u("y",A,k,x,v,_)}}else delete e.grid}function A(t,e){return n.coerce(r,g,l,t,e)}},contentDefaults:function(t,e){var r=e.grid;if(r&&r._domains){var n,i,o,a,s,l,u,d=t.grid||{},f=e._subplots,p=r._hasSubplotGrid,m=r.rows,g=r.columns,v="independent"===r.pattern,b=r._axisMap={};if(p){var y=d.subplots||[];l=r.subplots=new Array(m);var x=1;for(n=0;n{"use strict";var n=r(21197),i=r(46121).templatedArray,o=r(53644);t.exports=i("image",{visible:{valType:"boolean",dflt:!0,editType:"arraydraw",description:["Determines whether or not this image is visible."].join(" ")},source:{valType:"string",editType:"arraydraw",description:["Specifies the URL of the image to be used.","The URL must be accessible from the domain where the","plot code is run, and can be either relative or absolute."].join(" ")},layer:{valType:"enumerated",values:["below","above"],dflt:"above",editType:"arraydraw",description:["Specifies whether images are drawn below or above traces.","When `xref` and `yref` are both set to `paper`,","image is drawn below the entire plot area."].join(" ")},sizex:{valType:"number",dflt:0,editType:"arraydraw",description:["Sets the image container size horizontally.","The image will be sized based on the `position` value.","When `xref` is set to `paper`, units are sized relative","to the plot width.","When `xref` ends with ` domain`, units are sized relative","to the axis width."].join(" ")},sizey:{valType:"number",dflt:0,editType:"arraydraw",description:["Sets the image container size vertically.","The image will be sized based on the `position` value.","When `yref` is set to `paper`, units are sized relative","to the plot height.","When `yref` ends with ` domain`, units are sized relative","to the axis height."].join(" ")},sizing:{valType:"enumerated",values:["fill","contain","stretch"],dflt:"contain",editType:"arraydraw",description:["Specifies which dimension of the image to constrain."].join(" ")},opacity:{valType:"number",min:0,max:1,dflt:1,editType:"arraydraw",description:"Sets the opacity of the image."},x:{valType:"any",dflt:0,editType:"arraydraw",description:["Sets the image's x position.","When `xref` is set to `paper`, units are sized relative","to the plot height.","See `xref` for more info"].join(" ")},y:{valType:"any",dflt:0,editType:"arraydraw",description:["Sets the image's y position.","When `yref` is set to `paper`, units are sized relative","to the plot height.","See `yref` for more info"].join(" ")},xanchor:{valType:"enumerated",values:["left","center","right"],dflt:"left",editType:"arraydraw",description:"Sets the anchor for the x position"},yanchor:{valType:"enumerated",values:["top","middle","bottom"],dflt:"top",editType:"arraydraw",description:"Sets the anchor for the y position."},xref:{valType:"enumerated",values:["paper",n.idRegex.x.toString()],dflt:"paper",editType:"arraydraw",description:["Sets the images's x coordinate axis.",o.axisRefDescription("x","left","right")].join(" ")},yref:{valType:"enumerated",values:["paper",n.idRegex.y.toString()],dflt:"paper",editType:"arraydraw",description:["Sets the images's y coordinate axis.",o.axisRefDescription("y","bottom","top")].join(" ")},editType:"arraydraw"})},22470:(t,e,r)=>{"use strict";var n=r(7370),i=r(61814);t.exports=function(t,e,r,o){e=e||{};var a="log"===r&&"linear"===e.type,s="linear"===r&&"log"===e.type;if(a||s)for(var l,c,u=t._fullLayout.images,h=e._id.charAt(0),d=0;d{"use strict";var n=r(12822),i=r(75815),o=r(35677),a=r(3653);function s(t,e,r){function o(r,i){return n.coerce(t,e,a,r,i)}var s=o("source");if(!o("visible",!!s))return e;o("layer"),o("xanchor"),o("yanchor"),o("sizex"),o("sizey"),o("sizing"),o("opacity");for(var l={_fullLayout:r},c=["x","y"],u=0;u<2;u++){var h=c[u],d=i.coerceRef(t,e,l,h,"paper",void 0);"paper"!==d&&i.getFromId(l,d)._imgIndices.push(e._index),i.coercePosition(e,l,o,d,h,0)}return e}t.exports=function(t,e){o(t,e,{name:"images",handleItemDefaults:s})}},87030:(t,e,r)=>{"use strict";var n=r(27941),i=r(40666),o=r(75815),a=r(99246),s=r(25853);t.exports=function(t){var e,r,l=t._fullLayout,c=[],u={},h=[];for(r=0;r{"use strict";t.exports={moduleType:"component",name:"images",layoutAttributes:r(3653),supplyLayoutDefaults:r(96658),includeBasePlot:r(39859)("images"),draw:r(87030),convertCoords:r(22470)}},15524:(t,e,r)=>{"use strict";var n=r(75058),i=r(84226);t.exports={_isSubplotObj:!0,visible:{valType:"boolean",dflt:!0,editType:"legend",description:["Determines whether or not this legend is visible."].join(" ")},bgcolor:{valType:"color",editType:"legend",description:["Sets the legend background color.","Defaults to `layout.paper_bgcolor`."].join(" ")},bordercolor:{valType:"color",dflt:i.defaultLine,editType:"legend",description:"Sets the color of the border enclosing the legend."},borderwidth:{valType:"number",min:0,dflt:0,editType:"legend",description:"Sets the width (in px) of the border enclosing the legend."},font:n({editType:"legend",description:"Sets the font used to text the legend items."}),grouptitlefont:n({editType:"legend",description:["Sets the font for group titles in legend.","Defaults to `legend.font` with its size increased about 10%."].join(" ")}),orientation:{valType:"enumerated",values:["v","h"],dflt:"v",editType:"legend",description:"Sets the orientation of the legend."},traceorder:{valType:"flaglist",flags:["reversed","grouped"],extras:["normal"],editType:"legend",description:["Determines the order at which the legend items are displayed.","If *normal*, the items are displayed top-to-bottom in the same","order as the input data.","If *reversed*, the items are displayed in the opposite order","as *normal*.","If *grouped*, the items are displayed in groups","(when a trace `legendgroup` is provided).","if *grouped+reversed*, the items are displayed in the opposite order","as *grouped*."].join(" ")},tracegroupgap:{valType:"number",min:0,dflt:10,editType:"legend",description:["Sets the amount of vertical space (in px) between legend groups."].join(" ")},entrywidth:{valType:"number",min:0,editType:"legend",description:["Sets the width (in px or fraction) of the legend.","Use 0 to size the entry based on the text width,","when `entrywidthmode` is set to *pixels*."].join(" ")},entrywidthmode:{valType:"enumerated",values:["fraction","pixels"],dflt:"pixels",editType:"legend",description:"Determines what entrywidth means."},indentation:{valType:"number",min:-15,dflt:0,editType:"legend",description:"Sets the indentation (in px) of the legend entries."},itemsizing:{valType:"enumerated",values:["trace","constant"],dflt:"trace",editType:"legend",description:["Determines if the legend items symbols scale with their corresponding *trace* attributes","or remain *constant* independent of the symbol size on the graph."].join(" ")},itemwidth:{valType:"number",min:30,dflt:30,editType:"legend",description:"Sets the width (in px) of the legend item symbols (the part other than the title.text)."},itemclick:{valType:"enumerated",values:["toggle","toggleothers",!1],dflt:"toggle",editType:"legend",description:["Determines the behavior on legend item click.","*toggle* toggles the visibility of the item clicked on the graph.","*toggleothers* makes the clicked item the sole visible item on the graph.","*false* disables legend item click interactions."].join(" ")},itemdoubleclick:{valType:"enumerated",values:["toggle","toggleothers",!1],dflt:"toggleothers",editType:"legend",description:["Determines the behavior on legend item double-click.","*toggle* toggles the visibility of the item clicked on the graph.","*toggleothers* makes the clicked item the sole visible item on the graph.","*false* disables legend item double-click interactions."].join(" ")},groupclick:{valType:"enumerated",values:["toggleitem","togglegroup"],dflt:"togglegroup",editType:"legend",description:["Determines the behavior on legend group item click.","*toggleitem* toggles the visibility of the individual item clicked on the graph.","*togglegroup* toggles the visibility of all items in the same legendgroup as the item clicked on the graph."].join(" ")},x:{valType:"number",editType:"legend",description:["Sets the x position with respect to `xref` (in normalized coordinates) of the legend.","When `xref` is *paper*, defaults to *1.02* for vertical legends and","defaults to *0* for horizontal legends.","When `xref` is *container*, defaults to *1* for vertical legends and","defaults to *0* for horizontal legends.","Must be between *0* and *1* if `xref` is *container*.","and between *-2* and *3* if `xref` is *paper*."].join(" ")},xref:{valType:"enumerated",dflt:"paper",values:["container","paper"],editType:"layoutstyle",description:["Sets the container `x` refers to.","*container* spans the entire `width` of the plot.","*paper* refers to the width of the plotting area only."].join(" ")},xanchor:{valType:"enumerated",values:["auto","left","center","right"],dflt:"left",editType:"legend",description:["Sets the legend's horizontal position anchor.","This anchor binds the `x` position to the *left*, *center*","or *right* of the legend.","Value *auto* anchors legends to the right for `x` values greater than or equal to 2/3,","anchors legends to the left for `x` values less than or equal to 1/3 and","anchors legends with respect to their center otherwise."].join(" ")},y:{valType:"number",editType:"legend",description:["Sets the y position with respect to `yref` (in normalized coordinates) of the legend.","When `yref` is *paper*, defaults to *1* for vertical legends,","defaults to *-0.1* for horizontal legends on graphs w/o range sliders and","defaults to *1.1* for horizontal legends on graph with one or multiple range sliders.","When `yref` is *container*, defaults to *1*.","Must be between *0* and *1* if `yref` is *container*","and between *-2* and *3* if `yref` is *paper*."].join(" ")},yref:{valType:"enumerated",dflt:"paper",values:["container","paper"],editType:"layoutstyle",description:["Sets the container `y` refers to.","*container* spans the entire `height` of the plot.","*paper* refers to the height of the plotting area only."].join(" ")},yanchor:{valType:"enumerated",values:["auto","top","middle","bottom"],editType:"legend",description:["Sets the legend's vertical position anchor","This anchor binds the `y` position to the *top*, *middle*","or *bottom* of the legend.","Value *auto* anchors legends at their bottom for `y` values less than or equal to 1/3,","anchors legends to at their top for `y` values greater than or equal to 2/3 and","anchors legends with respect to their middle otherwise."].join(" ")},uirevision:{valType:"any",editType:"none",description:["Controls persistence of legend-driven changes in trace and pie label","visibility. 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r,i,a=m(t),l=a.anyFill,c=a.anyLine,h=a.showLine,d=a.showMarker,f=t[0],p=f.trace,g=!d&&!c&&!l&&u.hasText(p);function v(t,e,r,n){var i=o.nestedProperty(p,t).get(),a=o.isArrayOrTypedArray(i)&&e?e(i):i;if(b&&a&&void 0!==n&&(a=n),r){if(ar[1])return r[1]}return a}function y(t){return f._distinct&&f.index&&t[f.index]?t[f.index]:t[0]}if(d||g||h){var x={},w={};if(d){x.mc=v("marker.color",y),x.mx=v("marker.symbol",y),x.mo=v("marker.opacity",o.mean,[.2,1]),x.mlc=v("marker.line.color",y),x.mlw=v("marker.line.width",o.mean,[0,5],2),w.marker={sizeref:1,sizemin:1,sizemode:"diameter"};var k=v("marker.size",o.mean,[2,16],12);x.ms=k,w.marker.size=k}h&&(w.line={width:v("line.width",y,[0,10],5)}),g&&(x.tx="Aa",x.tp=v("textposition",y),x.ts=10,x.tc=v("textfont.color",y),x.tf=v("textfont.family",y),x.tw=v("textfont.weight",y),x.ty=v("textfont.style",y),x.tv=v("textfont.variant",y),x.tC=v("textfont.textcase",y),x.tE=v("textfont.lineposition",y),x.tS=v("textfont.shadow",y)),r=[o.minExtend(f,x)],(i=o.minExtend(p,w)).selectedpoints=null,i.texttemplate=null}var A=n.select(this).select("g.legendpoints"),M=A.selectAll("path.scatterpts").data(d?r:[]);M.enter().insert("path",":first-child").classed("scatterpts",!0).attr("transform",_),M.exit().remove(),M.call(s.pointStyle,i,e),d&&(r[0].mrc=3);var T=A.selectAll("g.pointtext").data(g?r:[]);T.enter().append("g").classed("pointtext",!0).append("text").attr("transform",_),T.exit().remove(),T.selectAll("text").call(s.textPointStyle,i,e)})).each((function(t){var 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f,p="in"===l?.5:2,m=(1+p)/2,g=(1-p)/2;for(i=0;i{"use strict";var n=r(47685),i=Object.keys(n),o=["drawline","drawopenpath","drawclosedpath","drawcircle","drawrect","eraseshape"],a=["v1hovermode","hoverclosest","hovercompare","togglehover","togglespikelines"].concat(o),s=[];i.forEach((function(t){!function(t){if(-1===a.indexOf(t._cat||t.name)){var e=t.name,r=(t._cat||t.name).toLowerCase();-1===s.indexOf(e)&&s.push(e),-1===s.indexOf(r)&&s.push(r)}}(n[t])})),s.sort(),t.exports={DRAW_MODES:o,backButtons:a,foreButtons:s}},90120:(t,e,r)=>{"use strict";var n=r(12822),i=r(17499),o=r(46121),a=r(62799);t.exports=function(t,e){var r=t.modebar||{},s=o.newContainer(e,"modebar");function l(t,e){return n.coerce(r,s,a,t,e)}l("orientation"),l("bgcolor",i.addOpacity(e.paper_bgcolor,.5));var c=i.contrast(i.rgb(e.modebar.bgcolor));l("color",i.addOpacity(c,.3)),l("activecolor",i.addOpacity(c,.7)),l("uirevision",e.uirevision),l("add"),l("remove")}},45828:(t,e,r)=>{"use 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e=u([],t),r=0;r1?(D=["toggleHover"],I=["resetViews"]):v?(O=["zoomInGeo","zoomOutGeo"],D=["hoverClosestGeo"],I=["resetGeo"]):g?(D=["hoverClosest3d"],I=["resetCameraDefault3d","resetCameraLastSave3d"]):w?(O=["zoomInMapbox","zoomOutMapbox"],D=["toggleHover"],I=["resetViewMapbox"]):k?(O=["zoomInMap","zoomOutMap"],D=["toggleHover"],I=["resetViewMap"]):x?D=["hoverClosestGl2d"]:b?D=["hoverClosestPie"]:T?(D=["hoverClosestCartesian","hoverCompareCartesian"],I=["resetViewSankey"]):D=["toggleHover"],m&&D.push("toggleSpikelines","hoverClosestCartesian","hoverCompareCartesian"),(function(t){for(var e=0;e{"use strict";var n=r(27941),i=r(7370),o=r(12822),a=r(50917),s=r(88566).version,l=new DOMParser;function c(t){this.container=t.container,this.element=document.createElement("div"),this.update(t.graphInfo,t.buttons),this.container.appendChild(this.element)}var u=c.prototype;u.update=function(t,e){this.graphInfo=t;var r=this.graphInfo._context,n=this.graphInfo._fullLayout,i="modebar-"+n._uid;this.element.setAttribute("id",i),this._uid=i,this.element.className="modebar","hover"===r.displayModeBar&&(this.element.className+=" modebar--hover ease-bg"),"v"===n.modebar.orientation&&(this.element.className+=" vertical",e=e.reverse());var a=n.modebar,s="hover"===r.displayModeBar?".js-plotly-plot .plotly:hover ":"";o.deleteRelatedStyleRule(i),o.addRelatedStyleRule(i,s+"#"+i+" .modebar-group","background-color: "+a.bgcolor),o.addRelatedStyleRule(i,"#"+i+" .modebar-btn .icon path","fill: "+a.color),o.addRelatedStyleRule(i,"#"+i+" .modebar-btn:hover .icon path","fill: "+a.activecolor),o.addRelatedStyleRule(i,"#"+i+" .modebar-btn.active .icon path","fill: "+a.activecolor);var l=!this.hasButtons(e),c=this.hasLogo!==r.displaylogo,u=this.locale!==r.locale;if(this.locale=r.locale,(l||c||u)&&(this.removeAllButtons(),this.updateButtons(e),r.watermark||r.displaylogo)){var h=this.getLogo();r.watermark&&(h.className=h.className+" watermark"),"v"===n.modebar.orientation?this.element.insertBefore(h,this.element.childNodes[0]):this.element.appendChild(h),this.hasLogo=!0}this.updateActiveButton()},u.updateButtons=function(t){var e=this;this.buttons=t,this.buttonElements=[],this.buttonsNames=[],this.buttons.forEach((function(t){var r=e.createGroup();t.forEach((function(t){var n=t.name;if(!n)throw new Error("must provide button 'name' in button config");if(-1!==e.buttonsNames.indexOf(n))throw new Error("button name '"+n+"' is taken");e.buttonsNames.push(n);var i=e.createButton(t);e.buttonElements.push(i),r.appendChild(i)})),e.element.appendChild(r)}))},u.createGroup=function(){var t=document.createElement("div");return t.className="modebar-group",t},u.createButton=function(t){var e=this,r=document.createElement("a");r.setAttribute("rel","tooltip"),r.className="modebar-btn";var i=t.title;void 0===i?i=t.name:"function"==typeof i&&(i=i(this.graphInfo)),(i||0===i)&&r.setAttribute("data-title",i),void 0!==t.attr&&r.setAttribute("data-attr",t.attr);var o=t.val;if(void 0!==o&&("function"==typeof o&&(o=o(this.graphInfo)),r.setAttribute("data-val",o)),"function"!=typeof t.click)throw new Error("must provide button 'click' function in button config");r.addEventListener("click",(function(r){t.click(e.graphInfo,r),e.updateActiveButton(r.currentTarget)})),r.setAttribute("data-toggle",t.toggle||!1),t.toggle&&n.select(r).classed("active",!0);var s=t.icon;return"function"==typeof s?r.appendChild(s()):r.appendChild(this.createIcon(s||a.question)),r.setAttribute("data-gravity",t.gravity||"n"),r},u.createIcon=function(t){var e,r=i(t.height)?Number(t.height):t.ascent-t.descent,n="http://www.w3.org/2000/svg";if(t.path){(e=document.createElementNS(n,"svg")).setAttribute("viewBox",[0,0,t.width,r].join(" ")),e.setAttribute("class","icon");var o=document.createElementNS(n,"path");o.setAttribute("d",t.path),t.transform?o.setAttribute("transform",t.transform):void 0!==t.ascent&&o.setAttribute("transform","matrix(1 0 0 -1 0 "+t.ascent+")"),e.appendChild(o)}return t.svg&&(e=l.parseFromString(t.svg,"application/xml").childNodes[0]),e.setAttribute("height","1em"),e.setAttribute("width","1em"),e},u.updateActiveButton=function(t){var e=this.graphInfo._fullLayout,r=void 0!==t?t.getAttribute("data-attr"):null;this.buttonElements.forEach((function(t){var i=t.getAttribute("data-val")||!0,a=t.getAttribute("data-attr"),s="true"===t.getAttribute("data-toggle"),l=n.select(t);if(s)a===r&&l.classed("active",!l.classed("active"));else{var c=null===a?a:o.nestedProperty(e,a).get();l.classed("active",c===i)}}))},u.hasButtons=function(t){var e=this.buttons;if(!e)return!1;if(t.length!==e.length)return!1;for(var r=0;r{"use strict";var n=r(75058),i=r(84226),o=(0,r(46121).templatedArray)("button",{visible:{valType:"boolean",dflt:!0,editType:"plot",description:"Determines whether or not this button is visible."},step:{valType:"enumerated",values:["month","year","day","hour","minute","second","all"],dflt:"month",editType:"plot",description:["The unit of measurement that the `count` value will set the range by."].join(" ")},stepmode:{valType:"enumerated",values:["backward","todate"],dflt:"backward",editType:"plot",description:["Sets the range update mode.","If *backward*, the range update shifts the start of range","back *count* times *step* milliseconds.","If *todate*, the range update shifts the start of range","back to the first timestamp from *count* times","*step* milliseconds back.","For example, with `step` set to *year* and `count` set to *1*","the range update shifts the start of the range back to","January 01 of the current year.","Month and year *todate* are currently available only","for the built-in (Gregorian) calendar."].join(" ")},count:{valType:"number",min:0,dflt:1,editType:"plot",description:["Sets the number of steps to take to update the range.","Use with `step` to specify the update interval."].join(" ")},label:{valType:"string",editType:"plot",description:"Sets the text label to appear on the button."},editType:"plot",description:["Sets the specifications for each buttons.","By default, a range selector comes with no buttons."].join(" ")});t.exports={visible:{valType:"boolean",editType:"plot",description:["Determines whether or not this range selector is visible.","Note that range selectors are only available for x axes of","`type` set to or auto-typed to *date*."].join(" ")},buttons:o,x:{valType:"number",min:-2,max:3,editType:"plot",description:"Sets the x position (in normalized coordinates) of the range selector."},xanchor:{valType:"enumerated",values:["auto","left","center","right"],dflt:"left",editType:"plot",description:["Sets the range selector's horizontal position anchor.","This anchor binds the `x` position to the *left*, *center*","or *right* of the range selector."].join(" ")},y:{valType:"number",min:-2,max:3,editType:"plot",description:"Sets the y position (in normalized coordinates) of the range selector."},yanchor:{valType:"enumerated",values:["auto","top","middle","bottom"],dflt:"bottom",editType:"plot",description:["Sets the range selector's vertical position anchor","This anchor binds the `y` position to the *top*, *middle*","or *bottom* of the range selector."].join(" ")},font:n({editType:"plot",description:"Sets the font of the range selector button text."}),bgcolor:{valType:"color",dflt:i.lightLine,editType:"plot",description:"Sets the background color of the range selector buttons."},activecolor:{valType:"color",editType:"plot",description:"Sets the background color of the active range selector button."},bordercolor:{valType:"color",dflt:i.defaultLine,editType:"plot",description:"Sets the color of the border enclosing the range selector."},borderwidth:{valType:"number",min:0,dflt:0,editType:"plot",description:"Sets the width (in px) of the border enclosing the range selector."},editType:"plot"}},12057:t=>{"use strict";t.exports={yPad:.02,minButtonWidth:30,rx:3,ry:3,lightAmount:25,darkAmount:10}},4088:(t,e,r)=>{"use strict";var n=r(12822),i=r(17499),o=r(46121),a=r(35677),s=r(76927),l=r(12057);function c(t,e,r,i){var o=i.calendar;function a(r,i){return n.coerce(t,e,s.buttons,r,i)}if(a("visible")){var l=a("step");"all"!==l&&(!o||"gregorian"===o||"month"!==l&&"year"!==l?a("stepmode"):e.stepmode="backward",a("count")),a("label")}}t.exports=function(t,e,r,u,h){var d=t.rangeselector||{},f=o.newContainer(e,"rangeselector");function p(t,e){return n.coerce(d,f,s,t,e)}if(p("visible",a(d,f,{name:"buttons",handleItemDefaults:c,calendar:h}).length>0)){var m=function(t,e,r){for(var n=r.filter((function(r){return e[r].anchor===t._id})),i=0,o=0;o{"use strict";var n=r(27941),i=r(25059),o=r(51137),a=r(17499),s=r(40666),l=r(12822),c=l.strTranslate,u=r(80394),h=r(99246),d=r(89701),f=d.LINE_SPACING,p=d.FROM_TL,m=d.FROM_BR,g=r(12057),v=r(98822);function b(t){return t._id}function y(t,e,r){var n=l.ensureSingle(t,"rect","selector-rect",(function(t){t.attr("shape-rendering","crispEdges")}));n.attr({rx:g.rx,ry:g.ry}),n.call(a.stroke,e.bordercolor).call(a.fill,function(t,e){return e._isActive||e._isHovered?t.activecolor:t.bgcolor}(e,r)).style("stroke-width",e.borderwidth+"px")}function x(t,e,r,n){var i,o;l.ensureSingle(t,"text","selector-text",(function(t){t.attr("text-anchor","middle")})).call(s.font,e.font).text((i=r,o=n._fullLayout._meta,i.label?o?l.templateString(i.label,o):i.label:"all"===i.step?"all":i.count+i.step.charAt(0))).call((function(t){u.convertToTspans(t,n)}))}t.exports=function(t){var e=t._fullLayout._infolayer.selectAll(".rangeselector").data(function(t){for(var e=h.list(t,"x",!0),r=[],n=0;n{"use strict";var n=r(55622),i=r(12822).titleCase;t.exports=function(t,e){var r=t._name,o={};if("all"===e.step)o[r+".autorange"]=!0;else{var a=function(t,e){var r,o=t.range,a=new Date(t.r2l(o[1])),s=e.step,l=n["utc"+i(s)],c=e.count;switch(e.stepmode){case"backward":r=t.l2r(+l.offset(a,-c));break;case"todate":var u=l.offset(a,-c);r=t.l2r(+l.ceil(u))}return[r,o[1]]}(t,e);o[r+".range[0]"]=a[0],o[r+".range[1]"]=a[1]}return o}},36404:(t,e,r)=>{"use strict";t.exports={moduleType:"component",name:"rangeselector",schema:{subplots:{xaxis:{rangeselector:r(76927)}}},layoutAttributes:r(76927),handleDefaults:r(4088),draw:r(58204)}},40959:(t,e,r)=>{"use strict";var n=r(84226);t.exports={bgcolor:{valType:"color",dflt:n.background,editType:"plot",description:"Sets the background color of the range slider."},bordercolor:{valType:"color",dflt:n.defaultLine,editType:"plot",description:"Sets the border color of the range slider."},borderwidth:{valType:"integer",dflt:0,min:0,editType:"plot",description:"Sets the border width of the range slider."},autorange:{valType:"boolean",dflt:!0,editType:"calc",impliedEdits:{"range[0]":void 0,"range[1]":void 0},description:["Determines whether or not the range slider range is","computed in relation to the input data.","If `range` is provided, then `autorange` is set to *false*."].join(" ")},range:{valType:"info_array",items:[{valType:"any",editType:"calc",impliedEdits:{"^autorange":!1}},{valType:"any",editType:"calc",impliedEdits:{"^autorange":!1}}],editType:"calc",impliedEdits:{autorange:!1},description:["Sets the range of the range slider.","If not set, defaults to the full xaxis range.","If the axis `type` is *log*, then you must take the","log of your desired range.","If the axis `type` is *date*, it should be date strings,","like date data, though Date objects and unix milliseconds","will be accepted and converted to strings.","If the axis `type` is *category*, it should be numbers,","using the scale where each category is assigned a serial","number from zero in the order it appears."].join(" ")},thickness:{valType:"number",dflt:.15,min:0,max:1,editType:"plot",description:["The height of the range slider as a fraction of the","total plot area height."].join(" ")},visible:{valType:"boolean",dflt:!0,editType:"calc",description:["Determines whether or not the range slider will be visible.","If visible, perpendicular axes will be set to `fixedrange`"].join(" ")},editType:"calc"}},99224:(t,e,r)=>{"use strict";var n=r(99246).list,i=r(19496).getAutoRange,o=r(92601);t.exports=function(t){for(var e=n(t,"x",!0),r=0;r{"use strict";t.exports={name:"rangeslider",containerClassName:"rangeslider-container",bgClassName:"rangeslider-bg",rangePlotClassName:"rangeslider-rangeplot",maskMinClassName:"rangeslider-mask-min",maskMaxClassName:"rangeslider-mask-max",slideBoxClassName:"rangeslider-slidebox",grabberMinClassName:"rangeslider-grabber-min",grabAreaMinClassName:"rangeslider-grabarea-min",handleMinClassName:"rangeslider-handle-min",grabberMaxClassName:"rangeslider-grabber-max",grabAreaMaxClassName:"rangeslider-grabarea-max",handleMaxClassName:"rangeslider-handle-max",maskMinOppAxisClassName:"rangeslider-mask-min-opp-axis",maskMaxOppAxisClassName:"rangeslider-mask-max-opp-axis",maskColor:"rgba(0,0,0,0.4)",maskOppAxisColor:"rgba(0,0,0,0.2)",slideBoxFill:"transparent",slideBoxCursor:"ew-resize",grabAreaFill:"transparent",grabAreaCursor:"col-resize",grabAreaWidth:10,handleWidth:4,handleRadius:1,handleStrokeWidth:1,extraPad:15}},4504:(t,e,r)=>{"use strict";var n=r(12822),i=r(46121),o=r(99246),a=r(40959),s=r(73290);t.exports=function(t,e,r){var l=t[r],c=e[r];if(l.rangeslider||e._requestRangeslider[c._id]){n.isPlainObject(l.rangeslider)||(l.rangeslider={});var u,h,d=l.rangeslider,f=i.newContainer(c,"rangeslider");if(_("visible")){_("bgcolor",e.plot_bgcolor),_("bordercolor"),_("borderwidth"),_("thickness"),_("autorange",!c.isValidRange(d.range)),_("range");var p=e._subplots;if(p)for(var m=p.cartesian.filter((function(t){return t.substr(0,t.indexOf("y"))===o.name2id(r)})).map((function(t){return t.substr(t.indexOf("y"),t.length)})),g=n.simpleMap(m,o.id2name),v=0;v{"use strict";var n=r(27941),i=r(25059),o=r(51137),a=r(12822),s=a.strTranslate,l=r(40666),c=r(17499),u=r(6883),h=r(29592),d=r(99246),f=r(19846),p=r(76292),m=r(92601);function g(t){return"number"==typeof t.clientX?t.clientX:t.touches&&t.touches.length>0?t.touches[0].clientX:0}function v(t,e,r,n){var i=a.ensureSingle(t,"rect",m.bgClassName,(function(t){t.attr({x:0,y:0,"shape-rendering":"crispEdges"})})),o=n.borderwidth%2==0?n.borderwidth:n.borderwidth-1,u=-n._offsetShift,h=l.crispRound(e,n.borderwidth);i.attr({width:n._width+o,height:n._height+o,transform:s(u,u),"stroke-width":h}).call(c.stroke,n.bordercolor).call(c.fill,n.bgcolor)}function b(t,e,r,n){var i=e._fullLayout;a.ensureSingleById(i._topdefs,"clipPath",n._clipId,(function(t){t.append("rect").attr({x:0,y:0})})).select("rect").attr({width:n._width,height:n._height})}function y(t,e,r,i){var s,c=e.calcdata,u=t.selectAll("g."+m.rangePlotClassName).data(r._subplotsWith,a.identity);u.enter().append("g").attr("class",(function(t){return m.rangePlotClassName+" "+t})).call(l.setClipUrl,i._clipId,e),u.order(),u.exit().remove(),u.each((function(t,a){var l=n.select(this),u=0===a,f=d.getFromId(e,t,"y"),p=f._name,m=i[p],g={data:[],layout:{xaxis:{type:r.type,domain:[0,1],range:i.range.slice(),calendar:r.calendar},width:i._width,height:i._height,margin:{t:0,b:0,l:0,r:0}},_context:e._context};r.rangebreaks&&(g.layout.xaxis.rangebreaks=r.rangebreaks),g.layout[p]={type:f.type,domain:[0,1],range:"match"!==m.rangemode?m.range.slice():f.range.slice(),calendar:f.calendar},f.rangebreaks&&(g.layout[p].rangebreaks=f.rangebreaks),o.supplyDefaults(g);var v=g._fullLayout.xaxis,b=g._fullLayout[p];v.clearCalc(),v.setScale(),b.clearCalc(),b.setScale();var y={id:t,plotgroup:l,xaxis:v,yaxis:b,isRangePlot:!0};u?s=y:(y.mainplot="xy",y.mainplotinfo=s),h.rangePlot(e,y,function(t,e){for(var r=[],n=0;n=n.max)e=j[r+1];else if(t=n.pmax)e=j[r+1];else if(tr._length||b+_<0)return;u=v+_,f=b+_;break;case l:if(x="col-resize",v+_>r._length)return;u=v+_,f=b;break;case c:if(x="col-resize",b+_<0)return;u=v,f=b+_;break;default:x="ew-resize",u=m,f=m+_}if(f{"use strict";var n=r(99246),i=r(80394),o=r(92601),a=r(89701).LINE_SPACING,s=o.name;function l(t){var e=t&&t[s];return e&&e.visible}e.isVisible=l,e.makeData=function(t){var e=n.list({_fullLayout:t},"x",!0),r=t.margin,i=[];if(!t._has("gl2d"))for(var o=0;o{"use strict";var n=r(12822),i=r(40959),o=r(73290),a=r(93729);t.exports={moduleType:"component",name:"rangeslider",schema:{subplots:{xaxis:{rangeslider:n.extendFlat({},i,{yaxis:o})}}},layoutAttributes:r(40959),handleDefaults:r(4504),calcAutorange:r(99224),draw:r(19260),isVisible:a.isVisible,makeData:a.makeData,autoMarginOpts:a.autoMarginOpts}},73290:t=>{"use strict";t.exports={_isSubplotObj:!0,rangemode:{valType:"enumerated",values:["auto","fixed","match"],dflt:"match",editType:"calc",description:["Determines whether or not the range of this axis in","the rangeslider use the same value than in the main plot","when zooming in/out.","If *auto*, the autorange will be used.","If *fixed*, the `range` is used.","If *match*, the current range of the corresponding y-axis on the main subplot is used."].join(" ")},range:{valType:"info_array",items:[{valType:"any",editType:"plot"},{valType:"any",editType:"plot"}],editType:"plot",description:["Sets the range of this axis for the rangeslider."].join(" ")},editType:"calc"}},65586:(t,e,r)=>{"use strict";var n=r(77061),i=r(98387).line,o=r(68057).T,a=r(98260).extendFlat,s=r(62309).overrideAll,l=r(46121).templatedArray,c=r(53644);t.exports=s(l("selection",{type:{valType:"enumerated",values:["rect","path"],description:["Specifies the selection type to be drawn.","If *rect*, a rectangle is drawn linking","(`x0`,`y0`), (`x1`,`y0`), (`x1`,`y1`) and (`x0`,`y1`).","If *path*, draw a custom SVG path using `path`."].join(" ")},xref:a({},n.xref,{description:["Sets the selection's x coordinate axis.",c.axisRefDescription("x","left","right")].join(" ")}),yref:a({},n.yref,{description:["Sets the selection's x coordinate axis.",c.axisRefDescription("y","bottom","top")].join(" ")}),x0:{valType:"any",description:"Sets the selection's starting x position."},x1:{valType:"any",description:"Sets the selection's end x position."},y0:{valType:"any",description:"Sets the selection's starting y position."},y1:{valType:"any",description:"Sets the selection's end y position."},path:{valType:"string",editType:"arraydraw",description:["For `type` *path* - a valid SVG path similar to `shapes.path` in data coordinates.","Allowed segments are: M, L and Z."].join(" ")},opacity:{valType:"number",min:0,max:1,dflt:.7,editType:"arraydraw",description:"Sets the opacity of the selection."},line:{color:i.color,width:a({},i.width,{min:1,dflt:1}),dash:a({},o,{dflt:"dot"})}}),"arraydraw","from-root")},76814:t=>{"use strict";t.exports={BENDPX:1.5,MINSELECT:12,SELECTDELAY:100,SELECTID:"-select"}},8037:(t,e,r)=>{"use strict";var n=r(12822),i=r(75815),o=r(35677),a=r(65586),s=r(23223);function l(t,e,r){function o(r,i){return n.coerce(t,e,a,r,i)}var l=o("path"),c="path"!==o("type",l?"path":"rect");c&&delete e.path,o("opacity"),o("line.color"),o("line.width"),o("line.dash");for(var u=["x","y"],h=0;h<2;h++){var d,f,p,m=u[h],g={_fullLayout:r},v=i.coerceRef(t,e,g,m);if((d=i.getFromId(g,v))._selectionIndices.push(e._index),p=s.rangeToShapePosition(d),f=s.shapePositionToRange(d),c){var b=m+"0",y=m+"1",x=t[b],_=t[y];t[b]=f(t[b],!0),t[y]=f(t[y],!0),i.coercePosition(e,g,o,v,b),i.coercePosition(e,g,o,v,y);var w=e[b],k=e[y];void 0!==w&&void 0!==k&&(e[b]=p(w),e[y]=p(k),t[b]=x,t[y]=_)}}c&&n.noneOrAll(t,e,["x0","x1","y0","y1"])}t.exports=function(t,e){o(t,e,{name:"selections",handleItemDefaults:l});for(var r=e.selections,n=0;n{"use strict";var n=r(59952).readPaths,i=r(49244),o=r(8867).clearOutlineControllers,a=r(17499),s=r(40666),l=r(46121).arrayEditor,c=r(23223),u=c.getPathString;function h(t){var e=t._fullLayout;for(var r in o(t),e._selectionLayer.selectAll("path").remove(),e._plots){var n=e._plots[r].selectionLayer;n&&n.selectAll("path").remove()}for(var i=0;i=0;A--){var M=r.append("path").attr(g).style("opacity",A?.1:v).call(a.stroke,y).call(a.fill,b).call(s.dashLine,A?"solid":_,A?4+x:x);if(p(M,t,o),w){var T=l(t.layout,"selections",o);M.style({cursor:"move"});var S={element:M.node(),plotinfo:f,gd:t,editHelpers:T,isActiveSelection:!0},C=n(c,t);i(C,M,S)}else M.style("pointer-events",A?"all":"none");k[A]=M}var E=k[0];k[1].node().addEventListener("click",(function(){return function(t,e){if(d(t)){var r=+e.node().getAttribute("data-index");if(r>=0){if(r===t._fullLayout._activeSelectionIndex)return void m(t);t._fullLayout._activeSelectionIndex=r,t._fullLayout._deactivateSelection=m,h(t)}}}(t,E)}))}(t._fullLayout._selectionLayer)}function p(t,e,r){var n=r.xref+r.yref;s.setClipUrl(t,"clip"+e._fullLayout._uid+n,e)}function m(t){d(t)&&t._fullLayout._activeSelectionIndex>=0&&(o(t),delete t._fullLayout._activeSelectionIndex,h(t))}t.exports={draw:h,drawOne:f,activateLastSelection:function(t){if(d(t)){var e=t._fullLayout.selections.length-1;t._fullLayout._activeSelectionIndex=e,t._fullLayout._deactivateSelection=m,h(t)}}}},21422:(t,e,r)=>{"use strict";var n=r(68057).T,i=r(98260).extendFlat;t.exports={newselection:{mode:{valType:"enumerated",values:["immediate","gradual"],dflt:"immediate",editType:"none",description:["Describes how a new selection is created.","If `immediate`, a new selection is created after first mouse up.","If `gradual`, a new selection is not created after first mouse.","By adding to and subtracting from the initial selection,","this option allows declaring extra outlines of the selection."].join(" ")},line:{color:{valType:"color",editType:"none",description:["Sets the line color.","By default uses either dark grey or white","to increase contrast with background color."].join(" ")},width:{valType:"number",min:1,dflt:1,editType:"none",description:"Sets the line width (in px)."},dash:i({},n,{dflt:"dot",editType:"none"}),editType:"none"},editType:"none"},activeselection:{fillcolor:{valType:"color",dflt:"rgba(0,0,0,0)",editType:"none",description:"Sets the color filling the active selection' interior."},opacity:{valType:"number",min:0,max:1,dflt:.5,editType:"none",description:"Sets the opacity of the active selection."},editType:"none"}}},80857:t=>{"use strict";t.exports=function(t,e,r){r("newselection.mode"),r("newselection.line.width")&&(r("newselection.line.color"),r("newselection.line.dash")),r("activeselection.fillcolor"),r("activeselection.opacity")}},63750:(t,e,r)=>{"use strict";var n=r(14295).selectMode,i=r(8867).clearOutline,o=r(59952),a=o.readPaths,s=o.writePaths,l=o.fixDatesForPaths;t.exports=function(t,e){if(t.length){var r=t[0][0];if(r){var o=r.getAttribute("d"),c=e.gd,u=c._fullLayout.newselection,h=e.plotinfo,d=h.xaxis,f=h.yaxis,p=e.isActiveSelection,m=e.dragmode,g=(c.layout||{}).selections||[];if(!n(m)&&void 0!==p){var v=c._fullLayout._activeSelectionIndex;if(v{"use strict";var n=r(12822).strTranslate;function i(t,e){switch(t.type){case"log":return t.p2d(e);case"date":return t.p2r(e,0,t.calendar);default:return t.p2r(e)}}t.exports={p2r:i,r2p:function(t,e){switch(t.type){case"log":return t.d2p(e);case"date":return t.r2p(e,0,t.calendar);default:return t.r2p(e)}},axValue:function(t){var e="y"===t._id.charAt(0)?1:0;return function(r){return i(t,r[e])}},getTransform:function(t){return n(t.xaxis._offset,t.yaxis._offset)}}},70059:(t,e,r)=>{"use strict";var n=r(70445),i=r(80191);t.exports={moduleType:"component",name:"selections",layoutAttributes:r(65586),supplyLayoutDefaults:r(8037),supplyDrawNewSelectionDefaults:r(80857),includeBasePlot:r(39859)("selections"),draw:n.draw,drawOne:n.drawOne,reselect:i.reselect,prepSelect:i.prepSelect,clearOutline:i.clearOutline,clearSelectionsCache:i.clearSelectionsCache,selectOnClick:i.selectOnClick}},80191:(t,e,r)=>{"use strict";var n=r(48439),i=r(53824),o=r(25059),a=r(40666).dashStyle,s=r(17499),l=r(70410),c=r(66811).makeEventData,u=r(14295),h=u.freeMode,d=u.rectMode,f=u.drawMode,p=u.openMode,m=u.selectMode,g=r(23223),v=r(6583),b=r(49244),y=r(8867).clearOutline,x=r(59952),_=x.handleEllipse,w=x.readPaths,k=r(81941).newShapes,A=r(63750),M=r(70445).activateLastSelection,T=r(12822),S=T.sorterAsc,C=r(92620),E=r(76324),L=r(99246).getFromId,z=r(86748),O=r(39004).redrawReglTraces,D=r(76814),I=D.MINSELECT,F=C.filter,R=C.tester,P=r(38554),j=P.p2r,N=P.axValue,B=P.getTransform;function U(t){return void 0!==t.subplot}function G(t,e,r,n,i,o,a){var s,l,c,u,h,d,f,m,g,v=e._hoverdata,y=e._fullLayout.clickmode.indexOf("event")>-1,x=[];if(function(t){return t&&Array.isArray(t)&&!0!==t[0].hoverOnBox}(v)){q(t,e,o);var _=function(t,e){var r,n,i=t[0],o=-1,a=[];for(n=0;n0?function(t,e){var r,n,i,o=[];for(i=0;i0&&o.push(r);if(1===o.length&&o[0]===e.searchInfo&&(n=e.searchInfo.cd[0].trace).selectedpoints.length===e.pointNumbers.length){for(i=0;i1)return!1;if((n+=e.selectedpoints.length)>1)return!1}return 1===n}(s)&&(d=J(_))){for(a&&a.remove(),g=0;g=0})(i)&&i._fullLayout._deactivateShape(i),function(t){return t._fullLayout._activeSelectionIndex>=0}(i)&&i._fullLayout._deactivateSelection(i);var a=i._fullLayout._zoomlayer,s=f(r),l=m(r);if(s||l){var c,u,h=a.selectAll(".select-outline-"+n.id);h&&i._fullLayout._outlining&&(s&&(c=k(h,t)),c&&o.call("_guiRelayout",i,{shapes:c}),l&&!U(t)&&(u=A(h,t)),u&&(i._fullLayout._noEmitSelectedAtStart=!0,o.call("_guiRelayout",i,{selections:u}).then((function(){e&&M(i)}))),i._fullLayout._outlining=!1)}n.selection={},n.selection.selectionDefs=t.selectionDefs=[],n.selection.mergedPolygons=t.mergedPolygons=[]}function Z(t){return t._id}function X(t,e,r,n){if(!t.calcdata)return[];var i,o,a,s=[],l=e.map(Z),c=r.map(Z);for(a=0;a0?n[0]:r;return!!e.selectedpoints&&e.selectedpoints.indexOf(i)>-1}function K(t,e,r){var n,i;for(n=0;n-1&&e;if(!o&&e){var et=at(t,!0);if(et.length){var nt=et[0].xref,ft=et[0].yref;if(nt&&ft){var pt=ct(et);ut([L(t,nt,"x"),L(t,ft,"y")])(Q,pt)}}t._fullLayout._noEmitSelectedAtStart?t._fullLayout._noEmitSelectedAtStart=!1:tt&&ht(t,Q),d._reselect=!1}if(!o&&d._deselect){var mt=d._deselect;(function(t,e,r){for(var n=0;n=0)A._fullLayout._deactivateShape(A);else if(!y){var r=M.clickmode;E.done(Tt).then((function(){if(E.clear(Tt),2===t){for(xt.remove(),J=0;J-1&&G(e,A,n.xaxes,n.yaxes,n.subplot,n,xt),"event"===r&&ht(A,void 0);l.click(A,e,z.id)})).catch(T.error)}},n.doneFn=function(){At.remove(),E.done(Tt).then((function(){E.clear(Tt),!S&&$&&n.selectionDefs&&($.subtract=yt,n.selectionDefs.push($),n.mergedPolygons.length=0,[].push.apply(n.mergedPolygons,Z)),(S||y)&&Y(n,S),n.doneFnCompleted&&n.doneFnCompleted(St),x&&ht(A,ot)})).catch(T.error)}},clearOutline:y,clearSelectionsCache:Y,selectOnClick:G}},39677:(t,e,r)=>{"use strict";var n=r(77061),i=r(75058),o=r(98387).line,a=r(68057).T,s=r(98260).extendFlat,l=r(46121).templatedArray,c=r(53644),u=r(3520),h=r(24131).LF,d=r(12086);t.exports=l("shape",{visible:s({},u.visible,{editType:"calc+arraydraw",description:["Determines whether or not this shape is visible.","If *legendonly*, the shape is not drawn,","but can appear as a legend item","(provided that the legend itself is visible)."].join(" ")}),showlegend:{valType:"boolean",dflt:!1,editType:"calc+arraydraw",description:["Determines whether or not this","shape is shown in the legend."].join(" ")},legend:s({},u.legend,{editType:"calc+arraydraw",description:["Sets the reference to a legend to show this shape in.","References to these legends are *legend*, *legend2*, *legend3*, etc.","Settings for these legends are set in the layout, under","`layout.legend`, `layout.legend2`, etc."].join(" ")}),legendgroup:s({},u.legendgroup,{editType:"calc+arraydraw",description:["Sets the legend group for this shape.","Traces and shapes part of the same legend group hide/show at the same time","when toggling legend items."].join(" ")}),legendgrouptitle:{text:s({},u.legendgrouptitle.text,{editType:"calc+arraydraw"}),font:i({editType:"calc+arraydraw",description:["Sets this legend group's title font."].join(" ")}),editType:"calc+arraydraw"},legendrank:s({},u.legendrank,{editType:"calc+arraydraw",description:["Sets the legend rank for this shape.","Items and groups with smaller ranks are presented on top/left side while","with *reversed* `legend.traceorder` they are on bottom/right side.","The default legendrank is 1000,","so that you can use ranks less than 1000 to place certain items before all unranked items,","and ranks greater than 1000 to go after all unranked items.","When having unranked or equal rank items shapes would be displayed after traces","i.e. according to their order in data and layout."].join(" ")}),legendwidth:s({},u.legendwidth,{editType:"calc+arraydraw",description:"Sets the width (in px or fraction) of the legend for this shape."}),type:{valType:"enumerated",values:["circle","rect","path","line"],editType:"calc+arraydraw",description:["Specifies the shape type to be drawn.","If *line*, a line is drawn from (`x0`,`y0`) to (`x1`,`y1`)","with respect to the axes' sizing mode.","If *circle*, a circle is drawn from","((`x0`+`x1`)/2, (`y0`+`y1`)/2))","with radius","(|(`x0`+`x1`)/2 - `x0`|, |(`y0`+`y1`)/2 -`y0`)|)","with respect to the axes' sizing mode.","If *rect*, a rectangle is drawn linking","(`x0`,`y0`), (`x1`,`y0`), (`x1`,`y1`), (`x0`,`y1`), (`x0`,`y0`)","with respect to the axes' sizing mode.","If *path*, draw a custom SVG path using `path`.","with respect to the axes' sizing mode."].join(" ")},layer:{valType:"enumerated",values:["below","above","between"],dflt:"above",editType:"arraydraw",description:["Specifies whether shapes are drawn below gridlines (*below*),","between gridlines and traces (*between*) or above traces (*above*)."].join(" ")},xref:s({},n.xref,{description:["Sets the shape's x coordinate axis.",c.axisRefDescription("x","left","right")].join(" ")}),xsizemode:{valType:"enumerated",values:["scaled","pixel"],dflt:"scaled",editType:"calc+arraydraw",description:["Sets the shapes's sizing mode along the x axis.","If set to *scaled*, `x0`, `x1` and x coordinates within `path` refer to","data values on the x axis or a fraction of the plot area's width","(`xref` set to *paper*).","If set to *pixel*, `xanchor` specifies the x position in terms","of data or plot fraction but `x0`, `x1` and x coordinates within `path`","are pixels relative to `xanchor`. This way, the shape can have","a fixed width while maintaining a position relative to data or","plot fraction."].join(" ")},xanchor:{valType:"any",editType:"calc+arraydraw",description:["Only relevant in conjunction with `xsizemode` set to *pixel*.","Specifies the anchor point on the x axis to which `x0`, `x1`","and x coordinates within `path` are relative to.","E.g. useful to attach a pixel sized shape to a certain data value.","No effect when `xsizemode` not set to *pixel*."].join(" ")},x0:{valType:"any",editType:"calc+arraydraw",description:["Sets the shape's starting x position.","See `type` and `xsizemode` for more info."].join(" ")},x1:{valType:"any",editType:"calc+arraydraw",description:["Sets the shape's end x position.","See `type` and `xsizemode` for more info."].join(" ")},x0shift:{valType:"number",dflt:0,min:-1,max:1,editType:"calc",description:["Shifts `x0` away from the center of the category when `xref` is a *category* or","*multicategory* axis. -0.5 corresponds to the start of the category and 0.5","corresponds to the end of the category."].join(" ")},x1shift:{valType:"number",dflt:0,min:-1,max:1,editType:"calc",description:["Shifts `x1` away from the center of the category when `xref` is a *category* or","*multicategory* axis. -0.5 corresponds to the start of the category and 0.5","corresponds to the end of the category."].join(" ")},yref:s({},n.yref,{description:["Sets the shape's y coordinate axis.",c.axisRefDescription("y","bottom","top")].join(" ")}),ysizemode:{valType:"enumerated",values:["scaled","pixel"],dflt:"scaled",editType:"calc+arraydraw",description:["Sets the shapes's sizing mode along the y axis.","If set to *scaled*, `y0`, `y1` and y coordinates within `path` refer to","data values on the y axis or a fraction of the plot area's height","(`yref` set to *paper*).","If set to *pixel*, `yanchor` specifies the y position in terms","of data or plot fraction but `y0`, `y1` and y coordinates within `path`","are pixels relative to `yanchor`. 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For lines, angle *auto*","is the same angle as the line. For all other shapes,","angle *auto* is horizontal."].join(" ")},xanchor:{valType:"enumerated",values:["auto","left","center","right"],dflt:"auto",editType:"calc+arraydraw",description:["Sets the label's horizontal position anchor","This anchor binds the specified `textposition` to the *left*, *center*","or *right* of the label text.","For example, if `textposition` is set to *top right* and","`xanchor` to *right* then the right-most portion of the","label text lines up with the right-most edge of the","shape."].join(" ")},yanchor:{valType:"enumerated",values:["top","middle","bottom"],editType:"calc+arraydraw",description:["Sets the label's vertical position anchor","This anchor binds the specified `textposition` to the *top*, *middle*","or *bottom* of the label text.","For example, if `textposition` is set to *top right* and","`yanchor` to *top* then the top-most portion of the","label text lines up with the top-most edge of the","shape."].join(" 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n=0,i=t.charAt(0),o=g.paramIsX[i],a=g.paramIsY[i],s=g.numParams[i];return i+t.substr(1).replace(g.paramRE,(function(t){return n>=s||(o[n]?t=e(t):a[n]&&(t=r(t)),n++),t}))}))}function M(t){_(t)&&t._fullLayout._activeShapeIndex>=0&&(u(t),delete t._fullLayout._activeShapeIndex,y(t))}t.exports={draw:y,drawOne:w,eraseActiveShape:function(t){if(_(t)){u(t);var e=t._fullLayout._activeShapeIndex,r=(t.layout||{}).shapes||[];if(e{"use strict";var n=r(62309).overrideAll,i=r(3520),o=r(75058),a=r(68057).T,s=r(98260).extendFlat,l=r(24131).LF,c=r(12086);t.exports=n({newshape:{visible:s({},i.visible,{description:["Determines whether or not new shape is visible.","If *legendonly*, the shape is not drawn,","but can appear as a legend item","(provided that the legend itself is visible)."].join(" ")}),showlegend:{valType:"boolean",dflt:!1,description:["Determines whether or not new","shape is shown in the legend."].join(" ")},legend:s({},i.legend,{description:["Sets the reference to a legend to show new shape in.","References to these legends are *legend*, *legend2*, *legend3*, etc.","Settings for these legends are set in the layout, under","`layout.legend`, `layout.legend2`, etc."].join(" ")}),legendgroup:s({},i.legendgroup,{description:["Sets the legend group for new shape.","Traces and shapes part of the same legend group hide/show at the same time","when toggling legend items."].join(" ")}),legendgrouptitle:{text:s({},i.legendgrouptitle.text,{}),font:o({description:["Sets this legend group's title font."].join(" ")})},legendrank:s({},i.legendrank,{description:["Sets the legend rank for new shape.","Items and groups with smaller ranks are presented on top/left side while","with *reversed* `legend.traceorder` they are on bottom/right side.","The default legendrank is 1000,","so that you can use ranks less than 1000 to place certain items before all unranked items,","and ranks greater than 1000 to go after all unranked items."].join(" ")}),legendwidth:s({},i.legendwidth,{description:"Sets the width (in px or fraction) of the legend for new shape."}),line:{color:{valType:"color",description:["Sets the line color.","By default uses either dark grey or white","to increase contrast with background color."].join(" ")},width:{valType:"number",min:0,dflt:4,description:"Sets the line width (in px)."},dash:s({},a,{dflt:"solid"})},fillcolor:{valType:"color",dflt:"rgba(0,0,0,0)",description:["Sets the color filling new shapes' interior.","Please note that if using a fillcolor with alpha greater than half,","drag inside the active shape starts moving the shape underneath,","otherwise a new shape could be started over."].join(" ")},fillrule:{valType:"enumerated",values:["evenodd","nonzero"],dflt:"evenodd",description:["Determines the path's interior.","For more info please visit https://developer.mozilla.org/en-US/docs/Web/SVG/Attribute/fill-rule"].join(" ")},opacity:{valType:"number",min:0,max:1,dflt:1,description:"Sets the opacity of new shapes."},layer:{valType:"enumerated",values:["below","above","between"],dflt:"above",description:["Specifies whether new shapes are drawn below gridlines (*below*),","between gridlines and traces (*between*) or above traces (*above*)."].join(" ")},drawdirection:{valType:"enumerated",values:["ortho","horizontal","vertical","diagonal"],dflt:"diagonal",description:["When `dragmode` is set to *drawrect*, *drawline* or *drawcircle*","this limits the drag to be horizontal, vertical or diagonal.","Using *diagonal* there is no limit e.g. in drawing lines in any direction.","*ortho* limits the draw to be either horizontal or vertical.","*horizontal* allows horizontal extend.","*vertical* allows vertical extend."].join(" ")},name:s({},i.name,{description:["Sets new shape name.","The name appears as the legend item."].join(" ")}),label:{text:{valType:"string",dflt:"",description:["Sets the text to display with the new shape.","It is also used for legend item if `name` is not provided."].join(" ")},texttemplate:l({newshape:!0},{keys:Object.keys(c)}),font:o({description:"Sets the new shape label text font."}),textposition:{valType:"enumerated",values:["top left","top center","top right","middle left","middle center","middle right","bottom left","bottom center","bottom right","start","middle","end"],description:["Sets the position of the label text relative to the new shape.","Supported values for rectangles, circles and paths are","*top left*, *top center*, *top right*, *middle left*,","*middle center*, *middle right*, *bottom left*, *bottom center*,","and *bottom right*.","Supported values for lines are *start*, *middle*, and *end*.","Default: *middle center* for rectangles, circles, and paths; *middle* for lines."].join(" ")},textangle:{valType:"angle",dflt:"auto",description:["Sets the angle at which the label text is drawn","with respect to the horizontal. For lines, angle *auto*","is the same angle as the line. For all other shapes,","angle *auto* is horizontal."].join(" ")},xanchor:{valType:"enumerated",values:["auto","left","center","right"],dflt:"auto",description:["Sets the label's horizontal position anchor","This anchor binds the specified `textposition` to the *left*, *center*","or *right* of the label text.","For example, if `textposition` is set to *top right* and","`xanchor` to *right* then the right-most portion of the","label text lines up with the right-most edge of the","new shape."].join(" ")},yanchor:{valType:"enumerated",values:["top","middle","bottom"],description:["Sets the label's vertical position anchor","This anchor binds the specified `textposition` to the *top*, *middle*","or *bottom* of the label text.","For example, if `textposition` is set to *top right* and","`yanchor` to *top* then the top-most portion of the","label text lines up with the top-most edge of the","new shape."].join(" ")},padding:{valType:"number",dflt:3,min:0,description:"Sets padding (in px) between edge of label and edge of new shape."}}},activeshape:{fillcolor:{valType:"color",dflt:"rgb(255,0,255)",description:"Sets the color filling the active shape' interior."},opacity:{valType:"number",min:0,max:1,dflt:.5,description:"Sets the opacity of the active shape."}}},"none","from-root")},81436:t=>{"use strict";t.exports={CIRCLE_SIDES:32,i000:0,i090:8,i180:16,i270:24,cos45:Math.cos(Math.PI/4),sin45:Math.sin(Math.PI/4),SQRT2:Math.sqrt(2)}},24815:(t,e,r)=>{"use strict";var n=r(17499),i=r(12822);t.exports=function(t,e,r){if(r("newshape.visible"),r("newshape.name"),r("newshape.showlegend"),r("newshape.legend"),r("newshape.legendwidth"),r("newshape.legendgroup"),r("newshape.legendgrouptitle.text"),i.coerceFont(r,"newshape.legendgrouptitle.font"),r("newshape.legendrank"),r("newshape.drawdirection"),r("newshape.layer"),r("newshape.fillcolor"),r("newshape.fillrule"),r("newshape.opacity"),r("newshape.line.width")){var o=(t||{}).plot_bgcolor||"#FFF";r("newshape.line.color",n.contrast(o)),r("newshape.line.dash")}var a="drawline"===t.dragmode,s=r("newshape.label.text"),l=r("newshape.label.texttemplate");if(s||l){r("newshape.label.textangle");var c=r("newshape.label.textposition",a?"middle":"middle center");r("newshape.label.xanchor"),r("newshape.label.yanchor",function(t,e){return t?"bottom":-1!==e.indexOf("top")?"top":-1!==e.indexOf("bottom")?"bottom":"middle"}(a,c)),r("newshape.label.padding"),i.coerceFont(r,"newshape.label.font",e.font)}r("activeshape.fillcolor"),r("activeshape.opacity")}},59952:(t,e,r)=>{"use strict";var n=r(37974),i=r(81436),o=i.CIRCLE_SIDES,a=i.SQRT2,s=r(38554),l=s.p2r,c=s.r2p,u=[0,3,4,5,6,1,2],h=[0,3,4,1,2];function d(t,e){return Math.abs(t-e)<=1e-6}function f(t,e){var r=e[1]-t[1],n=e[2]-t[2];return Math.sqrt(r*r+n*n)}e.writePaths=function(t){var e=t.length;if(!e)return"M0,0Z";for(var r="",n=0;n0&&l{"use strict";var n=r(14295),i=n.drawMode,o=n.openMode,a=r(81436),s=a.i000,l=a.i090,c=a.i180,u=a.i270,h=a.cos45,d=a.sin45,f=r(38554),p=f.p2r,m=f.r2p,g=r(8867).clearOutline,v=r(59952),b=v.readPaths,y=v.writePaths,x=v.ellipseOver,_=v.fixDatesForPaths;function w(t,e,r){var n,i=t[0][0],a=e.gd,f=i.getAttribute("d"),g=a._fullLayout.newshape,v=e.plotinfo,w=e.isActiveShape,k=v.xaxis,A=v.yaxis,M=!!v.domain||!v.xaxis,T=!!v.domain||!v.yaxis,S=o(r),C=b(f,a,v,w),E={editable:!0,visible:g.visible,name:g.name,showlegend:g.showlegend,legend:g.legend,legendwidth:g.legendwidth,legendgroup:g.legendgroup,legendgrouptitle:{text:g.legendgrouptitle.text,font:g.legendgrouptitle.font},legendrank:g.legendrank,label:g.label,xref:M?"paper":k._id,yref:T?"paper":A._id,layer:g.layer,opacity:g.opacity,line:{color:g.line.color,width:g.line.width,dash:g.line.dash}};if(S||(E.fillcolor=g.fillcolor,E.fillrule=g.fillrule),1===C.length&&(n=C[0]),n&&5===n.length&&"drawrect"===r)E.type="rect",E.x0=n[0][1],E.y0=n[0][2],E.x1=n[2][1],E.y1=n[2][2];else if(n&&"drawline"===r)E.type="line",E.x0=n[0][1],E.y0=n[0][2],E.x1=n[1][1],E.y1=n[1][2];else if(n&&"drawcircle"===r){E.type="circle";var L=n[s][1],z=n[l][1],O=n[c][1],D=n[u][1],I=n[s][2],F=n[l][2],R=n[c][2],P=n[u][2],j=v.xaxis&&("date"===v.xaxis.type||"log"===v.xaxis.type),N=v.yaxis&&("date"===v.yaxis.type||"log"===v.yaxis.type);j&&(L=m(v.xaxis,L),z=m(v.xaxis,z),O=m(v.xaxis,O),D=m(v.xaxis,D)),N&&(I=m(v.yaxis,I),F=m(v.yaxis,F),R=m(v.yaxis,R),P=m(v.yaxis,P));var B=(z+D)/2,U=(I+R)/2,G=x({x0:B,y0:U,x1:B+(D-z+O-L)/2*h,y1:U+(P-F+R-I)/2*d});j&&(G.x0=p(v.xaxis,G.x0),G.x1=p(v.xaxis,G.x1)),N&&(G.y0=p(v.yaxis,G.y0),G.y1=p(v.yaxis,G.y1)),E.x0=G.x0,E.y0=G.y0,E.x1=G.x1,E.y1=G.y1}else E.type="path",k&&A&&_(C,k,A),E.path=y(C),n=null;return E}t.exports={newShapes:function(t,e){if(t.length&&t[0][0]){var r=e.gd,n=e.isActiveShape,o=e.dragmode,a=(r.layout||{}).shapes||[];if(!i(o)&&void 0!==n){var s=r._fullLayout._activeShapeIndex;if(s{"use strict";t.exports={clearOutlineControllers:function(t){var e=t._fullLayout._zoomlayer;e&&e.selectAll(".outline-controllers").remove()},clearOutline:function(t){var e=t._fullLayout._zoomlayer;e&&e.selectAll(".select-outline").remove(),t._fullLayout._outlining=!1}}},23223:(t,e,r)=>{"use strict";var n=r(6583),i=r(12822),o=r(75815);function a(t,e){var r=0;return(e=e||0)&&t&&("category"===t.type||"multicategory"===t.type)&&(r=(t.r2p(1)-t.r2p(0))*e),r}e.rangeToShapePosition=function(t){return"log"===t.type?t.r2d:function(t){return t}},e.shapePositionToRange=function(t){return"log"===t.type?t.d2r:function(t){return t}},e.decodeDate=function(t){return function(e){return e.replace&&(e=e.replace("_"," ")),t(e)}},e.encodeDate=function(t){return function(e){return t(e).replace(" ","_")}},e.extractPathCoords=function(t,e,r){var o=[];return t.match(n.segmentRE).forEach((function(t){var a=e[t.charAt(0)].drawn;if(void 0!==a){var s=t.substr(1).match(n.paramRE);if(s&&!(s.lengthf&&(t="X"),t}));return o>f&&(p=p.replace(/[\s,]*X.*/,""),i.log("Ignoring extra params in segment "+t)),u+p}))}(r,l,u);if("pixel"===r.xsizemode){var M=l(r.xanchor);h=M+r.x0+_,d=M+r.x1+w}else h=l(r.x0)+_,d=l(r.x1)+w;if("pixel"===r.ysizemode){var T=u(r.yanchor);f=T-r.y0+k,p=T-r.y1+A}else f=u(r.y0)+k,p=u(r.y1)+A;if("line"===m)return"M"+h+","+f+"L"+d+","+p;if("rect"===m)return"M"+h+","+f+"H"+d+"V"+p+"H"+h+"Z";var S=(h+d)/2,C=(f+p)/2,E=Math.abs(S-h),L=Math.abs(C-f),z="A"+E+","+L,O=S+E+","+C;return"M"+O+z+" 0 1,1 "+S+","+(C-L)+z+" 0 0,1 "+O+"Z"}},60166:(t,e,r)=>{"use strict";var n=r(71422);t.exports={moduleType:"component",name:"shapes",layoutAttributes:r(39677),supplyLayoutDefaults:r(12138),supplyDrawNewShapeDefaults:r(24815),includeBasePlot:r(39859)("shapes"),calcAutorange:r(37358),draw:n.draw,drawOne:n.drawOne}},12086:t=>{"use strict";function e(t,e){return e?e.d2l(t):t}function r(t,e){return e?e.l2d(t):t}function n(t){return t.x0shift||0}function i(t){return t.x1shift||0}function o(t){return t.y0shift||0}function a(t){return t.y1shift||0}function s(t,r){return e(t.x1,r)+i(t)-e(t.x0,r)-n(t)}function l(t,r,n){return e(t.y1,n)+a(t)-e(t.y0,n)-o(t)}t.exports={x0:function(t){return t.x0},x1:function(t){return t.x1},y0:function(t){return t.y0},y1:function(t){return t.y1},slope:function(t,e,r){return"line"!==t.type?void 0:l(t,0,r)/s(t,e)},dx:s,dy:l,width:function(t,e){return Math.abs(s(t,e))},height:function(t,e,r){return Math.abs(l(t,0,r))},length:function(t,e,r){return"line"!==t.type?void 0:Math.sqrt(Math.pow(s(t,e),2)+Math.pow(l(t,0,r),2))},xcenter:function(t,o){return r((e(t.x1,o)+i(t)+e(t.x0,o)+n(t))/2,o)},ycenter:function(t,n,i){return r((e(t.y1,i)+a(t)+e(t.y0,i)+o(t))/2,i)}}},8421:(t,e,r)=>{"use strict";var n=r(75058),i=r(85538),o=r(98260).extendDeepAll,a=r(62309).overrideAll,s=r(46367),l=r(46121).templatedArray,c=r(92911),u=l("step",{visible:{valType:"boolean",dflt:!0,description:["Determines whether or not this step is included in the slider."].join(" ")},method:{valType:"enumerated",values:["restyle","relayout","animate","update","skip"],dflt:"restyle",description:["Sets the Plotly method to be called when the slider value is changed.","If the `skip` method is used, the API slider will function as normal","but will perform no API calls and will not bind automatically to state","updates. This may be used to create a component interface and attach to","slider events manually via JavaScript."].join(" ")},args:{valType:"info_array",freeLength:!0,items:[{valType:"any"},{valType:"any"},{valType:"any"}],description:["Sets the arguments values to be passed to the Plotly","method set in `method` on slide."].join(" ")},label:{valType:"string",description:"Sets the text label to appear on the slider"},value:{valType:"string",description:["Sets the value of the slider step, used to refer to the step programatically.","Defaults to the slider label if not provided."].join(" ")},execute:{valType:"boolean",dflt:!0,description:["When true, the API method is executed. When false, all other behaviors are the same","and command execution is skipped. This may be useful when hooking into, for example,","the `plotly_sliderchange` method and executing the API command manually without losing","the benefit of the slider automatically binding to the state of the plot through the","specification of `method` and `args`."].join(" ")}});t.exports=a(l("slider",{visible:{valType:"boolean",dflt:!0,description:["Determines whether or not the slider is visible."].join(" ")},active:{valType:"number",min:0,dflt:0,description:["Determines which button (by index starting from 0) is","considered active."].join(" ")},steps:u,lenmode:{valType:"enumerated",values:["fraction","pixels"],dflt:"fraction",description:["Determines whether this slider length","is set in units of plot *fraction* or in *pixels.","Use `len` to set the value."].join(" ")},len:{valType:"number",min:0,dflt:1,description:["Sets the length of the slider","This measure excludes the padding of both ends.","That is, the slider's length is this length minus the","padding on both ends."].join(" ")},x:{valType:"number",min:-2,max:3,dflt:0,description:"Sets the x position (in normalized coordinates) of the slider."},pad:o(i({editType:"arraydraw"}),{description:"Set the padding of the slider component along each side."},{t:{dflt:20}}),xanchor:{valType:"enumerated",values:["auto","left","center","right"],dflt:"left",description:["Sets the slider's horizontal position anchor.","This anchor binds the `x` position to the *left*, *center*","or *right* of the range selector."].join(" ")},y:{valType:"number",min:-2,max:3,dflt:0,description:"Sets the y position (in normalized coordinates) of the slider."},yanchor:{valType:"enumerated",values:["auto","top","middle","bottom"],dflt:"top",description:["Sets the slider's vertical position anchor","This anchor binds the `y` position to the *top*, *middle*","or *bottom* of the range selector."].join(" ")},transition:{duration:{valType:"number",min:0,dflt:150,description:"Sets the duration of the slider transition"},easing:{valType:"enumerated",values:s.transition.easing.values,dflt:"cubic-in-out",description:"Sets the easing function of the slider transition"}},currentvalue:{visible:{valType:"boolean",dflt:!0,description:["Shows the currently-selected value above the slider."].join(" ")},xanchor:{valType:"enumerated",values:["left","center","right"],dflt:"left",description:["The alignment of the value readout relative to the length of the slider."].join(" ")},offset:{valType:"number",dflt:10,description:["The amount of space, in pixels, between the current value label","and the slider."].join(" ")},prefix:{valType:"string",description:"When currentvalue.visible is true, this sets the prefix of the label."},suffix:{valType:"string",description:"When currentvalue.visible is true, this sets the suffix of the label."},font:n({description:"Sets the font of the current value label text."})},font:n({description:"Sets the font of the slider step labels."}),activebgcolor:{valType:"color",dflt:c.gripBgActiveColor,description:["Sets the background color of the slider grip","while dragging."].join(" ")},bgcolor:{valType:"color",dflt:c.railBgColor,description:"Sets the background color of the slider."},bordercolor:{valType:"color",dflt:c.railBorderColor,description:"Sets the color of the border enclosing the slider."},borderwidth:{valType:"number",min:0,dflt:c.railBorderWidth,description:"Sets the width (in px) of the border enclosing the slider."},ticklen:{valType:"number",min:0,dflt:c.tickLength,description:"Sets the length in pixels of step tick marks"},tickcolor:{valType:"color",dflt:c.tickColor,description:"Sets the color of the border enclosing the slider."},tickwidth:{valType:"number",min:0,dflt:1,description:"Sets the tick width (in px)."},minorticklen:{valType:"number",min:0,dflt:c.minorTickLength,description:"Sets the length in pixels of minor step tick marks"}}),"arraydraw","from-root")},92911:t=>{"use strict";t.exports={name:"sliders",containerClassName:"slider-container",groupClassName:"slider-group",inputAreaClass:"slider-input-area",railRectClass:"slider-rail-rect",railTouchRectClass:"slider-rail-touch-rect",gripRectClass:"slider-grip-rect",tickRectClass:"slider-tick-rect",inputProxyClass:"slider-input-proxy",labelsClass:"slider-labels",labelGroupClass:"slider-label-group",labelClass:"slider-label",currentValueClass:"slider-current-value",railHeight:5,menuIndexAttrName:"slider-active-index",autoMarginIdRoot:"slider-",minWidth:30,minHeight:30,textPadX:40,arrowOffsetX:4,railRadius:2,railWidth:5,railBorder:4,railBorderWidth:1,railBorderColor:"#bec8d9",railBgColor:"#f8fafc",railInset:8,stepInset:10,gripRadius:10,gripWidth:20,gripHeight:20,gripBorder:20,gripBorderWidth:1,gripBorderColor:"#bec8d9",gripBgColor:"#f6f8fa",gripBgActiveColor:"#dbdde0",labelPadding:8,labelOffset:0,tickWidth:1,tickColor:"#333",tickOffset:25,tickLength:7,minorTickOffset:25,minorTickColor:"#333",minorTickLength:4,currentValuePadding:8,currentValueInset:0}},60626:(t,e,r)=>{"use strict";var n=r(12822),i=r(35677),o=r(8421),a=r(92911).name,s=o.steps;function l(t,e,r){function a(r,i){return n.coerce(t,e,o,r,i)}for(var s=i(t,e,{name:"steps",handleItemDefaults:c}),l=0,u=0;u{"use strict";var n=r(27941),i=r(51137),o=r(17499),a=r(40666),s=r(12822),l=s.strTranslate,c=r(80394),u=r(46121).arrayEditor,h=r(92911),d=r(89701),f=d.LINE_SPACING,p=d.FROM_TL,m=d.FROM_BR;function g(t){return h.autoMarginIdRoot+t._index}function v(t){return t._index}function b(t,e){var r=a.tester.selectAll("g."+h.labelGroupClass).data(e._visibleSteps);r.enter().append("g").classed(h.labelGroupClass,!0);var o=0,l=0;r.each((function(t){var r=_(n.select(this),{step:t},e).node();if(r){var i=a.bBox(r);l=Math.max(l,i.height),o=Math.max(o,i.width)}})),r.remove();var u=e._dims={};u.inputAreaWidth=Math.max(h.railWidth,h.gripHeight);var d=t._fullLayout._size;u.lx=d.l+d.w*e.x,u.ly=d.t+d.h*(1-e.y),"fraction"===e.lenmode?u.outerLength=Math.round(d.w*e.len):u.outerLength=e.len,u.inputAreaStart=0,u.inputAreaLength=Math.round(u.outerLength-e.pad.l-e.pad.r);var f=(u.inputAreaLength-2*h.stepInset)/(e._stepCount-1),v=o+h.labelPadding;if(u.labelStride=Math.max(1,Math.ceil(v/f)),u.labelHeight=l,u.currentValueMaxWidth=0,u.currentValueHeight=0,u.currentValueTotalHeight=0,u.currentValueMaxLines=1,e.currentvalue.visible){var b=a.tester.append("g");r.each((function(t){var r=y(b,e,t.label),n=r.node()&&a.bBox(r.node())||{width:0,height:0},i=c.lineCount(r);u.currentValueMaxWidth=Math.max(u.currentValueMaxWidth,Math.ceil(n.width)),u.currentValueHeight=Math.max(u.currentValueHeight,Math.ceil(n.height)),u.currentValueMaxLines=Math.max(u.currentValueMaxLines,i)})),u.currentValueTotalHeight=u.currentValueHeight+e.currentvalue.offset,b.remove()}u.height=u.currentValueTotalHeight+h.tickOffset+e.ticklen+h.labelOffset+u.labelHeight+e.pad.t+e.pad.b;var x="left";s.isRightAnchor(e)&&(u.lx-=u.outerLength,x="right"),s.isCenterAnchor(e)&&(u.lx-=u.outerLength/2,x="center");var w="top";s.isBottomAnchor(e)&&(u.ly-=u.height,w="bottom"),s.isMiddleAnchor(e)&&(u.ly-=u.height/2,w="middle"),u.outerLength=Math.ceil(u.outerLength),u.height=Math.ceil(u.height),u.lx=Math.round(u.lx),u.ly=Math.round(u.ly);var k={y:e.y,b:u.height*m[w],t:u.height*p[w]};"fraction"===e.lenmode?(k.l=0,k.xl=e.x-e.len*p[x],k.r=0,k.xr=e.x+e.len*m[x]):(k.x=e.x,k.l=u.outerLength*p[x],k.r=u.outerLength*m[x]),i.autoMargin(t,g(e),k)}function y(t,e,r){if(e.currentvalue.visible){var n,i,o=e._dims;switch(e.currentvalue.xanchor){case"right":n=o.inputAreaLength-h.currentValueInset-o.currentValueMaxWidth,i="left";break;case"center":n=.5*o.inputAreaLength,i="middle";break;default:n=h.currentValueInset,i="left"}var l=s.ensureSingle(t,"text",h.labelClass,(function(t){t.attr({"text-anchor":i,"data-notex":1})})),u=e.currentvalue.prefix?e.currentvalue.prefix:"";if("string"==typeof r)u+=r;else{var d=e.steps[e.active].label,p=e._gd._fullLayout._meta;p&&(d=s.templateString(d,p)),u+=d}e.currentvalue.suffix&&(u+=e.currentvalue.suffix),l.call(a.font,e.currentvalue.font).text(u).call(c.convertToTspans,e._gd);var m=c.lineCount(l),g=(o.currentValueMaxLines+1-m)*e.currentvalue.font.size*f;return c.positionText(l,n,g),l}}function x(t,e,r){s.ensureSingle(t,"rect",h.gripRectClass,(function(n){n.call(M,e,t,r).style("pointer-events","all")})).attr({width:h.gripWidth,height:h.gripHeight,rx:h.gripRadius,ry:h.gripRadius}).call(o.stroke,r.bordercolor).call(o.fill,r.bgcolor).style("stroke-width",r.borderwidth+"px")}function _(t,e,r){var n=s.ensureSingle(t,"text",h.labelClass,(function(t){t.attr({"text-anchor":"middle","data-notex":1})})),i=e.step.label,o=r._gd._fullLayout._meta;return o&&(i=s.templateString(i,o)),n.call(a.font,r.font).text(i).call(c.convertToTspans,r._gd),n}function w(t,e){var r=s.ensureSingle(t,"g",h.labelsClass),i=e._dims,o=r.selectAll("g."+h.labelGroupClass).data(i.labelSteps);o.enter().append("g").classed(h.labelGroupClass,!0),o.exit().remove(),o.each((function(t){var r=n.select(this);r.call(_,t,e),a.setTranslate(r,C(e,t.fraction),h.tickOffset+e.ticklen+e.font.size*f+h.labelOffset+i.currentValueTotalHeight)}))}function k(t,e,r,n,i){var o=Math.round(n*(r._stepCount-1)),a=r._visibleSteps[o]._index;a!==r.active&&A(t,e,r,a,!0,i)}function A(t,e,r,n,o,a){var s=r.active;r.active=n,u(t.layout,h.name,r).applyUpdate("active",n);var l=r.steps[r.active];e.call(S,r,a),e.call(y,r),t.emit("plotly_sliderchange",{slider:r,step:r.steps[r.active],interaction:o,previousActive:s}),l&&l.method&&o&&(e._nextMethod?(e._nextMethod.step=l,e._nextMethod.doCallback=o,e._nextMethod.doTransition=a):(e._nextMethod={step:l,doCallback:o,doTransition:a},e._nextMethodRaf=window.requestAnimationFrame((function(){var r=e._nextMethod.step;r.method&&(r.execute&&i.executeAPICommand(t,r.method,r.args),e._nextMethod=null,e._nextMethodRaf=null)}))))}function M(t,e,r){if(!e._context.staticPlot){var i=r.node(),a=n.select(e);t.on("mousedown",l),t.on("touchstart",l)}function s(){return r.data()[0]}function l(){var t=s();e.emit("plotly_sliderstart",{slider:t});var l=r.select("."+h.gripRectClass);n.event.stopPropagation(),n.event.preventDefault(),l.call(o.fill,t.activebgcolor);var c=E(t,n.mouse(i)[0]);function u(){var t=s(),o=E(t,n.mouse(i)[0]);k(e,r,t,o,!1)}function d(){var t=s();t._dragging=!1,l.call(o.fill,t.bgcolor),a.on("mouseup",null),a.on("mousemove",null),a.on("touchend",null),a.on("touchmove",null),e.emit("plotly_sliderend",{slider:t,step:t.steps[t.active]})}k(e,r,t,c,!0),t._dragging=!0,a.on("mousemove",u),a.on("touchmove",u),a.on("mouseup",d),a.on("touchend",d)}}function T(t,e){var r=t.selectAll("rect."+h.tickRectClass).data(e._visibleSteps),i=e._dims;r.enter().append("rect").classed(h.tickRectClass,!0),r.exit().remove(),r.attr({width:e.tickwidth+"px","shape-rendering":"crispEdges"}),r.each((function(t,r){var s=r%i.labelStride==0,l=n.select(this);l.attr({height:s?e.ticklen:e.minorticklen}).call(o.fill,e.tickcolor),a.setTranslate(l,C(e,r/(e._stepCount-1))-.5*e.tickwidth,(s?h.tickOffset:h.minorTickOffset)+i.currentValueTotalHeight)}))}function S(t,e,r){for(var n=t.select("rect."+h.gripRectClass),i=0,o=0;o0&&(s=s.transition().duration(e.transition.duration).ease(e.transition.easing)),s.attr("transform",l(a-.5*h.gripWidth,e._dims.currentValueTotalHeight))}}function C(t,e){var r=t._dims;return r.inputAreaStart+h.stepInset+(r.inputAreaLength-2*h.stepInset)*Math.min(1,Math.max(0,e))}function E(t,e){var r=t._dims;return Math.min(1,Math.max(0,(e-h.stepInset-r.inputAreaStart)/(r.inputAreaLength-2*h.stepInset-2*r.inputAreaStart)))}function L(t,e,r){var n=r._dims,i=s.ensureSingle(t,"rect",h.railTouchRectClass,(function(n){n.call(M,e,t,r).style("pointer-events","all")}));i.attr({width:n.inputAreaLength,height:Math.max(n.inputAreaWidth,h.tickOffset+r.ticklen+n.labelHeight)}).call(o.fill,r.bgcolor).attr("opacity",0),a.setTranslate(i,0,n.currentValueTotalHeight)}function z(t,e){var r=e._dims,n=r.inputAreaLength-2*h.railInset,i=s.ensureSingle(t,"rect",h.railRectClass);i.attr({width:n,height:h.railWidth,rx:h.railRadius,ry:h.railRadius,"shape-rendering":"crispEdges"}).call(o.stroke,e.bordercolor).call(o.fill,e.bgcolor).style("stroke-width",e.borderwidth+"px"),a.setTranslate(i,h.railInset,.5*(r.inputAreaWidth-h.railWidth)+r.currentValueTotalHeight)}t.exports=function(t){var e=t._context.staticPlot,r=t._fullLayout,o=function(t,e){for(var r=t[h.name],n=[],i=0;i0?[0]:[]);function l(e){e._commandObserver&&(e._commandObserver.remove(),delete 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m,g=t._fullLayout,v=r.propContainer,b=r.propName,y=r.placeholder,x=r.traceIndex,_=r.avoid||{},w=r.attributes,k=r.transform,A=r.containerGroup,M=1,T=v.title,S=(T&&T.text?T.text:"").trim(),C=!1,E=T&&T.font?T.font:{},L=E.family,z=E.size,O=E.color,D=E.weight,I=E.style,F=E.variant,R=E.textcase,P=E.lineposition,j=E.shadow,N=!!r.subtitlePropName,B=r.subtitlePlaceholder,U=(v.title||{}).subtitle||{text:"",font:{}},G=U.text.trim(),V=!1,H=1,W=U.font,q=W.family,Y=W.size,Z=W.color,X=W.weight,$=W.style,J=W.variant,K=W.textcase,Q=W.lineposition,tt=W.shadow;"title.text"===b?m="titleText":-1!==b.indexOf("axis")?m="axisTitleText":b.indexOf(!0)&&(m="colorbarTitleText");var et=t._context.edits[m];function rt(t,e){return void 0!==t&&void 0!==e&&t.replace(p," % ")===e.replace(p," % ")}""===S?M=0:rt(S,y)&&(et||(S=""),M=.2,C=!0),N&&(""===G?H=0:rt(G,B)&&(et||(G=""),H=.2,V=!0)),r._meta?S=s.templateString(S,r._meta):g._meta&&(S=s.templateString(S,g._meta));var nt,it=S||G||et;A||(A=s.ensureSingle(g._infolayer,"g","g-"+e),nt=g._hColorbarMoveTitle);var ot=A.selectAll("text."+e).data(it?[0]:[]);ot.enter().append("text"),ot.text(S).attr("class",e),ot.exit().remove();var at=null,st=e+"-subtitle",lt=G||et;if(N&<&&((at=A.selectAll("text."+st).data(lt?[0]:[])).enter().append("text"),at.text(G).attr("class",st),at.exit().remove()),!it)return A;function ct(t,e){s.syncOrAsync([ut,ht],{title:t,subtitle:e})}function ut(r){var i,a=r.title,d=r.subtitle;if(!k&&nt&&(k={}),k?(i="",k.rotate&&(i+="rotate("+[k.rotate,w.x,w.y]+")"),(k.offset||nt)&&(i+=l(0,(k.offset||0)-(nt||0)))):i=null,a.attr("transform",i),a.style("opacity",M*u.opacity(O)).call(c.font,{color:u.rgb(O),size:n.round(z,2),family:L,weight:D,style:I,variant:F,textcase:R,shadow:j,lineposition:P}).attr(w).call(h.convertToTspans,t,(function(t){if(t){var e=n.select(t.node().parentNode).select("."+st);if(!e.empty()){var r=t.node().getBBox();if(r.height){var i=r.y+r.height+1.6*Y;e.attr("y",i)}}}})),d){var f=A.select("."+e+"-math-group"),p=a.node().getBBox(),m=f.node()?f.node().getBBox():void 0,g=m?m.y+m.height+1.6*Y:p.y+p.height+1.6*Y,v=s.extendFlat({},w,{y:g});d.attr("transform",i),d.style("opacity",H*u.opacity(Z)).call(c.font,{color:u.rgb(Z),size:n.round(Y,2),family:q,weight:X,style:$,variant:J,textcase:K,shadow:tt,lineposition:Q}).attr(v).call(h.convertToTspans,t)}return o.previousPromises(t)}function ht(e){var r=e.title,o=n.select(r.node().parentNode);if(_&&_.selection&&_.side&&S){o.attr("transform",null);var a=f[_.side],u="left"===_.side||"top"===_.side?-1:1,h=i(_.pad)?_.pad:2,d=c.bBox(o.node()),p={t:0,b:0,l:0,r:0},m=t._fullLayout._reservedMargin;for(var b in m)for(var y in m[b]){var x=m[b][y];p[y]=Math.max(p[y],x)}var w={left:p.l,top:p.t,right:g.width-p.r,bottom:g.height-p.b},k=_.maxShift||u*(w[_.side]-d[_.side]),A=0;if(k<0)A=k;else{var M=_.offsetLeft||0,T=_.offsetTop||0;d.left-=M,d.right-=M,d.top-=T,d.bottom-=T,_.selection.each((function(){var t=c.bBox(this);s.bBoxIntersect(d,t,h)&&(A=Math.max(A,u*(t[_.side]-d[a])+h))})),A=Math.min(k,A),v._titleScoot=Math.abs(A)}if(A>0||k<0){var C={left:[-A,0],right:[A,0],top:[0,-A],bottom:[0,A]}[_.side];o.attr("transform",l(C[0],C[1]))}}}function dt(t,e){t.text(e).on("mouseover.opacity",(function(){n.select(this).transition().duration(d.SHOW_PLACEHOLDER).style("opacity",1)})).on("mouseout.opacity",(function(){n.select(this).transition().duration(d.HIDE_PLACEHOLDER).style("opacity",0)}))}if(ot.call(ct,at),et&&(S?ot.on(".opacity",null):(dt(ot,y),C=!0),ot.call(h.makeEditable,{gd:t}).on("edit",(function(e){void 0!==x?a.call("_guiRestyle",t,b,e,x):a.call("_guiRelayout",t,b,e)})).on("cancel",(function(){this.text(this.attr("data-unformatted")).call(ct)})).on("input",(function(t){this.text(t||" ").call(h.positionText,w.x,w.y)})),N)){if(N&&!S){var ft=ot.node().getBBox(),pt=ft.y+ft.height+1.6*Y;at.attr("y",pt)}G?at.on(".opacity",null):(dt(at,B),V=!0),at.call(h.makeEditable,{gd:t}).on("edit",(function(e){a.call("_guiRelayout",t,"title.subtitle.text",e)})).on("cancel",(function(){this.text(this.attr("data-unformatted")).call(ct)})).on("input",(function(t){this.text(t||" ").call(h.positionText,at.attr("x"),at.attr("y"))}))}return ot.classed("js-placeholder",C),at&&at.classed("js-placeholder",V),A},SUBTITLE_PADDING_EM:1.6,SUBTITLE_PADDING_MATHJAX_EM:1.6}},40658:(t,e,r)=>{"use strict";var n=r(75058),i=r(84226),o=r(98260).extendFlat,a=r(62309).overrideAll,s=r(85538),l=r(46121).templatedArray,c=l("button",{visible:{valType:"boolean",description:"Determines whether or not this button is visible."},method:{valType:"enumerated",values:["restyle","relayout","animate","update","skip"],dflt:"restyle",description:["Sets the Plotly method to be called on click.","If the `skip` method is used, the API updatemenu will function as normal","but 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update menu's vertical position anchor","This anchor binds the `y` position to the *top*, *middle*","or *bottom* of the range selector."].join(" ")},pad:o(s({editType:"arraydraw"}),{description:"Sets the padding around the buttons or dropdown menu."}),font:n({description:"Sets the font of the update menu button text."}),bgcolor:{valType:"color",description:"Sets the background color of the update menu buttons."},bordercolor:{valType:"color",dflt:i.borderLine,description:"Sets the color of the border enclosing the update menu."},borderwidth:{valType:"number",min:0,dflt:1,editType:"arraydraw",description:"Sets the width (in px) of the border enclosing the update menu."}}),"arraydraw","from-root")},13518:t=>{"use strict";t.exports={name:"updatemenus",containerClassName:"updatemenu-container",headerGroupClassName:"updatemenu-header-group",headerClassName:"updatemenu-header",headerArrowClassName:"updatemenu-header-arrow",dropdownButtonGroupClassName:"updatemenu-dropdown-button-group",dropdownButtonClassName:"updatemenu-dropdown-button",buttonClassName:"updatemenu-button",itemRectClassName:"updatemenu-item-rect",itemTextClassName:"updatemenu-item-text",menuIndexAttrName:"updatemenu-active-index",autoMarginIdRoot:"updatemenu-",blankHeaderOpts:{label:" "},minWidth:30,minHeight:30,textPadX:24,arrowPadX:16,rx:2,ry:2,textOffsetX:12,textOffsetY:3,arrowOffsetX:4,gapButtonHeader:5,gapButton:2,activeColor:"#F4FAFF",hoverColor:"#F4FAFF",arrowSymbol:{left:"◄",right:"►",up:"▲",down:"▼"}}},42757:(t,e,r)=>{"use strict";var n=r(12822),i=r(35677),o=r(40658),a=r(13518).name,s=o.buttons;function l(t,e,r){function a(r,i){return 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`title.text`, the title's","contents used to be defined as the `title` attribute itself.","This behavior has been deprecated."].join(" ")},font:n({editType:"ticks",description:["Sets this axis' title font.","Note that the title's font used to be customized","by the now deprecated `titlefont` attribute."].join(" ")}),standoff:{valType:"number",min:0,editType:"ticks",description:["Sets the standoff distance (in px) between the axis labels and the title text","The default value is a function of the axis tick labels, the title `font.size`","and the axis `linewidth`.","Note that the axis title position is always constrained within the margins,","so the actual standoff distance is always less than the set or default value.","By setting `standoff` and turning on `automargin`, plotly.js will push the","margins to fit the axis title at given standoff distance."].join(" ")},editType:"ticks"},type:{valType:"enumerated",values:["-","linear","log","date","category","multicategory"],dflt:"-",editType:"calc",_noTemplating:!0,description:["Sets the axis type.","By default, plotly attempts to determined the axis type","by looking into the data of the traces that referenced","the axis in question."].join(" ")},autotypenumbers:{valType:"enumerated",values:["convert types","strict"],dflt:"convert types",editType:"calc",description:["Using *strict* a numeric string in trace data is not converted to a number.","Using *convert types* a numeric string in trace data may be","treated as a number during automatic axis `type` detection.","Defaults to layout.autotypenumbers."].join(" ")},autorange:{valType:"enumerated",values:[!0,!1,"reversed","min reversed","max reversed","min","max"],dflt:!0,editType:"axrange",impliedEdits:{"range[0]":void 0,"range[1]":void 0},description:["Determines whether or not the range of this axis is","computed in relation to the input data.","See `rangemode` for more info.","If `range` is provided and it has a value for both the","lower and upper bound, `autorange` is set to *false*.","Using *min* applies autorange only to set the minimum.","Using *max* applies autorange only to set the maximum.","Using *min reversed* applies autorange only to set the minimum on a reversed axis.","Using *max reversed* applies autorange only to set the maximum on a reversed axis.","Using *reversed* applies autorange on both ends and reverses the axis direction."].join(" ")},autorangeoptions:{minallowed:{valType:"any",editType:"plot",impliedEdits:{"range[0]":void 0,"range[1]":void 0},description:["Use this value exactly as autorange minimum."].join(" ")},maxallowed:{valType:"any",editType:"plot",impliedEdits:{"range[0]":void 0,"range[1]":void 0},description:["Use this value exactly as autorange maximum."].join(" ")},clipmin:{valType:"any",editType:"plot",impliedEdits:{"range[0]":void 0,"range[1]":void 0},description:["Clip autorange minimum if it goes beyond this value.","Has no effect when `autorangeoptions.minallowed` is provided."].join(" ")},clipmax:{valType:"any",editType:"plot",impliedEdits:{"range[0]":void 0,"range[1]":void 0},description:["Clip autorange maximum if it goes beyond this value.","Has no effect when `autorangeoptions.maxallowed` is provided."].join(" ")},include:{valType:"any",arrayOk:!0,editType:"plot",impliedEdits:{"range[0]":void 0,"range[1]":void 0},description:["Ensure this value is included in autorange."].join(" ")},editType:"plot"},rangemode:{valType:"enumerated",values:["normal","tozero","nonnegative"],dflt:"normal",editType:"plot",description:["If *normal*, the range is computed in relation to the extrema","of the input data.","If *tozero*`, the range extends to 0,","regardless of the input data","If *nonnegative*, the range is non-negative,","regardless of the input data.","Applies only to linear axes."].join(" ")},range:{valType:"info_array",items:[{valType:"any",editType:"axrange",impliedEdits:{"^autorange":!1},anim:!0},{valType:"any",editType:"axrange",impliedEdits:{"^autorange":!1},anim:!0}],editType:"axrange",impliedEdits:{autorange:!1},anim:!0,description:["Sets the range of this axis.","If the axis `type` is *log*, then you must take the log of your","desired range (e.g. to set the range from 1 to 100,","set the range from 0 to 2).","If the axis `type` is *date*, it should be date strings,","like date data, though Date objects and unix milliseconds","will be accepted and converted to strings.","If the axis `type` is *category*, it should be numbers,","using the scale where each category is assigned a serial","number from zero in the order it appears.","Leaving either or both elements `null` impacts the default `autorange`."].join(" ")},minallowed:{valType:"any",editType:"plot",impliedEdits:{"^autorange":!1},description:["Determines the minimum range of this axis."].join(" ")},maxallowed:{valType:"any",editType:"plot",impliedEdits:{"^autorange":!1},description:["Determines the maximum range of this axis."].join(" ")},fixedrange:{valType:"boolean",dflt:!1,editType:"calc",description:["Determines whether or not this axis is zoom-able.","If true, then zoom is disabled."].join(" ")},insiderange:{valType:"info_array",items:[{valType:"any",editType:"plot"},{valType:"any",editType:"plot"}],editType:"plot",description:["Could be used to set the desired inside range of this axis","(excluding the labels) when `ticklabelposition` of","the anchored axis has *inside*.","Not implemented for axes with `type` *log*.","This would be ignored when `range` is provided."].join(" ")},scaleanchor:{valType:"enumerated",values:[u.idRegex.x.toString(),u.idRegex.y.toString(),!1],editType:"plot",description:["If set to another axis id (e.g. `x2`, `y`), the range of this axis","changes together with the range of the corresponding axis","such that the scale of pixels per unit is in a constant ratio.","Both axes are still zoomable, but when you zoom one, the other will","zoom the same amount, keeping a fixed midpoint.","`constrain` and `constraintoward` determine how we enforce the constraint.","You can chain these, ie `yaxis: {scaleanchor: *x*}, xaxis2: {scaleanchor: *y*}`","but you can only link axes of the same `type`.","The linked axis can have the opposite letter (to constrain the aspect ratio)","or the same letter (to match scales across subplots).","Loops (`yaxis: {scaleanchor: *x*}, xaxis: {scaleanchor: *y*}` or longer) are redundant","and the last constraint encountered will be ignored to avoid possible","inconsistent constraints via `scaleratio`.","Note that setting axes simultaneously in both a `scaleanchor` and a `matches` constraint","is currently forbidden.","Setting `false` allows to remove a default constraint (occasionally,","you may need to prevent a default `scaleanchor` constraint from",'being applied, eg. when having an image trace `yaxis: {scaleanchor: "x"}`',"is set automatically in order for pixels to be rendered as squares,","setting `yaxis: {scaleanchor: false}` allows to remove the constraint)."].join(" ")},scaleratio:{valType:"number",min:0,dflt:1,editType:"plot",description:["If this axis is linked to another by `scaleanchor`, this determines the pixel","to unit scale ratio. For example, if this value is 10, then every unit on","this axis spans 10 times the number of pixels as a unit on the linked axis.","Use this for example to create an elevation profile where the vertical scale","is exaggerated a fixed amount with respect to the horizontal."].join(" ")},constrain:{valType:"enumerated",values:["range","domain"],editType:"plot",description:["If this axis needs to be compressed (either due to its own `scaleanchor` and","`scaleratio` or those of the other axis), determines how that happens:","by increasing the *range*, or by decreasing the *domain*.","Default is *domain* for axes containing image traces, *range* otherwise."].join(" ")},constraintoward:{valType:"enumerated",values:["left","center","right","top","middle","bottom"],editType:"plot",description:["If this axis needs to be compressed (either due to its own `scaleanchor` and","`scaleratio` or those of the other axis), determines which direction we push","the originally specified plot area. Options are *left*, *center* (default),","and *right* for x axes, and *top*, *middle* (default), and *bottom* for y axes."].join(" ")},matches:{valType:"enumerated",values:[u.idRegex.x.toString(),u.idRegex.y.toString()],editType:"calc",description:["If set to another axis id (e.g. `x2`, `y`), the range of this axis","will match the range of the corresponding axis in data-coordinates space.","Moreover, matching axes share auto-range values, category lists and","histogram auto-bins.","Note that setting axes simultaneously in both a `scaleanchor` and a `matches` constraint","is currently forbidden.","Moreover, note that matching axes must have the same `type`."].join(" ")},rangebreaks:s("rangebreak",{enabled:{valType:"boolean",dflt:!0,editType:"calc",description:["Determines whether this axis rangebreak is enabled or disabled.","Please note that `rangebreaks` only work for *date* axis type."].join(" ")},bounds:{valType:"info_array",items:[{valType:"any",editType:"calc"},{valType:"any",editType:"calc"}],editType:"calc",description:["Sets the lower and upper bounds of this axis rangebreak.","Can be used with `pattern`."].join(" ")},pattern:{valType:"enumerated",values:[d,h,""],editType:"calc",description:["Determines a pattern on the time line that generates breaks.","If *"+d+"* - days of the week in English e.g. 'Sunday' or `sun`","(matching is case-insensitive and considers only the first three characters),","as well as Sunday-based integers between 0 and 6.","If *"+h+"* - hour (24-hour clock) as decimal numbers between 0 and 24.","for more info.","Examples:","- { pattern: '"+d+"', bounds: [6, 1] }"," or simply { bounds: ['sat', 'mon'] }"," breaks from Saturday to Monday (i.e. skips the weekends).","- { pattern: '"+h+"', bounds: [17, 8] }"," breaks from 5pm to 8am (i.e. skips non-work hours)."].join(" ")},values:{valType:"info_array",freeLength:!0,editType:"calc",items:{valType:"any",editType:"calc"},description:["Sets the coordinate values corresponding to the rangebreaks.","An alternative to `bounds`.","Use `dvalue` to set the size of the values along the axis."].join(" ")},dvalue:{valType:"number",editType:"calc",min:0,dflt:c,description:["Sets the size of each `values` item.","The default is one day in milliseconds."].join(" ")},editType:"calc"}),tickmode:p,nticks:m(),tick0:g,dtick:v,ticklabelstep:{valType:"integer",min:1,dflt:1,editType:"ticks",description:["Sets the spacing between tick labels as compared to the spacing between ticks.","A value of 1 (default) means each tick gets a label.","A value of 2 means shows every 2nd label.","A larger value n means only every nth tick is labeled.","`tick0` determines which labels are shown.","Not implemented for axes with `type` *log* or *multicategory*, or when `tickmode` is *array*."].join(" ")},tickvals:b,ticktext:{valType:"data_array",editType:"ticks",description:["Sets the text displayed at the ticks position via `tickvals`.","Only has an effect if `tickmode` is set to *array*.","Used with `tickvals`."].join(" ")},ticks:y,tickson:{valType:"enumerated",values:["labels","boundaries"],dflt:"labels",editType:"ticks",description:["Determines where ticks and grid lines are drawn with respect to their","corresponding tick labels.","Only has an effect for axes of `type` *category* or *multicategory*.","When set to *boundaries*, ticks and grid lines are drawn half a category","to the left/bottom of labels."].join(" ")},ticklabelmode:{valType:"enumerated",values:["instant","period"],dflt:"instant",editType:"ticks",description:["Determines where tick labels are drawn with respect to their","corresponding ticks and grid lines.","Only has an effect for axes of `type` *date*","When set to *period*, tick labels are drawn in the middle of the period","between ticks."].join(" ")},ticklabelposition:{valType:"enumerated",values:["outside","inside","outside top","inside top","outside left","inside left","outside right","inside right","outside bottom","inside bottom"],dflt:"outside",editType:"calc",description:["Determines where tick labels are drawn with respect to the axis","Please note that","top or bottom has no effect on x axes or when `ticklabelmode` is set to *period*.","Similarly","left or right has no effect on y axes or when `ticklabelmode` is set to *period*.","Has no effect on *multicategory* axes or when `tickson` is set to *boundaries*.","When used on axes linked by `matches` or `scaleanchor`,","no extra padding for inside labels would be added by autorange,","so that the scales could match."].join(" ")},ticklabeloverflow:{valType:"enumerated",values:["allow","hide past div","hide past domain"],editType:"calc",description:["Determines how we handle tick labels that would overflow either the graph div or the domain of the axis.","The default value for inside tick labels is *hide past domain*.","Otherwise on *category* and *multicategory* axes the default is *allow*.","In other cases the default is *hide past div*."].join(" ")},ticklabelshift:{valType:"integer",dflt:0,editType:"ticks",description:["Shifts the tick labels by the specified number of pixels in parallel to the axis.","Positive values move the labels in the positive direction of the axis."].join(" ")},ticklabelstandoff:{valType:"integer",dflt:0,editType:"ticks",description:["Sets the standoff distance (in px) between the axis tick labels and their default position.","A positive `ticklabelstandoff` moves the labels farther away from the plot area","if `ticklabelposition` is *outside*, and deeper into the plot area if","`ticklabelposition` is *inside*. A negative `ticklabelstandoff` works in the opposite","direction, moving outside ticks towards the plot area and inside ticks towards","the outside. If the negative value is large enough, inside ticks can even end up","outside and vice versa."].join(" ")},ticklabelindex:{valType:"integer",arrayOk:!0,editType:"calc",description:["Only for axes with `type` *date* or *linear*.","Instead of drawing the major tick label, draw the label for the minor tick","that is n positions away from the major tick. E.g. to always draw the label for the","minor tick before each major tick, choose `ticklabelindex` -1. This is useful for date","axes with `ticklabelmode` *period* if you want to label the period that ends with each","major tick instead of the period that begins there."].join(" ")},mirror:{valType:"enumerated",values:[!0,"ticks",!1,"all","allticks"],dflt:!1,editType:"ticks+layoutstyle",description:["Determines if the axis lines or/and ticks are mirrored to","the opposite side of the plotting area.","If *true*, the axis lines are mirrored.","If *ticks*, the axis lines and ticks are mirrored.","If *false*, mirroring is disable.","If *all*, axis lines are mirrored on all shared-axes subplots.","If *allticks*, axis lines and ticks are mirrored","on all shared-axes subplots."].join(" ")},ticklen:x(),tickwidth:_(),tickcolor:w,showticklabels:{valType:"boolean",dflt:!0,editType:"ticks",description:"Determines whether or not the tick labels are drawn."},labelalias:{valType:"any",dflt:!1,editType:"ticks",description:["Replacement text for specific tick or hover labels.","For example using {US: 'USA', CA: 'Canada'} changes US to USA","and CA to Canada. The labels we would have shown must match","the keys exactly, after adding any tickprefix or ticksuffix.","For negative numbers the minus sign symbol used (U+2212) is wider than the regular ascii dash.","That means you need to use −1 instead of -1.","labelalias can be used with any axis type, and both keys (if needed)","and values (if desired) can include html-like tags or MathJax."].join(" ")},automargin:{valType:"flaglist",flags:["height","width","left","right","top","bottom"],extras:[!0,!1],dflt:!1,editType:"ticks",description:["Determines whether long tick labels automatically grow the figure","margins."].join(" ")},showspikes:{valType:"boolean",dflt:!1,editType:"modebar",description:["Determines whether or not spikes (aka droplines) are drawn for this axis.","Note: This only takes affect when hovermode = closest"].join(" ")},spikecolor:{valType:"color",dflt:null,editType:"none",description:"Sets the spike color. If undefined, will use the series color"},spikethickness:{valType:"number",dflt:3,editType:"none",description:"Sets the width (in px) of the zero line."},spikedash:a({},o,{dflt:"dash",editType:"none"}),spikemode:{valType:"flaglist",flags:["toaxis","across","marker"],dflt:"toaxis",editType:"none",description:["Determines the drawing mode for the spike line","If *toaxis*, the line is drawn from the data point to the axis the ","series is plotted on.","If *across*, the line is drawn across the entire plot area, and","supercedes *toaxis*.","If *marker*, then a marker dot is drawn on the axis the series is","plotted on"].join(" ")},spikesnap:{valType:"enumerated",values:["data","cursor","hovered data"],dflt:"hovered data",editType:"none",description:"Determines whether spikelines are stuck to the cursor or to the closest datapoints."},tickfont:n({editType:"ticks",description:"Sets the tick font."}),tickangle:{valType:"angle",dflt:"auto",editType:"ticks",description:["Sets the angle of the tick labels with respect to the horizontal.","For example, a `tickangle` of -90 draws the tick labels","vertically."].join(" ")},autotickangles:{valType:"info_array",freeLength:!0,items:{valType:"angle"},dflt:[0,30,90],editType:"ticks",description:["When `tickangle` is set to *auto*, it will be set to the first","angle in this array that is large enough to prevent label","overlap."].join(" ")},tickprefix:{valType:"string",dflt:"",editType:"ticks",description:"Sets a tick label prefix."},showtickprefix:{valType:"enumerated",values:["all","first","last","none"],dflt:"all",editType:"ticks",description:["If *all*, all tick labels are displayed with a prefix.","If *first*, only the first tick is displayed with a prefix.","If *last*, only the last tick is displayed with a suffix.","If *none*, tick prefixes are hidden."].join(" ")},ticksuffix:{valType:"string",dflt:"",editType:"ticks",description:"Sets a tick label suffix."},showticksuffix:{valType:"enumerated",values:["all","first","last","none"],dflt:"all",editType:"ticks",description:"Same as `showtickprefix` but for tick suffixes."},showexponent:{valType:"enumerated",values:["all","first","last","none"],dflt:"all",editType:"ticks",description:["If *all*, all exponents are shown besides their significands.","If *first*, only the exponent of the first tick is shown.","If *last*, only the exponent of the last tick is shown.","If *none*, no exponents appear."].join(" ")},exponentformat:{valType:"enumerated",values:["none","e","E","power","SI","B"],dflt:"B",editType:"ticks",description:["Determines a formatting rule for the tick exponents.","For example, consider the number 1,000,000,000.","If *none*, it appears as 1,000,000,000.","If *e*, 1e+9.","If *E*, 1E+9.","If *power*, 1x10^9 (with 9 in a super script).","If *SI*, 1G.","If *B*, 1B."].join(" ")},minexponent:{valType:"number",dflt:3,min:0,editType:"ticks",description:["Hide SI prefix for 10^n if |n| is below this number.","This only has an effect when `tickformat` is *SI* or *B*."].join(" ")},separatethousands:{valType:"boolean",dflt:!1,editType:"ticks",description:['If "true", even 4-digit integers are separated'].join(" ")},tickformat:{valType:"string",dflt:"",editType:"ticks",description:l("tick label")},tickformatstops:s("tickformatstop",{enabled:{valType:"boolean",dflt:!0,editType:"ticks",description:["Determines whether or not this stop is used.","If `false`, this stop is ignored even within its `dtickrange`."].join(" ")},dtickrange:{valType:"info_array",items:[{valType:"any",editType:"ticks"},{valType:"any",editType:"ticks"}],editType:"ticks",description:["range [*min*, *max*], where *min*, *max* - dtick values","which describe some zoom level, it is possible to omit *min*","or *max* value by passing *null*"].join(" ")},value:{valType:"string",dflt:"",editType:"ticks",description:["string - dtickformat for described zoom level, the same as *tickformat*"].join(" ")},editType:"ticks"}),hoverformat:{valType:"string",dflt:"",editType:"none",description:l("hover text")},showline:{valType:"boolean",dflt:!1,editType:"ticks+layoutstyle",description:["Determines whether or not a line bounding this axis is drawn."].join(" ")},linecolor:{valType:"color",dflt:i.defaultLine,editType:"layoutstyle",description:"Sets the axis line color."},linewidth:{valType:"number",min:0,dflt:1,editType:"ticks+layoutstyle",description:"Sets the width (in px) of the axis line."},showgrid:T,gridcolor:k,gridwidth:A(),griddash:M,zeroline:{valType:"boolean",editType:"ticks",description:["Determines whether or not a line is drawn at along the 0 value","of this axis.","If *true*, the zero line is drawn on top of the grid lines."].join(" ")},zerolinecolor:{valType:"color",dflt:i.defaultLine,editType:"ticks",description:"Sets the line color of the zero line."},zerolinewidth:{valType:"number",dflt:1,editType:"ticks",description:"Sets the width (in px) of the zero line."},showdividers:{valType:"boolean",dflt:!0,editType:"ticks",description:["Determines whether or not a dividers are drawn","between the category levels of this axis.","Only has an effect on *multicategory* axes."].join(" ")},dividercolor:{valType:"color",dflt:i.defaultLine,editType:"ticks",description:["Sets the color of the dividers","Only has an effect on *multicategory* axes."].join(" ")},dividerwidth:{valType:"number",dflt:1,editType:"ticks",description:["Sets the width (in px) of the dividers","Only has an effect on *multicategory* axes."].join(" ")},anchor:{valType:"enumerated",values:["free",u.idRegex.x.toString(),u.idRegex.y.toString()],editType:"plot",description:["If set to an opposite-letter axis id (e.g. `x2`, `y`), this axis is bound to","the corresponding opposite-letter axis.","If set to *free*, this axis' position is determined by `position`."].join(" ")},side:{valType:"enumerated",values:["top","bottom","left","right"],editType:"plot",description:["Determines whether a x (y) axis is positioned","at the *bottom* (*left*) or *top* (*right*)","of the plotting area."].join(" ")},overlaying:{valType:"enumerated",values:["free",u.idRegex.x.toString(),u.idRegex.y.toString()],editType:"plot",description:["If set a same-letter axis id, this axis is overlaid on top of","the corresponding same-letter axis, with traces and axes visible for both","axes.","If *false*, this axis does not overlay any same-letter axes.","In this case, for axes with overlapping domains only the highest-numbered","axis will be visible."].join(" ")},minor:{tickmode:f,nticks:m("minor"),tick0:g,dtick:v,tickvals:b,ticks:y,ticklen:x("minor"),tickwidth:_("minor"),tickcolor:w,gridcolor:k,gridwidth:A("minor"),griddash:M,showgrid:T,editType:"ticks"},layer:{valType:"enumerated",values:["above traces","below traces"],dflt:"above traces",editType:"plot",description:["Sets the layer on which this axis is displayed.","If *above traces*, this axis is displayed above all the subplot's traces","If *below traces*, this axis is displayed below all the subplot's traces,","but above the grid lines.","Useful when used together with scatter-like traces with `cliponaxis`","set to *false* to show markers and/or text nodes above this axis."].join(" ")},domain:{valType:"info_array",items:[{valType:"number",min:0,max:1,editType:"plot"},{valType:"number",min:0,max:1,editType:"plot"}],dflt:[0,1],editType:"plot",description:["Sets the domain of this axis (in plot fraction)."].join(" ")},position:{valType:"number",min:0,max:1,dflt:0,editType:"plot",description:["Sets the position of this axis in the plotting space","(in normalized coordinates).","Only has an effect if `anchor` is set to *free*."].join(" ")},autoshift:{valType:"boolean",dflt:!1,editType:"plot",description:["Automatically reposition the axis to avoid","overlap with other axes with the same `overlaying` value.","This repositioning will account for any `shift` amount applied to other","axes on the same side with `autoshift` is set to true.","Only has an effect if `anchor` is set to *free*."].join(" ")},shift:{valType:"number",editType:"plot",description:["Moves the axis a given number of pixels from where it would have been otherwise.","Accepts both positive and negative values, which will shift the axis either right","or left, respectively.","If `autoshift` is set to true, then this defaults to a padding of -3 if `side` is set to *left*.","and defaults to +3 if `side` is set to *right*. Defaults to 0 if `autoshift` is set to false.","Only has an effect if `anchor` is set to *free*."].join(" ")},categoryorder:{valType:"enumerated",values:["trace","category ascending","category descending","array","total ascending","total descending","min ascending","min descending","max ascending","max descending","sum ascending","sum descending","mean ascending","mean descending","geometric mean ascending","geometric mean descending","median ascending","median descending"],dflt:"trace",editType:"calc",description:["Specifies the ordering logic for the case of categorical variables.","By default, plotly uses *trace*, which specifies the order that is present in the data supplied.","Set `categoryorder` to *category ascending* or *category descending* if order should be determined by","the alphanumerical order of the category names.","Set `categoryorder` to *array* to derive the ordering from the attribute `categoryarray`. If a category","is not found in the `categoryarray` array, the sorting behavior for that attribute will be identical to","the *trace* mode. The unspecified categories will follow the categories in `categoryarray`.","Set `categoryorder` to *total ascending* or *total descending* if order should be determined by the","numerical order of the values.","Similarly, the order can be determined by the min, max, sum, mean, geometric mean or median of all the values."].join(" ")},categoryarray:{valType:"data_array",editType:"calc",description:["Sets the order in which categories on this axis appear.","Only has an effect if `categoryorder` is set to *array*.","Used with `categoryorder`."].join(" ")},uirevision:{valType:"any",editType:"none",description:["Controls persistence of user-driven changes in axis `range`,","`autorange`, and `title` if in `editable: true` configuration.","Defaults to `layout.uirevision`."].join(" ")},editType:"calc",_deprecated:{autotick:{valType:"boolean",editType:"ticks",description:["Obsolete.","Set `tickmode` to *auto* for old `autotick` *true* behavior.","Set `tickmode` to *linear* for `autotick` *false*."].join(" ")},title:{valType:"string",editType:"ticks",description:["Value of `title` is no longer a simple *string* but a set of sub-attributes.","To set the axis' title, please use `title.text` now."].join(" ")},titlefont:n({editType:"ticks",description:["Former `titlefont` is now the sub-attribute `font` of `title`.","To customize title font properties, please use `title.font` now."].join(" ")})}}},36741:(t,e,r)=>{"use strict";var n=r(12822),i=r(17499),o=r(66811).isUnifiedHover,a=r(85400),s=r(46121),l=r(13195),c=r(86130),u=r(25119),h=r(91200),d=r(69352),f=r(52869),p=r(99246),m=p.id2name,g=p.name2id,v=r(21197).AX_ID_PATTERN,b=r(25059),y=b.traceIs,x=b.getComponentMethod;function _(t,e,r){Array.isArray(t[e])?t[e].push(r):t[e]=[r]}t.exports=function(t,e,r){var b,w,k=e.autotypenumbers,A={},M={},T={},S={},C={},E={},L={},z={},O={},D={};for(b=0;b{"use strict";var n=r(18106).mix,i=r(84226),o=r(12822);t.exports=function(t,e,r,a){var s=(a=a||{}).dfltColor;function l(r,n){return 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i}}}(e,s,l);if(c)if("histogram"!==c.type||l!=={v:"y",h:"x"}[c.orientation||"v"]){var u=l+"calendar",h=c[u],d={noMultiCategory:!n(c,"cartesian")||n(c,"noMultiCategory")};if("box"===c.type&&c._hasPreCompStats&&l==={h:"x",v:"y"}[c.orientation||"v"]&&(d.noMultiCategory=!0),d.autotypenumbers=t.autotypenumbers,a(c,l)){var f=o(c),p=[];for(r=0;r{"use strict";var n=r(25059),i=r(12822);function o(t,e,r){var n,o,a,s=!1;if("data"===e.type)n=t._fullData[null!==e.traces?e.traces[0]:0];else{if("layout"!==e.type)return!1;n=t._fullLayout}return o=i.nestedProperty(n,e.prop).get(),(a=r[e.type]=r[e.type]||{}).hasOwnProperty(e.prop)&&a[e.prop]!==o&&(s=!0),a[e.prop]=o,{changed:s,value:o}}function a(t,e){var r=[],n=e[0],o={};if("string"==typeof n)o[n]=e[1];else{if(!i.isPlainObject(n))return r;o=n}return l(o,(function(t,e,n){r.push({type:"layout",prop:t,value:n})}),"",0),r}function s(t,e){var r,n,o,a,s=[];if(n=e[0],o=e[1],r=e[2],a={},"string"==typeof n)a[n]=o;else{if(!i.isPlainObject(n))return s;a=n,void 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n=r(98260).extendFlat;e.u=function(t,e){e=e||{};var r={valType:"info_array",editType:(t=t||{}).editType,items:[{valType:"number",min:0,max:1,editType:t.editType},{valType:"number",min:0,max:1,editType:t.editType}],dflt:[0,1]},i=t.name?t.name+" ":"",o=t.trace?"trace ":"subplot ",a=e.description?" "+e.description:"",s={x:n({},r,{description:["Sets the horizontal domain of this ",i,o,"(in plot fraction).",a].join("")}),y:n({},r,{description:["Sets the vertical domain of this ",i,o,"(in plot fraction).",a].join("")}),editType:t.editType};return t.noGridCell||(s.row={valType:"integer",min:0,dflt:0,editType:t.editType,description:["If there is a layout grid, use the domain ","for this row in the grid for this ",i,o,".",a].join("")},s.column={valType:"integer",min:0,dflt:0,editType:t.editType,description:["If there is a layout grid, use the domain ","for this column in the grid for this ",i,o,".",a].join("")}),s},e.N=function(t,e,r,n){var i=n&&n.x||[0,1],o=n&&n.y||[0,1],a=e.grid;if(a){var s=r("domain.column");void 0!==s&&(s{"use strict";t.exports=function(t){var e=t.variantValues,r=t.editType,n=t.colorEditType;void 0===n&&(n=r);var i={editType:r,valType:"integer",min:1,max:1e3,extras:["normal","bold"],dflt:"normal",description:["Sets the weight (or boldness) of the font."].join(" ")};t.noNumericWeightValues&&(i.valType="enumerated",i.values=i.extras,i.extras=void 0,i.min=void 0,i.max=void 0);var o={family:{valType:"string",noBlank:!0,strict:!0,editType:r,description:["HTML font family - the typeface that will be applied by the web browser.","The web browser will only be able to apply a font if it is available on the system","which it operates. Provide multiple font families, separated by commas, to indicate","the preference in which to apply fonts if they aren't available on the system.","The Chart Studio Cloud (at https://chart-studio.plotly.com or on-premise) generates images on a server,","where only a select number of","fonts are installed and supported.","These include *Arial*, *Balto*, *Courier New*, *Droid Sans*, *Droid Serif*,","*Droid Sans Mono*, *Gravitas One*, *Old Standard TT*, *Open Sans*, *Overpass*,","*PT Sans Narrow*, *Raleway*, *Times New Roman*."].join(" ")},size:{valType:"number",min:1,editType:r},color:{valType:"color",editType:n},weight:i,style:{editType:r,valType:"enumerated",values:["normal","italic"],dflt:"normal",description:["Sets whether a font should be styled with a normal or italic face from its family."].join(" ")},variant:t.noFontVariant?void 0:{editType:r,valType:"enumerated",values:e||["normal","small-caps","all-small-caps","all-petite-caps","petite-caps","unicase"],dflt:"normal",description:["Sets the variant of the font."].join(" ")},textcase:t.noFontTextcase?void 0:{editType:r,valType:"enumerated",values:["normal","word caps","upper","lower"],dflt:"normal",description:["Sets capitalization of text.","It can be used to make text appear in all-uppercase or all-lowercase,","or with each word capitalized."].join(" ")},lineposition:t.noFontLineposition?void 0:{editType:r,valType:"flaglist",flags:["under","over","through"],extras:["none"],dflt:"none",description:["Sets the kind of decoration line(s) with text,","such as an *under*, *over* or *through*","as well as combinations e.g. *under+over*, etc."].join(" ")},shadow:t.noFontShadow?void 0:{editType:r,valType:"string",dflt:t.autoShadowDflt?"auto":"none",description:["Sets the shape and color of the shadow behind text.","*auto* places minimal shadow and applies contrast text font color.","See https://developer.mozilla.org/en-US/docs/Web/CSS/text-shadow for additional options."].join(" ")},editType:r,description:""+(t.description||"")};return t.autoSize&&(o.size.dflt="auto"),t.autoColor&&(o.color.dflt="auto"),t.arrayOk&&(o.family.arrayOk=!0,o.weight.arrayOk=!0,o.style.arrayOk=!0,t.noFontVariant||(o.variant.arrayOk=!0),t.noFontTextcase||(o.textcase.arrayOk=!0),t.noFontLineposition||(o.lineposition.arrayOk=!0),t.noFontShadow||(o.shadow.arrayOk=!0),o.size.arrayOk=!0,o.color.arrayOk=!0),o}},53874:t=>{"use strict";t.exports={_isLinkedToArray:"frames_entry",group:{valType:"string",description:["An identifier that specifies the group to which the frame belongs,","used by animate to select a subset of frames."].join(" ")},name:{valType:"string",description:"A label by which to identify the frame"},traces:{valType:"any",description:["A list of trace indices that identify the respective traces in the","data attribute"].join(" ")},baseframe:{valType:"string",description:["The name of the frame into which this frame's properties are merged","before applying. This is used to unify properties and avoid needing","to specify the same values for the same properties in multiple frames."].join(" ")},data:{valType:"any",description:["A list of traces this frame modifies. The format is identical to the","normal trace definition."].join(" ")},layout:{valType:"any",description:["Layout properties which this frame modifies. The format is identical","to the normal layout definition."].join(" ")}}},47388:(t,e,r)=>{"use strict";var n=r(25059),i=r(21197).SUBPLOT_PATTERN;e.eV=function(t,e,r){var i,o=[],a=[];if(!(i="string"==typeof e?n.getModule(e).plot:"function"==typeof e?e:e.plot))return[o,t];for(var s=r,l=0;l{"use strict";var n=r(62309).overrideAll,i=r(53572),o=r(85833),a=r(47388).KO,s=r(12822),l=r(25853),c="gl3d",u="scene";e.name=c,e.attr=u,e.idRoot=u,e.idRegex=e.attrRegex=s.counterRegex("scene"),e.attributes=r(816),e.layoutAttributes=r(41019),e.baseLayoutAttrOverrides=n({hoverlabel:i.hoverlabel},"plot","nested"),e.supplyLayoutDefaults=r(13351),e.plot=function(t){for(var e=t._fullLayout,r=t._fullData,n=e._subplots[c],i=0;i{"use strict";t.exports={scene:{valType:"subplotid",dflt:"scene",editType:"calc+clearAxisTypes",description:["Sets a reference between this trace's 3D coordinate system and","a 3D scene.","If *scene* (the default value), the (x,y,z) coordinates refer to","`layout.scene`.","If *scene2*, the (x,y,z) coordinates refer to `layout.scene2`,","and so on."].join(" ")}}},82854:(t,e,r)=>{"use strict";var n=r(17499),i=r(86130),o=r(98260).extendFlat,a=r(62309).overrideAll;t.exports=a({visible:i.visible,showspikes:{valType:"boolean",dflt:!0,description:["Sets whether or not spikes starting from","data points to this axis' wall are shown on hover."].join(" ")},spikesides:{valType:"boolean",dflt:!0,description:["Sets whether or not spikes extending from the","projection data points to this axis' wall boundaries","are shown on hover."].join(" ")},spikethickness:{valType:"number",min:0,dflt:2,description:"Sets the thickness (in px) of the spikes."},spikecolor:{valType:"color",dflt:n.defaultLine,description:"Sets the color of the spikes."},showbackground:{valType:"boolean",dflt:!1,description:["Sets whether or not this axis' wall","has a background color."].join(" ")},backgroundcolor:{valType:"color",dflt:"rgba(204, 204, 204, 0.5)",description:"Sets the background color of this axis' wall."},showaxeslabels:{valType:"boolean",dflt:!0,description:"Sets whether or not this axis is labeled"},color:i.color,categoryorder:i.categoryorder,categoryarray:i.categoryarray,title:{text:i.title.text,font:i.title.font},type:o({},i.type,{values:["-","linear","log","date","category"]}),autotypenumbers:i.autotypenumbers,autorange:i.autorange,autorangeoptions:{minallowed:i.autorangeoptions.minallowed,maxallowed:i.autorangeoptions.maxallowed,clipmin:i.autorangeoptions.clipmin,clipmax:i.autorangeoptions.clipmax,include:i.autorangeoptions.include,editType:"plot"},rangemode:i.rangemode,minallowed:i.minallowed,maxallowed:i.maxallowed,range:o({},i.range,{items:[{valType:"any",editType:"plot",impliedEdits:{"^autorange":!1}},{valType:"any",editType:"plot",impliedEdits:{"^autorange":!1}}],anim:!1}),tickmode:i.minor.tickmode,nticks:i.nticks,tick0:i.tick0,dtick:i.dtick,tickvals:i.tickvals,ticktext:i.ticktext,ticks:i.ticks,mirror:i.mirror,ticklen:i.ticklen,tickwidth:i.tickwidth,tickcolor:i.tickcolor,showticklabels:i.showticklabels,labelalias:i.labelalias,tickfont:i.tickfont,tickangle:i.tickangle,tickprefix:i.tickprefix,showtickprefix:i.showtickprefix,ticksuffix:i.ticksuffix,showticksuffix:i.showticksuffix,showexponent:i.showexponent,exponentformat:i.exponentformat,minexponent:i.minexponent,separatethousands:i.separatethousands,tickformat:i.tickformat,tickformatstops:i.tickformatstops,hoverformat:i.hoverformat,showline:i.showline,linecolor:i.linecolor,linewidth:i.linewidth,showgrid:i.showgrid,gridcolor:o({},i.gridcolor,{dflt:"rgb(204, 204, 204)"}),gridwidth:i.gridwidth,zeroline:i.zeroline,zerolinecolor:i.zerolinecolor,zerolinewidth:i.zerolinewidth,_deprecated:{title:i._deprecated.title,titlefont:i._deprecated.titlefont}},"plot","from-root")},20049:(t,e,r)=>{"use strict";var n=r(18106).mix,i=r(12822),o=r(46121),a=r(82854),s=r(25119),l=r(91200),c=["xaxis","yaxis","zaxis"],u=13600/187;t.exports=function(t,e,r){var h,d;function f(t,e){return i.coerce(h,d,a,t,e)}for(var p=0;p{"use strict";var n=r(17235),i=r(12822),o=["xaxis","yaxis","zaxis"];function a(){this.bounds=[[-10,-10,-10],[10,10,10]],this.ticks=[[],[],[]],this.tickEnable=[!0,!0,!0],this.tickFont=["sans-serif","sans-serif","sans-serif"],this.tickSize=[12,12,12],this.tickFontWeight=["normal","normal","normal","normal"],this.tickFontStyle=["normal","normal","normal","normal"],this.tickFontVariant=["normal","normal","normal","normal"],this.tickAngle=[0,0,0],this.tickColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.tickPad=[18,18,18],this.labels=["x","y","z"],this.labelEnable=[!0,!0,!0],this.labelFont=["Open Sans","Open Sans","Open Sans"],this.labelSize=[20,20,20],this.labelFontWeight=["normal","normal","normal","normal"],this.labelFontStyle=["normal","normal","normal","normal"],this.labelFontVariant=["normal","normal","normal","normal"],this.labelColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.labelPad=[30,30,30],this.lineEnable=[!0,!0,!0],this.lineMirror=[!1,!1,!1],this.lineWidth=[1,1,1],this.lineColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.lineTickEnable=[!0,!0,!0],this.lineTickMirror=[!1,!1,!1],this.lineTickLength=[10,10,10],this.lineTickWidth=[1,1,1],this.lineTickColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.gridEnable=[!0,!0,!0],this.gridWidth=[1,1,1],this.gridColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.zeroEnable=[!0,!0,!0],this.zeroLineColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.zeroLineWidth=[2,2,2],this.backgroundEnable=[!0,!0,!0],this.backgroundColor=[[.8,.8,.8,.5],[.8,.8,.8,.5],[.8,.8,.8,.5]],this._defaultTickPad=this.tickPad.slice(),this._defaultLabelPad=this.labelPad.slice(),this._defaultLineTickLength=this.lineTickLength.slice()}a.prototype.merge=function(t,e){for(var r=this,a=0;a<3;++a){var s=e[o[a]];s.visible?(r.labels[a]=t._meta?i.templateString(s.title.text,t._meta):s.title.text,"font"in s.title&&(s.title.font.color&&(r.labelColor[a]=n(s.title.font.color)),s.title.font.family&&(r.labelFont[a]=s.title.font.family),s.title.font.size&&(r.labelSize[a]=s.title.font.size),s.title.font.weight&&(r.labelFontWeight[a]=s.title.font.weight),s.title.font.style&&(r.labelFontStyle[a]=s.title.font.style),s.title.font.variant&&(r.labelFontVariant[a]=s.title.font.variant)),"showline"in s&&(r.lineEnable[a]=s.showline),"linecolor"in s&&(r.lineColor[a]=n(s.linecolor)),"linewidth"in s&&(r.lineWidth[a]=s.linewidth),"showgrid"in s&&(r.gridEnable[a]=s.showgrid),"gridcolor"in s&&(r.gridColor[a]=n(s.gridcolor)),"gridwidth"in s&&(r.gridWidth[a]=s.gridwidth),"log"===s.type?r.zeroEnable[a]=!1:"zeroline"in s&&(r.zeroEnable[a]=s.zeroline),"zerolinecolor"in s&&(r.zeroLineColor[a]=n(s.zerolinecolor)),"zerolinewidth"in s&&(r.zeroLineWidth[a]=s.zerolinewidth),"ticks"in s&&s.ticks?r.lineTickEnable[a]=!0:r.lineTickEnable[a]=!1,"ticklen"in s&&(r.lineTickLength[a]=r._defaultLineTickLength[a]=s.ticklen),"tickcolor"in s&&(r.lineTickColor[a]=n(s.tickcolor)),"tickwidth"in s&&(r.lineTickWidth[a]=s.tickwidth),"tickangle"in s&&(r.tickAngle[a]="auto"===s.tickangle?-3600:Math.PI*-s.tickangle/180),"showticklabels"in s&&(r.tickEnable[a]=s.showticklabels),"tickfont"in s&&(s.tickfont.color&&(r.tickColor[a]=n(s.tickfont.color)),s.tickfont.family&&(r.tickFont[a]=s.tickfont.family),s.tickfont.size&&(r.tickSize[a]=s.tickfont.size),s.tickfont.weight&&(r.tickFontWeight[a]=s.tickfont.weight),s.tickfont.style&&(r.tickFontStyle[a]=s.tickfont.style),s.tickfont.variant&&(r.tickFontVariant[a]=s.tickfont.variant)),"mirror"in s?-1!==["ticks","all","allticks"].indexOf(s.mirror)?(r.lineTickMirror[a]=!0,r.lineMirror[a]=!0):!0===s.mirror?(r.lineTickMirror[a]=!1,r.lineMirror[a]=!0):(r.lineTickMirror[a]=!1,r.lineMirror[a]=!1):r.lineMirror[a]=!1,"showbackground"in s&&!1!==s.showbackground?(r.backgroundEnable[a]=!0,r.backgroundColor[a]=n(s.backgroundcolor)):r.backgroundEnable[a]=!1):(r.tickEnable[a]=!1,r.labelEnable[a]=!1,r.lineEnable[a]=!1,r.lineTickEnable[a]=!1,r.gridEnable[a]=!1,r.zeroEnable[a]=!1,r.backgroundEnable[a]=!1)}},t.exports=function(t,e){var r=new a;return r.merge(t,e),r}},13351:(t,e,r)=>{"use strict";var n=r(12822),i=r(17499),o=r(25059),a=r(84313),s=r(20049),l=r(41019),c=r(47388).KO,u="gl3d";function h(t,e,r,n){for(var a=r("bgcolor"),l=i.combine(a,n.paper_bgcolor),h=["up","center","eye"],d=0;d.999&&(g="turntable"):g="turntable")}else g="turntable";r("dragmode",g),r("hovermode",n.getDfltFromLayout("hovermode"))}t.exports=function(t,e,r){var i=e._basePlotModules.length>1;a(t,e,r,{type:u,attributes:l,handleDefaults:h,fullLayout:e,font:e.font,fullData:r,getDfltFromLayout:function(e){if(!i)return n.validate(t[e],l[e])?t[e]:void 0},autotypenumbersDflt:e.autotypenumbers,paper_bgcolor:e.paper_bgcolor,calendar:e.calendar})}},41019:(t,e,r)=>{"use strict";var n=r(82854),i=r(40365).u,o=r(98260).extendFlat,a=r(12822).counterRegex;function s(t,e,r){return{x:{valType:"number",dflt:t,editType:"camera"},y:{valType:"number",dflt:e,editType:"camera"},z:{valType:"number",dflt:r,editType:"camera"},editType:"camera"}}t.exports={_arrayAttrRegexps:[a("scene",".annotations",!0)],bgcolor:{valType:"color",dflt:"rgba(0,0,0,0)",editType:"plot"},camera:{up:o(s(0,0,1),{description:["Sets the (x,y,z) components of the 'up' camera vector.","This vector determines the up direction of this scene","with respect to the page.","The default is *{x: 0, y: 0, z: 1}* which means that","the z axis points up."].join(" ")}),center:o(s(0,0,0),{description:["Sets the (x,y,z) components of the 'center' camera vector","This vector determines the translation (x,y,z) space","about the center of this scene.","By default, there is no such translation."].join(" ")}),eye:o(s(1.25,1.25,1.25),{description:["Sets the (x,y,z) components of the 'eye' camera vector.","This vector determines the view point about the origin","of this scene."].join(" ")}),projection:{type:{valType:"enumerated",values:["perspective","orthographic"],dflt:"perspective",editType:"calc",description:["Sets the projection type. The projection type could be","either *perspective* or *orthographic*. The default is","*perspective*."].join(" ")},editType:"calc"},editType:"camera"},domain:i({name:"scene",editType:"plot"}),aspectmode:{valType:"enumerated",values:["auto","cube","data","manual"],dflt:"auto",editType:"plot",impliedEdits:{"aspectratio.x":void 0,"aspectratio.y":void 0,"aspectratio.z":void 0},description:["If *cube*, this scene's axes are drawn as a cube,","regardless of the axes' ranges.","If *data*, this scene's axes are drawn","in proportion with the axes' ranges.","If *manual*, this scene's axes are drawn","in proportion with the input of *aspectratio*","(the default behavior if *aspectratio* is provided).","If *auto*, this scene's axes are drawn","using the results of *data* except when one axis","is more than four times the size of the two others,","where in that case the results of *cube* are used."].join(" ")},aspectratio:{x:{valType:"number",min:0,editType:"plot",impliedEdits:{"^aspectmode":"manual"}},y:{valType:"number",min:0,editType:"plot",impliedEdits:{"^aspectmode":"manual"}},z:{valType:"number",min:0,editType:"plot",impliedEdits:{"^aspectmode":"manual"}},editType:"plot",impliedEdits:{aspectmode:"manual"},description:["Sets this scene's axis aspectratio."].join(" ")},xaxis:n,yaxis:n,zaxis:n,dragmode:{valType:"enumerated",values:["orbit","turntable","zoom","pan",!1],editType:"plot",description:["Determines the mode of drag interactions for this scene."].join(" ")},hovermode:{valType:"enumerated",values:["closest",!1],dflt:"closest",editType:"modebar",description:["Determines the mode of hover interactions for this scene."].join(" ")},uirevision:{valType:"any",editType:"none",description:["Controls persistence of user-driven changes in camera attributes.","Defaults to `layout.uirevision`."].join(" ")},editType:"plot",_deprecated:{cameraposition:{valType:"info_array",editType:"camera",description:"Obsolete. Use `camera` instead."}}}},63306:(t,e,r)=>{"use strict";var n=r(17235),i=["xaxis","yaxis","zaxis"];function o(){this.enabled=[!0,!0,!0],this.colors=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.drawSides=[!0,!0,!0],this.lineWidth=[1,1,1]}o.prototype.merge=function(t){for(var e=0;e<3;++e){var r=t[i[e]];r.visible?(this.enabled[e]=r.showspikes,this.colors[e]=n(r.spikecolor),this.drawSides[e]=r.spikesides,this.lineWidth[e]=r.spikethickness):(this.enabled[e]=!1,this.drawSides[e]=!1)}},t.exports=function(t){var e=new o;return e.merge(t),e}},1285:(t,e,r)=>{"use strict";t.exports=function(t){for(var e=t.axesOptions,r=t.glplot.axesPixels,s=t.fullSceneLayout,l=[[],[],[]],c=0;c<3;++c){var u=s[o[c]];if(u._length=(r[c].hi-r[c].lo)*r[c].pixelsPerDataUnit/t.dataScale[c],Math.abs(u._length)===1/0||isNaN(u._length))l[c]=[];else{u._input_range=u.range.slice(),u.range[0]=r[c].lo/t.dataScale[c],u.range[1]=r[c].hi/t.dataScale[c],u._m=1/(t.dataScale[c]*r[c].pixelsPerDataUnit),u.range[0]===u.range[1]&&(u.range[0]-=1,u.range[1]+=1);var h=u.tickmode;if("auto"===u.tickmode){u.tickmode="linear";var d=u.nticks||i.constrain(u._length/40,4,9);n.autoTicks(u,Math.abs(u.range[1]-u.range[0])/d)}for(var f=n.calcTicks(u,{msUTC:!0}),p=0;p/g," "));l[c]=f,u.tickmode=h}}for(e.ticks=l,c=0;c<3;++c)for(a[c]=.5*(t.glplot.bounds[0][c]+t.glplot.bounds[1][c]),p=0;p<2;++p)e.bounds[p][c]=t.glplot.bounds[p][c];t.contourLevels=function(t){for(var e=new Array(3),r=0;r<3;++r){for(var n=t[r],i=new Array(n.length),o=0;o{"use strict";function e(t,e){var r,n,i=[0,0,0,0];for(r=0;r<4;++r)for(n=0;n<4;++n)i[n]+=t[4*r+n]*e[r];return i}t.exports=function(t,r){return e(t.projection,e(t.view,e(t.model,[r[0],r[1],r[2],1])))}},85833:(t,e,r)=>{"use strict";var n,i,o=r(31845).gl_plot3d,a=o.createCamera,s=o.createScene,l=r(62945),c=r(17520),u=r(25059),h=r(12822),d=h.preserveDrawingBuffer(),f=r(75815),p=r(70410),m=r(17235),g=r(91203),v=r(40747),b=r(82678),y=r(63306),x=r(1285),_=r(19496).applyAutorangeOptions,w=!1;function k(t,e){var r=document.createElement("div"),n=t.container;this.graphDiv=t.graphDiv;var i=document.createElementNS("http://www.w3.org/2000/svg","svg");i.style.position="absolute",i.style.top=i.style.left="0px",i.style.width=i.style.height="100%",i.style["z-index"]=20,i.style["pointer-events"]="none",r.appendChild(i),this.svgContainer=i,r.id=t.id,r.style.position="absolute",r.style.top=r.style.left="0px",r.style.width=r.style.height="100%",n.appendChild(r),this.fullLayout=e,this.id=t.id||"scene",this.fullSceneLayout=e[this.id],this.plotArgs=[[],{},{}],this.axesOptions=b(e,e[this.id]),this.spikeOptions=y(e[this.id]),this.container=r,this.staticMode=!!t.staticPlot,this.pixelRatio=this.pixelRatio||t.plotGlPixelRatio||2,this.dataScale=[1,1,1],this.contourLevels=[[],[],[]],this.convertAnnotations=u.getComponentMethod("annotations3d","convert"),this.drawAnnotations=u.getComponentMethod("annotations3d","draw"),this.initializeGLPlot()}var A=k.prototype;A.prepareOptions=function(){var t=this,e={canvas:t.canvas,gl:t.gl,glOptions:{preserveDrawingBuffer:d,premultipliedAlpha:!0,antialias:!0},container:t.container,axes:t.axesOptions,spikes:t.spikeOptions,pickRadius:10,snapToData:!0,autoScale:!0,autoBounds:!1,cameraObject:t.camera,pixelRatio:t.pixelRatio};if(t.staticMode){if(!(i||(n=document.createElement("canvas"),i=l({canvas:n,preserveDrawingBuffer:!0,premultipliedAlpha:!0,antialias:!0}))))throw new Error("error creating static canvas/context for image server");e.gl=i,e.canvas=n}return e};var M=!0;A.tryCreatePlot=function(){var t=this,e=t.prepareOptions(),r=!0;try{t.glplot=s(e)}catch(n){if(t.staticMode||!M||d)r=!1;else{h.warn(["webgl setup failed possibly due to","false preserveDrawingBuffer config.","The mobile/tablet device may not be detected by is-mobile module.","Enabling preserveDrawingBuffer in second attempt to create webgl scene..."].join(" "));try{d=e.glOptions.preserveDrawingBuffer=!0,t.glplot=s(e)}catch(t){d=e.glOptions.preserveDrawingBuffer=!1,r=!1}}}return M=!1,r},A.initializeGLCamera=function(){var t=this,e=t.fullSceneLayout.camera,r="orthographic"===e.projection.type;t.camera=a(t.container,{center:[e.center.x,e.center.y,e.center.z],eye:[e.eye.x,e.eye.y,e.eye.z],up:[e.up.x,e.up.y,e.up.z],_ortho:r,zoomMin:.01,zoomMax:100,mode:"orbit"})},A.initializeGLPlot=function(){var t=this;if(t.initializeGLCamera(),!t.tryCreatePlot())return g(t);t.traces={},t.make4thDimension();var e=t.graphDiv,r=e.layout,n=function(){var e={};return t.isCameraChanged(r)&&(e[t.id+".camera"]=t.getCamera()),t.isAspectChanged(r)&&(e[t.id+".aspectratio"]=t.glplot.getAspectratio(),"manual"!==r[t.id].aspectmode&&(t.fullSceneLayout.aspectmode=r[t.id].aspectmode=e[t.id+".aspectmode"]="manual")),e},i=function(t){if(!1!==t.fullSceneLayout.dragmode){var e=n();t.saveLayout(r),t.graphDiv.emit("plotly_relayout",e)}};return t.glplot.canvas&&(t.glplot.canvas.addEventListener("mouseup",(function(){i(t)})),t.glplot.canvas.addEventListener("touchstart",(function(){w=!0})),t.glplot.canvas.addEventListener("wheel",(function(r){if(e._context._scrollZoom.gl3d){if(t.camera._ortho){var n=r.deltaX>r.deltaY?1.1:1/1.1,o=t.glplot.getAspectratio();t.glplot.setAspectratio({x:n*o.x,y:n*o.y,z:n*o.z})}i(t)}}),!!c&&{passive:!1}),t.glplot.canvas.addEventListener("mousemove",(function(){if(!1!==t.fullSceneLayout.dragmode&&0!==t.camera.mouseListener.buttons){var e=n();t.graphDiv.emit("plotly_relayouting",e)}})),t.staticMode||t.glplot.canvas.addEventListener("webglcontextlost",(function(r){e&&e.emit&&e.emit("plotly_webglcontextlost",{event:r,layer:t.id})}),!1)),t.glplot.oncontextloss=function(){t.recoverContext()},t.glplot.onrender=function(){t.render()},!0},A.render=function(){var t,e=this,r=e.graphDiv,n=e.svgContainer,i=e.container.getBoundingClientRect();r._fullLayout._calcInverseTransform(r);var o=r._fullLayout._invScaleX,a=r._fullLayout._invScaleY,s=i.width*o,l=i.height*a;n.setAttributeNS(null,"viewBox","0 0 "+s+" "+l),n.setAttributeNS(null,"width",s),n.setAttributeNS(null,"height",l),x(e),e.glplot.axes.update(e.axesOptions);for(var c=Object.keys(e.traces),u=null,d=e.glplot.selection,m=0;m")):"isosurface"===t.type||"volume"===t.type?(A.valueLabel=f.hoverLabelText(e._mockAxis,e._mockAxis.d2l(d.traceCoordinate[3]),t.valuehoverformat),C.push("value: "+A.valueLabel),d.textLabel&&C.push(d.textLabel),y=C.join("
")):y=d.textLabel;var E={x:d.traceCoordinate[0],y:d.traceCoordinate[1],z:d.traceCoordinate[2],data:_._input,fullData:_,curveNumber:_.index,pointNumber:k};p.appendArrayPointValue(E,_,k),t._module.eventData&&(E=_._module.eventData(E,d,_,{},k));var L={points:[E]};if(e.fullSceneLayout.hovermode){var z=[];p.loneHover({trace:_,x:(.5+.5*b[0]/b[3])*s,y:(.5-.5*b[1]/b[3])*l,xLabel:A.xLabel,yLabel:A.yLabel,zLabel:A.zLabel,text:y,name:u.name,color:p.castHoverOption(_,k,"bgcolor")||u.color,borderColor:p.castHoverOption(_,k,"bordercolor"),fontFamily:p.castHoverOption(_,k,"font.family"),fontSize:p.castHoverOption(_,k,"font.size"),fontColor:p.castHoverOption(_,k,"font.color"),nameLength:p.castHoverOption(_,k,"namelength"),textAlign:p.castHoverOption(_,k,"align"),hovertemplate:h.castOption(_,k,"hovertemplate"),hovertemplateLabels:h.extendFlat({},E,A),eventData:[E]},{container:n,gd:r,inOut_bbox:z}),E.bbox=z[0]}d.distance<5&&(d.buttons||w)?r.emit("plotly_click",L):r.emit("plotly_hover",L),this.oldEventData=L}else p.loneUnhover(n),this.oldEventData&&r.emit("plotly_unhover",this.oldEventData),this.oldEventData=void 0;e.drawAnnotations(e)},A.recoverContext=function(){var t=this;t.glplot.dispose();var e=function(){t.glplot.gl.isContextLost()?requestAnimationFrame(e):t.initializeGLPlot()?t.plot.apply(t,t.plotArgs):h.error("Catastrophic and unrecoverable WebGL error. Context lost.")};requestAnimationFrame(e)};var T=["xaxis","yaxis","zaxis"];function S(t,e,r){for(var n=t.fullSceneLayout,i=0;i<3;i++){var o=T[i],a=o.charAt(0),s=n[o],l=e[a],c=e[a+"calendar"],u=e["_"+a+"length"];if(h.isArrayOrTypedArray(l))for(var d,f=0;f<(u||l.length);f++)if(h.isArrayOrTypedArray(l[f]))for(var p=0;pv[1][a])v[0][a]=-1,v[1][a]=1;else{var O=v[1][a]-v[0][a];v[0][a]-=O/32,v[1][a]+=O/32}if(x=[v[0][a],v[1][a]],x=_(x,l),v[0][a]=x[0],v[1][a]=x[1],l.isReversed()){var D=v[0][a];v[0][a]=v[1][a],v[1][a]=D}}else x=l.range,v[0][a]=l.r2l(x[0]),v[1][a]=l.r2l(x[1]);v[0][a]===v[1][a]&&(v[0][a]-=1,v[1][a]+=1),b[a]=v[1][a]-v[0][a],l.range=[v[0][a],v[1][a]],l.limitRange(),n.glplot.setBounds(a,{min:l.range[0]*f[a],max:l.range[1]*f[a]})}var I=u.aspectmode;if("cube"===I)g=[1,1,1];else if("manual"===I){var F=u.aspectratio;g=[F.x,F.y,F.z]}else{if("auto"!==I&&"data"!==I)throw new Error("scene.js aspectRatio was not one of the enumerated types");var R=[1,1,1];for(a=0;a<3;++a){var P=y[c=(l=u[T[a]]).type];R[a]=Math.pow(P.acc,1/P.count)/f[a]}g="data"===I||Math.max.apply(null,R)/Math.min.apply(null,R)<=4?R:[1,1,1]}u.aspectratio.x=h.aspectratio.x=g[0],u.aspectratio.y=h.aspectratio.y=g[1],u.aspectratio.z=h.aspectratio.z=g[2],n.glplot.setAspectratio(u.aspectratio),n.viewInitial.aspectratio||(n.viewInitial.aspectratio={x:u.aspectratio.x,y:u.aspectratio.y,z:u.aspectratio.z}),n.viewInitial.aspectmode||(n.viewInitial.aspectmode=u.aspectmode);var j=u.domain||null,N=e._size||null;if(j&&N){var B=n.container.style;B.position="absolute",B.left=N.l+j.x[0]*N.w+"px",B.top=N.t+(1-j.y[1])*N.h+"px",B.width=N.w*(j.x[1]-j.x[0])+"px",B.height=N.h*(j.y[1]-j.y[0])+"px"}n.glplot.redraw()}},A.destroy=function(){var t=this;t.glplot&&(t.camera.mouseListener.enabled=!1,t.container.removeEventListener("wheel",t.camera.wheelListener),t.camera=null,t.glplot.dispose(),t.container.parentNode.removeChild(t.container),t.glplot=null)},A.getCamera=function(){var t,e=this;return e.camera.view.recalcMatrix(e.camera.view.lastT()),{up:{x:(t=e.camera).up[0],y:t.up[1],z:t.up[2]},center:{x:t.center[0],y:t.center[1],z:t.center[2]},eye:{x:t.eye[0],y:t.eye[1],z:t.eye[2]},projection:{type:!0===t._ortho?"orthographic":"perspective"}}},A.setViewport=function(t){var e,r=this,n=t.camera;r.camera.lookAt.apply(this,[[(e=n).eye.x,e.eye.y,e.eye.z],[e.center.x,e.center.y,e.center.z],[e.up.x,e.up.y,e.up.z]]),r.glplot.setAspectratio(t.aspectratio),"orthographic"===n.projection.type!==r.camera._ortho&&(r.glplot.redraw(),r.glplot.clearRGBA(),r.glplot.dispose(),r.initializeGLPlot())},A.isCameraChanged=function(t){var e=this.getCamera(),r=h.nestedProperty(t,this.id+".camera").get();function n(t,e,r,n){var i=["up","center","eye"],o=["x","y","z"];return e[i[r]]&&t[i[r]][o[n]]===e[i[r]][o[n]]}var i=!1;if(void 0===r)i=!0;else{for(var o=0;o<3;o++)for(var a=0;a<3;a++)if(!n(e,r,o,a)){i=!0;break}(!r.projection||e.projection&&e.projection.type!==r.projection.type)&&(i=!0)}return i},A.isAspectChanged=function(t){var e=this.glplot.getAspectratio(),r=h.nestedProperty(t,this.id+".aspectratio").get();return void 0===r||r.x!==e.x||r.y!==e.y||r.z!==e.z},A.saveLayout=function(t){var e,r,n,i,o,a,s=this,l=s.fullLayout,c=s.isCameraChanged(t),d=s.isAspectChanged(t),f=c||d;if(f){var p={};c&&(e=s.getCamera(),n=(r=h.nestedProperty(t,s.id+".camera")).get(),p[s.id+".camera"]=n),d&&(i=s.glplot.getAspectratio(),a=(o=h.nestedProperty(t,s.id+".aspectratio")).get(),p[s.id+".aspectratio"]=a),u.call("_storeDirectGUIEdit",t,l._preGUI,p),c&&(r.set(e),h.nestedProperty(l,s.id+".camera").set(e)),d&&(o.set(i),h.nestedProperty(l,s.id+".aspectratio").set(i),s.glplot.redraw())}return f},A.updateFx=function(t,e){var r=this,n=r.camera;if(n)if("orbit"===t)n.mode="orbit",n.keyBindingMode="rotate";else if("turntable"===t){n.up=[0,0,1],n.mode="turntable",n.keyBindingMode="rotate";var i=r.graphDiv,o=i._fullLayout,a=r.fullSceneLayout.camera,s=a.up.x,l=a.up.y,c=a.up.z;if(c/Math.sqrt(s*s+l*l+c*c)<.999){var d=r.id+".camera.up",f={x:0,y:0,z:1},p={};p[d]=f;var m=i.layout;u.call("_storeDirectGUIEdit",m,o._preGUI,p),a.up=f,h.nestedProperty(m,d).set(f)}}else n.keyBindingMode=t;r.fullSceneLayout.hovermode=e},A.toImage=function(t){var e=this;t||(t="png"),e.staticMode&&e.container.appendChild(n),e.glplot.redraw();var r=e.glplot.gl,i=r.drawingBufferWidth,o=r.drawingBufferHeight;r.bindFramebuffer(r.FRAMEBUFFER,null);var a=new Uint8Array(i*o*4);r.readPixels(0,0,i,o,r.RGBA,r.UNSIGNED_BYTE,a),function(t,e,r){for(var n=0,i=r-1;n0)for(var s=255/a,l=0;l<3;++l)t[o+l]=Math.min(s*t[o+l],255)}}(a,i,o);var s=document.createElement("canvas");s.width=i,s.height=o;var l,c=s.getContext("2d",{willReadFrequently:!0}),u=c.createImageData(i,o);switch(u.data.set(a),c.putImageData(u,0,0),t){case"jpeg":l=s.toDataURL("image/jpeg");break;case"webp":l=s.toDataURL("image/webp");break;default:l=s.toDataURL("image/png")}return e.staticMode&&e.container.removeChild(n),l},A.setConvert=function(){for(var t=0;t<3;t++){var e=this.fullSceneLayout[T[t]];f.setConvert(e,this.fullLayout),e.setScale=h.noop}},A.make4thDimension=function(){var t=this,e=t.graphDiv._fullLayout;t._mockAxis={type:"linear",showexponent:"all",exponentformat:"B"},f.setConvert(t._mockAxis,e)},t.exports=k},13195:(t,e,r)=>{"use strict";var n=r(75058),i=r(46367),o=r(84226),a=r(18360),s=r(21422),l=r(85538),c=r(98260).extendFlat,u=n({editType:"calc",description:["Sets the global font.","Note that fonts used in traces and other","layout components inherit from the global font."].join(" ")});u.family.dflt='"Open Sans", verdana, arial, sans-serif',u.size.dflt=12,u.color.dflt=o.defaultLine,t.exports={font:u,title:{text:{valType:"string",editType:"layoutstyle",description:["Sets the plot's title.","Note that before the existence of `title.text`, the title's","contents used to be defined as the `title` attribute itself.","This behavior has been deprecated."].join(" ")},font:n({editType:"layoutstyle",description:["Sets the title font.","Note that the title's font used to be customized","by the now deprecated `titlefont` attribute."].join(" ")}),subtitle:{text:{valType:"string",editType:"layoutstyle",description:"Sets the plot's subtitle."},font:n({editType:"layoutstyle",description:"Sets the subtitle font."}),editType:"layoutstyle"},xref:{valType:"enumerated",dflt:"container",values:["container","paper"],editType:"layoutstyle",description:["Sets the container `x` refers to.","*container* spans the entire `width` of the plot.","*paper* refers to the width of the plotting area only."].join(" ")},yref:{valType:"enumerated",dflt:"container",values:["container","paper"],editType:"layoutstyle",description:["Sets the container `y` refers to.","*container* spans the entire `height` of the plot.","*paper* refers to the height of the plotting area only."].join(" ")},x:{valType:"number",min:0,max:1,dflt:.5,editType:"layoutstyle",description:["Sets the x position with respect to `xref` in normalized","coordinates from *0* (left) to *1* (right)."].join(" ")},y:{valType:"number",min:0,max:1,dflt:"auto",editType:"layoutstyle",description:["Sets the y position with respect to `yref` in normalized","coordinates from *0* (bottom) to *1* (top).","*auto* places the baseline of the title onto the","vertical center of the top margin."].join(" ")},xanchor:{valType:"enumerated",dflt:"auto",values:["auto","left","center","right"],editType:"layoutstyle",description:["Sets the title's horizontal alignment with respect to its x position.","*left* means that the title starts at x,","*right* means 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When transitioning","lines, it may be desirable to disable this so that the number of points","along the resulting SVG path is unaffected."].join(" ")},editType:"plot"},connectgaps:{valType:"boolean",dflt:!1,editType:"calc",description:["Determines whether or not gaps","(i.e. {nan} or missing values)","in the provided data arrays are connected."].join(" ")},cliponaxis:{valType:"boolean",dflt:!0,editType:"plot",description:["Determines whether or not markers and text nodes","are clipped about the subplot axes.","To show markers and text nodes above axis lines and tick labels,","make sure to set `xaxis.layer` and `yaxis.layer` to *below traces*."].join(" ")},fill:{valType:"enumerated",values:["none","tozeroy","tozerox","tonexty","tonextx","toself","tonext"],editType:"calc",description:["Sets the area to fill with a solid color.","Defaults to *none* unless this trace is stacked, then it gets","*tonexty* (*tonextx*) if `orientation` is *v* (*h*)","Use with `fillcolor` if not *none*.","*tozerox* and *tozeroy* fill to x=0 and y=0 respectively.","*tonextx* and *tonexty* fill between the endpoints of this","trace and the endpoints of the trace before it, connecting those","endpoints with straight lines (to make a stacked area graph);","if there is no trace before it, they behave like *tozerox* and","*tozeroy*.","*toself* connects the endpoints of the trace (or each segment","of the trace if it has gaps) into a closed shape.","*tonext* fills the space between two traces if one completely","encloses the other (eg consecutive contour lines), and behaves like","*toself* if there is no trace before it. *tonext* should not be","used if one trace does not enclose the other.","Traces in a `stackgroup` will only fill to (or be filled to) other","traces in the same group. With multiple `stackgroup`s or some","traces stacked and some not, if fill-linked traces are not already","consecutive, the later ones will be pushed down in the drawing order."].join(" ")},fillcolor:f(!0),fillgradient:d({type:{valType:"enumerated",values:["radial","horizontal","vertical","none"],dflt:"none",editType:"calc",description:["Sets the type/orientation of the color gradient for the fill.","Defaults to *none*."].join(" ")},start:{valType:"number",editType:"calc",description:["Sets the gradient start value.","It is given as the absolute position on the axis determined by","the orientiation. E.g., if orientation is *horizontal*, the","gradient will be horizontal and start from the x-position","given by start. 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s.opacity(h.fillcolor)?D=h.fillcolor:s.opacity((h.line||{}).color)&&(D=h.line.color),n.extendFlat(t,{distance:t.maxHoverDistance,x0:O.x0,x1:O.x1,y0:O.y0,y1:O.y1,color:D,hovertemplate:!1}),delete t.index,h.text&&!n.isArrayOrTypedArray(h.text)?t.text=String(h.text):t.text=h.name,[t]}}},56384:(t,e,r)=>{"use strict";var n=r(677);t.exports={hasLines:n.hasLines,hasMarkers:n.hasMarkers,hasText:n.hasText,isBubble:n.isBubble,attributes:r(98387),layoutAttributes:r(49114),supplyDefaults:r(28724),crossTraceDefaults:r(30415),supplyLayoutDefaults:r(25229),calc:r(93459).calc,crossTraceCalc:r(30888),arraysToCalcdata:r(55508),plot:r(54461),colorbar:r(89927),formatLabels:r(23315),style:r(21905).style,styleOnSelect:r(21905).styleOnSelect,hoverPoints:r(2686),selectPoints:r(96414),animatable:!0,moduleType:"trace",name:"scatter",basePlotModule:r(29592),categories:["cartesian","svg","symbols","errorBarsOK","showLegend","scatter-like","zoomScale"],meta:{description:["The scatter trace type encompasses line 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8191&e||(r+=13,e>>>=13),127&e||(r+=7,e>>>=7),15&e||(r+=4,e>>>=4),3&e||(r+=2,e>>>=2),1&e||r++,r},o.prototype.bitLength=function(){var t=this.words[this.length-1],e=this._countBits(t);return 26*(this.length-1)+e},o.prototype.zeroBits=function(){if(this.isZero())return 0;for(var t=0,e=0;et.length?this.clone().ior(t):t.clone().ior(this)},o.prototype.uor=function(t){return this.length>t.length?this.clone().iuor(t):t.clone().iuor(this)},o.prototype.iuand=function(t){var e;e=this.length>t.length?t:this;for(var r=0;rt.length?this.clone().iand(t):t.clone().iand(this)},o.prototype.uand=function(t){return this.length>t.length?this.clone().iuand(t):t.clone().iuand(this)},o.prototype.iuxor=function(t){var e,r;this.length>t.length?(e=this,r=t):(e=t,r=this);for(var n=0;nt.length?this.clone().ixor(t):t.clone().ixor(this)},o.prototype.uxor=function(t){return this.length>t.length?this.clone().iuxor(t):t.clone().iuxor(this)},o.prototype.inotn=function(t){n("number"==typeof t&&t>=0);var e=0|Math.ceil(t/26),r=t%26;this._expand(e),r>0&&e--;for(var i=0;i0&&(this.words[i]=~this.words[i]&67108863>>26-r),this.strip()},o.prototype.notn=function(t){return this.clone().inotn(t)},o.prototype.setn=function(t,e){n("number"==typeof t&&t>=0);var r=t/26|0,i=t%26;return this._expand(r+1),this.words[r]=e?this.words[r]|1<t.length?(r=this,n=t):(r=t,n=this);for(var i=0,o=0;o>>26;for(;0!==i&&o>>26;if(this.length=r.length,0!==i)this.words[this.length]=i,this.length++;else if(r!==this)for(;ot.length?this.clone().iadd(t):t.clone().iadd(this)},o.prototype.isub=function(t){if(0!==t.negative){t.negative=0;var e=this.iadd(t);return t.negative=1,e._normSign()}if(0!==this.negative)return this.negative=0,this.iadd(t),this.negative=1,this._normSign();var r,n,i=this.cmp(t);if(0===i)return this.negative=0,this.length=1,this.words[0]=0,this;i>0?(r=this,n=t):(r=t,n=this);for(var o=0,a=0;a>26,this.words[a]=67108863&e;for(;0!==o&&a>26,this.words[a]=67108863&e;if(0===o&&a>>13,f=0|a[1],p=8191&f,m=f>>>13,g=0|a[2],v=8191&g,b=g>>>13,y=0|a[3],x=8191&y,_=y>>>13,w=0|a[4],k=8191&w,A=w>>>13,M=0|a[5],T=8191&M,S=M>>>13,C=0|a[6],E=8191&C,L=C>>>13,z=0|a[7],O=8191&z,D=z>>>13,I=0|a[8],F=8191&I,R=I>>>13,P=0|a[9],j=8191&P,N=P>>>13,B=0|s[0],U=8191&B,G=B>>>13,V=0|s[1],H=8191&V,W=V>>>13,q=0|s[2],Y=8191&q,Z=q>>>13,X=0|s[3],$=8191&X,J=X>>>13,K=0|s[4],Q=8191&K,tt=K>>>13,et=0|s[5],rt=8191&et,nt=et>>>13,it=0|s[6],ot=8191&it,at=it>>>13,st=0|s[7],lt=8191&st,ct=st>>>13,ut=0|s[8],ht=8191&ut,dt=ut>>>13,ft=0|s[9],pt=8191&ft,mt=ft>>>13;r.negative=t.negative^e.negative,r.length=19;var gt=(c+(n=Math.imul(h,U))|0)+((8191&(i=(i=Math.imul(h,G))+Math.imul(d,U)|0))<<13)|0;c=((o=Math.imul(d,G))+(i>>>13)|0)+(gt>>>26)|0,gt&=67108863,n=Math.imul(p,U),i=(i=Math.imul(p,G))+Math.imul(m,U)|0,o=Math.imul(m,G);var vt=(c+(n=n+Math.imul(h,H)|0)|0)+((8191&(i=(i=i+Math.imul(h,W)|0)+Math.imul(d,H)|0))<<13)|0;c=((o=o+Math.imul(d,W)|0)+(i>>>13)|0)+(vt>>>26)|0,vt&=67108863,n=Math.imul(v,U),i=(i=Math.imul(v,G))+Math.imul(b,U)|0,o=Math.imul(b,G),n=n+Math.imul(p,H)|0,i=(i=i+Math.imul(p,W)|0)+Math.imul(m,H)|0,o=o+Math.imul(m,W)|0;var bt=(c+(n=n+Math.imul(h,Y)|0)|0)+((8191&(i=(i=i+Math.imul(h,Z)|0)+Math.imul(d,Y)|0))<<13)|0;c=((o=o+Math.imul(d,Z)|0)+(i>>>13)|0)+(bt>>>26)|0,bt&=67108863,n=Math.imul(x,U),i=(i=Math.imul(x,G))+Math.imul(_,U)|0,o=Math.imul(_,G),n=n+Math.imul(v,H)|0,i=(i=i+Math.imul(v,W)|0)+Math.imul(b,H)|0,o=o+Math.imul(b,W)|0,n=n+Math.imul(p,Y)|0,i=(i=i+Math.imul(p,Z)|0)+Math.imul(m,Y)|0,o=o+Math.imul(m,Z)|0;var yt=(c+(n=n+Math.imul(h,$)|0)|0)+((8191&(i=(i=i+Math.imul(h,J)|0)+Math.imul(d,$)|0))<<13)|0;c=((o=o+Math.imul(d,J)|0)+(i>>>13)|0)+(yt>>>26)|0,yt&=67108863,n=Math.imul(k,U),i=(i=Math.imul(k,G))+Math.imul(A,U)|0,o=Math.imul(A,G),n=n+Math.imul(x,H)|0,i=(i=i+Math.imul(x,W)|0)+Math.imul(_,H)|0,o=o+Math.imul(_,W)|0,n=n+Math.imul(v,Y)|0,i=(i=i+Math.imul(v,Z)|0)+Math.imul(b,Y)|0,o=o+Math.imul(b,Z)|0,n=n+Math.imul(p,$)|0,i=(i=i+Math.imul(p,J)|0)+Math.imul(m,$)|0,o=o+Math.imul(m,J)|0;var xt=(c+(n=n+Math.imul(h,Q)|0)|0)+((8191&(i=(i=i+Math.imul(h,tt)|0)+Math.imul(d,Q)|0))<<13)|0;c=((o=o+Math.imul(d,tt)|0)+(i>>>13)|0)+(xt>>>26)|0,xt&=67108863,n=Math.imul(T,U),i=(i=Math.imul(T,G))+Math.imul(S,U)|0,o=Math.imul(S,G),n=n+Math.imul(k,H)|0,i=(i=i+Math.imul(k,W)|0)+Math.imul(A,H)|0,o=o+Math.imul(A,W)|0,n=n+Math.imul(x,Y)|0,i=(i=i+Math.imul(x,Z)|0)+Math.imul(_,Y)|0,o=o+Math.imul(_,Z)|0,n=n+Math.imul(v,$)|0,i=(i=i+Math.imul(v,J)|0)+Math.imul(b,$)|0,o=o+Math.imul(b,J)|0,n=n+Math.imul(p,Q)|0,i=(i=i+Math.imul(p,tt)|0)+Math.imul(m,Q)|0,o=o+Math.imul(m,tt)|0;var _t=(c+(n=n+Math.imul(h,rt)|0)|0)+((8191&(i=(i=i+Math.imul(h,nt)|0)+Math.imul(d,rt)|0))<<13)|0;c=((o=o+Math.imul(d,nt)|0)+(i>>>13)|0)+(_t>>>26)|0,_t&=67108863,n=Math.imul(E,U),i=(i=Math.imul(E,G))+Math.imul(L,U)|0,o=Math.imul(L,G),n=n+Math.imul(T,H)|0,i=(i=i+Math.imul(T,W)|0)+Math.imul(S,H)|0,o=o+Math.imul(S,W)|0,n=n+Math.imul(k,Y)|0,i=(i=i+Math.imul(k,Z)|0)+Math.imul(A,Y)|0,o=o+Math.imul(A,Z)|0,n=n+Math.imul(x,$)|0,i=(i=i+Math.imul(x,J)|0)+Math.imul(_,$)|0,o=o+Math.imul(_,J)|0,n=n+Math.imul(v,Q)|0,i=(i=i+Math.imul(v,tt)|0)+Math.imul(b,Q)|0,o=o+Math.imul(b,tt)|0,n=n+Math.imul(p,rt)|0,i=(i=i+Math.imul(p,nt)|0)+Math.imul(m,rt)|0,o=o+Math.imul(m,nt)|0;var wt=(c+(n=n+Math.imul(h,ot)|0)|0)+((8191&(i=(i=i+Math.imul(h,at)|0)+Math.imul(d,ot)|0))<<13)|0;c=((o=o+Math.imul(d,at)|0)+(i>>>13)|0)+(wt>>>26)|0,wt&=67108863,n=Math.imul(O,U),i=(i=Math.imul(O,G))+Math.imul(D,U)|0,o=Math.imul(D,G),n=n+Math.imul(E,H)|0,i=(i=i+Math.imul(E,W)|0)+Math.imul(L,H)|0,o=o+Math.imul(L,W)|0,n=n+Math.imul(T,Y)|0,i=(i=i+Math.imul(T,Z)|0)+Math.imul(S,Y)|0,o=o+Math.imul(S,Z)|0,n=n+Math.imul(k,$)|0,i=(i=i+Math.imul(k,J)|0)+Math.imul(A,$)|0,o=o+Math.imul(A,J)|0,n=n+Math.imul(x,Q)|0,i=(i=i+Math.imul(x,tt)|0)+Math.imul(_,Q)|0,o=o+Math.imul(_,tt)|0,n=n+Math.imul(v,rt)|0,i=(i=i+Math.imul(v,nt)|0)+Math.imul(b,rt)|0,o=o+Math.imul(b,nt)|0,n=n+Math.imul(p,ot)|0,i=(i=i+Math.imul(p,at)|0)+Math.imul(m,ot)|0,o=o+Math.imul(m,at)|0;var kt=(c+(n=n+Math.imul(h,lt)|0)|0)+((8191&(i=(i=i+Math.imul(h,ct)|0)+Math.imul(d,lt)|0))<<13)|0;c=((o=o+Math.imul(d,ct)|0)+(i>>>13)|0)+(kt>>>26)|0,kt&=67108863,n=Math.imul(F,U),i=(i=Math.imul(F,G))+Math.imul(R,U)|0,o=Math.imul(R,G),n=n+Math.imul(O,H)|0,i=(i=i+Math.imul(O,W)|0)+Math.imul(D,H)|0,o=o+Math.imul(D,W)|0,n=n+Math.imul(E,Y)|0,i=(i=i+Math.imul(E,Z)|0)+Math.imul(L,Y)|0,o=o+Math.imul(L,Z)|0,n=n+Math.imul(T,$)|0,i=(i=i+Math.imul(T,J)|0)+Math.imul(S,$)|0,o=o+Math.imul(S,J)|0,n=n+Math.imul(k,Q)|0,i=(i=i+Math.imul(k,tt)|0)+Math.imul(A,Q)|0,o=o+Math.imul(A,tt)|0,n=n+Math.imul(x,rt)|0,i=(i=i+Math.imul(x,nt)|0)+Math.imul(_,rt)|0,o=o+Math.imul(_,nt)|0,n=n+Math.imul(v,ot)|0,i=(i=i+Math.imul(v,at)|0)+Math.imul(b,ot)|0,o=o+Math.imul(b,at)|0,n=n+Math.imul(p,lt)|0,i=(i=i+Math.imul(p,ct)|0)+Math.imul(m,lt)|0,o=o+Math.imul(m,ct)|0;var At=(c+(n=n+Math.imul(h,ht)|0)|0)+((8191&(i=(i=i+Math.imul(h,dt)|0)+Math.imul(d,ht)|0))<<13)|0;c=((o=o+Math.imul(d,dt)|0)+(i>>>13)|0)+(At>>>26)|0,At&=67108863,n=Math.imul(j,U),i=(i=Math.imul(j,G))+Math.imul(N,U)|0,o=Math.imul(N,G),n=n+Math.imul(F,H)|0,i=(i=i+Math.imul(F,W)|0)+Math.imul(R,H)|0,o=o+Math.imul(R,W)|0,n=n+Math.imul(O,Y)|0,i=(i=i+Math.imul(O,Z)|0)+Math.imul(D,Y)|0,o=o+Math.imul(D,Z)|0,n=n+Math.imul(E,$)|0,i=(i=i+Math.imul(E,J)|0)+Math.imul(L,$)|0,o=o+Math.imul(L,J)|0,n=n+Math.imul(T,Q)|0,i=(i=i+Math.imul(T,tt)|0)+Math.imul(S,Q)|0,o=o+Math.imul(S,tt)|0,n=n+Math.imul(k,rt)|0,i=(i=i+Math.imul(k,nt)|0)+Math.imul(A,rt)|0,o=o+Math.imul(A,nt)|0,n=n+Math.imul(x,ot)|0,i=(i=i+Math.imul(x,at)|0)+Math.imul(_,ot)|0,o=o+Math.imul(_,at)|0,n=n+Math.imul(v,lt)|0,i=(i=i+Math.imul(v,ct)|0)+Math.imul(b,lt)|0,o=o+Math.imul(b,ct)|0,n=n+Math.imul(p,ht)|0,i=(i=i+Math.imul(p,dt)|0)+Math.imul(m,ht)|0,o=o+Math.imul(m,dt)|0;var Mt=(c+(n=n+Math.imul(h,pt)|0)|0)+((8191&(i=(i=i+Math.imul(h,mt)|0)+Math.imul(d,pt)|0))<<13)|0;c=((o=o+Math.imul(d,mt)|0)+(i>>>13)|0)+(Mt>>>26)|0,Mt&=67108863,n=Math.imul(j,H),i=(i=Math.imul(j,W))+Math.imul(N,H)|0,o=Math.imul(N,W),n=n+Math.imul(F,Y)|0,i=(i=i+Math.imul(F,Z)|0)+Math.imul(R,Y)|0,o=o+Math.imul(R,Z)|0,n=n+Math.imul(O,$)|0,i=(i=i+Math.imul(O,J)|0)+Math.imul(D,$)|0,o=o+Math.imul(D,J)|0,n=n+Math.imul(E,Q)|0,i=(i=i+Math.imul(E,tt)|0)+Math.imul(L,Q)|0,o=o+Math.imul(L,tt)|0,n=n+Math.imul(T,rt)|0,i=(i=i+Math.imul(T,nt)|0)+Math.imul(S,rt)|0,o=o+Math.imul(S,nt)|0,n=n+Math.imul(k,ot)|0,i=(i=i+Math.imul(k,at)|0)+Math.imul(A,ot)|0,o=o+Math.imul(A,at)|0,n=n+Math.imul(x,lt)|0,i=(i=i+Math.imul(x,ct)|0)+Math.imul(_,lt)|0,o=o+Math.imul(_,ct)|0,n=n+Math.imul(v,ht)|0,i=(i=i+Math.imul(v,dt)|0)+Math.imul(b,ht)|0,o=o+Math.imul(b,dt)|0;var Tt=(c+(n=n+Math.imul(p,pt)|0)|0)+((8191&(i=(i=i+Math.imul(p,mt)|0)+Math.imul(m,pt)|0))<<13)|0;c=((o=o+Math.imul(m,mt)|0)+(i>>>13)|0)+(Tt>>>26)|0,Tt&=67108863,n=Math.imul(j,Y),i=(i=Math.imul(j,Z))+Math.imul(N,Y)|0,o=Math.imul(N,Z),n=n+Math.imul(F,$)|0,i=(i=i+Math.imul(F,J)|0)+Math.imul(R,$)|0,o=o+Math.imul(R,J)|0,n=n+Math.imul(O,Q)|0,i=(i=i+Math.imul(O,tt)|0)+Math.imul(D,Q)|0,o=o+Math.imul(D,tt)|0,n=n+Math.imul(E,rt)|0,i=(i=i+Math.imul(E,nt)|0)+Math.imul(L,rt)|0,o=o+Math.imul(L,nt)|0,n=n+Math.imul(T,ot)|0,i=(i=i+Math.imul(T,at)|0)+Math.imul(S,ot)|0,o=o+Math.imul(S,at)|0,n=n+Math.imul(k,lt)|0,i=(i=i+Math.imul(k,ct)|0)+Math.imul(A,lt)|0,o=o+Math.imul(A,ct)|0,n=n+Math.imul(x,ht)|0,i=(i=i+Math.imul(x,dt)|0)+Math.imul(_,ht)|0,o=o+Math.imul(_,dt)|0;var St=(c+(n=n+Math.imul(v,pt)|0)|0)+((8191&(i=(i=i+Math.imul(v,mt)|0)+Math.imul(b,pt)|0))<<13)|0;c=((o=o+Math.imul(b,mt)|0)+(i>>>13)|0)+(St>>>26)|0,St&=67108863,n=Math.imul(j,$),i=(i=Math.imul(j,J))+Math.imul(N,$)|0,o=Math.imul(N,J),n=n+Math.imul(F,Q)|0,i=(i=i+Math.imul(F,tt)|0)+Math.imul(R,Q)|0,o=o+Math.imul(R,tt)|0,n=n+Math.imul(O,rt)|0,i=(i=i+Math.imul(O,nt)|0)+Math.imul(D,rt)|0,o=o+Math.imul(D,nt)|0,n=n+Math.imul(E,ot)|0,i=(i=i+Math.imul(E,at)|0)+Math.imul(L,ot)|0,o=o+Math.imul(L,at)|0,n=n+Math.imul(T,lt)|0,i=(i=i+Math.imul(T,ct)|0)+Math.imul(S,lt)|0,o=o+Math.imul(S,ct)|0,n=n+Math.imul(k,ht)|0,i=(i=i+Math.imul(k,dt)|0)+Math.imul(A,ht)|0,o=o+Math.imul(A,dt)|0;var Ct=(c+(n=n+Math.imul(x,pt)|0)|0)+((8191&(i=(i=i+Math.imul(x,mt)|0)+Math.imul(_,pt)|0))<<13)|0;c=((o=o+Math.imul(_,mt)|0)+(i>>>13)|0)+(Ct>>>26)|0,Ct&=67108863,n=Math.imul(j,Q),i=(i=Math.imul(j,tt))+Math.imul(N,Q)|0,o=Math.imul(N,tt),n=n+Math.imul(F,rt)|0,i=(i=i+Math.imul(F,nt)|0)+Math.imul(R,rt)|0,o=o+Math.imul(R,nt)|0,n=n+Math.imul(O,ot)|0,i=(i=i+Math.imul(O,at)|0)+Math.imul(D,ot)|0,o=o+Math.imul(D,at)|0,n=n+Math.imul(E,lt)|0,i=(i=i+Math.imul(E,ct)|0)+Math.imul(L,lt)|0,o=o+Math.imul(L,ct)|0,n=n+Math.imul(T,ht)|0,i=(i=i+Math.imul(T,dt)|0)+Math.imul(S,ht)|0,o=o+Math.imul(S,dt)|0;var Et=(c+(n=n+Math.imul(k,pt)|0)|0)+((8191&(i=(i=i+Math.imul(k,mt)|0)+Math.imul(A,pt)|0))<<13)|0;c=((o=o+Math.imul(A,mt)|0)+(i>>>13)|0)+(Et>>>26)|0,Et&=67108863,n=Math.imul(j,rt),i=(i=Math.imul(j,nt))+Math.imul(N,rt)|0,o=Math.imul(N,nt),n=n+Math.imul(F,ot)|0,i=(i=i+Math.imul(F,at)|0)+Math.imul(R,ot)|0,o=o+Math.imul(R,at)|0,n=n+Math.imul(O,lt)|0,i=(i=i+Math.imul(O,ct)|0)+Math.imul(D,lt)|0,o=o+Math.imul(D,ct)|0,n=n+Math.imul(E,ht)|0,i=(i=i+Math.imul(E,dt)|0)+Math.imul(L,ht)|0,o=o+Math.imul(L,dt)|0;var Lt=(c+(n=n+Math.imul(T,pt)|0)|0)+((8191&(i=(i=i+Math.imul(T,mt)|0)+Math.imul(S,pt)|0))<<13)|0;c=((o=o+Math.imul(S,mt)|0)+(i>>>13)|0)+(Lt>>>26)|0,Lt&=67108863,n=Math.imul(j,ot),i=(i=Math.imul(j,at))+Math.imul(N,ot)|0,o=Math.imul(N,at),n=n+Math.imul(F,lt)|0,i=(i=i+Math.imul(F,ct)|0)+Math.imul(R,lt)|0,o=o+Math.imul(R,ct)|0,n=n+Math.imul(O,ht)|0,i=(i=i+Math.imul(O,dt)|0)+Math.imul(D,ht)|0,o=o+Math.imul(D,dt)|0;var zt=(c+(n=n+Math.imul(E,pt)|0)|0)+((8191&(i=(i=i+Math.imul(E,mt)|0)+Math.imul(L,pt)|0))<<13)|0;c=((o=o+Math.imul(L,mt)|0)+(i>>>13)|0)+(zt>>>26)|0,zt&=67108863,n=Math.imul(j,lt),i=(i=Math.imul(j,ct))+Math.imul(N,lt)|0,o=Math.imul(N,ct),n=n+Math.imul(F,ht)|0,i=(i=i+Math.imul(F,dt)|0)+Math.imul(R,ht)|0,o=o+Math.imul(R,dt)|0;var Ot=(c+(n=n+Math.imul(O,pt)|0)|0)+((8191&(i=(i=i+Math.imul(O,mt)|0)+Math.imul(D,pt)|0))<<13)|0;c=((o=o+Math.imul(D,mt)|0)+(i>>>13)|0)+(Ot>>>26)|0,Ot&=67108863,n=Math.imul(j,ht),i=(i=Math.imul(j,dt))+Math.imul(N,ht)|0,o=Math.imul(N,dt);var Dt=(c+(n=n+Math.imul(F,pt)|0)|0)+((8191&(i=(i=i+Math.imul(F,mt)|0)+Math.imul(R,pt)|0))<<13)|0;c=((o=o+Math.imul(R,mt)|0)+(i>>>13)|0)+(Dt>>>26)|0,Dt&=67108863;var It=(c+(n=Math.imul(j,pt))|0)+((8191&(i=(i=Math.imul(j,mt))+Math.imul(N,pt)|0))<<13)|0;return c=((o=Math.imul(N,mt))+(i>>>13)|0)+(It>>>26)|0,It&=67108863,l[0]=gt,l[1]=vt,l[2]=bt,l[3]=yt,l[4]=xt,l[5]=_t,l[6]=wt,l[7]=kt,l[8]=At,l[9]=Mt,l[10]=Tt,l[11]=St,l[12]=Ct,l[13]=Et,l[14]=Lt,l[15]=zt,l[16]=Ot,l[17]=Dt,l[18]=It,0!==c&&(l[19]=c,r.length++),r};function m(t,e,r){return(new g).mulp(t,e,r)}function g(t,e){this.x=t,this.y=e}Math.imul||(p=f),o.prototype.mulTo=function(t,e){var r,n=this.length+t.length;return r=10===this.length&&10===t.length?p(this,t,e):n<63?f(this,t,e):n<1024?function(t,e,r){r.negative=e.negative^t.negative,r.length=t.length+e.length;for(var n=0,i=0,o=0;o>>26)|0)>>>26,a&=67108863}r.words[o]=s,n=a,a=i}return 0!==n?r.words[o]=n:r.length--,r.strip()}(this,t,e):m(this,t,e),r},g.prototype.makeRBT=function(t){for(var e=new Array(t),r=o.prototype._countBits(t)-1,n=0;n>=1;return n},g.prototype.permute=function(t,e,r,n,i,o){for(var a=0;a>>=1)i++;return 1<>>=13,r[2*a+1]=8191&o,o>>>=13;for(a=2*e;a>=26,e+=i/67108864|0,e+=o>>>26,this.words[r]=67108863&o}return 0!==e&&(this.words[r]=e,this.length++),this},o.prototype.muln=function(t){return this.clone().imuln(t)},o.prototype.sqr=function(){return this.mul(this)},o.prototype.isqr=function(){return this.imul(this.clone())},o.prototype.pow=function(t){var e=function(t){for(var e=new Array(t.bitLength()),r=0;r>>i}return e}(t);if(0===e.length)return new o(1);for(var r=this,n=0;n=0);var e,r=t%26,i=(t-r)/26,o=67108863>>>26-r<<26-r;if(0!==r){var a=0;for(e=0;e>>26-r}a&&(this.words[e]=a,this.length++)}if(0!==i){for(e=this.length-1;e>=0;e--)this.words[e+i]=this.words[e];for(e=0;e=0),i=e?(e-e%26)/26:0;var o=t%26,a=Math.min((t-o)/26,this.length),s=67108863^67108863>>>o<a)for(this.length-=a,c=0;c=0&&(0!==u||c>=i);c--){var h=0|this.words[c];this.words[c]=u<<26-o|h>>>o,u=h&s}return l&&0!==u&&(l.words[l.length++]=u),0===this.length&&(this.words[0]=0,this.length=1),this.strip()},o.prototype.ishrn=function(t,e,r){return n(0===this.negative),this.iushrn(t,e,r)},o.prototype.shln=function(t){return this.clone().ishln(t)},o.prototype.ushln=function(t){return this.clone().iushln(t)},o.prototype.shrn=function(t){return this.clone().ishrn(t)},o.prototype.ushrn=function(t){return this.clone().iushrn(t)},o.prototype.testn=function(t){n("number"==typeof t&&t>=0);var e=t%26,r=(t-e)/26,i=1<=0);var e=t%26,r=(t-e)/26;if(n(0===this.negative,"imaskn works only with positive numbers"),this.length<=r)return this;if(0!==e&&r++,this.length=Math.min(r,this.length),0!==e){var i=67108863^67108863>>>e<=67108864;e++)this.words[e]-=67108864,e===this.length-1?this.words[e+1]=1:this.words[e+1]++;return this.length=Math.max(this.length,e+1),this},o.prototype.isubn=function(t){if(n("number"==typeof t),n(t<67108864),t<0)return this.iaddn(-t);if(0!==this.negative)return this.negative=0,this.iaddn(t),this.negative=1,this;if(this.words[0]-=t,1===this.length&&this.words[0]<0)this.words[0]=-this.words[0],this.negative=1;else for(var e=0;e>26)-(l/67108864|0),this.words[i+r]=67108863&o}for(;i>26,this.words[i+r]=67108863&o;if(0===s)return this.strip();for(n(-1===s),s=0,i=0;i>26,this.words[i]=67108863&o;return this.negative=1,this.strip()},o.prototype._wordDiv=function(t,e){var r=(this.length,t.length),n=this.clone(),i=t,a=0|i.words[i.length-1];0!=(r=26-this._countBits(a))&&(i=i.ushln(r),n.iushln(r),a=0|i.words[i.length-1]);var s,l=n.length-i.length;if("mod"!==e){(s=new o(null)).length=l+1,s.words=new Array(s.length);for(var c=0;c=0;h--){var d=67108864*(0|n.words[i.length+h])+(0|n.words[i.length+h-1]);for(d=Math.min(d/a|0,67108863),n._ishlnsubmul(i,d,h);0!==n.negative;)d--,n.negative=0,n._ishlnsubmul(i,1,h),n.isZero()||(n.negative^=1);s&&(s.words[h]=d)}return s&&s.strip(),n.strip(),"div"!==e&&0!==r&&n.iushrn(r),{div:s||null,mod:n}},o.prototype.divmod=function(t,e,r){return n(!t.isZero()),this.isZero()?{div:new o(0),mod:new o(0)}:0!==this.negative&&0===t.negative?(s=this.neg().divmod(t,e),"mod"!==e&&(i=s.div.neg()),"div"!==e&&(a=s.mod.neg(),r&&0!==a.negative&&a.iadd(t)),{div:i,mod:a}):0===this.negative&&0!==t.negative?(s=this.divmod(t.neg(),e),"mod"!==e&&(i=s.div.neg()),{div:i,mod:s.mod}):this.negative&t.negative?(s=this.neg().divmod(t.neg(),e),"div"!==e&&(a=s.mod.neg(),r&&0!==a.negative&&a.isub(t)),{div:s.div,mod:a}):t.length>this.length||this.cmp(t)<0?{div:new o(0),mod:this}:1===t.length?"div"===e?{div:this.divn(t.words[0]),mod:null}:"mod"===e?{div:null,mod:new o(this.modn(t.words[0]))}:{div:this.divn(t.words[0]),mod:new o(this.modn(t.words[0]))}:this._wordDiv(t,e);var i,a,s},o.prototype.div=function(t){return this.divmod(t,"div",!1).div},o.prototype.mod=function(t){return this.divmod(t,"mod",!1).mod},o.prototype.umod=function(t){return this.divmod(t,"mod",!0).mod},o.prototype.divRound=function(t){var e=this.divmod(t);if(e.mod.isZero())return e.div;var r=0!==e.div.negative?e.mod.isub(t):e.mod,n=t.ushrn(1),i=t.andln(1),o=r.cmp(n);return o<0||1===i&&0===o?e.div:0!==e.div.negative?e.div.isubn(1):e.div.iaddn(1)},o.prototype.modn=function(t){n(t<=67108863);for(var e=(1<<26)%t,r=0,i=this.length-1;i>=0;i--)r=(e*r+(0|this.words[i]))%t;return r},o.prototype.idivn=function(t){n(t<=67108863);for(var e=0,r=this.length-1;r>=0;r--){var i=(0|this.words[r])+67108864*e;this.words[r]=i/t|0,e=i%t}return this.strip()},o.prototype.divn=function(t){return this.clone().idivn(t)},o.prototype.egcd=function(t){n(0===t.negative),n(!t.isZero());var e=this,r=t.clone();e=0!==e.negative?e.umod(t):e.clone();for(var i=new o(1),a=new o(0),s=new o(0),l=new o(1),c=0;e.isEven()&&r.isEven();)e.iushrn(1),r.iushrn(1),++c;for(var u=r.clone(),h=e.clone();!e.isZero();){for(var d=0,f=1;!(e.words[0]&f)&&d<26;++d,f<<=1);if(d>0)for(e.iushrn(d);d-- >0;)(i.isOdd()||a.isOdd())&&(i.iadd(u),a.isub(h)),i.iushrn(1),a.iushrn(1);for(var p=0,m=1;!(r.words[0]&m)&&p<26;++p,m<<=1);if(p>0)for(r.iushrn(p);p-- >0;)(s.isOdd()||l.isOdd())&&(s.iadd(u),l.isub(h)),s.iushrn(1),l.iushrn(1);e.cmp(r)>=0?(e.isub(r),i.isub(s),a.isub(l)):(r.isub(e),s.isub(i),l.isub(a))}return{a:s,b:l,gcd:r.iushln(c)}},o.prototype._invmp=function(t){n(0===t.negative),n(!t.isZero());var e=this,r=t.clone();e=0!==e.negative?e.umod(t):e.clone();for(var i,a=new o(1),s=new o(0),l=r.clone();e.cmpn(1)>0&&r.cmpn(1)>0;){for(var c=0,u=1;!(e.words[0]&u)&&c<26;++c,u<<=1);if(c>0)for(e.iushrn(c);c-- >0;)a.isOdd()&&a.iadd(l),a.iushrn(1);for(var h=0,d=1;!(r.words[0]&d)&&h<26;++h,d<<=1);if(h>0)for(r.iushrn(h);h-- >0;)s.isOdd()&&s.iadd(l),s.iushrn(1);e.cmp(r)>=0?(e.isub(r),a.isub(s)):(r.isub(e),s.isub(a))}return(i=0===e.cmpn(1)?a:s).cmpn(0)<0&&i.iadd(t),i},o.prototype.gcd=function(t){if(this.isZero())return t.abs();if(t.isZero())return this.abs();var e=this.clone(),r=t.clone();e.negative=0,r.negative=0;for(var n=0;e.isEven()&&r.isEven();n++)e.iushrn(1),r.iushrn(1);for(;;){for(;e.isEven();)e.iushrn(1);for(;r.isEven();)r.iushrn(1);var i=e.cmp(r);if(i<0){var o=e;e=r,r=o}else if(0===i||0===r.cmpn(1))break;e.isub(r)}return r.iushln(n)},o.prototype.invm=function(t){return this.egcd(t).a.umod(t)},o.prototype.isEven=function(){return!(1&this.words[0])},o.prototype.isOdd=function(){return!(1&~this.words[0])},o.prototype.andln=function(t){return this.words[0]&t},o.prototype.bincn=function(t){n("number"==typeof t);var e=t%26,r=(t-e)/26,i=1<>>26,s&=67108863,this.words[a]=s}return 0!==o&&(this.words[a]=o,this.length++),this},o.prototype.isZero=function(){return 1===this.length&&0===this.words[0]},o.prototype.cmpn=function(t){var e,r=t<0;if(0!==this.negative&&!r)return-1;if(0===this.negative&&r)return 1;if(this.strip(),this.length>1)e=1;else{r&&(t=-t),n(t<=67108863,"Number is too big");var i=0|this.words[0];e=i===t?0:it.length)return 1;if(this.length=0;r--){var n=0|this.words[r],i=0|t.words[r];if(n!==i){ni&&(e=1);break}}return e},o.prototype.gtn=function(t){return 1===this.cmpn(t)},o.prototype.gt=function(t){return 1===this.cmp(t)},o.prototype.gten=function(t){return this.cmpn(t)>=0},o.prototype.gte=function(t){return this.cmp(t)>=0},o.prototype.ltn=function(t){return-1===this.cmpn(t)},o.prototype.lt=function(t){return-1===this.cmp(t)},o.prototype.lten=function(t){return this.cmpn(t)<=0},o.prototype.lte=function(t){return this.cmp(t)<=0},o.prototype.eqn=function(t){return 0===this.cmpn(t)},o.prototype.eq=function(t){return 0===this.cmp(t)},o.red=function(t){return new k(t)},o.prototype.toRed=function(t){return n(!this.red,"Already a number in reduction context"),n(0===this.negative,"red works only with positives"),t.convertTo(this)._forceRed(t)},o.prototype.fromRed=function(){return n(this.red,"fromRed works only with numbers in reduction context"),this.red.convertFrom(this)},o.prototype._forceRed=function(t){return this.red=t,this},o.prototype.forceRed=function(t){return n(!this.red,"Already a number in reduction context"),this._forceRed(t)},o.prototype.redAdd=function(t){return n(this.red,"redAdd works only with red numbers"),this.red.add(this,t)},o.prototype.redIAdd=function(t){return n(this.red,"redIAdd works only with red numbers"),this.red.iadd(this,t)},o.prototype.redSub=function(t){return n(this.red,"redSub works only with red numbers"),this.red.sub(this,t)},o.prototype.redISub=function(t){return n(this.red,"redISub works only with red numbers"),this.red.isub(this,t)},o.prototype.redShl=function(t){return n(this.red,"redShl works only with red numbers"),this.red.shl(this,t)},o.prototype.redMul=function(t){return n(this.red,"redMul works only with red numbers"),this.red._verify2(this,t),this.red.mul(this,t)},o.prototype.redIMul=function(t){return n(this.red,"redMul works only with red numbers"),this.red._verify2(this,t),this.red.imul(this,t)},o.prototype.redSqr=function(){return n(this.red,"redSqr works only with red numbers"),this.red._verify1(this),this.red.sqr(this)},o.prototype.redISqr=function(){return n(this.red,"redISqr works only with red numbers"),this.red._verify1(this),this.red.isqr(this)},o.prototype.redSqrt=function(){return n(this.red,"redSqrt works only with red numbers"),this.red._verify1(this),this.red.sqrt(this)},o.prototype.redInvm=function(){return n(this.red,"redInvm works only with red numbers"),this.red._verify1(this),this.red.invm(this)},o.prototype.redNeg=function(){return n(this.red,"redNeg works only with red numbers"),this.red._verify1(this),this.red.neg(this)},o.prototype.redPow=function(t){return n(this.red&&!t.red,"redPow(normalNum)"),this.red._verify1(this),this.red.pow(this,t)};var v={k256:null,p224:null,p192:null,p25519:null};function b(t,e){this.name=t,this.p=new o(e,16),this.n=this.p.bitLength(),this.k=new o(1).iushln(this.n).isub(this.p),this.tmp=this._tmp()}function y(){b.call(this,"k256","ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f")}function x(){b.call(this,"p224","ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001")}function _(){b.call(this,"p192","ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff")}function w(){b.call(this,"25519","7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed")}function k(t){if("string"==typeof t){var e=o._prime(t);this.m=e.p,this.prime=e}else n(t.gtn(1),"modulus must be greater than 1"),this.m=t,this.prime=null}function A(t){k.call(this,t),this.shift=this.m.bitLength(),this.shift%26!=0&&(this.shift+=26-this.shift%26),this.r=new o(1).iushln(this.shift),this.r2=this.imod(this.r.sqr()),this.rinv=this.r._invmp(this.m),this.minv=this.rinv.mul(this.r).isubn(1).div(this.m),this.minv=this.minv.umod(this.r),this.minv=this.r.sub(this.minv)}b.prototype._tmp=function(){var t=new o(null);return t.words=new Array(Math.ceil(this.n/13)),t},b.prototype.ireduce=function(t){var e,r=t;do{this.split(r,this.tmp),e=(r=(r=this.imulK(r)).iadd(this.tmp)).bitLength()}while(e>this.n);var n=e0?r.isub(this.p):void 0!==r.strip?r.strip():r._strip(),r},b.prototype.split=function(t,e){t.iushrn(this.n,0,e)},b.prototype.imulK=function(t){return t.imul(this.k)},i(y,b),y.prototype.split=function(t,e){for(var r=4194303,n=Math.min(t.length,9),i=0;i>>22,o=a}o>>>=22,t.words[i-10]=o,0===o&&t.length>10?t.length-=10:t.length-=9},y.prototype.imulK=function(t){t.words[t.length]=0,t.words[t.length+1]=0,t.length+=2;for(var e=0,r=0;r>>=26,t.words[r]=i,e=n}return 0!==e&&(t.words[t.length++]=e),t},o._prime=function(t){if(v[t])return v[t];var e;if("k256"===t)e=new y;else if("p224"===t)e=new x;else if("p192"===t)e=new _;else{if("p25519"!==t)throw new Error("Unknown prime "+t);e=new w}return v[t]=e,e},k.prototype._verify1=function(t){n(0===t.negative,"red works only with positives"),n(t.red,"red works only with red numbers")},k.prototype._verify2=function(t,e){n(!(t.negative|e.negative),"red 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v=[{family:this.labelFont[0],style:this.labelFontStyle[0],weight:this.labelFontWeight[0],variant:this.labelFontVariant[0]},{family:this.labelFont[1],style:this.labelFontStyle[1],weight:this.labelFontWeight[1],variant:this.labelFontVariant[1]},{family:this.labelFont[2],style:this.labelFontStyle[2],weight:this.labelFontWeight[2],variant:this.labelFontVariant[2]}],b=[{family:this.tickFont[0],style:this.tickFontStyle[0],weight:this.tickFontWeight[0],variant:this.tickFontVariant[0]},{family:this.tickFont[1],style:this.tickFontStyle[1],weight:this.tickFontWeight[1],variant:this.tickFontVariant[1]},{family:this.tickFont[2],style:this.tickFontStyle[2],weight:this.tickFontWeight[2],variant:this.tickFontVariant[2]}];this._text?this._text&&(g||u)&&this._text.update(this.bounds,this.labels,v,this.ticks,b):this._text=n(this.gl,this.bounds,this.labels,v,this.ticks,b),this._lines&&u&&(this._lines.dispose(),this._lines=null),this._lines||(this._lines=i(this.gl,this.bounds,this.ticks))};var g=[new m,new m,new m];function v(t,e,r,n,i){for(var o=t.primalOffset,a=t.primalMinor,s=t.mirrorOffset,l=t.mirrorMinor,c=n[e],u=0;u<3;++u)if(e!==u){var h=o,d=s,f=a,p=l;c&1<0?(f[u]=-1,p[u]=0):(f[u]=0,p[u]=1)}}var b=[0,0,0],y={model:l,view:l,projection:l,_ortho:!1};p.isOpaque=function(){return!0},p.isTransparent=function(){return!1},p.drawTransparent=function(t){};var x=[0,0,0],_=[0,0,0],w=[0,0,0];p.draw=function(t){t=t||y;for(var e=this.gl,r=t.model||l,n=t.view||l,i=t.projection||l,o=this.bounds,s=t._ortho||!1,c=a(r,n,i,o,s),u=c.cubeEdges,h=c.axis,f=n[12],p=n[13],m=n[14],k=n[15],A=(s?2:1)*this.pixelRatio*(i[3]*f+i[7]*p+i[11]*m+i[15]*k)/e.drawingBufferHeight,M=0;M<3;++M)this.lastCubeProps.cubeEdges[M]=u[M],this.lastCubeProps.axis[M]=h[M];var T=g;for(M=0;M<3;++M)v(g[M],M,this.bounds,u,h);e=this.gl;var S,C,E,L=b;for(M=0;M<3;++M)this.backgroundEnable[M]?L[M]=h[M]:L[M]=0;for(this._background.draw(r,n,i,o,L,this.backgroundColor),this._lines.bind(r,n,i,this),M=0;M<3;++M){var z=[0,0,0];h[M]>0?z[M]=o[1][M]:z[M]=o[0][M];for(var O=0;O<2;++O){var D=(M+1+O)%3,I=(M+1+(1^O))%3;this.gridEnable[D]&&this._lines.drawGrid(D,I,this.bounds,z,this.gridColor[D],this.gridWidth[D]*this.pixelRatio)}for(O=0;O<2;++O)D=(M+1+O)%3,I=(M+1+(1^O))%3,this.zeroEnable[I]&&Math.min(o[0][I],o[1][I])<=0&&Math.max(o[0][I],o[1][I])>=0&&this._lines.drawZero(D,I,this.bounds,z,this.zeroLineColor[I],this.zeroLineWidth[I]*this.pixelRatio)}for(M=0;M<3;++M){this.lineEnable[M]&&this._lines.drawAxisLine(M,this.bounds,T[M].primalOffset,this.lineColor[M],this.lineWidth[M]*this.pixelRatio),this.lineMirror[M]&&this._lines.drawAxisLine(M,this.bounds,T[M].mirrorOffset,this.lineColor[M],this.lineWidth[M]*this.pixelRatio);var F=d(x,T[M].primalMinor),R=d(_,T[M].mirrorMinor),P=this.lineTickLength;for(O=0;O<3;++O){var j=A/r[5*O];F[O]*=P[O]*j,R[O]*=P[O]*j}this.lineTickEnable[M]&&this._lines.drawAxisTicks(M,T[M].primalOffset,F,this.lineTickColor[M],this.lineTickWidth[M]*this.pixelRatio),this.lineTickMirror[M]&&this._lines.drawAxisTicks(M,T[M].mirrorOffset,R,this.lineTickColor[M],this.lineTickWidth[M]*this.pixelRatio)}function N(t){(E=[0,0,0])[t]=1}function B(t,e,r){var n=(t+1)%3,i=(t+2)%3,o=e[n],a=e[i],s=r[n],l=r[i];o>0&&l>0||o>0&&l<0||o<0&&l>0||o<0&&l<0?N(n):(a>0&&s>0||a>0&&s<0||a<0&&s>0||a<0&&s<0)&&N(i)}for(this._lines.unbind(),this._text.bind(r,n,i,this.pixelRatio),M=0;M<3;++M){var U=T[M].primalMinor,G=T[M].mirrorMinor,V=d(w,T[M].primalOffset);for(O=0;O<3;++O)this.lineTickEnable[M]&&(V[O]+=A*U[O]*Math.max(this.lineTickLength[O],0)/r[5*O]);var H=[0,0,0];if(H[M]=1,this.tickEnable[M]){for(-3600===this.tickAngle[M]?(this.tickAngle[M]=0,this.tickAlign[M]="auto"):this.tickAlign[M]=-1,C=1,"auto"===(S=[this.tickAlign[M],.5,C])[0]?S[0]=0:S[0]=parseInt(""+S[0]),E=[0,0,0],B(M,U,G),O=0;O<3;++O)V[O]+=A*U[O]*this.tickPad[O]/r[5*O];this._text.drawTicks(M,this.tickSize[M],this.tickAngle[M],V,this.tickColor[M],H,E,S)}if(this.labelEnable[M]){for(C=0,E=[0,0,0],this.labels[M].length>4&&(N(M),C=1),"auto"===(S=[this.labelAlign[M],.5,C])[0]?S[0]=0:S[0]=parseInt(""+S[0]),O=0;O<3;++O)V[O]+=A*U[O]*this.labelPad[O]/r[5*O];V[M]+=.5*(o[0][M]+o[1][M]),this._text.drawLabel(M,this.labelSize[M],this.labelAngle[M],V,this.labelColor[M],[0,0,0],E,S)}}this._text.unbind()},p.dispose=function(){this._text.dispose(),this._lines.dispose(),this._background.dispose(),this._lines=null,this._text=null,this._background=null,this.gl=null}},5304:function(t,e,r){"use strict";t.exports=function(t){for(var e=[],r=[],s=0,l=0;l<3;++l)for(var c=(l+1)%3,u=(l+2)%3,h=[0,0,0],d=[0,0,0],f=-1;f<=1;f+=2){r.push(s,s+2,s+1,s+1,s+2,s+3),h[l]=f,d[l]=f;for(var p=-1;p<=1;p+=2){h[c]=p;for(var m=-1;m<=1;m+=2)h[u]=m,e.push(h[0],h[1],h[2],d[0],d[1],d[2]),s+=1}var g=c;c=u,u=g}var v=n(t,new Float32Array(e)),b=n(t,new Uint16Array(r),t.ELEMENT_ARRAY_BUFFER),y=i(t,[{buffer:v,type:t.FLOAT,size:3,offset:0,stride:24},{buffer:v,type:t.FLOAT,size:3,offset:12,stride:24}],b),x=o(t);return x.attributes.position.location=0,x.attributes.normal.location=1,new a(t,v,y,x)};var n=r(2762),i=r(8116),o=r(1879).bg;function a(t,e,r,n){this.gl=t,this.buffer=e,this.vao=r,this.shader=n}var s=a.prototype;s.draw=function(t,e,r,n,i,o){for(var a=!1,s=0;s<3;++s)a=a||i[s];if(a){var l=this.gl;l.enable(l.POLYGON_OFFSET_FILL),l.polygonOffset(1,2),this.shader.bind(),this.shader.uniforms={model:t,view:e,projection:r,bounds:n,enable:i,colors:o},this.vao.bind(),this.vao.draw(this.gl.TRIANGLES,36),this.vao.unbind(),l.disable(l.POLYGON_OFFSET_FILL)}},s.dispose=function(){this.vao.dispose(),this.buffer.dispose(),this.shader.dispose()}},6429:function(t,e,r){"use strict";t.exports=function(t,e,r,o,f){i(s,e,t),i(s,r,s);for(var b=0,y=0;y<2;++y){u[2]=o[y][2];for(var x=0;x<2;++x){u[1]=o[x][1];for(var _=0;_<2;++_)u[0]=o[_][0],d(l[b],u,s),b+=1}}var w=-1;for(y=0;y<8;++y){for(var k=l[y][3],A=0;A<3;++A)c[y][A]=l[y][A]/k;f&&(c[y][2]*=-1),k<0&&(w<0||c[y][2]C&&(w|=1<C&&(w|=1<c[y][1])&&(R=y);var P=-1;for(y=0;y<3;++y)(N=R^1<c[j][0]&&(j=N))}var B=m;B[0]=B[1]=B[2]=0,B[n.log2(P^R)]=R&P,B[n.log2(R^j)]=R&j;var U=7^j;U===w||U===F?(U=7^P,B[n.log2(j^U)]=U&j):B[n.log2(P^U)]=U&P;var G=g,V=w;for(M=0;M<3;++M)G[M]=V&1< HALF_PI) && (b <= ONE_AND_HALF_PI)) ?\n b - PI :\n b;\n}\n\nfloat look_horizontal_or_vertical(float a, float ratio) {\n // ratio controls the ratio between being horizontal to (vertical + horizontal)\n // if ratio is set to 0.5 then it is 50%, 50%.\n // when using a higher ratio e.g. 0.75 the result would\n // likely be more horizontal than vertical.\n\n float b = positive_angle(a);\n\n return\n (b < ( ratio) * HALF_PI) ? 0.0 :\n (b < (2.0 - ratio) * HALF_PI) ? -HALF_PI :\n (b < (2.0 + ratio) * HALF_PI) ? 0.0 :\n (b < (4.0 - ratio) * HALF_PI) ? HALF_PI :\n 0.0;\n}\n\nfloat roundTo(float a, float b) {\n return float(b * floor((a + 0.5 * b) / b));\n}\n\nfloat look_round_n_directions(float a, int n) {\n float b = positive_angle(a);\n float div = TWO_PI / float(n);\n float c = roundTo(b, div);\n return look_upwards(c);\n}\n\nfloat applyAlignOption(float rawAngle, float delta) {\n return\n (option > 2) ? look_round_n_directions(rawAngle + delta, option) : // option 3-n: round to n directions\n (option == 2) ? look_horizontal_or_vertical(rawAngle + delta, hv_ratio) : // horizontal or vertical\n (option == 1) ? rawAngle + delta : // use free angle, and flip to align with one direction of the axis\n (option == 0) ? look_upwards(rawAngle) : // use free angle, and stay upwards\n (option ==-1) ? 0.0 : // useful for backward compatibility, all texts remains horizontal\n rawAngle; // otherwise return back raw input angle\n}\n\nbool isAxisTitle = (axis.x == 0.0) &&\n (axis.y == 0.0) &&\n (axis.z == 0.0);\n\nvoid main() {\n //Compute world offset\n float axisDistance = position.z;\n vec3 dataPosition = axisDistance * axis + offset;\n\n float beta = angle; // i.e. user defined attributes for each tick\n\n float axisAngle;\n float clipAngle;\n float flip;\n\n if (enableAlign) {\n axisAngle = (isAxisTitle) ? HALF_PI :\n computeViewAngle(dataPosition, dataPosition + axis);\n clipAngle = computeViewAngle(dataPosition, dataPosition + alignDir);\n\n axisAngle += (sin(axisAngle) < 0.0) ? PI : 0.0;\n clipAngle += (sin(clipAngle) < 0.0) ? PI : 0.0;\n\n flip = (dot(vec2(cos(axisAngle), sin(axisAngle)),\n vec2(sin(clipAngle),-cos(clipAngle))) > 0.0) ? 1.0 : 0.0;\n\n beta += applyAlignOption(clipAngle, flip * PI);\n }\n\n //Compute plane offset\n vec2 planeCoord = position.xy * pixelScale;\n\n mat2 planeXform = scale * mat2(\n cos(beta), sin(beta),\n -sin(beta), cos(beta)\n );\n\n vec2 viewOffset = 2.0 * planeXform * planeCoord / resolution;\n\n //Compute clip position\n vec3 clipPosition = project(dataPosition);\n\n //Apply text offset in clip coordinates\n clipPosition += vec3(viewOffset, 0.0);\n\n //Done\n gl_Position = vec4(clipPosition, 1.0);\n}\n"]),l=n(["precision highp float;\n#define GLSLIFY 1\n\nuniform vec4 color;\nvoid main() {\n gl_FragColor = color;\n}"]);e.Q=function(t){return i(t,s,l,null,[{name:"position",type:"vec3"}])};var c=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position;\nattribute vec3 normal;\n\nuniform mat4 model, view, projection;\nuniform vec3 enable;\nuniform vec3 bounds[2];\n\nvarying vec3 colorChannel;\n\nvoid main() {\n\n vec3 signAxis = sign(bounds[1] - bounds[0]);\n\n vec3 realNormal = signAxis * normal;\n\n if(dot(realNormal, enable) > 0.0) {\n vec3 minRange = min(bounds[0], bounds[1]);\n vec3 maxRange = max(bounds[0], bounds[1]);\n vec3 nPosition = mix(minRange, maxRange, 0.5 * (position + 1.0));\n gl_Position = projection * (view * (model * vec4(nPosition, 1.0)));\n } else {\n gl_Position = vec4(0,0,0,0);\n }\n\n colorChannel = abs(realNormal);\n}\n"]),u=n(["precision highp float;\n#define GLSLIFY 1\n\nuniform vec4 colors[3];\n\nvarying vec3 colorChannel;\n\nvoid main() {\n gl_FragColor = colorChannel.x * colors[0] +\n colorChannel.y * colors[1] +\n colorChannel.z * colors[2];\n}"]);e.bg=function(t){return i(t,c,u,null,[{name:"position",type:"vec3"},{name:"normal",type:"vec3"}])}},4935:function(t,e,r){"use strict";t.exports=function(t,e,r,n,a,l){var c=i(t),h=o(t,[{buffer:c,size:3}]),d=s(t);d.attributes.position.location=0;var f=new u(t,d,c,h);return f.update(e,r,n,a,l),f};var i=r(2762),o=r(8116),a=r(4359),s=r(1879).Q,l=window||n.global||{},c=l.__TEXT_CACHE||{};function u(t,e,r,n){this.gl=t,this.shader=e,this.buffer=r,this.vao=n,this.tickOffset=this.tickCount=this.labelOffset=this.labelCount=null}l.__TEXT_CACHE={};var h=u.prototype,d=[0,0];h.bind=function(t,e,r,n){this.vao.bind(),this.shader.bind();var i=this.shader.uniforms;i.model=t,i.view=e,i.projection=r,i.pixelScale=n,d[0]=this.gl.drawingBufferWidth,d[1]=this.gl.drawingBufferHeight,this.shader.uniforms.resolution=d},h.unbind=function(){this.vao.unbind()},h.update=function(t,e,r,n,i){var o=[];function s(t,e,r,n,i,s){var l=[r.style,r.weight,r.variant,r.family].join("_"),u=c[l];u||(u=c[l]={});var h=u[e];h||(h=u[e]=function(t,e){try{return a(t,e)}catch(e){return console.warn('error vectorizing text:"'+t+'" error:',e),{cells:[],positions:[]}}}(e,{triangles:!0,font:r.family,fontStyle:r.style,fontWeight:r.weight,fontVariant:r.variant,textAlign:"center",textBaseline:"middle",lineSpacing:i,styletags:s}));for(var d=(n||12)/12,f=h.positions,p=h.cells,m=0,g=p.length;m=0;--b){var y=f[v[b]];o.push(d*y[0],-d*y[1],t)}}for(var l=[0,0,0],u=[0,0,0],h=[0,0,0],d=[0,0,0],f={breaklines:!0,bolds:!0,italics:!0,subscripts:!0,superscripts:!0},p=0;p<3;++p){h[p]=o.length/3|0,s(.5*(t[0][p]+t[1][p]),e[p],r[p],12,1.25,f),d[p]=(o.length/3|0)-h[p],l[p]=o.length/3|0;for(var m=0;m=0&&(i=r.length-n-1);var o=Math.pow(10,i),a=Math.round(t*e*o),s=a+"";if(s.indexOf("e")>=0)return s;var l=a/o,c=a%o;a<0?(l=0|-Math.ceil(l),c=0|-c):(l=0|Math.floor(l),c|=0);var u=""+l;if(a<0&&(u="-"+u),i){for(var h=""+c;h.length=t[0][i];--a)o.push({x:a*e[i],text:r(e[i],a)});n.push(o)}return n},e.equal=function(t,e){for(var r=0;r<3;++r){if(t[r].length!==e[r].length)return!1;for(var n=0;nr)throw new Error("gl-buffer: If resizing buffer, must not specify offset");return t.bufferSubData(e,o,i),r}function u(t,e){for(var r=n.malloc(t.length,e),i=t.length,o=0;o=0;--n){if(e[n]!==r)return!1;r*=t[n]}return!0}(t.shape,t.stride))0===t.offset&&t.data.length===t.shape[0]?this.length=c(this.gl,this.type,this.length,this.usage,t.data,e):this.length=c(this.gl,this.type,this.length,this.usage,t.data.subarray(t.offset,t.shape[0]),e);else{var s=n.malloc(t.size,r),l=o(s,t.shape);i.assign(l,t),this.length=c(this.gl,this.type,this.length,this.usage,e<0?s:s.subarray(0,t.size),e),n.free(s)}}else if(Array.isArray(t)){var h;h=this.type===this.gl.ELEMENT_ARRAY_BUFFER?u(t,"uint16"):u(t,"float32"),this.length=c(this.gl,this.type,this.length,this.usage,e<0?h:h.subarray(0,t.length),e),n.free(h)}else if("object"==typeof t&&"number"==typeof t.length)this.length=c(this.gl,this.type,this.length,this.usage,t,e);else{if("number"!=typeof t&&void 0!==t)throw new Error("gl-buffer: Invalid data type");if(e>=0)throw new Error("gl-buffer: Cannot specify offset when resizing buffer");(t|=0)<=0&&(t=1),this.gl.bufferData(this.type,0|t,this.usage),this.length=t}},t.exports=function(t,e,r,n){if(r=r||t.ARRAY_BUFFER,n=n||t.DYNAMIC_DRAW,r!==t.ARRAY_BUFFER&&r!==t.ELEMENT_ARRAY_BUFFER)throw new Error("gl-buffer: Invalid type for webgl buffer, must be either gl.ARRAY_BUFFER or gl.ELEMENT_ARRAY_BUFFER");if(n!==t.DYNAMIC_DRAW&&n!==t.STATIC_DRAW&&n!==t.STREAM_DRAW)throw new Error("gl-buffer: Invalid usage for buffer, must be either gl.DYNAMIC_DRAW, gl.STATIC_DRAW or gl.STREAM_DRAW");var i=t.createBuffer(),o=new s(t,r,i,0,n);return o.update(e),o}},6405:function(t,e,r){"use strict";var n=r(2931);t.exports=function(t,e){var r=t.positions,i=t.vectors,o={positions:[],vertexIntensity:[],vertexIntensityBounds:t.vertexIntensityBounds,vectors:[],cells:[],coneOffset:t.coneOffset,colormap:t.colormap};if(0===t.positions.length)return e&&(e[0]=[0,0,0],e[1]=[0,0,0]),o;for(var a=0,s=1/0,l=-1/0,c=1/0,u=-1/0,h=1/0,d=-1/0,f=null,p=null,m=[],g=1/0,v=!1,b="raw"===t.coneSizemode,y=0;ya&&(a=n.length(_)),y&&!b){var w=2*n.distance(f,x)/(n.length(p)+n.length(_));w?(g=Math.min(g,w),v=!1):v=!0}v||(f=x,p=_),m.push(_)}var k=[s,c,h],A=[l,u,d];e&&(e[0]=k,e[1]=A),0===a&&(a=1);var M=1/a;isFinite(g)||(g=1),o.vectorScale=g;var T=t.coneSize||(b?1:.5);t.absoluteConeSize&&(T=t.absoluteConeSize*M),o.coneScale=T,y=0;for(var S=0;y=1},f.isTransparent=function(){return this.opacity<1},f.pickSlots=1,f.setPickBase=function(t){this.pickId=t},f.update=function(t){t=t||{};var e=this.gl;this.dirty=!0,"lightPosition"in t&&(this.lightPosition=t.lightPosition),"opacity"in t&&(this.opacity=t.opacity),"ambient"in t&&(this.ambientLight=t.ambient),"diffuse"in t&&(this.diffuseLight=t.diffuse),"specular"in t&&(this.specularLight=t.specular),"roughness"in t&&(this.roughness=t.roughness),"fresnel"in t&&(this.fresnel=t.fresnel),void 0!==t.tubeScale&&(this.tubeScale=t.tubeScale),void 0!==t.vectorScale&&(this.vectorScale=t.vectorScale),void 0!==t.coneScale&&(this.coneScale=t.coneScale),void 0!==t.coneOffset&&(this.coneOffset=t.coneOffset),t.colormap&&(this.texture.shape=[256,256],this.texture.minFilter=e.LINEAR_MIPMAP_LINEAR,this.texture.magFilter=e.LINEAR,this.texture.setPixels(function(t){for(var e=u({colormap:t,nshades:256,format:"rgba"}),r=new Uint8Array(1024),n=0;n<256;++n){for(var i=e[n],o=0;o<3;++o)r[4*n+o]=i[o];r[4*n+3]=255*i[3]}return c(r,[256,256,4],[4,0,1])}(t.colormap)),this.texture.generateMipmap());var r=t.cells,n=t.positions,i=t.vectors;if(n&&r&&i){var o=[],a=[],s=[],l=[],h=[];this.cells=r,this.positions=n,this.vectors=i;var d=t.meshColor||[1,1,1,1],f=t.vertexIntensity,p=1/0,m=-1/0;if(f)if(t.vertexIntensityBounds)p=+t.vertexIntensityBounds[0],m=+t.vertexIntensityBounds[1];else for(var g=0;g0){var m=this.triShader;m.bind(),m.uniforms=c,this.triangleVAO.bind(),e.drawArrays(e.TRIANGLES,0,3*this.triangleCount),this.triangleVAO.unbind()}},f.drawPick=function(t){t=t||{};for(var e=this.gl,r=t.model||h,n=t.view||h,i=t.projection||h,o=[[-1e6,-1e6,-1e6],[1e6,1e6,1e6]],a=0;a<3;++a)o[0][a]=Math.max(o[0][a],this.clipBounds[0][a]),o[1][a]=Math.min(o[1][a],this.clipBounds[1][a]);this._model=[].slice.call(r),this._view=[].slice.call(n),this._projection=[].slice.call(i),this._resolution=[e.drawingBufferWidth,e.drawingBufferHeight];var s={model:r,view:n,projection:i,clipBounds:o,tubeScale:this.tubeScale,vectorScale:this.vectorScale,coneScale:this.coneScale,coneOffset:this.coneOffset,pickId:this.pickId/255},l=this.pickShader;l.bind(),l.uniforms=s,this.triangleCount>0&&(this.triangleVAO.bind(),e.drawArrays(e.TRIANGLES,0,3*this.triangleCount),this.triangleVAO.unbind())},f.pick=function(t){if(!t)return null;if(t.id!==this.pickId)return null;var e=t.value[0]+256*t.value[1]+65536*t.value[2],r=this.cells[e],n=this.positions[r[1]].slice(0,3),i={position:n,dataCoordinate:n,index:Math.floor(r[1]/48)};return"cone"===this.traceType?i.index=Math.floor(r[1]/48):"streamtube"===this.traceType&&(i.intensity=this.intensity[r[1]],i.velocity=this.vectors[r[1]].slice(0,3),i.divergence=this.vectors[r[1]][3],i.index=e),i},f.dispose=function(){this.texture.dispose(),this.triShader.dispose(),this.pickShader.dispose(),this.triangleVAO.dispose(),this.trianglePositions.dispose(),this.triangleVectors.dispose(),this.triangleColors.dispose(),this.triangleUVs.dispose(),this.triangleIds.dispose()},t.exports=function(t,e,r){var s=r.shaders;1===arguments.length&&(t=(e=t).gl);var l=function(t,e){var r=n(t,e.meshShader.vertex,e.meshShader.fragment,null,e.meshShader.attributes);return r.attributes.position.location=0,r.attributes.color.location=2,r.attributes.uv.location=3,r.attributes.vector.location=4,r}(t,s),u=function(t,e){var r=n(t,e.pickShader.vertex,e.pickShader.fragment,null,e.pickShader.attributes);return r.attributes.position.location=0,r.attributes.id.location=1,r.attributes.vector.location=4,r}(t,s),h=a(t,c(new Uint8Array([255,255,255,255]),[1,1,4]));h.generateMipmap(),h.minFilter=t.LINEAR_MIPMAP_LINEAR,h.magFilter=t.LINEAR;var f=i(t),p=i(t),m=i(t),g=i(t),v=i(t),b=new d(t,h,l,u,f,p,v,m,g,o(t,[{buffer:f,type:t.FLOAT,size:4},{buffer:v,type:t.UNSIGNED_BYTE,size:4,normalized:!0},{buffer:m,type:t.FLOAT,size:4},{buffer:g,type:t.FLOAT,size:2},{buffer:p,type:t.FLOAT,size:4}]),r.traceType||"cone");return b.update(e),b}},614:function(t,e,r){var n=r(3236),i=n(["precision highp float;\n\nprecision highp float;\n#define GLSLIFY 1\n\nvec3 getOrthogonalVector(vec3 v) {\n // Return up-vector for only-z vector.\n // Return ax + by + cz = 0, a point that lies on the plane that has v as a normal and that isn't (0,0,0).\n // From the above if-statement we have ||a|| > 0 U ||b|| > 0.\n // Assign z = 0, x = -b, y = a:\n // a*-b + b*a + c*0 = -ba + ba + 0 = 0\n if (v.x*v.x > v.z*v.z || v.y*v.y > v.z*v.z) {\n return normalize(vec3(-v.y, v.x, 0.0));\n } else {\n return normalize(vec3(0.0, v.z, -v.y));\n }\n}\n\n// Calculate the cone vertex and normal at the given index.\n//\n// The returned vertex is for a cone with its top at origin and height of 1.0,\n// pointing in the direction of the vector attribute.\n//\n// Each cone is made up of a top vertex, a center base vertex and base perimeter vertices.\n// These vertices are used to make up the triangles of the cone by the following:\n// segment + 0 top vertex\n// segment + 1 perimeter vertex a+1\n// segment + 2 perimeter vertex a\n// segment + 3 center base vertex\n// segment + 4 perimeter vertex a\n// segment + 5 perimeter vertex a+1\n// Where segment is the number of the radial segment * 6 and a is the angle at that radial segment.\n// To go from index to segment, floor(index / 6)\n// To go from segment to angle, 2*pi * (segment/segmentCount)\n// To go from index to segment index, index - (segment*6)\n//\nvec3 getConePosition(vec3 d, float rawIndex, float coneOffset, out vec3 normal) {\n\n const float segmentCount = 8.0;\n\n float index = rawIndex - floor(rawIndex /\n (segmentCount * 6.0)) *\n (segmentCount * 6.0);\n\n float segment = floor(0.001 + index/6.0);\n float segmentIndex = index - (segment*6.0);\n\n normal = -normalize(d);\n\n if (segmentIndex > 2.99 && segmentIndex < 3.01) {\n return mix(vec3(0.0), -d, coneOffset);\n }\n\n float nextAngle = (\n (segmentIndex > 0.99 && segmentIndex < 1.01) ||\n (segmentIndex > 4.99 && segmentIndex < 5.01)\n ) ? 1.0 : 0.0;\n float angle = 2.0 * 3.14159 * ((segment + nextAngle) / segmentCount);\n\n vec3 v1 = mix(d, vec3(0.0), coneOffset);\n vec3 v2 = v1 - d;\n\n vec3 u = getOrthogonalVector(d);\n vec3 v = normalize(cross(u, d));\n\n vec3 x = u * cos(angle) * length(d)*0.25;\n vec3 y = v * sin(angle) * length(d)*0.25;\n vec3 v3 = v2 + x + y;\n if (segmentIndex < 3.0) {\n vec3 tx = u * sin(angle);\n vec3 ty = v * -cos(angle);\n vec3 tangent = tx + ty;\n normal = normalize(cross(v3 - v1, tangent));\n }\n\n if (segmentIndex == 0.0) {\n return mix(d, vec3(0.0), coneOffset);\n }\n return v3;\n}\n\nattribute vec3 vector;\nattribute vec4 color, position;\nattribute vec2 uv;\n\nuniform float vectorScale, coneScale, coneOffset;\nuniform mat4 model, view, projection, inverseModel;\nuniform vec3 eyePosition, lightPosition;\n\nvarying vec3 f_normal, f_lightDirection, f_eyeDirection, f_data, f_position;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n // Scale the vector magnitude to stay constant with\n // model & view changes.\n vec3 normal;\n vec3 XYZ = getConePosition(mat3(model) * ((vectorScale * coneScale) * vector), position.w, coneOffset, normal);\n vec4 conePosition = model * vec4(position.xyz, 1.0) + vec4(XYZ, 0.0);\n\n //Lighting geometry parameters\n vec4 cameraCoordinate = view * conePosition;\n cameraCoordinate.xyz /= cameraCoordinate.w;\n f_lightDirection = lightPosition - cameraCoordinate.xyz;\n f_eyeDirection = eyePosition - cameraCoordinate.xyz;\n f_normal = normalize((vec4(normal, 0.0) * inverseModel).xyz);\n\n // vec4 m_position = model * vec4(conePosition, 1.0);\n vec4 t_position = view * conePosition;\n gl_Position = projection * t_position;\n\n f_color = color;\n f_data = conePosition.xyz;\n f_position = position.xyz;\n f_uv = uv;\n}\n"]),o=n(["#extension GL_OES_standard_derivatives : enable\n\nprecision highp float;\n#define GLSLIFY 1\n\nfloat beckmannDistribution(float x, float roughness) {\n float NdotH = max(x, 0.0001);\n float cos2Alpha = NdotH * NdotH;\n float tan2Alpha = (cos2Alpha - 1.0) / cos2Alpha;\n float roughness2 = roughness * roughness;\n float denom = 3.141592653589793 * roughness2 * cos2Alpha * cos2Alpha;\n return exp(tan2Alpha / roughness2) / denom;\n}\n\nfloat cookTorranceSpecular(\n vec3 lightDirection,\n vec3 viewDirection,\n vec3 surfaceNormal,\n float roughness,\n float fresnel) {\n\n float VdotN = max(dot(viewDirection, surfaceNormal), 0.0);\n float LdotN = max(dot(lightDirection, surfaceNormal), 0.0);\n\n //Half angle vector\n vec3 H = normalize(lightDirection + viewDirection);\n\n //Geometric term\n float NdotH = max(dot(surfaceNormal, H), 0.0);\n float VdotH = max(dot(viewDirection, H), 0.000001);\n float LdotH = max(dot(lightDirection, H), 0.000001);\n float G1 = (2.0 * NdotH * VdotN) / VdotH;\n float G2 = (2.0 * NdotH * LdotN) / LdotH;\n float G = min(1.0, min(G1, G2));\n \n //Distribution term\n float D = beckmannDistribution(NdotH, roughness);\n\n //Fresnel term\n float F = pow(1.0 - VdotN, fresnel);\n\n //Multiply terms and done\n return G * F * D / max(3.14159265 * VdotN, 0.000001);\n}\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float roughness, fresnel, kambient, kdiffuse, kspecular, opacity;\nuniform sampler2D texture;\n\nvarying vec3 f_normal, f_lightDirection, f_eyeDirection, f_data, f_position;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n vec3 N = normalize(f_normal);\n vec3 L = normalize(f_lightDirection);\n vec3 V = normalize(f_eyeDirection);\n\n if(gl_FrontFacing) {\n N = -N;\n }\n\n float specular = min(1.0, max(0.0, cookTorranceSpecular(L, V, N, roughness, fresnel)));\n float diffuse = min(kambient + kdiffuse * max(dot(N, L), 0.0), 1.0);\n\n vec4 surfaceColor = f_color * texture2D(texture, f_uv);\n vec4 litColor = surfaceColor.a * vec4(diffuse * surfaceColor.rgb + kspecular * vec3(1,1,1) * specular, 1.0);\n\n gl_FragColor = litColor * opacity;\n}\n"]),a=n(["precision highp float;\n\nprecision highp float;\n#define GLSLIFY 1\n\nvec3 getOrthogonalVector(vec3 v) {\n // Return up-vector for only-z vector.\n // Return ax + by + cz = 0, a point that lies on the plane that has v as a normal and that isn't (0,0,0).\n // From the above if-statement we have ||a|| > 0 U ||b|| > 0.\n // Assign z = 0, x = -b, y = a:\n // a*-b + b*a + c*0 = -ba + ba + 0 = 0\n if (v.x*v.x > v.z*v.z || v.y*v.y > v.z*v.z) {\n return normalize(vec3(-v.y, v.x, 0.0));\n } else {\n return normalize(vec3(0.0, v.z, -v.y));\n }\n}\n\n// Calculate the cone vertex and normal at the given index.\n//\n// The returned vertex is for a cone with its top at origin and height of 1.0,\n// pointing in the direction of the vector attribute.\n//\n// Each cone is made up of a top vertex, a center base vertex and base perimeter vertices.\n// These vertices are used to make up the triangles of the cone by the following:\n// segment + 0 top vertex\n// segment + 1 perimeter vertex a+1\n// segment + 2 perimeter vertex a\n// segment + 3 center base vertex\n// segment + 4 perimeter vertex a\n// segment + 5 perimeter vertex a+1\n// Where segment is the number of the radial segment * 6 and a is the angle at that radial segment.\n// To go from index to segment, floor(index / 6)\n// To go from segment to angle, 2*pi * (segment/segmentCount)\n// To go from index to segment index, index - (segment*6)\n//\nvec3 getConePosition(vec3 d, float rawIndex, float coneOffset, out vec3 normal) {\n\n const float segmentCount = 8.0;\n\n float index = rawIndex - floor(rawIndex /\n (segmentCount * 6.0)) *\n (segmentCount * 6.0);\n\n float segment = floor(0.001 + index/6.0);\n float segmentIndex = index - (segment*6.0);\n\n normal = -normalize(d);\n\n if (segmentIndex > 2.99 && segmentIndex < 3.01) {\n return mix(vec3(0.0), -d, coneOffset);\n }\n\n float nextAngle = (\n (segmentIndex > 0.99 && segmentIndex < 1.01) ||\n (segmentIndex > 4.99 && segmentIndex < 5.01)\n ) ? 1.0 : 0.0;\n float angle = 2.0 * 3.14159 * ((segment + nextAngle) / segmentCount);\n\n vec3 v1 = mix(d, vec3(0.0), coneOffset);\n vec3 v2 = v1 - d;\n\n vec3 u = getOrthogonalVector(d);\n vec3 v = normalize(cross(u, d));\n\n vec3 x = u * cos(angle) * length(d)*0.25;\n vec3 y = v * sin(angle) * length(d)*0.25;\n vec3 v3 = v2 + x + y;\n if (segmentIndex < 3.0) {\n vec3 tx = u * sin(angle);\n vec3 ty = v * -cos(angle);\n vec3 tangent = tx + ty;\n normal = normalize(cross(v3 - v1, tangent));\n }\n\n if (segmentIndex == 0.0) {\n return mix(d, vec3(0.0), coneOffset);\n }\n return v3;\n}\n\nattribute vec4 vector;\nattribute vec4 position;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\nuniform float vectorScale, coneScale, coneOffset;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n vec3 normal;\n vec3 XYZ = getConePosition(mat3(model) * ((vectorScale * coneScale) * vector.xyz), position.w, coneOffset, normal);\n vec4 conePosition = model * vec4(position.xyz, 1.0) + vec4(XYZ, 0.0);\n gl_Position = projection * (view * conePosition);\n f_id = id;\n f_position = position.xyz;\n}\n"]),s=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float pickId;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n\n gl_FragColor = vec4(pickId, f_id.xyz);\n}"]);e.meshShader={vertex:i,fragment:o,attributes:[{name:"position",type:"vec4"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"},{name:"vector",type:"vec3"}]},e.pickShader={vertex:a,fragment:s,attributes:[{name:"position",type:"vec4"},{name:"id",type:"vec4"},{name:"vector",type:"vec3"}]}},737:function(t){t.exports={0:"NONE",1:"ONE",2:"LINE_LOOP",3:"LINE_STRIP",4:"TRIANGLES",5:"TRIANGLE_STRIP",6:"TRIANGLE_FAN",256:"DEPTH_BUFFER_BIT",512:"NEVER",513:"LESS",514:"EQUAL",515:"LEQUAL",516:"GREATER",517:"NOTEQUAL",518:"GEQUAL",519:"ALWAYS",768:"SRC_COLOR",769:"ONE_MINUS_SRC_COLOR",770:"SRC_ALPHA",771:"ONE_MINUS_SRC_ALPHA",772:"DST_ALPHA",773:"ONE_MINUS_DST_ALPHA",774:"DST_COLOR",775:"ONE_MINUS_DST_COLOR",776:"SRC_ALPHA_SATURATE",1024:"STENCIL_BUFFER_BIT",1028:"FRONT",1029:"BACK",1032:"FRONT_AND_BACK",1280:"INVALID_ENUM",1281:"INVALID_VALUE",1282:"INVALID_OPERATION",1285:"OUT_OF_MEMORY",1286:"INVALID_FRAMEBUFFER_OPERATION",2304:"CW",2305:"CCW",2849:"LINE_WIDTH",2884:"CULL_FACE",2885:"CULL_FACE_MODE",2886:"FRONT_FACE",2928:"DEPTH_RANGE",2929:"DEPTH_TEST",2930:"DEPTH_WRITEMASK",2931:"DEPTH_CLEAR_VALUE",2932:"DEPTH_FUNC",2960:"STENCIL_TEST",2961:"STENCIL_CLEAR_VALUE",2962:"STENCIL_FUNC",2963:"STENCIL_VALUE_MASK",2964:"STENCIL_FAIL",2965:"STENCIL_PASS_DEPTH_FAIL",2966:"STENCIL_PASS_DEPTH_PASS",2967:"STENCIL_REF",2968:"STENCIL_WRITEMASK",2978:"VIEWPORT",3024:"DITHER",3042:"BLEND",3088:"SCISSOR_BOX",3089:"SCISSOR_TEST",3106:"COLOR_CLEAR_VALUE",3107:"COLOR_WRITEMASK",3317:"UNPACK_ALIGNMENT",3333:"PACK_ALIGNMENT",3379:"MAX_TEXTURE_SIZE",3386:"MAX_VIEWPORT_DIMS",3408:"SUBPIXEL_BITS",3410:"RED_BITS",3411:"GREEN_BITS",3412:"BLUE_BITS",3413:"ALPHA_BITS",3414:"DEPTH_BITS",3415:"STENCIL_BITS",3553:"TEXTURE_2D",4352:"DONT_CARE",4353:"FASTEST",4354:"NICEST",5120:"BYTE",5121:"UNSIGNED_BYTE",5122:"SHORT",5123:"UNSIGNED_SHORT",5124:"INT",5125:"UNSIGNED_INT",5126:"FLOAT",5386:"INVERT",5890:"TEXTURE",6401:"STENCIL_INDEX",6402:"DEPTH_COMPONENT",6406:"ALPHA",6407:"RGB",6408:"RGBA",6409:"LUMINANCE",6410:"LUMINANCE_ALPHA",7680:"KEEP",7681:"REPLACE",7682:"INCR",7683:"DECR",7936:"VENDOR",7937:"RENDERER",7938:"VERSION",9728:"NEAREST",9729:"LINEAR",9984:"NEAREST_MIPMAP_NEAREST",9985:"LINEAR_MIPMAP_NEAREST",9986:"NEAREST_MIPMAP_LINEAR",9987:"LINEAR_MIPMAP_LINEAR",10240:"TEXTURE_MAG_FILTER",10241:"TEXTURE_MIN_FILTER",10242:"TEXTURE_WRAP_S",10243:"TEXTURE_WRAP_T",10497:"REPEAT",10752:"POLYGON_OFFSET_UNITS",16384:"COLOR_BUFFER_BIT",32769:"CONSTANT_COLOR",32770:"ONE_MINUS_CONSTANT_COLOR",32771:"CONSTANT_ALPHA",32772:"ONE_MINUS_CONSTANT_ALPHA",32773:"BLEND_COLOR",32774:"FUNC_ADD",32777:"BLEND_EQUATION_RGB",32778:"FUNC_SUBTRACT",32779:"FUNC_REVERSE_SUBTRACT",32819:"UNSIGNED_SHORT_4_4_4_4",32820:"UNSIGNED_SHORT_5_5_5_1",32823:"POLYGON_OFFSET_FILL",32824:"POLYGON_OFFSET_FACTOR",32854:"RGBA4",32855:"RGB5_A1",32873:"TEXTURE_BINDING_2D",32926:"SAMPLE_ALPHA_TO_COVERAGE",32928:"SAMPLE_COVERAGE",32936:"SAMPLE_BUFFERS",32937:"SAMPLES",32938:"SAMPLE_COVERAGE_VALUE",32939:"SAMPLE_COVERAGE_INVERT",32968:"BLEND_DST_RGB",32969:"BLEND_SRC_RGB",32970:"BLEND_DST_ALPHA",32971:"BLEND_SRC_ALPHA",33071:"CLAMP_TO_EDGE",33170:"GENERATE_MIPMAP_HINT",33189:"DEPTH_COMPONENT16",33306:"DEPTH_STENCIL_ATTACHMENT",33635:"UNSIGNED_SHORT_5_6_5",33648:"MIRRORED_REPEAT",33901:"ALIASED_POINT_SIZE_RANGE",33902:"ALIASED_LINE_WIDTH_RANGE",33984:"TEXTURE0",33985:"TEXTURE1",33986:"TEXTURE2",33987:"TEXTURE3",33988:"TEXTURE4",33989:"TEXTURE5",33990:"TEXTURE6",33991:"TEXTURE7",33992:"TEXTURE8",33993:"TEXTURE9",33994:"TEXTURE10",33995:"TEXTURE11",33996:"TEXTURE12",33997:"TEXTURE13",33998:"TEXTURE14",33999:"TEXTURE15",34e3:"TEXTURE16",34001:"TEXTURE17",34002:"TEXTURE18",34003:"TEXTURE19",34004:"TEXTURE20",34005:"TEXTURE21",34006:"TEXTURE22",34007:"TEXTURE23",34008:"TEXTURE24",34009:"TEXTURE25",34010:"TEXTURE26",34011:"TEXTURE27",34012:"TEXTURE28",34013:"TEXTURE29",34014:"TEXTURE30",34015:"TEXTURE31",34016:"ACTIVE_TEXTURE",34024:"MAX_RENDERBUFFER_SIZE",34041:"DEPTH_STENCIL",34055:"INCR_WRAP",34056:"DECR_WRAP",34067:"TEXTURE_CUBE_MAP",34068:"TEXTURE_BINDING_CUBE_MAP",34069:"TEXTURE_CUBE_MAP_POSITIVE_X",34070:"TEXTURE_CUBE_MAP_NEGATIVE_X",34071:"TEXTURE_CUBE_MAP_POSITIVE_Y",34072:"TEXTURE_CUBE_MAP_NEGATIVE_Y",34073:"TEXTURE_CUBE_MAP_POSITIVE_Z",34074:"TEXTURE_CUBE_MAP_NEGATIVE_Z",34076:"MAX_CUBE_MAP_TEXTURE_SIZE",34338:"VERTEX_ATTRIB_ARRAY_ENABLED",34339:"VERTEX_ATTRIB_ARRAY_SIZE",34340:"VERTEX_ATTRIB_ARRAY_STRIDE",34341:"VERTEX_ATTRIB_ARRAY_TYPE",34342:"CURRENT_VERTEX_ATTRIB",34373:"VERTEX_ATTRIB_ARRAY_POINTER",34466:"NUM_COMPRESSED_TEXTURE_FORMATS",34467:"COMPRESSED_TEXTURE_FORMATS",34660:"BUFFER_SIZE",34661:"BUFFER_USAGE",34816:"STENCIL_BACK_FUNC",34817:"STENCIL_BACK_FAIL",34818:"STENCIL_BACK_PASS_DEPTH_FAIL",34819:"STENCIL_BACK_PASS_DEPTH_PASS",34877:"BLEND_EQUATION_ALPHA",34921:"MAX_VERTEX_ATTRIBS",34922:"VERTEX_ATTRIB_ARRAY_NORMALIZED",34930:"MAX_TEXTURE_IMAGE_UNITS",34962:"ARRAY_BUFFER",34963:"ELEMENT_ARRAY_BUFFER",34964:"ARRAY_BUFFER_BINDING",34965:"ELEMENT_ARRAY_BUFFER_BINDING",34975:"VERTEX_ATTRIB_ARRAY_BUFFER_BINDING",35040:"STREAM_DRAW",35044:"STATIC_DRAW",35048:"DYNAMIC_DRAW",35632:"FRAGMENT_SHADER",35633:"VERTEX_SHADER",35660:"MAX_VERTEX_TEXTURE_IMAGE_UNITS",35661:"MAX_COMBINED_TEXTURE_IMAGE_UNITS",35663:"SHADER_TYPE",35664:"FLOAT_VEC2",35665:"FLOAT_VEC3",35666:"FLOAT_VEC4",35667:"INT_VEC2",35668:"INT_VEC3",35669:"INT_VEC4",35670:"BOOL",35671:"BOOL_VEC2",35672:"BOOL_VEC3",35673:"BOOL_VEC4",35674:"FLOAT_MAT2",35675:"FLOAT_MAT3",35676:"FLOAT_MAT4",35678:"SAMPLER_2D",35680:"SAMPLER_CUBE",35712:"DELETE_STATUS",35713:"COMPILE_STATUS",35714:"LINK_STATUS",35715:"VALIDATE_STATUS",35716:"INFO_LOG_LENGTH",35717:"ATTACHED_SHADERS",35718:"ACTIVE_UNIFORMS",35719:"ACTIVE_UNIFORM_MAX_LENGTH",35720:"SHADER_SOURCE_LENGTH",35721:"ACTIVE_ATTRIBUTES",35722:"ACTIVE_ATTRIBUTE_MAX_LENGTH",35724:"SHADING_LANGUAGE_VERSION",35725:"CURRENT_PROGRAM",36003:"STENCIL_BACK_REF",36004:"STENCIL_BACK_VALUE_MASK",36005:"STENCIL_BACK_WRITEMASK",36006:"FRAMEBUFFER_BINDING",36007:"RENDERBUFFER_BINDING",36048:"FRAMEBUFFER_ATTACHMENT_OBJECT_TYPE",36049:"FRAMEBUFFER_ATTACHMENT_OBJECT_NAME",36050:"FRAMEBUFFER_ATTACHMENT_TEXTURE_LEVEL",36051:"FRAMEBUFFER_ATTACHMENT_TEXTURE_CUBE_MAP_FACE",36053:"FRAMEBUFFER_COMPLETE",36054:"FRAMEBUFFER_INCOMPLETE_ATTACHMENT",36055:"FRAMEBUFFER_INCOMPLETE_MISSING_ATTACHMENT",36057:"FRAMEBUFFER_INCOMPLETE_DIMENSIONS",36061:"FRAMEBUFFER_UNSUPPORTED",36064:"COLOR_ATTACHMENT0",36096:"DEPTH_ATTACHMENT",36128:"STENCIL_ATTACHMENT",36160:"FRAMEBUFFER",36161:"RENDERBUFFER",36162:"RENDERBUFFER_WIDTH",36163:"RENDERBUFFER_HEIGHT",36164:"RENDERBUFFER_INTERNAL_FORMAT",36168:"STENCIL_INDEX8",36176:"RENDERBUFFER_RED_SIZE",36177:"RENDERBUFFER_GREEN_SIZE",36178:"RENDERBUFFER_BLUE_SIZE",36179:"RENDERBUFFER_ALPHA_SIZE",36180:"RENDERBUFFER_DEPTH_SIZE",36181:"RENDERBUFFER_STENCIL_SIZE",36194:"RGB565",36336:"LOW_FLOAT",36337:"MEDIUM_FLOAT",36338:"HIGH_FLOAT",36339:"LOW_INT",36340:"MEDIUM_INT",36341:"HIGH_INT",36346:"SHADER_COMPILER",36347:"MAX_VERTEX_UNIFORM_VECTORS",36348:"MAX_VARYING_VECTORS",36349:"MAX_FRAGMENT_UNIFORM_VECTORS",37440:"UNPACK_FLIP_Y_WEBGL",37441:"UNPACK_PREMULTIPLY_ALPHA_WEBGL",37442:"CONTEXT_LOST_WEBGL",37443:"UNPACK_COLORSPACE_CONVERSION_WEBGL",37444:"BROWSER_DEFAULT_WEBGL"}},5171:function(t,e,r){var n=r(737);t.exports=function(t){return n[t]}},9165:function(t,e,r){"use strict";t.exports=function(t){var e=t.gl,r=n(e),a=i(e,[{buffer:r,type:e.FLOAT,size:3,offset:0,stride:40},{buffer:r,type:e.FLOAT,size:4,offset:12,stride:40},{buffer:r,type:e.FLOAT,size:3,offset:28,stride:40}]),l=o(e);l.attributes.position.location=0,l.attributes.color.location=1,l.attributes.offset.location=2;var c=new s(e,r,a,l);return c.update(t),c};var n=r(2762),i=r(8116),o=r(3436),a=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1];function s(t,e,r,n){this.gl=t,this.shader=n,this.buffer=e,this.vao=r,this.pixelRatio=1,this.bounds=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.lineWidth=[1,1,1],this.capSize=[10,10,10],this.lineCount=[0,0,0],this.lineOffset=[0,0,0],this.opacity=1,this.hasAlpha=!1}var l=s.prototype;function c(t,e){for(var r=0;r<3;++r)t[0][r]=Math.min(t[0][r],e[r]),t[1][r]=Math.max(t[1][r],e[r])}l.isOpaque=function(){return!this.hasAlpha},l.isTransparent=function(){return this.hasAlpha},l.drawTransparent=l.draw=function(t){var e=this.gl,r=this.shader.uniforms;this.shader.bind();var n=r.view=t.view||a,i=r.projection=t.projection||a;r.model=t.model||a,r.clipBounds=this.clipBounds,r.opacity=this.opacity;var o=n[12],s=n[13],l=n[14],c=n[15],u=(t._ortho?2:1)*this.pixelRatio*(i[3]*o+i[7]*s+i[11]*l+i[15]*c)/e.drawingBufferHeight;this.vao.bind();for(var h=0;h<3;++h)e.lineWidth(this.lineWidth[h]*this.pixelRatio),r.capSize=this.capSize[h]*u,this.lineCount[h]&&e.drawArrays(e.LINES,this.lineOffset[h],this.lineCount[h]);this.vao.unbind()};var u=function(){for(var t=new Array(3),e=0;e<3;++e){for(var r=[],n=1;n<=2;++n)for(var i=-1;i<=1;i+=2){var o=[0,0,0];o[(n+e)%3]=i,r.push(o)}t[e]=r}return t}();function h(t,e,r,n){for(var i=u[n],o=0;o0&&((f=u.slice())[s]+=p[1][s],i.push(u[0],u[1],u[2],m[0],m[1],m[2],m[3],0,0,0,f[0],f[1],f[2],m[0],m[1],m[2],m[3],0,0,0),c(this.bounds,f),a+=2+h(i,f,m,s))}this.lineCount[s]=a-this.lineOffset[s]}this.buffer.update(i)}},l.dispose=function(){this.shader.dispose(),this.buffer.dispose(),this.vao.dispose()}},3436:function(t,e,r){"use strict";var n=r(3236),i=r(9405),o=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position, offset;\nattribute vec4 color;\nuniform mat4 model, view, projection;\nuniform float capSize;\nvarying vec4 fragColor;\nvarying vec3 fragPosition;\n\nvoid main() {\n vec4 worldPosition = model * vec4(position, 1.0);\n worldPosition = (worldPosition / worldPosition.w) + vec4(capSize * offset, 0.0);\n gl_Position = projection * (view * worldPosition);\n fragColor = color;\n fragPosition = position;\n}"]),a=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float opacity;\nvarying vec3 fragPosition;\nvarying vec4 fragColor;\n\nvoid main() {\n if (\n outOfRange(clipBounds[0], clipBounds[1], fragPosition) ||\n fragColor.a * opacity == 0.\n ) discard;\n\n gl_FragColor = opacity * fragColor;\n}"]);t.exports=function(t){return i(t,o,a,null,[{name:"position",type:"vec3"},{name:"color",type:"vec4"},{name:"offset",type:"vec3"}])}},2260:function(t,e,r){"use strict";var n=r(7766);t.exports=function(t,e,r,n){i||(i=t.FRAMEBUFFER_UNSUPPORTED,o=t.FRAMEBUFFER_INCOMPLETE_ATTACHMENT,a=t.FRAMEBUFFER_INCOMPLETE_DIMENSIONS,s=t.FRAMEBUFFER_INCOMPLETE_MISSING_ATTACHMENT);var c=t.getExtension("WEBGL_draw_buffers");if(!l&&c&&function(t,e){var r=t.getParameter(e.MAX_COLOR_ATTACHMENTS_WEBGL);l=new Array(r+1);for(var n=0;n<=r;++n){for(var i=new Array(r),o=0;ou||r<0||r>u)throw new Error("gl-fbo: Parameters are too large for FBO");var h=1;if("color"in(n=n||{})){if((h=Math.max(0|n.color,0))<0)throw new Error("gl-fbo: Must specify a nonnegative number of colors");if(h>1){if(!c)throw new Error("gl-fbo: Multiple draw buffer extension not supported");if(h>t.getParameter(c.MAX_COLOR_ATTACHMENTS_WEBGL))throw new Error("gl-fbo: Context does not support "+h+" draw buffers")}}var d=t.UNSIGNED_BYTE,f=t.getExtension("OES_texture_float");if(n.float&&h>0){if(!f)throw new Error("gl-fbo: Context does not support floating point textures");d=t.FLOAT}else n.preferFloat&&h>0&&f&&(d=t.FLOAT);var m=!0;"depth"in n&&(m=!!n.depth);var g=!1;return"stencil"in n&&(g=!!n.stencil),new p(t,e,r,d,h,m,g,c)};var i,o,a,s,l=null;function c(t){return[t.getParameter(t.FRAMEBUFFER_BINDING),t.getParameter(t.RENDERBUFFER_BINDING),t.getParameter(t.TEXTURE_BINDING_2D)]}function u(t,e){t.bindFramebuffer(t.FRAMEBUFFER,e[0]),t.bindRenderbuffer(t.RENDERBUFFER,e[1]),t.bindTexture(t.TEXTURE_2D,e[2])}function h(t){switch(t){case i:throw new Error("gl-fbo: Framebuffer unsupported");case o:throw new Error("gl-fbo: Framebuffer incomplete attachment");case a:throw new Error("gl-fbo: Framebuffer incomplete dimensions");case s:throw new Error("gl-fbo: Framebuffer incomplete missing attachment");default:throw new Error("gl-fbo: Framebuffer failed for unspecified reason")}}function d(t,e,r,i,o,a){if(!i)return null;var s=n(t,e,r,o,i);return s.magFilter=t.NEAREST,s.minFilter=t.NEAREST,s.mipSamples=1,s.bind(),t.framebufferTexture2D(t.FRAMEBUFFER,a,t.TEXTURE_2D,s.handle,0),s}function f(t,e,r,n,i){var o=t.createRenderbuffer();return t.bindRenderbuffer(t.RENDERBUFFER,o),t.renderbufferStorage(t.RENDERBUFFER,n,e,r),t.framebufferRenderbuffer(t.FRAMEBUFFER,i,t.RENDERBUFFER,o),o}function p(t,e,r,n,i,o,a,s){this.gl=t,this._shape=[0|e,0|r],this._destroyed=!1,this._ext=s,this.color=new Array(i);for(var p=0;p1&&s.drawBuffersWEBGL(l[a]);var b=r.getExtension("WEBGL_depth_texture");b?p?t.depth=d(r,i,o,b.UNSIGNED_INT_24_8_WEBGL,r.DEPTH_STENCIL,r.DEPTH_STENCIL_ATTACHMENT):m&&(t.depth=d(r,i,o,r.UNSIGNED_SHORT,r.DEPTH_COMPONENT,r.DEPTH_ATTACHMENT)):m&&p?t._depth_rb=f(r,i,o,r.DEPTH_STENCIL,r.DEPTH_STENCIL_ATTACHMENT):m?t._depth_rb=f(r,i,o,r.DEPTH_COMPONENT16,r.DEPTH_ATTACHMENT):p&&(t._depth_rb=f(r,i,o,r.STENCIL_INDEX,r.STENCIL_ATTACHMENT));var y=r.checkFramebufferStatus(r.FRAMEBUFFER);if(y!==r.FRAMEBUFFER_COMPLETE){for(t._destroyed=!0,r.bindFramebuffer(r.FRAMEBUFFER,null),r.deleteFramebuffer(t.handle),t.handle=null,t.depth&&(t.depth.dispose(),t.depth=null),t._depth_rb&&(r.deleteRenderbuffer(t._depth_rb),t._depth_rb=null),v=0;vi||r<0||r>i)throw new Error("gl-fbo: Can't resize FBO, invalid dimensions");t._shape[0]=e,t._shape[1]=r;for(var o=c(n),a=0;a>8*f&255;this.pickOffset=r,i.bind();var p=i.uniforms;p.viewTransform=t,p.pickOffset=e,p.shape=this.shape;var m=i.attributes;return this.positionBuffer.bind(),m.position.pointer(),this.weightBuffer.bind(),m.weight.pointer(s.UNSIGNED_BYTE,!1),this.idBuffer.bind(),m.pickId.pointer(s.UNSIGNED_BYTE,!1),s.drawArrays(s.TRIANGLES,0,a),r+this.shape[0]*this.shape[1]}}}(),h.pick=function(t,e,r){var n=this.pickOffset,i=this.shape[0]*this.shape[1];if(r=n+i)return null;var o=r-n,a=this.xData,s=this.yData;return{object:this,pointId:o,dataCoord:[a[o%this.shape[0]],s[o/this.shape[0]|0]]}},h.update=function(t){var e=(t=t||{}).shape||[0,0],r=t.x||i(e[0]),a=t.y||i(e[1]),s=t.z||new Float32Array(e[0]*e[1]),l=!1!==t.zsmooth;this.xData=r,this.yData=a;var c,u,h,f,p=t.colorLevels||[0],m=t.colorValues||[0,0,0,1],g=p.length,v=this.bounds;l?(c=v[0]=r[0],u=v[1]=a[0],h=v[2]=r[r.length-1],f=v[3]=a[a.length-1]):(c=v[0]=r[0]+(r[1]-r[0])/2,u=v[1]=a[0]+(a[1]-a[0])/2,h=v[2]=r[r.length-1]+(r[r.length-1]-r[r.length-2])/2,f=v[3]=a[a.length-1]+(a[a.length-1]-a[a.length-2])/2);var b=1/(h-c),y=1/(f-u),x=e[0],_=e[1];this.shape=[x,_];var w=(l?(x-1)*(_-1):x*_)*(d.length>>>1);this.numVertices=w;for(var k=o.mallocUint8(4*w),A=o.mallocFloat32(2*w),M=o.mallocUint8(2*w),T=o.mallocUint32(w),S=0,C=l?x-1:x,E=l?_-1:_,L=0;L max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform sampler2D dashTexture;\nuniform float dashScale;\nuniform float opacity;\n\nvarying vec3 worldPosition;\nvarying float pixelArcLength;\nvarying vec4 fragColor;\n\nvoid main() {\n if (\n outOfRange(clipBounds[0], clipBounds[1], worldPosition) ||\n fragColor.a * opacity == 0.\n ) discard;\n\n float dashWeight = texture2D(dashTexture, vec2(dashScale * pixelArcLength, 0)).r;\n if(dashWeight < 0.5) {\n discard;\n }\n gl_FragColor = fragColor * opacity;\n}\n"]),s=n(["precision highp float;\n#define GLSLIFY 1\n\n#define FLOAT_MAX 1.70141184e38\n#define FLOAT_MIN 1.17549435e-38\n\n// https://github.com/mikolalysenko/glsl-read-float/blob/master/index.glsl\nvec4 packFloat(float v) {\n float av = abs(v);\n\n //Handle special cases\n if(av < FLOAT_MIN) {\n return vec4(0.0, 0.0, 0.0, 0.0);\n } else if(v > FLOAT_MAX) {\n return vec4(127.0, 128.0, 0.0, 0.0) / 255.0;\n } else if(v < -FLOAT_MAX) {\n return vec4(255.0, 128.0, 0.0, 0.0) / 255.0;\n }\n\n vec4 c = vec4(0,0,0,0);\n\n //Compute exponent and mantissa\n float e = floor(log2(av));\n float m = av * pow(2.0, -e) - 1.0;\n\n //Unpack mantissa\n c[1] = floor(128.0 * m);\n m -= c[1] / 128.0;\n c[2] = floor(32768.0 * m);\n m -= c[2] / 32768.0;\n c[3] = floor(8388608.0 * m);\n\n //Unpack exponent\n float ebias = e + 127.0;\n c[0] = floor(ebias / 2.0);\n ebias -= c[0] * 2.0;\n c[1] += floor(ebias) * 128.0;\n\n //Unpack sign bit\n c[0] += 128.0 * step(0.0, -v);\n\n //Scale back to range\n return c / 255.0;\n}\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform float pickId;\nuniform vec3 clipBounds[2];\n\nvarying vec3 worldPosition;\nvarying float pixelArcLength;\nvarying vec4 fragColor;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], worldPosition)) discard;\n\n gl_FragColor = vec4(pickId/255.0, packFloat(pixelArcLength).xyz);\n}"]),l=[{name:"position",type:"vec3"},{name:"nextPosition",type:"vec3"},{name:"arcLength",type:"float"},{name:"lineWidth",type:"float"},{name:"color",type:"vec4"}];e.createShader=function(t){return i(t,o,a,null,l)},e.createPickShader=function(t){return i(t,o,s,null,l)}},5714:function(t,e,r){"use strict";t.exports=function(t){var e=t.gl||t.scene&&t.scene.gl,r=h(e);r.attributes.position.location=0,r.attributes.nextPosition.location=1,r.attributes.arcLength.location=2,r.attributes.lineWidth.location=3,r.attributes.color.location=4;var a=d(e);a.attributes.position.location=0,a.attributes.nextPosition.location=1,a.attributes.arcLength.location=2,a.attributes.lineWidth.location=3,a.attributes.color.location=4;for(var s=n(e),l=i(e,[{buffer:s,size:3,offset:0,stride:48},{buffer:s,size:3,offset:12,stride:48},{buffer:s,size:1,offset:24,stride:48},{buffer:s,size:1,offset:28,stride:48},{buffer:s,size:4,offset:32,stride:48}]),u=c(new Array(1024),[256,1,4]),f=0;f<1024;++f)u.data[f]=255;var p=o(e,u);p.wrap=e.REPEAT;var m=new v(e,r,a,s,l,p);return m.update(t),m};var n=r(2762),i=r(8116),o=r(7766),a=new Uint8Array(4),s=new Float32Array(a.buffer),l=r(2478),c=r(9618),u=r(7319),h=u.createShader,d=u.createPickShader,f=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1];function p(t,e){for(var r=0,n=0;n<3;++n){var i=t[n]-e[n];r+=i*i}return Math.sqrt(r)}function m(t){for(var e=[[-1e6,-1e6,-1e6],[1e6,1e6,1e6]],r=0;r<3;++r)e[0][r]=Math.max(t[0][r],e[0][r]),e[1][r]=Math.min(t[1][r],e[1][r]);return e}function g(t,e,r,n){this.arcLength=t,this.position=e,this.index=r,this.dataCoordinate=n}function v(t,e,r,n,i,o){this.gl=t,this.shader=e,this.pickShader=r,this.buffer=n,this.vao=i,this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.points=[],this.arcLength=[],this.vertexCount=0,this.bounds=[[0,0,0],[0,0,0]],this.pickId=0,this.lineWidth=1,this.texture=o,this.dashScale=1,this.opacity=1,this.hasAlpha=!1,this.dirty=!0,this.pixelRatio=1}var b=v.prototype;b.isTransparent=function(){return this.hasAlpha},b.isOpaque=function(){return!this.hasAlpha},b.pickSlots=1,b.setPickBase=function(t){this.pickId=t},b.drawTransparent=b.draw=function(t){if(this.vertexCount){var e=this.gl,r=this.shader,n=this.vao;r.bind(),r.uniforms={model:t.model||f,view:t.view||f,projection:t.projection||f,clipBounds:m(this.clipBounds),dashTexture:this.texture.bind(),dashScale:this.dashScale/this.arcLength[this.arcLength.length-1],opacity:this.opacity,screenShape:[e.drawingBufferWidth,e.drawingBufferHeight],pixelRatio:this.pixelRatio},n.bind(),n.draw(e.TRIANGLE_STRIP,this.vertexCount),n.unbind()}},b.drawPick=function(t){if(this.vertexCount){var e=this.gl,r=this.pickShader,n=this.vao;r.bind(),r.uniforms={model:t.model||f,view:t.view||f,projection:t.projection||f,pickId:this.pickId,clipBounds:m(this.clipBounds),screenShape:[e.drawingBufferWidth,e.drawingBufferHeight],pixelRatio:this.pixelRatio},n.bind(),n.draw(e.TRIANGLE_STRIP,this.vertexCount),n.unbind()}},b.update=function(t){var e,r;this.dirty=!0;var n=!!t.connectGaps;"dashScale"in t&&(this.dashScale=t.dashScale),this.hasAlpha=!1,"opacity"in t&&(this.opacity=+t.opacity,this.opacity<1&&(this.hasAlpha=!0));var i=[],o=[],a=[],s=0,u=0,h=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],d=t.position||t.positions;if(d){var f=t.color||t.colors||[0,0,0,1],m=t.lineWidth||1,g=!1;t:for(e=1;e0){for(var w=0;w<24;++w)i.push(i[i.length-12]);u+=2,g=!0}continue t}h[0][r]=Math.min(h[0][r],x[r],_[r]),h[1][r]=Math.max(h[1][r],x[r],_[r])}Array.isArray(f[0])?(v=f.length>e-1?f[e-1]:f.length>0?f[f.length-1]:[0,0,0,1],b=f.length>e?f[e]:f.length>0?f[f.length-1]:[0,0,0,1]):v=b=f,3===v.length&&(v=[v[0],v[1],v[2],1]),3===b.length&&(b=[b[0],b[1],b[2],1]),!this.hasAlpha&&v[3]<1&&(this.hasAlpha=!0),y=Array.isArray(m)?m.length>e-1?m[e-1]:m.length>0?m[m.length-1]:[0,0,0,1]:m;var k=s;if(s+=p(x,_),g){for(r=0;r<2;++r)i.push(x[0],x[1],x[2],_[0],_[1],_[2],k,y,v[0],v[1],v[2],v[3]);u+=2,g=!1}i.push(x[0],x[1],x[2],_[0],_[1],_[2],k,y,v[0],v[1],v[2],v[3],x[0],x[1],x[2],_[0],_[1],_[2],k,-y,v[0],v[1],v[2],v[3],_[0],_[1],_[2],x[0],x[1],x[2],s,-y,b[0],b[1],b[2],b[3],_[0],_[1],_[2],x[0],x[1],x[2],s,y,b[0],b[1],b[2],b[3]),u+=4}}if(this.buffer.update(i),o.push(s),a.push(d[d.length-1].slice()),this.bounds=h,this.vertexCount=u,this.points=a,this.arcLength=o,"dashes"in t){var A=t.dashes.slice();for(A.unshift(0),e=1;e1.0001)return null;v+=g[h]}return Math.abs(v-1)>.001?null:[d,s(t,g),g]}},840:function(t,e,r){var n=r(3236),i=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position, normal;\nattribute vec4 color;\nattribute vec2 uv;\n\nuniform mat4 model\n , view\n , projection\n , inverseModel;\nuniform vec3 eyePosition\n , lightPosition;\n\nvarying vec3 f_normal\n , f_lightDirection\n , f_eyeDirection\n , f_data;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvec4 project(vec3 p) {\n return projection * (view * (model * vec4(p, 1.0)));\n}\n\nvoid main() {\n gl_Position = project(position);\n\n //Lighting geometry parameters\n vec4 cameraCoordinate = view * vec4(position , 1.0);\n cameraCoordinate.xyz /= cameraCoordinate.w;\n f_lightDirection = lightPosition - cameraCoordinate.xyz;\n f_eyeDirection = eyePosition - cameraCoordinate.xyz;\n f_normal = normalize((vec4(normal, 0.0) * inverseModel).xyz);\n\n f_color = color;\n f_data = position;\n f_uv = uv;\n}\n"]),o=n(["#extension GL_OES_standard_derivatives : enable\n\nprecision highp float;\n#define GLSLIFY 1\n\nfloat beckmannDistribution(float x, float roughness) {\n float NdotH = max(x, 0.0001);\n float cos2Alpha = NdotH * NdotH;\n float tan2Alpha = (cos2Alpha - 1.0) / cos2Alpha;\n float roughness2 = roughness * roughness;\n float denom = 3.141592653589793 * roughness2 * cos2Alpha * cos2Alpha;\n return exp(tan2Alpha / roughness2) / denom;\n}\n\nfloat cookTorranceSpecular(\n vec3 lightDirection,\n vec3 viewDirection,\n vec3 surfaceNormal,\n float roughness,\n float fresnel) {\n\n float VdotN = max(dot(viewDirection, surfaceNormal), 0.0);\n float LdotN = max(dot(lightDirection, surfaceNormal), 0.0);\n\n //Half angle vector\n vec3 H = normalize(lightDirection + viewDirection);\n\n //Geometric term\n float NdotH = max(dot(surfaceNormal, H), 0.0);\n float VdotH = max(dot(viewDirection, H), 0.000001);\n float LdotH = max(dot(lightDirection, H), 0.000001);\n float G1 = (2.0 * NdotH * VdotN) / VdotH;\n float G2 = (2.0 * NdotH * LdotN) / LdotH;\n float G = min(1.0, min(G1, G2));\n \n //Distribution term\n float D = beckmannDistribution(NdotH, roughness);\n\n //Fresnel term\n float F = pow(1.0 - VdotN, fresnel);\n\n //Multiply terms and done\n return G * F * D / max(3.14159265 * VdotN, 0.000001);\n}\n\n//#pragma glslify: beckmann = require(glsl-specular-beckmann) // used in gl-surface3d\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float roughness\n , fresnel\n , kambient\n , kdiffuse\n , kspecular;\nuniform sampler2D texture;\n\nvarying vec3 f_normal\n , f_lightDirection\n , f_eyeDirection\n , f_data;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n if (f_color.a == 0.0 ||\n outOfRange(clipBounds[0], clipBounds[1], f_data)\n ) discard;\n\n vec3 N = normalize(f_normal);\n vec3 L = normalize(f_lightDirection);\n vec3 V = normalize(f_eyeDirection);\n\n if(gl_FrontFacing) {\n N = -N;\n }\n\n float specular = min(1.0, max(0.0, cookTorranceSpecular(L, V, N, roughness, fresnel)));\n //float specular = max(0.0, beckmann(L, V, N, roughness)); // used in gl-surface3d\n\n float diffuse = min(kambient + kdiffuse * max(dot(N, L), 0.0), 1.0);\n\n vec4 surfaceColor = vec4(f_color.rgb, 1.0) * texture2D(texture, f_uv);\n vec4 litColor = surfaceColor.a * vec4(diffuse * surfaceColor.rgb + kspecular * vec3(1,1,1) * specular, 1.0);\n\n gl_FragColor = litColor * f_color.a;\n}\n"]),a=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 uv;\n\nuniform mat4 model, view, projection;\n\nvarying vec4 f_color;\nvarying vec3 f_data;\nvarying vec2 f_uv;\n\nvoid main() {\n gl_Position = projection * (view * (model * vec4(position, 1.0)));\n f_color = color;\n f_data = position;\n f_uv = uv;\n}"]),s=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform sampler2D texture;\nuniform float opacity;\n\nvarying vec4 f_color;\nvarying vec3 f_data;\nvarying vec2 f_uv;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_data)) discard;\n\n gl_FragColor = f_color * texture2D(texture, f_uv) * opacity;\n}"]),l=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 uv;\nattribute float pointSize;\n\nuniform mat4 model, view, projection;\nuniform vec3 clipBounds[2];\n\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0.0, 0.0 ,0.0 ,0.0);\n } else {\n gl_Position = projection * (view * (model * vec4(position, 1.0)));\n }\n gl_PointSize = pointSize;\n f_color = color;\n f_uv = uv;\n}"]),c=n(["precision highp float;\n#define GLSLIFY 1\n\nuniform sampler2D texture;\nuniform float opacity;\n\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n vec2 pointR = gl_PointCoord.xy - vec2(0.5, 0.5);\n if(dot(pointR, pointR) > 0.25) {\n discard;\n }\n gl_FragColor = f_color * texture2D(texture, f_uv) * opacity;\n}"]),u=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n gl_Position = projection * (view * (model * vec4(position, 1.0)));\n f_id = id;\n f_position = position;\n}"]),h=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float pickId;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n\n gl_FragColor = vec4(pickId, f_id.xyz);\n}"]),d=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute float pointSize;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\nuniform vec3 clipBounds[2];\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0.0, 0.0, 0.0, 0.0);\n } else {\n gl_Position = projection * (view * (model * vec4(position, 1.0)));\n gl_PointSize = pointSize;\n }\n f_id = id;\n f_position = position;\n}"]),f=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position;\n\nuniform mat4 model, view, projection;\n\nvoid main() {\n gl_Position = projection * (view * (model * vec4(position, 1.0)));\n}"]),p=n(["precision highp float;\n#define GLSLIFY 1\n\nuniform vec3 contourColor;\n\nvoid main() {\n gl_FragColor = vec4(contourColor, 1.0);\n}\n"]);e.meshShader={vertex:i,fragment:o,attributes:[{name:"position",type:"vec3"},{name:"normal",type:"vec3"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"}]},e.wireShader={vertex:a,fragment:s,attributes:[{name:"position",type:"vec3"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"}]},e.pointShader={vertex:l,fragment:c,attributes:[{name:"position",type:"vec3"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"},{name:"pointSize",type:"float"}]},e.pickShader={vertex:u,fragment:h,attributes:[{name:"position",type:"vec3"},{name:"id",type:"vec4"}]},e.pointPickShader={vertex:d,fragment:h,attributes:[{name:"position",type:"vec3"},{name:"pointSize",type:"float"},{name:"id",type:"vec4"}]},e.contourShader={vertex:f,fragment:p,attributes:[{name:"position",type:"vec3"}]}},7201:function(t,e,r){"use strict";var n=r(9405),i=r(2762),o=r(8116),a=r(7766),s=r(8406),l=r(6760),c=r(7608),u=r(9618),h=r(6729),d=r(7765),f=r(1888),p=r(840),m=r(7626),g=p.meshShader,v=p.wireShader,b=p.pointShader,y=p.pickShader,x=p.pointPickShader,_=p.contourShader,w=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1];function k(t,e,r,n,i,o,a,s,l,c,u,h,d,f,p,m,g,v,b,y,x,_,k,A,M,T,S){this.gl=t,this.pixelRatio=1,this.cells=[],this.positions=[],this.intensity=[],this.texture=e,this.dirty=!0,this.triShader=r,this.lineShader=n,this.pointShader=i,this.pickShader=o,this.pointPickShader=a,this.contourShader=s,this.trianglePositions=l,this.triangleColors=u,this.triangleNormals=d,this.triangleUVs=h,this.triangleIds=c,this.triangleVAO=f,this.triangleCount=0,this.lineWidth=1,this.edgePositions=p,this.edgeColors=g,this.edgeUVs=v,this.edgeIds=m,this.edgeVAO=b,this.edgeCount=0,this.pointPositions=y,this.pointColors=_,this.pointUVs=k,this.pointSizes=A,this.pointIds=x,this.pointVAO=M,this.pointCount=0,this.contourLineWidth=1,this.contourPositions=T,this.contourVAO=S,this.contourCount=0,this.contourColor=[0,0,0],this.contourEnable=!0,this.pickVertex=!0,this.pickId=1,this.bounds=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.lightPosition=[1e5,1e5,0],this.ambientLight=.8,this.diffuseLight=.8,this.specularLight=2,this.roughness=.5,this.fresnel=1.5,this.opacity=1,this.hasAlpha=!1,this.opacityscale=!1,this._model=w,this._view=w,this._projection=w,this._resolution=[1,1]}var A=k.prototype;function M(t,e){if(!e)return 1;if(!e.length)return 1;for(var r=0;rt&&r>0){var n=(e[r][0]-t)/(e[r][0]-e[r-1][0]);return e[r][1]*(1-n)+n*e[r-1][1]}}return 1}function T(t){var e=n(t,b.vertex,b.fragment);return e.attributes.position.location=0,e.attributes.color.location=2,e.attributes.uv.location=3,e.attributes.pointSize.location=4,e}function S(t){var e=n(t,y.vertex,y.fragment);return e.attributes.position.location=0,e.attributes.id.location=1,e}function C(t){var e=n(t,x.vertex,x.fragment);return e.attributes.position.location=0,e.attributes.id.location=1,e.attributes.pointSize.location=4,e}function E(t){var e=n(t,_.vertex,_.fragment);return e.attributes.position.location=0,e}A.isOpaque=function(){return!this.hasAlpha},A.isTransparent=function(){return this.hasAlpha},A.pickSlots=1,A.setPickBase=function(t){this.pickId=t},A.highlight=function(t){if(t&&this.contourEnable){for(var e=d(this.cells,this.intensity,t.intensity),r=e.cells,n=e.vertexIds,i=e.vertexWeights,o=r.length,a=f.mallocFloat32(6*o),s=0,l=0;l0&&((h=this.triShader).bind(),h.uniforms=s,this.triangleVAO.bind(),e.drawArrays(e.TRIANGLES,0,3*this.triangleCount),this.triangleVAO.unbind()),this.edgeCount>0&&this.lineWidth>0&&((h=this.lineShader).bind(),h.uniforms=s,this.edgeVAO.bind(),e.lineWidth(this.lineWidth*this.pixelRatio),e.drawArrays(e.LINES,0,2*this.edgeCount),this.edgeVAO.unbind()),this.pointCount>0&&((h=this.pointShader).bind(),h.uniforms=s,this.pointVAO.bind(),e.drawArrays(e.POINTS,0,this.pointCount),this.pointVAO.unbind()),this.contourEnable&&this.contourCount>0&&this.contourLineWidth>0&&((h=this.contourShader).bind(),h.uniforms=s,this.contourVAO.bind(),e.drawArrays(e.LINES,0,this.contourCount),this.contourVAO.unbind())},A.drawPick=function(t){t=t||{};for(var e=this.gl,r=t.model||w,n=t.view||w,i=t.projection||w,o=[[-1e6,-1e6,-1e6],[1e6,1e6,1e6]],a=0;a<3;++a)o[0][a]=Math.max(o[0][a],this.clipBounds[0][a]),o[1][a]=Math.min(o[1][a],this.clipBounds[1][a]);this._model=[].slice.call(r),this._view=[].slice.call(n),this._projection=[].slice.call(i),this._resolution=[e.drawingBufferWidth,e.drawingBufferHeight];var s,l={model:r,view:n,projection:i,clipBounds:o,pickId:this.pickId/255};(s=this.pickShader).bind(),s.uniforms=l,this.triangleCount>0&&(this.triangleVAO.bind(),e.drawArrays(e.TRIANGLES,0,3*this.triangleCount),this.triangleVAO.unbind()),this.edgeCount>0&&(this.edgeVAO.bind(),e.lineWidth(this.lineWidth*this.pixelRatio),e.drawArrays(e.LINES,0,2*this.edgeCount),this.edgeVAO.unbind()),this.pointCount>0&&((s=this.pointPickShader).bind(),s.uniforms=l,this.pointVAO.bind(),e.drawArrays(e.POINTS,0,this.pointCount),this.pointVAO.unbind())},A.pick=function(t){if(!t)return null;if(t.id!==this.pickId)return null;for(var e=t.value[0]+256*t.value[1]+65536*t.value[2],r=this.cells[e],n=this.positions,i=new Array(r.length),o=0;oi[A]&&(r.uniforms.dataAxis=c,r.uniforms.screenOffset=u,r.uniforms.color=g[t],r.uniforms.angle=v[t],o.drawArrays(o.TRIANGLES,i[A],i[M]-i[A]))),b[t]&&k&&(u[1^t]-=T*f*y[t],r.uniforms.dataAxis=h,r.uniforms.screenOffset=u,r.uniforms.color=x[t],r.uniforms.angle=_[t],o.drawArrays(o.TRIANGLES,w,k)),u[1^t]=T*s[2+(1^t)]-1,p[t+2]&&(u[1^t]+=T*f*m[t+2],Ai[A]&&(r.uniforms.dataAxis=c,r.uniforms.screenOffset=u,r.uniforms.color=g[t+2],r.uniforms.angle=v[t+2],o.drawArrays(o.TRIANGLES,i[A],i[M]-i[A]))),b[t+2]&&k&&(u[1^t]+=T*f*y[t+2],r.uniforms.dataAxis=h,r.uniforms.screenOffset=u,r.uniforms.color=x[t+2],r.uniforms.angle=_[t+2],o.drawArrays(o.TRIANGLES,w,k))}),m.drawTitle=function(){var t=[0,0],e=[0,0];return function(){var r=this.plot,n=this.shader,i=r.gl,o=r.screenBox,a=r.titleCenter,s=r.titleAngle,l=r.titleColor,c=r.pixelRatio;if(this.titleCount){for(var u=0;u<2;++u)e[u]=2*(a[u]*c-o[u])/(o[2+u]-o[u])-1;n.bind(),n.uniforms.dataAxis=t,n.uniforms.screenOffset=e,n.uniforms.angle=s,n.uniforms.color=l,i.drawArrays(i.TRIANGLES,this.titleOffset,this.titleCount)}}}(),m.bind=(d=[0,0],f=[0,0],p=[0,0],function(){var t=this.plot,e=this.shader,r=t._tickBounds,n=t.dataBox,i=t.screenBox,o=t.viewBox;e.bind();for(var a=0;a<2;++a){var s=r[a],l=r[a+2]-s,c=.5*(n[a+2]+n[a]),u=n[a+2]-n[a],h=o[a],m=o[a+2]-h,g=i[a],v=i[a+2]-g;f[a]=2*l/u*m/v,d[a]=2*(s-c)/u*m/v}p[1]=2*t.pixelRatio/(i[3]-i[1]),p[0]=p[1]*(i[3]-i[1])/(i[2]-i[0]),e.uniforms.dataScale=f,e.uniforms.dataShift=d,e.uniforms.textScale=p,this.vbo.bind(),e.attributes.textCoordinate.pointer()}),m.update=function(t){var e,r,n,i,a,s=[],l=t.ticks,c=t.bounds;for(a=0;a<2;++a){var u=[Math.floor(s.length/3)],h=[-1/0],d=l[a];for(e=0;e=0){var m=e[p]-n[p]*(e[p+2]-e[p])/(n[p+2]-n[p]);0===p?a.drawLine(m,e[1],m,e[3],f[p],d[p]):a.drawLine(e[0],m,e[2],m,f[p],d[p])}}for(p=0;p=0;--t)this.objects[t].dispose();for(this.objects.length=0,t=this.overlays.length-1;t>=0;--t)this.overlays[t].dispose();this.overlays.length=0,this.gl=null},c.addObject=function(t){this.objects.indexOf(t)<0&&(this.objects.push(t),this.setDirty())},c.removeObject=function(t){for(var e=this.objects,r=0;rMath.abs(e))c.rotate(o,0,0,-t*r*Math.PI*p.rotateSpeed/window.innerWidth);else if(!p._ortho){var a=-p.zoomSpeed*i*e/window.innerHeight*(o-c.lastT())/20;c.pan(o,0,0,h*(Math.exp(a)-1))}}}),!0)},p.enableMouseListeners(),p};var n=r(3025),i=r(6296),o=r(351),a=r(8512),s=r(24),l=r(7520)},799:function(t,e,r){var n=r(3236),i=r(9405),o=n(["precision mediump float;\n#define GLSLIFY 1\nattribute vec2 position;\nvarying vec2 uv;\nvoid main() {\n uv = position;\n gl_Position = vec4(position, 0, 1);\n}"]),a=n(["precision mediump float;\n#define GLSLIFY 1\n\nuniform sampler2D accumBuffer;\nvarying vec2 uv;\n\nvoid main() {\n vec4 accum = texture2D(accumBuffer, 0.5 * (uv + 1.0));\n gl_FragColor = min(vec4(1,1,1,1), accum);\n}"]);t.exports=function(t){return i(t,o,a,null,[{name:"position",type:"vec2"}])}},4100:function(t,e,r){"use strict";var n=r(4437),i=r(3837),o=r(5445),a=r(4449),s=r(3589),l=r(2260),c=r(7169),u=r(351),h=r(4772),d=r(4040),f=r(799),p=r(9216)({tablet:!0,featureDetect:!0});function m(){this.mouse=[-1,-1],this.screen=null,this.distance=1/0,this.index=null,this.dataCoordinate=null,this.dataPosition=null,this.object=null,this.data=null}function g(t){var e=Math.round(Math.log(Math.abs(t))/Math.log(10));if(e<0){var r=Math.round(Math.pow(10,-e));return Math.ceil(t*r)/r}return e>0?(r=Math.round(Math.pow(10,e)),Math.ceil(t/r)*r):Math.ceil(t)}function v(t){return"boolean"!=typeof t||t}t.exports={createScene:function(t){(t=t||{}).camera=t.camera||{};var e=t.canvas;e||(e=document.createElement("canvas"),t.container?t.container.appendChild(e):document.body.appendChild(e));var r=t.gl;if(r||(t.glOptions&&(p=!!t.glOptions.preserveDrawingBuffer),r=function(t,e){var r=null;try{(r=t.getContext("webgl",e))||(r=t.getContext("experimental-webgl",e))}catch(t){return null}return r}(e,t.glOptions||{premultipliedAlpha:!0,antialias:!0,preserveDrawingBuffer:p})),!r)throw new Error("webgl not supported");var b=t.bounds||[[-10,-10,-10],[10,10,10]],y=new m,x=l(r,r.drawingBufferWidth,r.drawingBufferHeight,{preferFloat:!p}),_=f(r),w=t.cameraObject&&!0===t.cameraObject._ortho||t.camera.projection&&"orthographic"===t.camera.projection.type||!1,k={eye:t.camera.eye||[2,0,0],center:t.camera.center||[0,0,0],up:t.camera.up||[0,1,0],zoomMin:t.camera.zoomMax||.1,zoomMax:t.camera.zoomMin||100,mode:t.camera.mode||"turntable",_ortho:w},A=t.axes||{},M=i(r,A);M.enable=!A.disable;var T=t.spikes||{},S=a(r,T),C=[],E=[],L=[],z=[],O=!0,D=!0,I={view:null,projection:new Array(16),model:new Array(16),_ortho:!1},F=(D=!0,[r.drawingBufferWidth,r.drawingBufferHeight]),R=t.cameraObject||n(e,k),P={gl:r,contextLost:!1,pixelRatio:t.pixelRatio||1,canvas:e,selection:y,camera:R,axes:M,axesPixels:null,spikes:S,bounds:b,objects:C,shape:F,aspect:t.aspectRatio||[1,1,1],pickRadius:t.pickRadius||10,zNear:t.zNear||.01,zFar:t.zFar||1e3,fovy:t.fovy||Math.PI/4,clearColor:t.clearColor||[0,0,0,0],autoResize:v(t.autoResize),autoBounds:v(t.autoBounds),autoScale:!!t.autoScale,autoCenter:v(t.autoCenter),clipToBounds:v(t.clipToBounds),snapToData:!!t.snapToData,onselect:t.onselect||null,onrender:t.onrender||null,onclick:t.onclick||null,cameraParams:I,oncontextloss:null,mouseListener:null,_stopped:!1,getAspectratio:function(){return{x:this.aspect[0],y:this.aspect[1],z:this.aspect[2]}},setAspectratio:function(t){this.aspect[0]=t.x,this.aspect[1]=t.y,this.aspect[2]=t.z,D=!0},setBounds:function(t,e){this.bounds[0][t]=e.min,this.bounds[1][t]=e.max},setClearColor:function(t){this.clearColor=t},clearRGBA:function(){this.gl.clearColor(this.clearColor[0],this.clearColor[1],this.clearColor[2],this.clearColor[3]),this.gl.clear(this.gl.COLOR_BUFFER_BIT|this.gl.DEPTH_BUFFER_BIT)}},j=[r.drawingBufferWidth/P.pixelRatio|0,r.drawingBufferHeight/P.pixelRatio|0];function N(){if(!P._stopped&&P.autoResize){var t=e.parentNode,r=1,n=1;t&&t!==document.body?(r=t.clientWidth,n=t.clientHeight):(r=window.innerWidth,n=window.innerHeight);var i=0|Math.ceil(r*P.pixelRatio),o=0|Math.ceil(n*P.pixelRatio);if(i!==e.width||o!==e.height){e.width=i,e.height=o;var a=e.style;a.position=a.position||"absolute",a.left="0px",a.top="0px",a.width=r+"px",a.height=n+"px",O=!0}}}function B(){for(var t=C.length,e=z.length,n=0;n0&&0===L[e-1];)L.pop(),z.pop().dispose()}function U(){if(P.contextLost)return!0;r.isContextLost()&&(P.contextLost=!0,P.mouseListener.enabled=!1,P.selection.object=null,P.oncontextloss&&P.oncontextloss())}P.autoResize&&N(),window.addEventListener("resize",N),P.update=function(t){P._stopped||(t=t||{},O=!0,D=!0)},P.add=function(t){P._stopped||(t.axes=M,C.push(t),E.push(-1),O=!0,D=!0,B())},P.remove=function(t){if(!P._stopped){var e=C.indexOf(t);e<0||(C.splice(e,1),E.pop(),O=!0,D=!0,B())}},P.dispose=function(){if(!P._stopped&&(P._stopped=!0,window.removeEventListener("resize",N),e.removeEventListener("webglcontextlost",U),P.mouseListener.enabled=!1,!P.contextLost)){M.dispose(),S.dispose();for(var t=0;ty.distance)continue;for(var c=0;c 1.0) {\n discard;\n }\n baseColor = mix(borderColor, color, step(radius, centerFraction));\n gl_FragColor = vec4(baseColor.rgb * baseColor.a, baseColor.a);\n }\n}\n"]),e.pickVertex=n(["precision mediump float;\n#define GLSLIFY 1\n\nattribute vec2 position;\nattribute vec4 pickId;\n\nuniform mat3 matrix;\nuniform float pointSize;\nuniform vec4 pickOffset;\n\nvarying vec4 fragId;\n\nvoid main() {\n vec3 hgPosition = matrix * vec3(position, 1);\n gl_Position = vec4(hgPosition.xy, 0, hgPosition.z);\n gl_PointSize = pointSize;\n\n vec4 id = pickId + pickOffset;\n id.y += floor(id.x / 256.0);\n id.x -= floor(id.x / 256.0) * 256.0;\n\n id.z += floor(id.y / 256.0);\n id.y -= floor(id.y / 256.0) * 256.0;\n\n id.w += floor(id.z / 256.0);\n id.z -= floor(id.z / 256.0) * 256.0;\n\n fragId = id;\n}\n"]),e.pickFragment=n(["precision mediump float;\n#define GLSLIFY 1\n\nvarying vec4 fragId;\n\nvoid main() {\n float radius = length(2.0 * gl_PointCoord.xy - 1.0);\n if(radius > 1.0) {\n discard;\n }\n gl_FragColor = fragId / 255.0;\n}\n"])},4696:function(t,e,r){"use strict";var n=r(9405),i=r(2762),o=r(1888),a=r(6640);function s(t,e,r,n,i){this.plot=t,this.offsetBuffer=e,this.pickBuffer=r,this.shader=n,this.pickShader=i,this.sizeMin=.5,this.sizeMinCap=2,this.sizeMax=20,this.areaRatio=1,this.pointCount=0,this.color=[1,0,0,1],this.borderColor=[0,0,0,1],this.blend=!1,this.pickOffset=0,this.points=null}t.exports=function(t,e){var r=t.gl,o=new s(t,i(r),i(r),n(r,a.pointVertex,a.pointFragment),n(r,a.pickVertex,a.pickFragment));return o.update(e),t.addObject(o),o};var l,c,u=s.prototype;u.dispose=function(){this.shader.dispose(),this.pickShader.dispose(),this.offsetBuffer.dispose(),this.pickBuffer.dispose(),this.plot.removeObject(this)},u.update=function(t){var e;function r(e,r){return e in t?t[e]:r}t=t||{},this.sizeMin=r("sizeMin",.5),this.sizeMax=r("sizeMax",20),this.color=r("color",[1,0,0,1]).slice(),this.areaRatio=r("areaRatio",1),this.borderColor=r("borderColor",[0,0,0,1]).slice(),this.blend=r("blend",!1);var n=t.positions.length>>>1,i=t.positions instanceof Float32Array,a=t.idToIndex instanceof Int32Array&&t.idToIndex.length>=n,s=t.positions,l=i?s:o.mallocFloat32(s.length),c=a?t.idToIndex:o.mallocInt32(n);if(i||l.set(s),!a)for(l.set(s),e=0;e>>1;for(r=0;r=e[0]&&o<=e[2]&&a>=e[1]&&a<=e[3]&&n++}return n}(this.points,i),u=this.plot.pickPixelRatio*Math.max(Math.min(this.sizeMinCap,this.sizeMin),Math.min(this.sizeMax,this.sizeMax/Math.pow(s,.33333)));l[0]=2/o,l[4]=2/a,l[6]=-2*i[0]/o-1,l[7]=-2*i[1]/a-1,this.offsetBuffer.bind(),r.bind(),r.attributes.position.pointer(),r.uniforms.matrix=l,r.uniforms.color=this.color,r.uniforms.borderColor=this.borderColor,r.uniforms.pointCloud=u<5,r.uniforms.pointSize=u,r.uniforms.centerFraction=Math.min(1,Math.max(0,Math.sqrt(1-this.areaRatio))),e&&(c[0]=255&t,c[1]=t>>8&255,c[2]=t>>16&255,c[3]=t>>24&255,this.pickBuffer.bind(),r.attributes.pickId.pointer(n.UNSIGNED_BYTE),r.uniforms.pickOffset=c,this.pickOffset=t);var h=n.getParameter(n.BLEND),d=n.getParameter(n.DITHER);return h&&!this.blend&&n.disable(n.BLEND),d&&n.disable(n.DITHER),n.drawArrays(n.POINTS,0,this.pointCount),h&&!this.blend&&n.enable(n.BLEND),d&&n.enable(n.DITHER),t+this.pointCount}),u.draw=u.unifiedDraw,u.drawPick=u.unifiedDraw,u.pick=function(t,e,r){var n=this.pickOffset,i=this.pointCount;if(r=n+i)return null;var o=r-n,a=this.points;return{object:this,pointId:o,dataCoord:[a[2*o],a[2*o+1]]}}},783:function(t){t.exports=function(t,e,r,n){var i,o,a,s,l,c=e[0],u=e[1],h=e[2],d=e[3],f=r[0],p=r[1],m=r[2],g=r[3];return(o=c*f+u*p+h*m+d*g)<0&&(o=-o,f=-f,p=-p,m=-m,g=-g),1-o>1e-6?(i=Math.acos(o),a=Math.sin(i),s=Math.sin((1-n)*i)/a,l=Math.sin(n*i)/a):(s=1-n,l=n),t[0]=s*c+l*f,t[1]=s*u+l*p,t[2]=s*h+l*m,t[3]=s*d+l*g,t}},5964:function(t){"use strict";t.exports=function(t){return t||0===t?t.toString():""}},9366:function(t,e,r){"use strict";var n=r(4359);t.exports=function(t,e,r){var o=[e.style,e.weight,e.variant,e.family].join("_"),a=i[o];if(a||(a=i[o]={}),t in a)return a[t];var s={textAlign:"center",textBaseline:"middle",lineHeight:1,font:e.family,fontStyle:e.style,fontWeight:e.weight,fontVariant:e.variant,lineSpacing:1.25,styletags:{breaklines:!0,bolds:!0,italics:!0,subscripts:!0,superscripts:!0},triangles:!0},l=n(t,s);s.triangles=!1;var c,u,h=n(t,s);if(r&&1!==r){for(c=0;c max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 glyph;\nattribute vec4 id;\n\nuniform vec4 highlightId;\nuniform float highlightScale;\nuniform mat4 model, view, projection;\nuniform vec3 clipBounds[2];\n\nvarying vec4 interpColor;\nvarying vec4 pickId;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0,0,0,0);\n } else {\n float scale = 1.0;\n if(distance(highlightId, id) < 0.0001) {\n scale = highlightScale;\n }\n\n vec4 worldPosition = model * vec4(position, 1);\n vec4 viewPosition = view * worldPosition;\n viewPosition = viewPosition / viewPosition.w;\n vec4 clipPosition = projection * (viewPosition + scale * vec4(glyph.x, -glyph.y, 0, 0));\n\n gl_Position = clipPosition;\n interpColor = color;\n pickId = id;\n dataCoordinate = position;\n }\n}"]),a=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 glyph;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\nuniform vec2 screenSize;\nuniform vec3 clipBounds[2];\nuniform float highlightScale, pixelRatio;\nuniform vec4 highlightId;\n\nvarying vec4 interpColor;\nvarying vec4 pickId;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0,0,0,0);\n } else {\n float scale = pixelRatio;\n if(distance(highlightId.bgr, id.bgr) < 0.001) {\n scale *= highlightScale;\n }\n\n vec4 worldPosition = model * vec4(position, 1.0);\n vec4 viewPosition = view * worldPosition;\n vec4 clipPosition = projection * viewPosition;\n clipPosition /= clipPosition.w;\n\n gl_Position = clipPosition + vec4(screenSize * scale * vec2(glyph.x, -glyph.y), 0.0, 0.0);\n interpColor = color;\n pickId = id;\n dataCoordinate = position;\n }\n}"]),s=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 glyph;\nattribute vec4 id;\n\nuniform float highlightScale;\nuniform vec4 highlightId;\nuniform vec3 axes[2];\nuniform mat4 model, view, projection;\nuniform vec2 screenSize;\nuniform vec3 clipBounds[2];\nuniform float scale, pixelRatio;\n\nvarying vec4 interpColor;\nvarying vec4 pickId;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0,0,0,0);\n } else {\n float lscale = pixelRatio * scale;\n if(distance(highlightId, id) < 0.0001) {\n lscale *= highlightScale;\n }\n\n vec4 clipCenter = projection * (view * (model * vec4(position, 1)));\n vec3 dataPosition = position + 0.5*lscale*(axes[0] * glyph.x + axes[1] * glyph.y) * clipCenter.w * screenSize.y;\n vec4 clipPosition = projection * (view * (model * vec4(dataPosition, 1)));\n\n gl_Position = clipPosition;\n interpColor = color;\n pickId = id;\n dataCoordinate = dataPosition;\n }\n}\n"]),l=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 fragClipBounds[2];\nuniform float opacity;\n\nvarying vec4 interpColor;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (\n outOfRange(fragClipBounds[0], fragClipBounds[1], dataCoordinate) ||\n interpColor.a * opacity == 0.\n ) discard;\n gl_FragColor = interpColor * opacity;\n}\n"]),c=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 fragClipBounds[2];\nuniform float pickGroup;\n\nvarying vec4 pickId;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (outOfRange(fragClipBounds[0], fragClipBounds[1], dataCoordinate)) discard;\n\n gl_FragColor = vec4(pickGroup, pickId.bgr);\n}"]),u=[{name:"position",type:"vec3"},{name:"color",type:"vec4"},{name:"glyph",type:"vec2"},{name:"id",type:"vec4"}],h={vertex:o,fragment:l,attributes:u},d={vertex:a,fragment:l,attributes:u},f={vertex:s,fragment:l,attributes:u},p={vertex:o,fragment:c,attributes:u},m={vertex:a,fragment:c,attributes:u},g={vertex:s,fragment:c,attributes:u};function v(t,e){var r=n(t,e),i=r.attributes;return i.position.location=0,i.color.location=1,i.glyph.location=2,i.id.location=3,r}e.createPerspective=function(t){return v(t,h)},e.createOrtho=function(t){return v(t,d)},e.createProject=function(t){return v(t,f)},e.createPickPerspective=function(t){return v(t,p)},e.createPickOrtho=function(t){return v(t,m)},e.createPickProject=function(t){return v(t,g)}},8418:function(t,e,r){"use strict";var n=r(5219),i=r(2762),o=r(8116),a=r(1888),s=r(6760),l=r(1283),c=r(9366),u=r(5964),h=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],d=ArrayBuffer,f=DataView;function p(t){return Array.isArray(t)||function(t){return d.isView(t)&&!(t instanceof f)}(t)}function m(t,e){var r=t[0],n=t[1],i=t[2],o=t[3];return t[0]=e[0]*r+e[4]*n+e[8]*i+e[12]*o,t[1]=e[1]*r+e[5]*n+e[9]*i+e[13]*o,t[2]=e[2]*r+e[6]*n+e[10]*i+e[14]*o,t[3]=e[3]*r+e[7]*n+e[11]*i+e[15]*o,t}function g(t,e,r,n){return m(n,n),m(n,n),m(n,n)}function v(t,e){this.index=t,this.dataCoordinate=this.position=e}function b(t){return!0===t||t>1?1:t}function y(t,e,r,n,i,o,a,s,l,c,u,h){this.gl=t,this.pixelRatio=1,this.shader=e,this.orthoShader=r,this.projectShader=n,this.pointBuffer=i,this.colorBuffer=o,this.glyphBuffer=a,this.idBuffer=s,this.vao=l,this.vertexCount=0,this.lineVertexCount=0,this.opacity=1,this.hasAlpha=!1,this.lineWidth=0,this.projectScale=[2/3,2/3,2/3],this.projectOpacity=[1,1,1],this.projectHasAlpha=!1,this.pickId=0,this.pickPerspectiveShader=c,this.pickOrthoShader=u,this.pickProjectShader=h,this.points=[],this._selectResult=new v(0,[0,0,0]),this.useOrtho=!0,this.bounds=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],this.axesProject=[!0,!0,!0],this.axesBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.highlightId=[1,1,1,1],this.highlightScale=2,this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.dirty=!0}t.exports=function(t){var e=t.gl,r=l.createPerspective(e),n=l.createOrtho(e),a=l.createProject(e),s=l.createPickPerspective(e),c=l.createPickOrtho(e),u=l.createPickProject(e),h=i(e),d=i(e),f=i(e),p=i(e),m=new y(e,r,n,a,h,d,f,p,o(e,[{buffer:h,size:3,type:e.FLOAT},{buffer:d,size:4,type:e.FLOAT},{buffer:f,size:2,type:e.FLOAT},{buffer:p,size:4,type:e.UNSIGNED_BYTE,normalized:!0}]),s,c,u);return m.update(t),m};var x=y.prototype;x.pickSlots=1,x.setPickBase=function(t){this.pickId=t},x.isTransparent=function(){if(this.hasAlpha)return!0;for(var t=0;t<3;++t)if(this.axesProject[t]&&this.projectHasAlpha)return!0;return!1},x.isOpaque=function(){if(!this.hasAlpha)return!0;for(var t=0;t<3;++t)if(this.axesProject[t]&&!this.projectHasAlpha)return!0;return!1};var _=[0,0],w=[0,0,0],k=[0,0,0],A=[0,0,0,1],M=[0,0,0,1],T=h.slice(),S=[0,0,0],C=[[0,0,0],[0,0,0]];function E(t){return t[0]=t[1]=t[2]=0,t}function L(t,e){return t[0]=e[0],t[1]=e[1],t[2]=e[2],t[3]=1,t}function z(t,e,r,n){return t[0]=e[0],t[1]=e[1],t[2]=e[2],t[r]=n,t}var O=[[-1e8,-1e8,-1e8],[1e8,1e8,1e8]];function D(t,e,r,n,i,o,a){var l=r.gl;if((o===r.projectHasAlpha||a)&&function(t,e,r,n){var i,o=e.axesProject,a=e.gl,l=t.uniforms,c=r.model||h,u=r.view||h,d=r.projection||h,f=e.axesBounds,p=function(t){for(var e=C,r=0;r<2;++r)for(var n=0;n<3;++n)e[r][n]=Math.max(Math.min(t[r][n],1e8),-1e8);return e}(e.clipBounds);i=e.axes&&e.axes.lastCubeProps?e.axes.lastCubeProps.axis:[1,1,1],_[0]=2/a.drawingBufferWidth,_[1]=2/a.drawingBufferHeight,t.bind(),l.view=u,l.projection=d,l.screenSize=_,l.highlightId=e.highlightId,l.highlightScale=e.highlightScale,l.clipBounds=p,l.pickGroup=e.pickId/255,l.pixelRatio=n;for(var m=0;m<3;++m)if(o[m]){l.scale=e.projectScale[m],l.opacity=e.projectOpacity[m];for(var v=T,b=0;b<16;++b)v[b]=0;for(b=0;b<4;++b)v[5*b]=1;v[5*m]=0,i[m]<0?v[12+m]=f[0][m]:v[12+m]=f[1][m],s(v,c,v),l.model=v;var y=(m+1)%3,x=(m+2)%3,O=E(w),D=E(k);O[y]=1,D[x]=1;var I=g(0,0,0,L(A,O)),F=g(0,0,0,L(M,D));if(Math.abs(I[1])>Math.abs(F[1])){var R=I;I=F,F=R,R=O,O=D,D=R;var P=y;y=x,x=P}I[0]<0&&(O[y]=-1),F[1]>0&&(D[x]=-1);var j=0,N=0;for(b=0;b<4;++b)j+=Math.pow(c[4*y+b],2),N+=Math.pow(c[4*x+b],2);O[y]/=Math.sqrt(j),D[x]/=Math.sqrt(N),l.axes[0]=O,l.axes[1]=D,l.fragClipBounds[0]=z(S,p[0],m,-1e8),l.fragClipBounds[1]=z(S,p[1],m,1e8),e.vao.bind(),e.vao.draw(a.TRIANGLES,e.vertexCount),e.lineWidth>0&&(a.lineWidth(e.lineWidth*n),e.vao.draw(a.LINES,e.lineVertexCount,e.vertexCount)),e.vao.unbind()}}(e,r,n,i),o===r.hasAlpha||a){t.bind();var c=t.uniforms;c.model=n.model||h,c.view=n.view||h,c.projection=n.projection||h,_[0]=2/l.drawingBufferWidth,_[1]=2/l.drawingBufferHeight,c.screenSize=_,c.highlightId=r.highlightId,c.highlightScale=r.highlightScale,c.fragClipBounds=O,c.clipBounds=r.axes.bounds,c.opacity=r.opacity,c.pickGroup=r.pickId/255,c.pixelRatio=i,r.vao.bind(),r.vao.draw(l.TRIANGLES,r.vertexCount),r.lineWidth>0&&(l.lineWidth(r.lineWidth*i),r.vao.draw(l.LINES,r.lineVertexCount,r.vertexCount)),r.vao.unbind()}}function I(t,e,r,i){var o;o=p(t)?e=this.pointCount||e<0)return null;var r=this.points[e],n=this._selectResult;n.index=e;for(var i=0;i<3;++i)n.position[i]=n.dataCoordinate[i]=r[i];return n},x.highlight=function(t){if(t){var e=t.index,r=255&e,n=e>>8&255,i=e>>16&255;this.highlightId=[r/255,n/255,i/255,0]}else this.highlightId=[1,1,1,1]},x.update=function(t){if("perspective"in(t=t||{})&&(this.useOrtho=!t.perspective),"orthographic"in t&&(this.useOrtho=!!t.orthographic),"lineWidth"in t&&(this.lineWidth=t.lineWidth),"project"in t)if(p(t.project))this.axesProject=t.project;else{var e=!!t.project;this.axesProject=[e,e,e]}if("projectScale"in t)if(p(t.projectScale))this.projectScale=t.projectScale.slice();else{var r=+t.projectScale;this.projectScale=[r,r,r]}if(this.projectHasAlpha=!1,"projectOpacity"in t){p(t.projectOpacity)?this.projectOpacity=t.projectOpacity.slice():(r=+t.projectOpacity,this.projectOpacity=[r,r,r]);for(var n=0;n<3;++n)this.projectOpacity[n]=b(this.projectOpacity[n]),this.projectOpacity[n]<1&&(this.projectHasAlpha=!0)}this.hasAlpha=!1,"opacity"in t&&(this.opacity=b(t.opacity),this.opacity<1&&(this.hasAlpha=!0)),this.dirty=!0;var i,o,s=t.position,l={family:t.font||"normal",style:t.fontStyle||"normal",weight:t.fontWeight||"normal",variant:t.fontVariant||"normal"},c=t.alignment||[0,0];if(2===c.length)i=c[0],o=c[1];else for(i=[],o=[],n=0;n0){var D=0,F=x,R=[0,0,0,1],P=[0,0,0,1],j=p(f)&&p(f[0]),N=p(v)&&p(v[0]);t:for(n=0;n0?1-S[0][0]:Y<0?1+S[1][0]:1,Z*=Z>0?1-S[0][1]:Z<0?1+S[1][1]:1],$=M.cells||[],J=M.positions||[];for(A=0;A<$.length;++A)for(var K=$[A],Q=0;Q<3;++Q){for(var tt=0;tt<3;++tt)E[3*D+tt]=k[tt];for(tt=0;tt<4;++tt)L[4*D+tt]=R[tt];O[D]=y;var et=J[K[Q]];z[2*D]=V*(W*et[0]-q*et[1]+X[0]),z[2*D+1]=V*(q*et[0]+W*et[1]+X[1]),D+=1}for($=T.edges,J=T.positions,A=0;A<$.length;++A)for(K=$[A],Q=0;Q<2;++Q){for(tt=0;tt<3;++tt)E[3*F+tt]=k[tt];for(tt=0;tt<4;++tt)L[4*F+tt]=P[tt];O[F]=y,et=J[K[Q]],z[2*F]=V*(W*et[0]-q*et[1]+X[0]),z[2*F+1]=V*(q*et[0]+W*et[1]+X[1]),F+=1}}}this.bounds=[u,h],this.points=s,this.pointCount=s.length,this.vertexCount=x,this.lineVertexCount=_,this.pointBuffer.update(E),this.colorBuffer.update(L),this.glyphBuffer.update(z),this.idBuffer.update(O),a.free(E),a.free(L),a.free(z),a.free(O)},x.dispose=function(){this.shader.dispose(),this.orthoShader.dispose(),this.pickPerspectiveShader.dispose(),this.pickOrthoShader.dispose(),this.vao.dispose(),this.pointBuffer.dispose(),this.colorBuffer.dispose(),this.glyphBuffer.dispose(),this.idBuffer.dispose()}},4298:function(t,e,r){"use strict";var n=r(3236);e.boxVertex=n(["precision mediump float;\n#define GLSLIFY 1\n\nattribute vec2 vertex;\n\nuniform vec2 cornerA, cornerB;\n\nvoid main() {\n gl_Position = vec4(mix(cornerA, cornerB, vertex), 0, 1);\n}\n"]),e.boxFragment=n(["precision mediump float;\n#define GLSLIFY 1\n\nuniform vec4 color;\n\nvoid main() {\n gl_FragColor = color;\n}\n"])},3161:function(t,e,r){"use strict";var n=r(9405),i=r(2762),o=r(4298);function a(t,e,r){this.plot=t,this.boxBuffer=e,this.boxShader=r,this.enabled=!0,this.selectBox=[1/0,1/0,-1/0,-1/0],this.borderColor=[0,0,0,1],this.innerFill=!1,this.innerColor=[0,0,0,.25],this.outerFill=!0,this.outerColor=[0,0,0,.5],this.borderWidth=10}t.exports=function(t,e){var r=t.gl,s=new a(t,i(r,[0,0,0,1,1,0,1,1]),n(r,o.boxVertex,o.boxFragment));return s.update(e),t.addOverlay(s),s};var s=a.prototype;s.draw=function(){if(this.enabled){var t=this.plot,e=this.selectBox,r=this.borderWidth,n=(this.innerFill,this.innerColor),i=(this.outerFill,this.outerColor),o=this.borderColor,a=t.box,s=t.screenBox,l=t.dataBox,c=t.viewBox,u=t.pixelRatio,h=(e[0]-l[0])*(c[2]-c[0])/(l[2]-l[0])+c[0],d=(e[1]-l[1])*(c[3]-c[1])/(l[3]-l[1])+c[1],f=(e[2]-l[0])*(c[2]-c[0])/(l[2]-l[0])+c[0],p=(e[3]-l[1])*(c[3]-c[1])/(l[3]-l[1])+c[1];if(h=Math.max(h,c[0]),d=Math.max(d,c[1]),f=Math.min(f,c[2]),p=Math.min(p,c[3]),!(f0){var v=r*u;a.drawBox(h-v,d-v,f+v,d+v,o),a.drawBox(h-v,p-v,f+v,p+v,o),a.drawBox(h-v,d-v,h+v,p+v,o),a.drawBox(f-v,d-v,f+v,p+v,o)}}}},s.update=function(t){t=t||{},this.innerFill=!!t.innerFill,this.outerFill=!!t.outerFill,this.innerColor=(t.innerColor||[0,0,0,.5]).slice(),this.outerColor=(t.outerColor||[0,0,0,.5]).slice(),this.borderColor=(t.borderColor||[0,0,0,1]).slice(),this.borderWidth=t.borderWidth||0,this.selectBox=(t.selectBox||this.selectBox).slice()},s.dispose=function(){this.boxBuffer.dispose(),this.boxShader.dispose(),this.plot.removeOverlay(this)}},3589:function(t,e,r){"use strict";t.exports=function(t,e){var r=e[0],o=e[1];return new l(t,n(t,r,o,{}),i.mallocUint8(r*o*4))};var n=r(2260),i=r(1888),o=r(9618),a=r(8828).nextPow2;function s(t,e,r,n,i){this.coord=[t,e],this.id=r,this.value=n,this.distance=i}function l(t,e,r){this.gl=t,this.fbo=e,this.buffer=r,this._readTimeout=null;var n=this;this._readCallback=function(){n.gl&&(e.bind(),t.readPixels(0,0,e.shape[0],e.shape[1],t.RGBA,t.UNSIGNED_BYTE,n.buffer),n._readTimeout=null)}}var c=l.prototype;Object.defineProperty(c,"shape",{get:function(){return this.gl?this.fbo.shape.slice():[0,0]},set:function(t){if(this.gl){this.fbo.shape=t;var e=this.fbo.shape[0],r=this.fbo.shape[1];if(r*e*4>this.buffer.length){i.free(this.buffer);for(var n=this.buffer=i.mallocUint8(a(r*e*4)),o=0;or)for(t=r;te)for(t=e;t=0){for(var k=0|w.type.charAt(w.type.length-1),A=new Array(k),M=0;M=0;)T+=1;_[b]=T}var S=new Array(r.length);function C(){d.program=a.program(f,d._vref,d._fref,x,_);for(var t=0;t=0){if((p=d.charCodeAt(d.length-1)-48)<2||p>4)throw new n("","Invalid data type for attribute "+h+": "+d);s(t,e,f[0],i,p,o,h)}else{if(!(d.indexOf("mat")>=0))throw new n("","Unknown data type for attribute "+h+": "+d);var p;if((p=d.charCodeAt(d.length-1)-48)<2||p>4)throw new n("","Invalid data type for attribute "+h+": "+d);l(t,e,f,i,p,o,h)}}}return 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// a*-b + b*a + c*0 = -ba + ba + 0 = 0\n if (v.x*v.x > v.z*v.z || v.y*v.y > v.z*v.z) {\n return normalize(vec3(-v.y, v.x, 0.0));\n } else {\n return normalize(vec3(0.0, v.z, -v.y));\n }\n}\n\n// Calculate the tube vertex and normal at the given index.\n//\n// The returned vertex is for a tube ring with its center at origin, radius of length(d), pointing in the direction of d.\n//\n// Each tube segment is made up of a ring of vertices.\n// These vertices are used to make up the triangles of the tube by connecting them together in the vertex array.\n// The indexes of tube segments run from 0 to 8.\n//\nvec3 getTubePosition(vec3 d, float index, out vec3 normal) {\n float segmentCount = 8.0;\n\n float angle = 2.0 * 3.14159 * (index / segmentCount);\n\n vec3 u = getOrthogonalVector(d);\n vec3 v = normalize(cross(u, d));\n\n vec3 x = u * cos(angle) * length(d);\n vec3 y = v * sin(angle) * length(d);\n vec3 v3 = x + y;\n\n normal = normalize(v3);\n\n return v3;\n}\n\nattribute vec4 vector;\nattribute vec4 color, position;\nattribute vec2 uv;\n\nuniform float vectorScale, tubeScale;\nuniform mat4 model, view, projection, inverseModel;\nuniform vec3 eyePosition, lightPosition;\n\nvarying vec3 f_normal, f_lightDirection, f_eyeDirection, f_data, f_position;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n // Scale the vector magnitude to stay constant with\n // model & view changes.\n vec3 normal;\n vec3 XYZ = getTubePosition(mat3(model) * (tubeScale * vector.w * normalize(vector.xyz)), position.w, normal);\n vec4 tubePosition = model * vec4(position.xyz, 1.0) + vec4(XYZ, 0.0);\n\n //Lighting geometry parameters\n vec4 cameraCoordinate = view * tubePosition;\n cameraCoordinate.xyz /= cameraCoordinate.w;\n f_lightDirection = lightPosition - cameraCoordinate.xyz;\n f_eyeDirection = eyePosition - cameraCoordinate.xyz;\n f_normal = normalize((vec4(normal, 0.0) * inverseModel).xyz);\n\n // vec4 m_position = model * vec4(tubePosition, 1.0);\n vec4 t_position = view * tubePosition;\n gl_Position = projection * t_position;\n\n f_color = color;\n f_data = tubePosition.xyz;\n f_position = position.xyz;\n f_uv = uv;\n}\n"]),o=n(["#extension GL_OES_standard_derivatives : enable\n\nprecision highp float;\n#define GLSLIFY 1\n\nfloat beckmannDistribution(float x, float roughness) {\n float NdotH = max(x, 0.0001);\n float cos2Alpha = NdotH * NdotH;\n float tan2Alpha = (cos2Alpha - 1.0) / cos2Alpha;\n float roughness2 = roughness * roughness;\n float denom = 3.141592653589793 * roughness2 * cos2Alpha * cos2Alpha;\n return exp(tan2Alpha / roughness2) / denom;\n}\n\nfloat cookTorranceSpecular(\n vec3 lightDirection,\n vec3 viewDirection,\n vec3 surfaceNormal,\n float roughness,\n float fresnel) {\n\n float VdotN = max(dot(viewDirection, surfaceNormal), 0.0);\n float LdotN = max(dot(lightDirection, surfaceNormal), 0.0);\n\n //Half angle vector\n vec3 H = normalize(lightDirection + viewDirection);\n\n //Geometric term\n float NdotH = max(dot(surfaceNormal, H), 0.0);\n float VdotH = max(dot(viewDirection, H), 0.000001);\n float LdotH = max(dot(lightDirection, H), 0.000001);\n float G1 = (2.0 * NdotH * VdotN) / VdotH;\n float G2 = (2.0 * NdotH * LdotN) / LdotH;\n float G = min(1.0, min(G1, G2));\n \n //Distribution term\n float D = beckmannDistribution(NdotH, roughness);\n\n //Fresnel term\n float F = pow(1.0 - VdotN, fresnel);\n\n //Multiply terms and done\n return G * F * D / max(3.14159265 * VdotN, 0.000001);\n}\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float roughness, fresnel, kambient, kdiffuse, kspecular, opacity;\nuniform sampler2D texture;\n\nvarying vec3 f_normal, f_lightDirection, f_eyeDirection, f_data, f_position;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n vec3 N = normalize(f_normal);\n vec3 L = normalize(f_lightDirection);\n vec3 V = normalize(f_eyeDirection);\n\n if(gl_FrontFacing) {\n N = -N;\n }\n\n float specular = min(1.0, max(0.0, cookTorranceSpecular(L, V, N, roughness, fresnel)));\n float diffuse = min(kambient + kdiffuse * max(dot(N, L), 0.0), 1.0);\n\n vec4 surfaceColor = f_color * texture2D(texture, f_uv);\n vec4 litColor = surfaceColor.a * vec4(diffuse * surfaceColor.rgb + kspecular * vec3(1,1,1) * specular, 1.0);\n\n gl_FragColor = litColor * opacity;\n}\n"]),a=n(["precision highp float;\n\nprecision highp float;\n#define GLSLIFY 1\n\nvec3 getOrthogonalVector(vec3 v) {\n // Return up-vector for only-z vector.\n // Return ax + by + cz = 0, a point that lies on 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cos(angle) * length(d);\n vec3 y = v * sin(angle) * length(d);\n vec3 v3 = x + y;\n\n normal = normalize(v3);\n\n return v3;\n}\n\nattribute vec4 vector;\nattribute vec4 position;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\nuniform float tubeScale;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n vec3 normal;\n vec3 XYZ = getTubePosition(mat3(model) * (tubeScale * vector.w * normalize(vector.xyz)), position.w, normal);\n vec4 tubePosition = model * vec4(position.xyz, 1.0) + vec4(XYZ, 0.0);\n\n gl_Position = projection * (view * tubePosition);\n f_id = id;\n f_position = position.xyz;\n}\n"]),s=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n 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x,_,w,k,A,M,T=o[0][p],S=o[0][v],C=o[1][m],E=o[1][b],L=o[2][g],z=(l-T)/(S-T),O=(c-C)/(E-C),D=(u-L)/(o[2][y]-L);switch(isFinite(z)||(z=.5),isFinite(O)||(O=.5),isFinite(D)||(D=.5),r.reversedX&&(p=h-1-p,v=h-1-v),r.reversedY&&(m=d-1-m,b=d-1-b),r.reversedZ&&(g=f-1-g,y=f-1-y),r.filled){case 5:A=g,M=y,w=m*f,k=b*f,x=p*f*d,_=v*f*d;break;case 4:A=g,M=y,x=p*f,_=v*f,w=m*f*h,k=b*f*h;break;case 3:w=m,k=b,A=g*d,M=y*d,x=p*d*f,_=v*d*f;break;case 2:w=m,k=b,x=p*d,_=v*d,A=g*d*h,M=y*d*h;break;case 1:x=p,_=v,A=g*h,M=y*h,w=m*h*f,k=b*h*f;break;default:x=p,_=v,w=m*h,k=b*h,A=g*h*d,M=y*h*d}var I=i[x+w+A],F=i[x+w+M],R=i[x+k+A],P=i[x+k+M],j=i[_+w+A],N=i[_+w+M],B=i[_+k+A],U=i[_+k+M],G=n.create(),V=n.create(),H=n.create(),W=n.create();n.lerp(G,I,j,z),n.lerp(V,F,N,z),n.lerp(H,R,B,z),n.lerp(W,P,U,z);var q=n.create(),Y=n.create();n.lerp(q,G,H,O),n.lerp(Y,V,W,O);var Z=n.create();return n.lerp(Z,q,Y,D),Z}(e,t,f)},m=t.getDivergence||function(t,e){var r=n.create(),i=1e-4;n.add(r,t,[i,0,0]);var o=p(r);n.subtract(o,o,e),n.scale(o,o,1/i),n.add(r,t,[0,i,0]);var a=p(r);n.subtract(a,a,e),n.scale(a,a,1/i),n.add(r,t,[0,0,i]);var s=p(r);return n.subtract(s,s,e),n.scale(s,s,1/i),n.add(r,o,a),n.add(r,r,s),r},g=[],v=e[0][0],b=e[0][1],y=e[0][2],x=e[1][0],_=e[1][1],w=e[1][2],k=function(t){var e=t[0],r=t[1],n=t[2];return!(ex||r_||nw)},A=10*n.distance(e[0],e[1])/c,M=A*A,T=1,S=0,C=r.length;C>1&&(T=function(t){for(var e=[],r=[],n=[],i={},o={},a={},s=t.length,c=0;cS&&(S=P),F.push(P),g.push({points:z,velocities:O,divergences:F});for(var j=0;j<100*c&&z.lengthM&&n.scale(N,N,A/Math.sqrt(B)),n.add(N,N,L),D=p(N),n.squaredDistance(I,N)-M>-1e-4*M&&(z.push(N),I=N,O.push(D),R=m(N,D),P=n.length(R),isFinite(P)&&P>S&&(S=P),F.push(P)),L=N}}var U=function(t,e,r,o){for(var a=0,s=0;s0)for(k=0;k<8;k++){var A=(k+1)%8;c.push(d[k],f[k],f[A],f[A],d[A],d[k]),h.push(b,v,v,v,b,b),p.push(m,g,g,g,m,m);var M=c.length;u.push([M-6,M-5,M-4],[M-3,M-2,M-1])}var T=d;d=f,f=T;var S=b;b=v,v=S;var C=m;m=g,g=C}return{positions:c,cells:u,vectors:h,vertexIntensity:p}}(t,r,o,a)})),h=[],d=[],f=[],p=[];for(s=0;s max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 lowerBound, upperBound;\nuniform float contourTint;\nuniform vec4 contourColor;\nuniform sampler2D colormap;\nuniform vec3 clipBounds[2];\nuniform float roughness, fresnel, kambient, kdiffuse, kspecular, opacity;\nuniform float vertexColor;\n\nvarying float value, kill;\nvarying vec3 worldCoordinate;\nvarying vec3 lightDirection, eyeDirection, surfaceNormal;\nvarying vec4 vColor;\n\nvoid main() {\n if (\n kill > 0.0 ||\n vColor.a == 0.0 ||\n outOfRange(clipBounds[0], clipBounds[1], worldCoordinate)\n ) discard;\n\n vec3 N = normalize(surfaceNormal);\n vec3 V = normalize(eyeDirection);\n vec3 L = normalize(lightDirection);\n\n if(gl_FrontFacing) {\n N = -N;\n }\n\n float specular = max(beckmannSpecular(L, V, N, roughness), 0.);\n float diffuse = min(kambient + kdiffuse * max(dot(N, L), 0.0), 1.0);\n\n //decide how to interpolate color — in vertex or in fragment\n vec4 surfaceColor =\n step(vertexColor, .5) * texture2D(colormap, vec2(value, value)) +\n step(.5, vertexColor) * vColor;\n\n vec4 litColor = surfaceColor.a * vec4(diffuse * surfaceColor.rgb + kspecular * vec3(1,1,1) * specular, 1.0);\n\n gl_FragColor = mix(litColor, contourColor, contourTint) * opacity;\n}\n"]),s=i(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec4 uv;\nattribute float f;\n\nuniform vec3 objectOffset;\nuniform mat3 permutation;\nuniform mat4 model, view, projection;\nuniform float height, zOffset;\nuniform sampler2D colormap;\n\nvarying float value, kill;\nvarying vec3 worldCoordinate;\nvarying vec2 planeCoordinate;\nvarying vec3 lightDirection, eyeDirection, surfaceNormal;\nvarying vec4 vColor;\n\nvoid main() {\n vec3 dataCoordinate = permutation * vec3(uv.xy, height);\n worldCoordinate = objectOffset + dataCoordinate;\n mat4 objectOffsetTranslation = mat4(1.0) + mat4(vec4(0), vec4(0), vec4(0), vec4(objectOffset, 0));\n vec4 worldPosition = (model * objectOffsetTranslation) * vec4(dataCoordinate, 1.0);\n\n vec4 clipPosition = projection * (view * worldPosition);\n clipPosition.z += zOffset;\n\n gl_Position = clipPosition;\n value = f + objectOffset.z;\n kill = -1.0;\n planeCoordinate = uv.zw;\n\n vColor = texture2D(colormap, vec2(value, value));\n\n //Don't do lighting for contours\n surfaceNormal = vec3(1,0,0);\n eyeDirection = vec3(0,1,0);\n lightDirection = vec3(0,0,1);\n}\n"]),l=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec2 shape;\nuniform vec3 clipBounds[2];\nuniform float pickId;\n\nvarying float value, kill;\nvarying vec3 worldCoordinate;\nvarying vec2 planeCoordinate;\nvarying vec3 surfaceNormal;\n\nvec2 splitFloat(float v) {\n float vh = 255.0 * v;\n float upper = floor(vh);\n float lower = fract(vh);\n return vec2(upper / 255.0, floor(lower * 16.0) / 16.0);\n}\n\nvoid main() {\n if ((kill > 0.0) ||\n (outOfRange(clipBounds[0], clipBounds[1], worldCoordinate))) discard;\n\n vec2 ux = splitFloat(planeCoordinate.x / shape.x);\n vec2 uy = splitFloat(planeCoordinate.y / shape.y);\n gl_FragColor = vec4(pickId, ux.x, uy.x, ux.y + (uy.y/16.0));\n}\n"]);e.createShader=function(t){var e=n(t,o,a,null,[{name:"uv",type:"vec4"},{name:"f",type:"vec3"},{name:"normal",type:"vec3"}]);return e.attributes.uv.location=0,e.attributes.f.location=1,e.attributes.normal.location=2,e},e.createPickShader=function(t){var e=n(t,o,l,null,[{name:"uv",type:"vec4"},{name:"f",type:"vec3"},{name:"normal",type:"vec3"}]);return e.attributes.uv.location=0,e.attributes.f.location=1,e.attributes.normal.location=2,e},e.createContourShader=function(t){var e=n(t,s,a,null,[{name:"uv",type:"vec4"},{name:"f",type:"float"}]);return e.attributes.uv.location=0,e.attributes.f.location=1,e},e.createPickContourShader=function(t){var e=n(t,s,l,null,[{name:"uv",type:"vec4"},{name:"f",type:"float"}]);return e.attributes.uv.location=0,e.attributes.f.location=1,e}},9499:function(t,e,r){"use strict";t.exports=function(t){var e=t.gl,r=b(e),n=x(e),s=y(e),l=_(e),c=i(e),u=o(e,[{buffer:c,size:4,stride:w,offset:0},{buffer:c,size:3,stride:w,offset:16},{buffer:c,size:3,stride:w,offset:28}]),h=i(e),d=o(e,[{buffer:h,size:4,stride:20,offset:0},{buffer:h,size:1,stride:20,offset:16}]),f=i(e),p=o(e,[{buffer:f,size:2,type:e.FLOAT}]),m=a(e,1,S,e.RGBA,e.UNSIGNED_BYTE);m.minFilter=e.LINEAR,m.magFilter=e.LINEAR;var g=new C(e,[0,0],[[0,0,0],[0,0,0]],r,n,c,u,m,s,l,h,d,f,p,[0,0,0]),v={levels:[[],[],[]]};for(var k in t)v[k]=t[k];return v.colormap=v.colormap||"jet",g.update(v),g};var n=r(8828),i=r(2762),o=r(8116),a=r(7766),s=r(1888),l=r(6729),c=r(5298),u=r(9994),h=r(9618),d=r(3711),f=r(6760),p=r(7608),m=r(2478),g=r(6199),v=r(990),b=v.createShader,y=v.createContourShader,x=v.createPickShader,_=v.createPickContourShader,w=40,k=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],A=[[0,0],[0,1],[1,0],[1,1],[1,0],[0,1]],M=[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]];function T(t,e,r,n,i){this.position=t,this.index=e,this.uv=r,this.level=n,this.dataCoordinate=i}!function(){for(var t=0;t<3;++t){var e=M[t],r=(t+2)%3;e[(t+1)%3+0]=1,e[r+3]=1,e[t+6]=1}}();var S=256;function C(t,e,r,n,i,o,a,l,c,u,d,f,p,m,g){this.gl=t,this.shape=e,this.bounds=r,this.objectOffset=g,this.intensityBounds=[],this._shader=n,this._pickShader=i,this._coordinateBuffer=o,this._vao=a,this._colorMap=l,this._contourShader=c,this._contourPickShader=u,this._contourBuffer=d,this._contourVAO=f,this._contourOffsets=[[],[],[]],this._contourCounts=[[],[],[]],this._vertexCount=0,this._pickResult=new T([0,0,0],[0,0],[0,0],[0,0,0],[0,0,0]),this._dynamicBuffer=p,this._dynamicVAO=m,this._dynamicOffsets=[0,0,0],this._dynamicCounts=[0,0,0],this.contourWidth=[1,1,1],this.contourLevels=[[1],[1],[1]],this.contourTint=[0,0,0],this.contourColor=[[.5,.5,.5,1],[.5,.5,.5,1],[.5,.5,.5,1]],this.showContour=!0,this.showSurface=!0,this.enableHighlight=[!0,!0,!0],this.highlightColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.highlightTint=[1,1,1],this.highlightLevel=[-1,-1,-1],this.enableDynamic=[!0,!0,!0],this.dynamicLevel=[NaN,NaN,NaN],this.dynamicColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.dynamicTint=[1,1,1],this.dynamicWidth=[1,1,1],this.axesBounds=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],this.surfaceProject=[!1,!1,!1],this.contourProject=[[!1,!1,!1],[!1,!1,!1],[!1,!1,!1]],this.colorBounds=[!1,!1],this._field=[h(s.mallocFloat(1024),[0,0]),h(s.mallocFloat(1024),[0,0]),h(s.mallocFloat(1024),[0,0])],this.pickId=1,this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.snapToData=!1,this.pixelRatio=1,this.opacity=1,this.lightPosition=[10,1e4,0],this.ambientLight=.8,this.diffuseLight=.8,this.specularLight=2,this.roughness=.5,this.fresnel=1.5,this.vertexColor=0,this.dirty=!0}var E=C.prototype;E.genColormap=function(t,e){var r=!1,n=u([l({colormap:t,nshades:S,format:"rgba"}).map((function(t,n){var i=e?function(t,e){if(!e)return 1;if(!e.length)return 1;for(var r=0;rt&&r>0){var n=(e[r][0]-t)/(e[r][0]-e[r-1][0]);return e[r][1]*(1-n)+n*e[r-1][1]}}return 1}(n/255,e):t[3];return i<1&&(r=!0),[t[0],t[1],t[2],255*i]}))]);return c.divseq(n,255),this.hasAlphaScale=r,n},E.isTransparent=function(){return this.opacity<1||this.hasAlphaScale},E.isOpaque=function(){return!this.isTransparent()},E.pickSlots=1,E.setPickBase=function(t){this.pickId=t};var L=[0,0,0],z={showSurface:!1,showContour:!1,projections:[k.slice(),k.slice(),k.slice()],clipBounds:[[[0,0,0],[0,0,0]],[[0,0,0],[0,0,0]],[[0,0,0],[0,0,0]]]};function O(t,e){var r,n,i,o=e.axes&&e.axes.lastCubeProps.axis||L,a=e.showSurface,s=e.showContour;for(r=0;r<3;++r)for(a=a||e.surfaceProject[r],n=0;n<3;++n)s=s||e.contourProject[r][n];for(r=0;r<3;++r){var l=z.projections[r];for(n=0;n<16;++n)l[n]=0;for(n=0;n<4;++n)l[5*n]=1;l[5*r]=0,l[12+r]=e.axesBounds[+(o[r]>0)][r],f(l,t.model,l);var c=z.clipBounds[r];for(i=0;i<2;++i)for(n=0;n<3;++n)c[i][n]=t.clipBounds[i][n];c[0][r]=-1e8,c[1][r]=1e8}return z.showSurface=a,z.showContour=s,z}var D={model:k,view:k,projection:k,inverseModel:k.slice(),lowerBound:[0,0,0],upperBound:[0,0,0],colorMap:0,clipBounds:[[0,0,0],[0,0,0]],height:0,contourTint:0,contourColor:[0,0,0,1],permutation:[1,0,0,0,1,0,0,0,1],zOffset:-1e-4,objectOffset:[0,0,0],kambient:1,kdiffuse:1,kspecular:1,lightPosition:[1e3,1e3,1e3],eyePosition:[0,0,0],roughness:1,fresnel:1,opacity:1,vertexColor:0},I=k.slice(),F=[1,0,0,0,1,0,0,0,1];function R(t,e){t=t||{};var r=this.gl;r.disable(r.CULL_FACE),this._colorMap.bind(0);var n=D;n.model=t.model||k,n.view=t.view||k,n.projection=t.projection||k,n.lowerBound=[this.bounds[0][0],this.bounds[0][1],this.colorBounds[0]||this.bounds[0][2]],n.upperBound=[this.bounds[1][0],this.bounds[1][1],this.colorBounds[1]||this.bounds[1][2]],n.objectOffset=this.objectOffset,n.contourColor=this.contourColor[0],n.inverseModel=p(n.inverseModel,n.model);for(var i=0;i<2;++i)for(var o=n.clipBounds[i],a=0;a<3;++a)o[a]=Math.min(Math.max(this.clipBounds[i][a],-1e8),1e8);n.kambient=this.ambientLight,n.kdiffuse=this.diffuseLight,n.kspecular=this.specularLight,n.roughness=this.roughness,n.fresnel=this.fresnel,n.opacity=this.opacity,n.height=0,n.permutation=F,n.vertexColor=this.vertexColor;var s=I;for(f(s,n.view,n.model),f(s,n.projection,s),p(s,s),i=0;i<3;++i)n.eyePosition[i]=s[12+i]/s[15];var l=s[15];for(i=0;i<3;++i)l+=this.lightPosition[i]*s[4*i+3];for(i=0;i<3;++i){var c=s[12+i];for(a=0;a<3;++a)c+=s[4*a+i]*this.lightPosition[a];n.lightPosition[i]=c/l}var u=O(n,this);if(u.showSurface){for(this._shader.bind(),this._shader.uniforms=n,this._vao.bind(),this.showSurface&&this._vertexCount&&this._vao.draw(r.TRIANGLES,this._vertexCount),i=0;i<3;++i)this.surfaceProject[i]&&this.vertexCount&&(this._shader.uniforms.model=u.projections[i],this._shader.uniforms.clipBounds=u.clipBounds[i],this._vao.draw(r.TRIANGLES,this._vertexCount));this._vao.unbind()}if(u.showContour){var h=this._contourShader;n.kambient=1,n.kdiffuse=0,n.kspecular=0,n.opacity=1,h.bind(),h.uniforms=n;var d=this._contourVAO;for(d.bind(),i=0;i<3;++i)for(h.uniforms.permutation=M[i],r.lineWidth(this.contourWidth[i]*this.pixelRatio),a=0;a>4)/16)/255,i=Math.floor(n),o=n-i,a=e[1]*(t.value[1]+(15&t.value[2])/16)/255,s=Math.floor(a),l=a-s;i+=1,s+=1;var c=r.position;c[0]=c[1]=c[2]=0;for(var u=0;u<2;++u)for(var h=u?o:1-o,d=0;d<2;++d)for(var f=i+u,p=s+d,g=h*(d?l:1-l),v=0;v<3;++v)c[v]+=this._field[v].get(f,p)*g;for(var b=this._pickResult.level,y=0;y<3;++y)if(b[y]=m.le(this.contourLevels[y],c[y]),b[y]<0)this.contourLevels[y].length>0&&(b[y]=0);else if(b[y]Math.abs(_-c[y])&&(b[y]+=1)}for(r.index[0]=o<.5?i:i+1,r.index[1]=l<.5?s:s+1,r.uv[0]=n/e[0],r.uv[1]=a/e[1],v=0;v<3;++v)r.dataCoordinate[v]=this._field[v].get(r.index[0],r.index[1]);return r},E.padField=function(t,e){var r=e.shape.slice(),n=t.shape.slice();c.assign(t.lo(1,1).hi(r[0],r[1]),e),c.assign(t.lo(1).hi(r[0],1),e.hi(r[0],1)),c.assign(t.lo(1,n[1]-1).hi(r[0],1),e.lo(0,r[1]-1).hi(r[0],1)),c.assign(t.lo(0,1).hi(1,r[1]),e.hi(1)),c.assign(t.lo(n[0]-1,1).hi(1,r[1]),e.lo(r[0]-1)),t.set(0,0,e.get(0,0)),t.set(0,n[1]-1,e.get(0,r[1]-1)),t.set(n[0]-1,0,e.get(r[0]-1,0)),t.set(n[0]-1,n[1]-1,e.get(r[0]-1,r[1]-1))},E.update=function(t){t=t||{},this.objectOffset=t.objectOffset||this.objectOffset,this.dirty=!0,"contourWidth"in t&&(this.contourWidth=j(t.contourWidth,Number)),"showContour"in t&&(this.showContour=j(t.showContour,Boolean)),"showSurface"in t&&(this.showSurface=!!t.showSurface),"contourTint"in t&&(this.contourTint=j(t.contourTint,Boolean)),"contourColor"in t&&(this.contourColor=B(t.contourColor)),"contourProject"in t&&(this.contourProject=j(t.contourProject,(function(t){return j(t,Boolean)}))),"surfaceProject"in t&&(this.surfaceProject=t.surfaceProject),"dynamicColor"in t&&(this.dynamicColor=B(t.dynamicColor)),"dynamicTint"in t&&(this.dynamicTint=j(t.dynamicTint,Number)),"dynamicWidth"in t&&(this.dynamicWidth=j(t.dynamicWidth,Number)),"opacity"in t&&(this.opacity=t.opacity),"opacityscale"in t&&(this.opacityscale=t.opacityscale),"colorBounds"in t&&(this.colorBounds=t.colorBounds),"vertexColor"in t&&(this.vertexColor=t.vertexColor?1:0),"colormap"in t&&this._colorMap.setPixels(this.genColormap(t.colormap,this.opacityscale));var e=t.field||t.coords&&t.coords[2]||null,r=!1;if(e||(e=this._field[2].shape[0]||this._field[2].shape[2]?this._field[2].lo(1,1).hi(this._field[2].shape[0]-2,this._field[2].shape[1]-2):this._field[2].hi(0,0)),"field"in t||"coords"in t){var i=(e.shape[0]+2)*(e.shape[1]+2);i>this._field[2].data.length&&(s.freeFloat(this._field[2].data),this._field[2].data=s.mallocFloat(n.nextPow2(i))),this._field[2]=h(this._field[2].data,[e.shape[0]+2,e.shape[1]+2]),this.padField(this._field[2],e),this.shape=e.shape.slice();for(var o=this.shape,a=0;a<2;++a)this._field[2].size>this._field[a].data.length&&(s.freeFloat(this._field[a].data),this._field[a].data=s.mallocFloat(this._field[2].size)),this._field[a]=h(this._field[a].data,[o[0]+2,o[1]+2]);if(t.coords){var l=t.coords;if(!Array.isArray(l)||3!==l.length)throw new Error("gl-surface: invalid coordinates for x/y");for(a=0;a<2;++a){var c=l[a];for(v=0;v<2;++v)if(c.shape[v]!==o[v])throw new Error("gl-surface: coords have incorrect shape");this.padField(this._field[a],c)}}else if(t.ticks){var u=t.ticks;if(!Array.isArray(u)||2!==u.length)throw new Error("gl-surface: invalid ticks");for(a=0;a<2;++a){var f=u[a];if((Array.isArray(f)||f.length)&&(f=h(f)),f.shape[0]!==o[a])throw new Error("gl-surface: invalid tick length");var p=h(f.data,o);p.stride[a]=f.stride[0],p.stride[1^a]=0,this.padField(this._field[a],p)}}else{for(a=0;a<2;++a){var m=[0,0];m[a]=1,this._field[a]=h(this._field[a].data,[o[0]+2,o[1]+2],m,0)}this._field[0].set(0,0,0);for(var v=0;v0){for(var yt=0;yt<5;++yt)K.pop();U-=1}continue t}K.push(nt[0],nt[1],at[0],at[1],nt[2]),U+=1}}rt.push(U)}this._contourOffsets[Q]=et,this._contourCounts[Q]=rt}var xt=s.mallocFloat(K.length);for(a=0;as||a[1]<0||a[1]>s)throw new Error("gl-texture2d: Invalid texture size");var l=p(a,e.stride.slice()),c=0;"float32"===r?c=t.FLOAT:"float64"===r?(c=t.FLOAT,l=!1,r="float32"):"uint8"===r?c=t.UNSIGNED_BYTE:(c=t.UNSIGNED_BYTE,l=!1,r="uint8");var h,f,g=0;if(2===a.length)g=t.LUMINANCE,a=[a[0],a[1],1],e=n(e.data,a,[e.stride[0],e.stride[1],1],e.offset);else{if(3!==a.length)throw new Error("gl-texture2d: Invalid shape for texture");if(1===a[2])g=t.ALPHA;else if(2===a[2])g=t.LUMINANCE_ALPHA;else if(3===a[2])g=t.RGB;else{if(4!==a[2])throw new Error("gl-texture2d: Invalid shape for pixel coords");g=t.RGBA}}c!==t.FLOAT||t.getExtension("OES_texture_float")||(c=t.UNSIGNED_BYTE,l=!1);var v=e.size;if(l)h=0===e.offset&&e.data.length===v?e.data:e.data.subarray(e.offset,e.offset+v);else{var b=[a[2],a[2]*a[0],1];f=o.malloc(v,r);var y=n(f,a,b,0);"float32"!==r&&"float64"!==r||c!==t.UNSIGNED_BYTE?i.assign(y,e):u(y,e),h=f.subarray(0,v)}var x=m(t);return t.texImage2D(t.TEXTURE_2D,0,g,a[0],a[1],0,g,c,h),l||o.free(f),new d(t,x,a[0],a[1],g,c)}(t,e)}throw new Error("gl-texture2d: Invalid arguments for texture2d constructor")};var a=null,s=null,l=null;function c(t){return"undefined"!=typeof HTMLCanvasElement&&t instanceof HTMLCanvasElement||"undefined"!=typeof HTMLImageElement&&t instanceof HTMLImageElement||"undefined"!=typeof HTMLVideoElement&&t instanceof HTMLVideoElement||"undefined"!=typeof ImageData&&t instanceof ImageData}var u=function(t,e){i.muls(t,e,255)};function h(t,e,r){var n=t.gl,i=n.getParameter(n.MAX_TEXTURE_SIZE);if(e<0||e>i||r<0||r>i)throw new Error("gl-texture2d: Invalid texture size");return t._shape=[e,r],t.bind(),n.texImage2D(n.TEXTURE_2D,0,t.format,e,r,0,t.format,t.type,null),t._mipLevels=[0],t}function d(t,e,r,n,i,o){this.gl=t,this.handle=e,this.format=i,this.type=o,this._shape=[r,n],this._mipLevels=[0],this._magFilter=t.NEAREST,this._minFilter=t.NEAREST,this._wrapS=t.CLAMP_TO_EDGE,this._wrapT=t.CLAMP_TO_EDGE,this._anisoSamples=1;var a=this,s=[this._wrapS,this._wrapT];Object.defineProperties(s,[{get:function(){return a._wrapS},set:function(t){return a.wrapS=t}},{get:function(){return a._wrapT},set:function(t){return a.wrapT=t}}]),this._wrapVector=s;var l=[this._shape[0],this._shape[1]];Object.defineProperties(l,[{get:function(){return a._shape[0]},set:function(t){return a.width=t}},{get:function(){return a._shape[1]},set:function(t){return a.height=t}}]),this._shapeVector=l}var f=d.prototype;function p(t,e){return 3===t.length?1===e[2]&&e[1]===t[0]*t[2]&&e[0]===t[2]:1===e[0]&&e[1]===t[0]}function m(t){var e=t.createTexture();return t.bindTexture(t.TEXTURE_2D,e),t.texParameteri(t.TEXTURE_2D,t.TEXTURE_MIN_FILTER,t.NEAREST),t.texParameteri(t.TEXTURE_2D,t.TEXTURE_MAG_FILTER,t.NEAREST),t.texParameteri(t.TEXTURE_2D,t.TEXTURE_WRAP_S,t.CLAMP_TO_EDGE),t.texParameteri(t.TEXTURE_2D,t.TEXTURE_WRAP_T,t.CLAMP_TO_EDGE),e}function g(t,e,r,n,i){var o=t.getParameter(t.MAX_TEXTURE_SIZE);if(e<0||e>o||r<0||r>o)throw new Error("gl-texture2d: Invalid texture shape");if(i===t.FLOAT&&!t.getExtension("OES_texture_float"))throw new Error("gl-texture2d: Floating point textures not supported on this platform");var a=m(t);return 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6:u.push([t-.5-.25*(-n-r+o+i)/(n-r+i-o),e-.5-.25*(-i-r+o+n)/(i-r+n-o)]);break;case 7:u.push([t-.75-.25*(o+i-2*d)/(i-o),e-.75-.25*(o+n-2*d)/(n-o)]);break;case 8:u.push([t-.75-.25*(-o-i+2*d)/(o-i),e-.75-.25*(-o-n+2*d)/(o-n)]);break;case 9:u.push([t-.5-.25*(n+r+-o-i)/(r-n+o-i),e-.5-.25*(i+r+-o-n)/(r-i+o-n)]);break;case 10:u.push([t-.5-.5*(-n-r-o-i+4*d)/(n-r+o-i),e-.5]);break;case 11:u.push([t-.25-.25*(-o-i+2*d)/(o-i),e-.75-.25*(i+r-2*d)/(r-i)]);break;case 12:u.push([t-.5,e-.5-.5*(-i-r-o-n+4*d)/(i-r+o-n)]);break;case 13:u.push([t-.75-.25*(n+r-2*d)/(r-n),e-.25-.25*(-o-n+2*d)/(o-n)]);break;case 14:u.push([t-.25-.25*(-n-r+2*d)/(n-r),e-.25-.25*(-i-r+2*d)/(i-r)])}},cell:function(t,e,r,n,i,o,a,s,l){i?s.push([t,e]):s.push([e,t])}});return function(t,e){var r=[],i=[];return n(t,r,i,e),{positions:r,cells:i}}}},a={}},529:function(t,e,r){"use strict";t.exports=function t(e,r,n){var o=(n=n||{}).fontStyle||"normal",s=n.fontWeight||"normal",l=n.fontVariant||"normal",c=[o,s,l,e].join("_"),u=a[c];u||(u=a[c]={" ":{data:new Float32Array(0),shape:.2}});var h=u[r];if(!h)if(r.length<=1||!/\d/.test(r))h=u[r]=function(t){for(var e=t.cells,r=t.positions,n=new Float32Array(6*e.length),i=0,o=0,a=0;a0&&(m+=.02);var v=new Float32Array(p),b=0,y=-.5*m;for(g=0;gMath.max(r,n)?i[2]=1:r>Math.max(e,n)?i[0]=1:i[1]=1;for(var o=0,a=0,l=0;l<3;++l)o+=t[l]*t[l],a+=i[l]*t[l];for(l=0;l<3;++l)i[l]-=a/o*t[l];return s(i,i),i}function d(t,e,r,i,o,a,s,l){this.center=n(r),this.up=n(i),this.right=n(o),this.radius=n([a]),this.angle=n([s,l]),this.angle.bounds=[[-1/0,-Math.PI/2],[1/0,Math.PI/2]],this.setDistanceLimits(t,e),this.computedCenter=this.center.curve(0),this.computedUp=this.up.curve(0),this.computedRight=this.right.curve(0),this.computedRadius=this.radius.curve(0),this.computedAngle=this.angle.curve(0),this.computedToward=[0,0,0],this.computedEye=[0,0,0],this.computedMatrix=new Array(16);for(var c=0;c<16;++c)this.computedMatrix[c]=.5;this.recalcMatrix(0)}var f=d.prototype;f.setDistanceLimits=function(t,e){t=t>0?Math.log(t):-1/0,e=e>0?Math.log(e):1/0,e=Math.max(e,t),this.radius.bounds[0][0]=t,this.radius.bounds[1][0]=e},f.getDistanceLimits=function(t){var e=this.radius.bounds[0];return t?(t[0]=Math.exp(e[0][0]),t[1]=Math.exp(e[1][0]),t):[Math.exp(e[0][0]),Math.exp(e[1][0])]},f.recalcMatrix=function(t){this.center.curve(t),this.up.curve(t),this.right.curve(t),this.radius.curve(t),this.angle.curve(t);for(var e=this.computedUp,r=this.computedRight,n=0,i=0,o=0;o<3;++o)i+=e[o]*r[o],n+=e[o]*e[o];var l=Math.sqrt(n),u=0;for(o=0;o<3;++o)r[o]-=e[o]*i/n,u+=r[o]*r[o],e[o]/=l;var h=Math.sqrt(u);for(o=0;o<3;++o)r[o]/=h;var d=this.computedToward;a(d,e,r),s(d,d);var f=Math.exp(this.computedRadius[0]),p=this.computedAngle[0],m=this.computedAngle[1],g=Math.cos(p),v=Math.sin(p),b=Math.cos(m),y=Math.sin(m),x=this.computedCenter,_=g*b,w=v*b,k=y,A=-g*y,M=-v*y,T=b,S=this.computedEye,C=this.computedMatrix;for(o=0;o<3;++o){var E=_*r[o]+w*d[o]+k*e[o];C[4*o+1]=A*r[o]+M*d[o]+T*e[o],C[4*o+2]=E,C[4*o+3]=0}var L=C[1],z=C[5],O=C[9],D=C[2],I=C[6],F=C[10],R=z*F-O*I,P=O*D-L*F,j=L*I-z*D,N=c(R,P,j);for(R/=N,P/=N,j/=N,C[0]=R,C[4]=P,C[8]=j,o=0;o<3;++o)S[o]=x[o]+C[2+4*o]*f;for(o=0;o<3;++o){u=0;for(var B=0;B<3;++B)u+=C[o+4*B]*S[B];C[12+o]=-u}C[15]=1},f.getMatrix=function(t,e){this.recalcMatrix(t);var r=this.computedMatrix;if(e){for(var n=0;n<16;++n)e[n]=r[n];return e}return r};var p=[0,0,0];f.rotate=function(t,e,r,n){if(this.angle.move(t,e,r),n){this.recalcMatrix(t);var i=this.computedMatrix;p[0]=i[2],p[1]=i[6],p[2]=i[10];for(var a=this.computedUp,s=this.computedRight,l=this.computedToward,c=0;c<3;++c)i[4*c]=a[c],i[4*c+1]=s[c],i[4*c+2]=l[c];for(o(i,i,n,p),c=0;c<3;++c)a[c]=i[4*c],s[c]=i[4*c+1];this.up.set(t,a[0],a[1],a[2]),this.right.set(t,s[0],s[1],s[2])}},f.pan=function(t,e,r,n){e=e||0,r=r||0,n=n||0,this.recalcMatrix(t);var i=this.computedMatrix,o=(Math.exp(this.computedRadius[0]),i[1]),a=i[5],s=i[9],l=c(o,a,s);o/=l,a/=l,s/=l;var u=i[0],h=i[4],d=i[8],f=u*o+h*a+d*s,p=c(u-=o*f,h-=a*f,d-=s*f),m=(u/=p)*e+o*r,g=(h/=p)*e+a*r,v=(d/=p)*e+s*r;this.center.move(t,m,g,v);var b=Math.exp(this.computedRadius[0]);b=Math.max(1e-4,b+n),this.radius.set(t,Math.log(b))},f.translate=function(t,e,r,n){this.center.move(t,e||0,r||0,n||0)},f.setMatrix=function(t,e,r,n){var o=1;"number"==typeof r&&(o=0|r),(o<0||o>3)&&(o=1);var a=(o+2)%3;e||(this.recalcMatrix(t),e=this.computedMatrix);var s=e[o],l=e[o+4],h=e[o+8];if(n){var d=Math.abs(s),f=Math.abs(l),p=Math.abs(h),m=Math.max(d,f,p);d===m?(s=s<0?-1:1,l=h=0):p===m?(h=h<0?-1:1,s=l=0):(l=l<0?-1:1,s=h=0)}else{var g=c(s,l,h);s/=g,l/=g,h/=g}var v,b,y=e[a],x=e[a+4],_=e[a+8],w=y*s+x*l+_*h,k=c(y-=s*w,x-=l*w,_-=h*w),A=l*(_/=k)-h*(x/=k),M=h*(y/=k)-s*_,T=s*x-l*y,S=c(A,M,T);if(A/=S,M/=S,T/=S,this.center.jump(t,H,W,q),this.radius.idle(t),this.up.jump(t,s,l,h),this.right.jump(t,y,x,_),2===o){var C=e[1],E=e[5],L=e[9],z=C*y+E*x+L*_,O=C*A+E*M+L*T;v=R<0?-Math.PI/2:Math.PI/2,b=Math.atan2(O,z)}else{var D=e[2],I=e[6],F=e[10],R=D*s+I*l+F*h,P=D*y+I*x+F*_,j=D*A+I*M+F*T;v=Math.asin(u(R)),b=Math.atan2(j,P)}this.angle.jump(t,b,v),this.recalcMatrix(t);var N=e[2],B=e[6],U=e[10],G=this.computedMatrix;i(G,e);var V=G[15],H=G[12]/V,W=G[13]/V,q=G[14]/V,Y=Math.exp(this.computedRadius[0]);this.center.jump(t,H-N*Y,W-B*Y,q-U*Y)},f.lastT=function(){return 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enableEndMiter;\n\nconst float REVERSE_THRESHOLD = -.875;\nconst float MIN_DIFF = 1e-6;\n\n// TODO: possible optimizations: avoid overcalculating all for vertices and calc just one instead\n// TODO: precalculate dot products, normalize things beforehead etc.\n// TODO: refactor to rectangular algorithm\n\nfloat distToLine(vec2 p, vec2 a, vec2 b) {\n\tvec2 diff = b - a;\n\tvec2 perp = normalize(vec2(-diff.y, diff.x));\n\treturn dot(p - a, perp);\n}\n\nbool isNaN( float val ){\n return ( val < 0.0 || 0.0 < val || val == 0.0 ) ? false : true;\n}\n\nvoid main() {\n\tvec2 aCoord = aCoord, bCoord = bCoord, prevCoord = prevCoord, nextCoord = nextCoord;\n\n vec2 adjustedScale;\n adjustedScale.x = (abs(scale.x) < MIN_DIFF) ? MIN_DIFF : scale.x;\n adjustedScale.y = (abs(scale.y) < MIN_DIFF) ? MIN_DIFF : scale.y;\n\n vec2 scaleRatio = adjustedScale * viewport.zw;\n\tvec2 normalWidth = thickness / scaleRatio;\n\n\tfloat lineStart = 1. - lineEnd;\n\tfloat lineBot = 1. - lineTop;\n\n\tfragColor = (lineStart * aColor + lineEnd * bColor) / 255.;\n\n\tif (isNaN(aCoord.x) || isNaN(aCoord.y) || isNaN(bCoord.x) || isNaN(bCoord.y)) return;\n\n\tif (aCoord == prevCoord) prevCoord = aCoord + normalize(bCoord - aCoord);\n\tif (bCoord == nextCoord) nextCoord = bCoord - normalize(bCoord - aCoord);\n\n\n\tvec2 prevDiff = aCoord - prevCoord;\n\tvec2 currDiff = bCoord - aCoord;\n\tvec2 nextDiff = nextCoord - bCoord;\n\n\tvec2 prevTangent = normalize(prevDiff * scaleRatio);\n\tvec2 currTangent = normalize(currDiff * scaleRatio);\n\tvec2 nextTangent = normalize(nextDiff * scaleRatio);\n\n\tvec2 prevNormal = vec2(-prevTangent.y, prevTangent.x);\n\tvec2 currNormal = vec2(-currTangent.y, currTangent.x);\n\tvec2 nextNormal = vec2(-nextTangent.y, nextTangent.x);\n\n\tvec2 startJoinDirection = normalize(prevTangent - currTangent);\n\tvec2 endJoinDirection = normalize(currTangent - nextTangent);\n\n\t// collapsed/unidirectional segment cases\n\t// FIXME: there should be more elegant solution\n\tvec2 prevTanDiff = abs(prevTangent - currTangent);\n\tvec2 nextTanDiff = abs(nextTangent - currTangent);\n\tif (max(prevTanDiff.x, prevTanDiff.y) < MIN_DIFF) {\n\t\tstartJoinDirection = currNormal;\n\t}\n\tif (max(nextTanDiff.x, nextTanDiff.y) < MIN_DIFF) {\n\t\tendJoinDirection = currNormal;\n\t}\n\tif (aCoord == bCoord) {\n\t\tendJoinDirection = startJoinDirection;\n\t\tcurrNormal = prevNormal;\n\t\tcurrTangent = prevTangent;\n\t}\n\n\ttangent = currTangent;\n\n\t//calculate join shifts relative to normals\n\tfloat startJoinShift = dot(currNormal, startJoinDirection);\n\tfloat endJoinShift = dot(currNormal, endJoinDirection);\n\n\tfloat startMiterRatio = abs(1. / startJoinShift);\n\tfloat endMiterRatio = abs(1. / endJoinShift);\n\n\tvec2 startJoin = startJoinDirection * startMiterRatio;\n\tvec2 endJoin = endJoinDirection * endMiterRatio;\n\n\tvec2 startTopJoin, startBotJoin, endTopJoin, endBotJoin;\n\tstartTopJoin = sign(startJoinShift) * startJoin * .5;\n\tstartBotJoin = -startTopJoin;\n\n\tendTopJoin = sign(endJoinShift) * endJoin * .5;\n\tendBotJoin = -endTopJoin;\n\n\tvec2 aTopCoord = aCoord + normalWidth * startTopJoin;\n\tvec2 bTopCoord = bCoord + normalWidth * endTopJoin;\n\tvec2 aBotCoord = aCoord + normalWidth * startBotJoin;\n\tvec2 bBotCoord = bCoord + normalWidth * endBotJoin;\n\n\t//miter anti-clipping\n\tfloat baClipping = distToLine(bCoord, aCoord, aBotCoord) / dot(normalize(normalWidth * endBotJoin), normalize(normalWidth.yx * vec2(-startBotJoin.y, startBotJoin.x)));\n\tfloat abClipping = distToLine(aCoord, bCoord, bTopCoord) / dot(normalize(normalWidth * startBotJoin), normalize(normalWidth.yx * vec2(-endBotJoin.y, endBotJoin.x)));\n\n\t//prevent close to reverse direction switch\n\tbool prevReverse = dot(currTangent, prevTangent) <= REVERSE_THRESHOLD && abs(dot(currTangent, prevNormal)) * min(length(prevDiff), length(currDiff)) < length(normalWidth * currNormal);\n\tbool nextReverse = dot(currTangent, nextTangent) <= REVERSE_THRESHOLD && abs(dot(currTangent, nextNormal)) * min(length(nextDiff), length(currDiff)) < length(normalWidth * currNormal);\n\n\tif (prevReverse) {\n\t\t//make join rectangular\n\t\tvec2 miterShift = normalWidth * startJoinDirection * miterLimit * .5;\n\t\tfloat normalAdjust = 1. - min(miterLimit / startMiterRatio, 1.);\n\t\taBotCoord = aCoord + miterShift - normalAdjust * normalWidth * currNormal * .5;\n\t\taTopCoord = aCoord + miterShift + normalAdjust * normalWidth * currNormal * .5;\n\t}\n\telse if (!nextReverse && baClipping > 0. && baClipping < length(normalWidth * endBotJoin)) {\n\t\t//handle miter clipping\n\t\tbTopCoord -= normalWidth * endTopJoin;\n\t\tbTopCoord += normalize(endTopJoin * normalWidth) * baClipping;\n\t}\n\n\tif (nextReverse) {\n\t\t//make join rectangular\n\t\tvec2 miterShift = normalWidth * endJoinDirection * miterLimit * .5;\n\t\tfloat normalAdjust = 1. - min(miterLimit / endMiterRatio, 1.);\n\t\tbBotCoord = bCoord + miterShift - normalAdjust * normalWidth * currNormal * .5;\n\t\tbTopCoord = bCoord + miterShift + normalAdjust * normalWidth * currNormal * .5;\n\t}\n\telse if (!prevReverse && abClipping > 0. && abClipping < length(normalWidth * startBotJoin)) {\n\t\t//handle miter clipping\n\t\taBotCoord -= normalWidth * startBotJoin;\n\t\taBotCoord += normalize(startBotJoin * normalWidth) * abClipping;\n\t}\n\n\tvec2 aTopPosition = (aTopCoord) * adjustedScale + translate;\n\tvec2 aBotPosition = (aBotCoord) * adjustedScale + translate;\n\n\tvec2 bTopPosition = (bTopCoord) * adjustedScale + translate;\n\tvec2 bBotPosition = (bBotCoord) * adjustedScale + translate;\n\n\t//position is normalized 0..1 coord on the screen\n\tvec2 position = (aTopPosition * lineTop + aBotPosition * lineBot) * lineStart + (bTopPosition * lineTop + bBotPosition * lineBot) * lineEnd;\n\n\tstartCoord = aCoord * scaleRatio + translate * viewport.zw + viewport.xy;\n\tendCoord = bCoord * scaleRatio + translate * viewport.zw + viewport.xy;\n\n\tgl_Position = vec4(position * 2.0 - 1.0, depth, 1);\n\n\tenableStartMiter = step(dot(currTangent, prevTangent), .5);\n\tenableEndMiter = step(dot(currTangent, nextTangent), .5);\n\n\t//bevel miter cutoffs\n\tif (miterMode == 1.) {\n\t\tif (enableStartMiter == 1.) {\n\t\t\tvec2 startMiterWidth = vec2(startJoinDirection) * thickness * miterLimit * .5;\n\t\t\tstartCutoff = vec4(aCoord, aCoord);\n\t\t\tstartCutoff.zw += vec2(-startJoinDirection.y, startJoinDirection.x) / scaleRatio;\n\t\t\tstartCutoff = startCutoff * scaleRatio.xyxy + translate.xyxy * viewport.zwzw;\n\t\t\tstartCutoff += viewport.xyxy;\n\t\t\tstartCutoff += startMiterWidth.xyxy;\n\t\t}\n\n\t\tif (enableEndMiter == 1.) {\n\t\t\tvec2 endMiterWidth = vec2(endJoinDirection) * thickness * miterLimit * .5;\n\t\t\tendCutoff = vec4(bCoord, bCoord);\n\t\t\tendCutoff.zw += vec2(-endJoinDirection.y, endJoinDirection.x) / scaleRatio;\n\t\t\tendCutoff = endCutoff * scaleRatio.xyxy + translate.xyxy * viewport.zwzw;\n\t\t\tendCutoff += viewport.xyxy;\n\t\t\tendCutoff += endMiterWidth.xyxy;\n\t\t}\n\t}\n\n\t//round miter cutoffs\n\telse if (miterMode == 2.) {\n\t\tif (enableStartMiter == 1.) {\n\t\t\tvec2 startMiterWidth = vec2(startJoinDirection) * thickness * abs(dot(startJoinDirection, currNormal)) * .5;\n\t\t\tstartCutoff = vec4(aCoord, aCoord);\n\t\t\tstartCutoff.zw += vec2(-startJoinDirection.y, startJoinDirection.x) / scaleRatio;\n\t\t\tstartCutoff = startCutoff * scaleRatio.xyxy + translate.xyxy * viewport.zwzw;\n\t\t\tstartCutoff += viewport.xyxy;\n\t\t\tstartCutoff += startMiterWidth.xyxy;\n\t\t}\n\n\t\tif (enableEndMiter == 1.) {\n\t\t\tvec2 endMiterWidth = vec2(endJoinDirection) * thickness * abs(dot(endJoinDirection, currNormal)) * .5;\n\t\t\tendCutoff = vec4(bCoord, bCoord);\n\t\t\tendCutoff.zw += 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CSSStyleSheet;this._styles={noCell:s,noEnvs:l,noShape:c,noProperties:u},this._shadow.adoptedStyleSheets=[...r.getRootNode().adoptedStyleSheets,s,l,c,u],this._options=new f.O(this._root,(t=>this.positionSettingsModal(t)),e),this._options.modal.shadow.adoptedStyleSheets=[...this._options.modal.shadow.adoptedStyleSheets,s,l,c,u],this._colorReset=this._options.getModalElement("atom-color-reset"),this._colorMoreOptions=this._options.getModalElement("atom-color-more-options"),this._colorMoreOptions.disabled=!0,this._connectOptions(),this._trajectoryOptions=this._options.getModalElement("trajectory-settings-group"),this.positionSettingsModal=t=>{const e=this._root.getBoundingClientRect();return{left:e.left+e.width/2-t.width/2,top:e.top+20}},this._root.addEventListener("wheel",(t=>{if(t.isTrusted){t.preventDefault(),t.stopImmediatePropagation();const e=new Event("wheel");Object.assign(e,{ctrlKey:!0,detail:t.detail,wheelDelta:t.wheelDelta,pageX:t.pageX,pageY:t.pageY}),i()(t.target,"event.target"),t.target.dispatchEvent(e)}}),{capture:!0}),window.addEventListener("resize",(()=>this.resize())),window.requestAnimationFrame((()=>{window.dispatchEvent(new Event("resize"))}))}refreshOptions(t,e){const r=this._options.modal.shadow.adoptedStyleSheets;this._options.remove(),this._options=new f.O(this._root,(t=>this.positionSettingsModal(t)),e),this._options.modal.shadow.adoptedStyleSheets=r,this._colorReset=this._options.getModalElement("atom-color-reset"),this._colorMoreOptions=this._options.getModalElement("atom-color-more-options"),this._trajectoryOptions=this._options.getModalElement("trajectory-settings-group"),this._colorReset.disabled=!0,this._colorMoreOptions.disabled=!0,this._connectOptions(),t?this._options.environments.activated.enable():this._options.environments.activated.disable()}remove(){null!==this._root.parentElement&&(this._root.parentElement.innerHTML=""),this._options.remove()}resize(){this._viewer.resize(),this._updateColorBar()}natoms(){return void 0===this._current?void 0:this._current.structure.size}set environments(t){this._environments=t}load(t,e,r={},n){let a,s,l,c,h;if(this.resize(),this._properties=e,void 0!==this._highlighted&&(a=this._defaultCutoff(this._highlighted.center)),this._environments=r.environments,s=void 0===r.keepOrientation?this._options.keepOrientation.value:r.keepOrientation,void 0===r.supercell?[l,c,h]=[this._options.supercell[0].value,this._options.supercell[1].value,this._options.supercell[2].value]:([l,c,h]=r.supercell,this._options.supercell[0].value=l,this._options.supercell[1].value=c,this._options.supercell[2].value=h),void 0===this._initialSupercell&&(this._initialSupercell=[l,c,h],this._resetSupercell.innerHTML=`reset ${l}x${c}x${h} supercell`),void 0===t.cell?this._styles.noCell.replaceSync(".chsp-hide-if-no-cell { display: none; }"):this._styles.noCell.replaceSync(""),this._showSupercellInfo(),void 0!==r.trajectory&&r.trajectory?this._trajectoryOptions.style.display="block":this._trajectoryOptions.style.display="none",this._options.unitCell.value&&void 0!==this._current&&this._viewer.removeUnitCell(this._current.model),this._viewer.removeAllModels(),void 0!==this._current)for(const t of this._current.atomLabels)this._viewer.removeLabel(t);void 0!==this._highlighted&&(this._viewer.removeModel(this._highlighted.model),this._highlighted=void 0),this._current={model:this._viewer.addModel(),structure:t,atomLabels:[]},function(t,e){if(void 0!==e.cell){const r=e.cell,n=new o.Matrix3(r[0],r[3],r[6],r[1],r[4],r[7],r[2],r[5],r[8]);t.setCrystMatrix(n)}const r=[];for(let t=0;t{n&&n()}))}_setEnvironmentInteractions(){if(void 0===this._environments)return;const t=this._environments.filter((t=>void 0!==t)).map((t=>t.center));for(const t of this._viewer.selectedAtoms({}))t.clickable=!1,t.hoverable=!1;i()(void 0!==this._current,"this._current !== undefined"),this._viewer.setClickable({model:this._current.model,index:t},!0,(t=>this._selectAtom(t))),this._setHoverable(t)}highlight(t){let e;void 0!==this._highlighted&&(e=this._defaultCutoff(this._highlighted.center)),this._changeHighlighted(t,e),this._updateStyle();const r=this._options.environments.center.value;void 0!==this._highlighted&&r&&(this._options.keepOrientation.value||this._resetView(),this._centerView()),this._viewer.render()}applySettings(t){this._options.applySettings(t)}saveSettings(){return this._options.saveSettings()}onSettingChange(t){this._options.onSettingChange(t)}exportPNG(){return this._viewer.pngURI()}_setHoverable(t){i()(void 0!==this._current,"this._current !== undefined"),this._viewer.setHoverDuration(0);const e=this.natoms();i()(void 0!==e,"n_atoms !== undefined");const r=new Map;this._viewer.setHoverable({model:this._current.model,index:t},!0,(t=>{if(i()(void 0!==t.index,"atom.index !== undefined"),void 0!==r.get(t.index))return;const e=this._viewer.addModel();e.addAtoms([t]),e.setStyle({},this._centralStyle(.3));const n=e.selectedAtoms({});n[0].clickable=!1,n[0].hoverable=!1,r.set(t.index,e),this._viewer.render()}),(t=>{i()(void 0!==t.index,"atom.index !== undefined");const e=r.get(t.index);void 0!==e&&(this._viewer.removeModel(e),r.delete(t.index),this._viewer.render())}))}_connectOptions(){const t=()=>{this._updateStyle(),this._viewer.render()};this._options.spaceFilling.onchange.push(t),this._options.bonds.onchange.push(t),this._options.atoms.onchange.push(t),this._options.atomLabels.onchange.push((t=>{if(void 0!==this._current)if(t){i()(0===this._current.atomLabels.length,"this._current.atomLabels.length === 0");const t=this._current.structure;for(let e=0;ethis._addAxes(t))),this._options.rotation.onchange.push((t=>{t?this._viewer.spin("vy"):this._viewer.spin(!1)})),this._options.unitCell.onchange.push((t=>{void 0!==this._current&&(t?this._viewer.addUnitCell(this._current.model,{box:{color:"black"},astyle:{hidden:!0},bstyle:{hidden:!0},cstyle:{hidden:!0}}):this._viewer.removeUnitCell(this._current.model),this._viewer.render())})),this._options.shape.onchange.push((()=>{void 0!==this._current&&(this._updateStyle(),this._viewer.render())}));const e=()=>{if(this._showSupercellInfo(),void 0===this._current)return;const t=this._current.model.selectedAtoms({});this._current.model.removeAtoms(t.splice(this._current.structure.size));const e=this._options.supercell[0].value,r=this._options.supercell[1].value,n=this._options.supercell[2].value;if(1===e&&1===r&&1===n||this._viewer.replicateUnitCell(this._options.supercell[0].value,this._options.supercell[1].value,this._options.supercell[2].value,this._current.model),u(this._current.model.selectedAtoms({})),void 0!==this._highlighted){const t=this._defaultCutoff(this._highlighted.center);this._changeHighlighted(this._highlighted.center,t)}this._environmentsEnabled()&&this._setEnvironmentInteractions(),this._updateStyle(),this._viewer.render()};this._options.supercell[0].onchange.push(e),this._options.supercell[1].onchange.push(e),this._options.supercell[2].onchange.push(e),this._options.environments.bgColor.onchange.push(t),this._options.environments.bgStyle.onchange.push(t),this._options.environments.cutoff.onchange.push((()=>{if(void 0!==this._highlighted){const t=this._defaultCutoff(this._highlighted.center);this._changeHighlighted(this._highlighted.center,t)}t()})),this._options.environments.center.onchange.push((t=>{this._options.keepOrientation.value||this._resetView(),t&&this._centerView(),this._viewer.render()})),this._options.environments.activated.onchange.push((e=>{if(this._enableEnvironmentSettings(e),e){i()(void 0!==this._lastHighlighted,"this._lastHighlighted !== undefined"),this._options.environments.cutoff.value=this._lastHighlighted.cutoff;const t=this._lastHighlighted.center,e=this._defaultCutoff(t);this._changeHighlighted(t,e)}else i()(void 0!==this._highlighted,"this._highlighted !== undefined"),this._viewer.removeModel(this._highlighted.model),this._lastHighlighted={center:this._highlighted.center,cutoff:this._options.environments.cutoff.value};t()})),this._options.color.property.onchange.push((()=>{const e=this._options.color.property.value;if("element"!==e){this._options.color.transform.enable(),this._options.color.transform.value="linear",this._options.color.min.enable(),this._options.color.max.enable(),this._colorReset.disabled=!1,this._colorMoreOptions.disabled=!1,this._options.color.palette.enable();const t=this._colorValues(e,"linear");t.some((t=>null===t))&&(0,h.R4)("The selected structure has undefined properties for some atoms, these atoms will be colored in light gray.");const{max:r,min:n}=(0,h.GI)(t);this._options.color.min.value=Number.NEGATIVE_INFINITY,this._options.color.max.value=r,this._options.color.min.value=n,this._setScaleStep([n,r])}else this._options.color.transform.disable(),this._options.color.min.disable(),this._options.color.max.disable(),this._options.getModalElement("atom-color-extra").classList.contains("show")&&this._colorMoreOptions.click(),this._colorReset.disabled=!0,this._colorMoreOptions.disabled=!0,this._options.color.palette.disable(),this._viewer.setColorByElement({},o.elementColors.Jmol);this._updateColorBar(),t()}));const r=e=>{const r=this._options.color.min.value,n=this._options.color.max.value;if(r>n)return(0,h.R4)("The inserted min and max values in color are such that min > max! The last inserted value was reset."),void("min"===e?this._options.color.min.reset():this._options.color.max.reset());this._setScaleStep([r,n]),this._updateColorBar(),t()};this._options.color.transform.onchange.push((()=>{const e=this._options.color.property.value;i()("element"!==e,"property !== 'element'");const r=this._options.color.transform.value,n=this._colorValues(e,r),{min:o,max:a}=(0,h.GI)(n);this._options.color.min.value=Number.NEGATIVE_INFINITY,this._options.color.max.value=a,this._options.color.min.value=o,this._setScaleStep([o,a]),this._updateColorBar(),t()})),this._options.color.min.onchange.push((()=>{r("min"),t()})),this._options.color.max.onchange.push((()=>{r("max"),t()})),this._colorReset.addEventListener("click",(()=>{const e=JSON.parse(JSON.stringify(this._properties))[this._options.color.property.value].filter((t=>!isNaN(Number(t)))),[r,n]=[Math.min(...e),Math.max(...e)];this._options.color.min.value=r,this._options.color.max.value=n,this._setScaleStep([r,n]),this._updateColorBar(),t()})),this._options.color.palette.onchange.push((()=>{this._updateColorBar(),t()})),this._resetEnvCutoff=this._options.getModalElement("env-reset"),this._resetEnvCutoff.onclick=()=>{i()(void 0!==this._highlighted,"this._highlighted !== undefined"),this._options.environments.cutoff.value=this._defaultCutoff(this._highlighted.center),t()},this._options.getModalElement("align-x").onclick=()=>this._viewAlong([1,0,0]),this._options.getModalElement("align-y").onclick=()=>this._viewAlong([0,1,0]),this._options.getModalElement("align-z").onclick=()=>this._viewAlong([0,0,1]),this._options.getModalElement("align-a").onclick=()=>{if(void 0===this._current||void 0===this._current.structure.cell)return;const t=this._current.structure.cell,e=[t[0],t[1],t[2]];this._viewAlong(e)},this._options.getModalElement("align-b").onclick=()=>{if(void 0===this._current||void 0===this._current.structure.cell)return;const t=this._current.structure.cell,e=[t[3],t[4],t[5]];this._viewAlong(e)},this._options.getModalElement("align-c").onclick=()=>{if(void 0===this._current||void 0===this._current.structure.cell)return;const t=this._current.structure.cell,e=[t[6],t[7],t[8]];this._viewAlong(e)},this._resetSupercell=this._options.getModalElement("reset-supercell"),this._resetSupercell.onclick=()=>{i()(void 0!==this._initialSupercell,"this._initialSupercell !== undefined"),this._options.supercell[0].value=this._initialSupercell[0],this._options.supercell[1].value=this._initialSupercell[1],this._options.supercell[2].value=this._initialSupercell[2]},this._root.ondblclick=()=>{this._resetView(),this._options.environments.center.value&&this._centerView(),this._viewer.render()}}_selectAtom(t){i()(void 0!==t.serial,"atom.serial !== undefined"),this.onselect(t.serial)}_updateStyle(){void 0!==this._current&&(""!==this._options.shape.value&&this._addShapes(),this._environmentsEnabled()?(i()(void 0!==this._highlighted,"this._highlighted !== undefined"),this._current.model.setStyle({},this._hiddenStyle()),this._current.model.setStyle({index:this._highlighted.center},this._centralStyle(.4),!0),this._highlighted.model.setStyle({},this._mainStyle())):this._current.model.setStyle({},this._mainStyle()))}_addAxes(t){if(void 0!==this._axes&&(this._viewer.removeShape(this._axes[0].arrow),this._viewer.removeLabel(this._axes[0].label),this._viewer.removeShape(this._axes[1].arrow),this._viewer.removeLabel(this._axes[1].label),this._viewer.removeShape(this._axes[2].arrow),this._viewer.removeLabel(this._axes[2].label),this._axes=void 0),"off"===t);else if("xyz"===t)this._axes=[this._addLabeledArrow([2,0,0],"red","X"),this._addLabeledArrow([0,2,0],"green","Y"),this._addLabeledArrow([0,0,2],"blue","Z")];else if("abc"===t){if(void 0===this._current||void 0===this._current.structure.cell)return;const t=this._current.structure.cell,e=[t[0],t[1],t[2]],r=[t[3],t[4],t[5]],n=[t[6],t[7],t[8]];this._axes=[this._addLabeledArrow(e,"red","A"),this._addLabeledArrow(r,"green","B"),this._addLabeledArrow(n,"blue","C")]}this._viewer.render()}_addShapes(){if(void 0===this._current)return;if(""===this._options.shape.value)return;this._viewer.removeAllShapes(),this._options.unitCell.value&&this._viewer.addUnitCell(this._current.model,{box:{color:"black"},astyle:{hidden:!0},bstyle:{hidden:!0},cstyle:{hidden:!0}}),this._addAxes(this._options.axes.value),i()(0===this._current.atomLabels.length,"this._current.atomLabels.length === 0");const t=this._current.structure;i()(!(void 0===t.shapes),"!(structure.shapes === undefined)");const e=this._options.shape.value.split(","),r={vertexArr:[],normalArr:[],faceArr:[],color:[]},n=this._colorFunction(),a={};for(const s of e){if(""===s)continue;i()(s in t.shapes,"shape in structure.shapes");const e=t.shapes[s];let l=this._options.supercell[0].value,c=this._options.supercell[1].value,u=this._options.supercell[2].value,h=this._current.structure.cell;void 0===h&&(h=[1,0,0,0,1,0,0,0,1],(l>1||c>1||u>1)&&(l=1,c=1,u=1));for(let s=0;s0&&this._viewer.addCustom(r),this._viewer.render()}_mainStyle(){const t={};return this._options.atoms.value&&(t.sphere={scale:this._options.spaceFilling.value?1:.22,colorfunc:this._colorFunction()}),this._options.bonds.value&&(t.stick={radius:.15,colorfunc:this._colorFunction()}),t}_colorValues(t,e){i()(void 0!==this._properties,"this._properties !== undefined"),i()(Object.keys(this._properties).includes(t),"Object.keys(this._properties).includes(property)");let r=JSON.parse(JSON.stringify(this._properties[t])),n=t=>t;return"log"===e?n=Math.log10:"sqrt"===e?n=Math.sqrt:"inverse"===e&&(n=t=>1/t),r=r.map((t=>null===t||isNaN(t)?t:n(t))),r}_colorFunction(){if(void 0===this._properties)return;const t=this._options.color.property.value;if("element"===t)return;const e=this._options.color.transform.value,r=this._colorValues(t,e),n=this._options.color.min.value,a=this._options.color.max.value,s=p.s[this._options.color.palette.value],l=[];for(let t=0;t{i()(void 0!==t.serial,"atom.serial !== undefined");const e=r[t.serial];return null===e?14540253:isNaN(e)?2236962:Number.isFinite(n)&&Number.isFinite(a)?c.valueToHex(e):2236962}}_hiddenStyle(){const t={},e=this._options.environments.bgStyle.value;"hide"===e||("licorice"===e||"ball-stick"===e?(t.stick={radius:.149,opacity:g(),hidden:!this._options.bonds.value},"ball-stick"===e&&""===this._options.shape.value&&(t.sphere={scale:this._options.spaceFilling.value?.999:.219,opacity:g()})):(0,h.HB)());const r=this._options.environments.bgColor.value;return"CPK"===r||("grey"===r?(void 0!==t.stick&&(t.stick.color=8421504),void 0!==t.sphere&&(t.sphere.color=8421504)):"property"===r?(void 0!==t.stick&&(t.stick={radius:.149,opacity:g(),hidden:!this._options.bonds.value,colorfunc:this._colorFunction()}),void 0!==t.sphere&&(t.sphere={scale:this._options.spaceFilling.value?.999:.219,opacity:g(),colorfunc:this._colorFunction()})):(0,h.HB)()),t}_centralStyle(t){return{sphere:{scale:t,color:"green",opacity:g()}}}_showSupercellInfo(){const t=this._options.supercell[0].value,e=this._options.supercell[1].value,r=this._options.supercell[2].value;this._cellInfo.innerText=1!==t||1!==e||1!==r?`${t}x${e}x${r} supercell`:""}_environmentsEnabled(){return void 0!==this._highlighted&&!this._resetEnvCutoff.disabled}_enableEnvironmentSettings(t){const e=this._options.getModalElement("env-activated").nextElementSibling;i()(null!==e,"toggle !== null");const r=this._resetEnvCutoff;if(t){if(this._environmentsEnabled())return;r.disabled=!1,e.innerText="Disable",this._options.environments.cutoff.enable(),this._options.environments.bgStyle.enable(),this._options.environments.bgColor.enable()}else{if(!this._environmentsEnabled())return;r.disabled=!0,e.innerText="Enable",this._options.environments.cutoff.disable(),this._options.environments.bgStyle.disable(),this._options.environments.bgColor.disable()}}_defaultCutoff(t){i()(void 0!==this._environments,"this._environments !== undefined");const e=this._environments[t];return i()(void 0!==e,"environment !== undefined"),e.cutoff}_changeHighlighted(t,e){if(void 0!==this._highlighted&&this._viewer.removeModel(this._highlighted.model),void 0===t)this._options.environments.cutoff.value=0,this._highlighted=void 0;else{if(void 0===this._environments)throw Error("can not highlight an atom without having a list of environments");const r=this._environments[t];if(void 0===r)throw Error(`can not highlight 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this.current!==t.environment&&(this.current=t.environment,!0)}activate(){this.marker.classList.toggle("chsp-active-pin",!0)}deactivate(){this.marker.classList.toggle("chsp-active-pin",!1)}remove(){o()(null!==this.marker.parentNode,"this.marker.parentNode !== null"),this.marker.parentNode.removeChild(this.marker)}toggleVisible(t){this.marker.style.display=t?"block":"none"}}var T=__webpack_require__(50112),S=__webpack_require__(45127),C=__webpack_require__(17136),E=__webpack_require__(90170);const L=["circle","square","diamond","cross","x"];function z(t){return L[t%L.length]}class O extends S.W2{constructor(t){o()(t.length>0,"validProperties.length > 0"),super(),this.max=new S.Je("number",NaN),this.min=new S.Je("number",NaN),this.property=new S.Je("string",t[0]),this.scale=new S.Je("string","linear"),this.property.validate=(0,S.qP)(t,"axis"),this.scale.validate=(0,S.qP)(["linear","log"],"axis scale")}disable(){this.max.disable(),this.min.disable(),this.scale.disable()}enable(){this.max.enable(),this.min.enable(),this.scale.enable()}}class D extends S.W2{constructor(t,e,r,n={}){super();const i=Object.keys(e);if(i.length<2)throw new Error("Cannot show a map because the dataset contains fewer than two properties.");this.x=new O(i),this.y=new O(i),this.z=new O(i.concat([""])),this.symbol=new S.Je("string","");const o=[""];for(const t in e)void 0!==e[t].string&&o.push(t);this.symbol.validate=(0,S.qP)(o,"symbol"),this.palette=new S.Je("string","inferno"),this.palette.validate=(0,S.qP)(Object.keys(C.s),"palette"),this.color={mode:new S.Je("string","linear"),property:new S.Je("string",""),min:new S.Je("number",NaN),max:new S.Je("number",NaN)},this.color.property.validate=(0,S.qP)(i.concat([""]),"color"),this.color.mode.validate=(0,S.qP)(["linear","log","sqrt","inverse"],"mode"),this.size={factor:new S.Je("number",50),mode:new S.Je("string","linear"),property:new S.Je("string","")},this.size.property.validate=(0,S.qP)(i.concat([""]),"size"),this.size.factor.validate=t=>{if(t<1||t>100)throw Error(`size factor must be between 0 and 100, got ${t}`)},this.size.mode.validate=(0,S.qP)(["linear","log","sqrt","inverse","flip-linear","proportional"],"mode"),this.markerOutline=new S.Je("boolean",!0),this.joinPoints=new S.Je("boolean",!1),this.x.property.value=i[0],this.y.property.value=i[1],this.z.property.value="",i.length>2?this.color.property.value=i[2]:this.color.property.value="",this._positionSettingsModal=r;const{openModal:a,modal:s}=this._createSettingsHTML();this._modal=s,this._openModal=a,t.appendChild(this._openModal),this._bind(e),this.applySettings(n)}getModalElement(t){return(0,s.VT)(t,this._modal.shadow)}applySettings(t){if("size"in t){const e=t.size;"mode"in e&&"constant"===e.mode&&(delete e.mode,e.property="")}if("color"in t){const e=t.color;"scale"in e&&(e.mode=e.scale,delete e.scale)}super.applySettings(t)}remove(){this._modal.remove(),this._openModal.remove()}is3D(){return""!==this.z.property.value}hasColors(){return""!==this.color.property.value}hovertemplate(){if(this.hasColors()){let t=this.color.property.value;switch(this.color.mode.value){case"inverse":t=`(${t})-1`;break;case"log":t=`log(${t})`;break;case"sqrt":t=`sqrt(${t})`}return t+": %{marker.color:.2f}"}return"%{x:.2f}, %{y:.2f}"}calculateColors(t){let e=this.color.mode.value;const{min:r,max:n}=(0,s.GI)(t);return n===r&&(e="fixed"),t.map((t=>{let r=.5;switch(e){case"inverse":r=1/t;break;case"log":r=Math.log10(t);break;case"sqrt":r=Math.sqrt(t);break;case"linear":r=1*t;break;default:r=.5}return isNaN(r)?"#aaaaaa":r}))}calculateSizes(t){const e=(t=>{const e=Math.log(1/6),r=(Math.log(6)-e)/99;return Math.exp(e+r*(t-1))})(this.size.factor.value);let r=this.size.mode.value;const{min:n,max:i}=(0,s.GI)(t),o=this.is3D()?800:300,a=n>0?n:1e-6*(i-n),l=t.map((t=>{let s=.3;switch(i===n?r="fixed":s=(t-n)/(i-n),r){case"proportional":s=t/Math.abs(i);break;case"inverse":s=a/t;break;case"log":s=Math.log(t/a)/Math.log(i/a);break;case"sqrt":s=Math.sqrt(t/Math.abs(i));break;case"linear":s*=1;break;case"flip-linear":s=1-s;break;default:s=.3-.1}return s+=.1,o*s*e}));return l.some((t=>isNaN(t)||t<0))?((0,s.R4)(`After applying the selected scaling mode ${r}, some point sizesevaluated to invalid values. These points will be displayed at the minimum size.`),l.map((t=>isNaN(t)?.1*o*e:t))):l}getSymbols(t){o()(void 0!==t.string,"property.string !== undefined");const e=t.string.strings().length;return this.is3D()?(e>L.length&&(0,s.R4)(`${e} symbols are required, but we only have ${L.length}. Some symbols will be repeated`),t.values.map(z)):t.values}_createSettingsHTML(){const t=document.createElement("template");t.innerHTML=`\n
${E.A}
\n `;const e=t.content.firstChild;t.innerHTML='\n';const r=t.content.querySelector(".modal");o()(null!==r&&r instanceof HTMLElement,"modalElement !== null && modalElement instanceof HTMLElement");const n=r.querySelector(".modal-dialog");o()(null!==n&&n instanceof HTMLElement,"modalDialog !== null && modalDialog instanceof HTMLElement"),(0,s.eB)(n,".modal-header");const i=new T.A(r);return i.shadow.adoptedStyleSheets=[v.A,b.A],d.A.initialize(r),e.addEventListener("click",(()=>{if(null===n.getAttribute("data-initial-modal-positions-set")){n.setAttribute("data-initial-modal-positions-set","true"),n.parentNode.style.display="block",n.style.width=n.offsetWidth/1.5+"px",n.style.minWidth="500px",n.style.margin="0",n.style.position="fixed";const{top:t,left:e}=this._positionSettingsModal(n.getBoundingClientRect());n.style.top=`${t}px`,n.style.left=`${e}px`}i.open()})),r.addEventListener("keydown",(t=>{t.stopPropagation()})),{openModal:e,modal:i}}_bind(t){const e=this.getModalElement("map-x-property");e.options.length=0;for(const r in t)e.options.add(new Option(r,r));this.x.property.bind(e,"value"),this.x.min.bind(this.getModalElement("map-x-min"),"value"),this.x.max.bind(this.getModalElement("map-x-max"),"value"),this.x.scale.bind(this.getModalElement("map-x-scale"),"value");const r=this.getModalElement("map-y-property");r.options.length=0;for(const e in t)r.options.add(new Option(e,e));this.y.property.bind(r,"value"),this.y.min.bind(this.getModalElement("map-y-min"),"value"),this.y.max.bind(this.getModalElement("map-y-max"),"value"),this.y.scale.bind(this.getModalElement("map-y-scale"),"value");const n=this.getModalElement("map-z-property");n.options.length=0,n.options.add(new Option("none",""));for(const e in t)n.options.add(new Option(e,e));this.z.property.bind(n,"value"),this.z.min.bind(this.getModalElement("map-z-min"),"value"),this.z.max.bind(this.getModalElement("map-z-max"),"value"),this.z.scale.bind(this.getModalElement("map-z-scale"),"value");const i=this.getModalElement("map-color-property");i.options.length=0,i.options.add(new Option("fixed",""));for(const e in t)i.options.add(new Option(e,e));this.color.property.bind(i,"value"),this.color.mode.bind(this.getModalElement("map-color-transform"),"value"),this.color.min.bind(this.getModalElement("map-color-min"),"value"),this.color.max.bind(this.getModalElement("map-color-max"),"value");const o=this.getModalElement("map-color-palette");o.length=0;for(const t in C.s)o.options.add(new Option(t,t));this.palette.bind(o,"value");const a=this.getModalElement("map-symbol-property");a.options.length=0,a.options.add(new Option("fixed",""));for(const e in t)void 0!==t[e].string&&a.options.add(new Option(e,e));this.symbol.bind(a,"value");const s=this.getModalElement("map-size-property");s.options.length=0,s.options.add(new Option("fixed",""));for(const e in t)s.options.add(new Option(e,e));this.size.property.bind(s,"value"),this.size.factor.bind(this.getModalElement("map-size-factor"),"value"),this.size.mode.bind(this.getModalElement("map-size-transform"),"value"),this.markerOutline.bind(this.getModalElement("map-marker-outline"),"checked"),this.joinPoints.bind(this.getModalElement("map-join-points"),"checked")}colorScale(){return C.s[this.palette.value]}setLogLabel(t,e){const r=this.getModalElement(`map-${e}-min-label`),n=this.getModalElement(`map-${e}-max-label`);"log"===t.scale.value?(r.innerHTML="min: 10^",n.innerHTML="max: 10^"):(r.innerHTML="min:",n.innerHTML="max:")}}const I='\n\n \n \n\n\x3c!--Icon taken from www.uxwing.com and edited in Inkscape--\x3e\n\n';const F={coloraxis:{cmax:0,cmin:0,colorbar:{len:1,thickness:20,title:{text:"",side:"right",font:{size:15}},y:0,yanchor:"bottom"},colorscale:[],showscale:!0},hovermode:"closest",legend:{itemclick:!1,itemdoubleclick:!1,tracegroupgap:5,y:1,yanchor:"top"},margin:{b:50,l:50,r:50,t:50},scene:{camera:{projection:{type:"orthographic"}},xaxis:{showspikes:!1,title:""},yaxis:{showspikes:!1,title:""},zaxis:{showspikes:!1,title:""}},showlegend:!0,xaxis:{range:void 0,title:"",type:"linear",zeroline:!1},yaxis:{range:void 0,title:"",type:"linear",zeroline:!1},zaxis:{range:void 0,title:"",type:"linear",zeroline:!1}},R={displayModeBar:!0,displaylogo:!1,responsive:!0,scrollZoom:!0,modeBarButtonsToRemove:["hoverClosestCartesian","hoverCompareCartesian","toggleSpikelines","autoScale2d","zoomIn2d","zoomOut2d","select2d","lasso2d","hoverClosest3d","tableRotation","resetCameraLastSave3d","toImage"],modeBarButtonsToAdd:[[{name:"Download PNG",icon:{width:400,height:447,path:j(I)},click:function(t){c().downloadImage(t,{filename:"chemiscope-map",format:"png",width:Math.max(t._fullLayout.width,600),height:Math.max(t._fullLayout.width,600)}).catch((t=>setTimeout((()=>{throw t}))))}}],[{name:"Download SVG",icon:{width:400,height:447,path:j('\n\n \n \n \n\x3c!--Icon taken from www.uxwing.com and edited in Inkscape--\x3e\n\n')},click:function(t){c().downloadImage(t,{filename:"chemiscope-map",format:"svg",width:Math.max(t._fullLayout.width,600),height:Math.max(t._fullLayout.height,600)}).catch((t=>setTimeout((()=>{throw t}))))}}]]};class P{constructor(t,e,r,n,i){this._getAxisRange=(t,e,r)=>{const n=!isNaN(t),i=!isNaN(e);if(n&&i){if(t<=e)return[t,e];(0,s.R4)(`The inserted min and max values in ${r} are such that min > max!The default values will be used.`)}return[n?t:void 0,i?e:void 0]},this._indexer=r,this._target=n,this.onselect=()=>{},this.activeChanged=()=>{},this._selected=new Map;const o=(0,s.V6)(t),a=document.createElement("div");a.style.setProperty("height","100%"),o.appendChild(a),this._shadow=a.attachShadow({mode:"open"}),this._root=document.createElement("div"),this._root.style.setProperty("height","100%"),this._shadow.appendChild(this._root),""===this._root.style.position&&(this._root.style.position="relative"),this._plot=document.createElement("div"),this._plot.style.width="100%",this._plot.style.height="100%",this._root.appendChild(this._plot),this._data=new A(i);const l=this._getCurrentProperties();var c;this._options=new D(this._root,l,(t=>this.positionSettingsModal(t)),e),this._colorReset=this._options.getModalElement("map-color-reset"),this._connectSettings(),this.positionSettingsModal=t=>{const e=this._root.getBoundingClientRect();return{left:e.left+e.width/2-t.width/2,top:e.top+20}},this._createPlot(),this._shadow.adoptedStyleSheets=[v.A,b.A,u,(c=this._plot,h(c._fullLayout._modeBar._uid))]}switchTarget(t){return e=this,r=void 0,i=function*(){if(t!==this._target){if(this._target=t,this._handleMarkers(),void 0!==this._active){const t=this._selected.get(this._active);void 0!==t&&this.onselect(this._indexer.fromEnvironment(t.current,this._target))}this._setupMapOptions(),this._connectSettings(),yield this._react(this._getTraces(),this._getLayout())}},new((n=void 0)||(n=Promise))((function(t,o){function a(t){try{l(i.next(t))}catch(t){o(t)}}function s(t){try{l(i.throw(t))}catch(t){o(t)}}function l(e){var r;e.done?t(e.value):(r=e.value,r instanceof n?r:new n((function(t){t(r)}))).then(a,s)}l((i=i.apply(e,r||[])).next())}));var e,r,n,i}_handleMarkers(){var t;for(const[e,r]of this._selected.entries()){if("structure"===this._target)r.current=this._indexer.fromEnvironment(r.current,"atom").structure;else{const e=null===(t=this._indexer.fromStructure(r.current,"atom"))||void 0===t?void 0:t.environment;o()(void 0!==e,"environment !== undefined"),r.current=e}this._selected.set(e,r)}}remove(){var t;this._shadow.host.remove(),this._options.remove(),null===(t=document.getElementById("js-plotly-tester"))||void 0===t||t.remove(),this._plotFix.disable()}select(t){if(void 0===this._active)throw Error("tries to update selected environment, but there is no active marker");if(void 0===t.environment){const e=this._indexer.fromStructureAtom(this._target,t.structure,t.atom);if(void 0===e){const e=void 0===t.atom?"":` / atom ${t.atom}`;throw Error(`can not find the environnement for structure ${t.structure}`+e)}t=e}const e=this._selected.get(this._active);o()(void 0!==e,"data !== undefined"),e.select(t)&&this._updateMarkers()}setActive(t){if(void 0!==this._active){const t=this._selected.get(this._active);o()(void 0!==t,"oldData !== undefined"),t.deactivate()}this._active=t;const e=this._selected.get(this._active);o()(void 0!==e,"data !== undefined"),e.activate(),this._is3D()&&this._restyle({"marker.size":this._sizes(1)},1)}addMarker(t,e,r){o()(!this._selected.has(t),"!this._selected.has(guid)");const n=new M(t,e,r.environment);this._root.appendChild(n.marker),n.marker.onclick=()=>{this.setActive(t),this.activeChanged(t,this._indexer.fromEnvironment(n.current,this._target))},this._selected.set(t,n),this._updateMarkers([n]),this.setActive(t)}removeMarker(t){this._active===t&&(1===this._selected.size?this._active=void 0:this.setActive((0,s.o)(this._selected,t)));const e=this._selected.get(t);o()(void 0!==e,"data !== undefined"),e.remove(),this._selected.delete(t),this._updateMarkers()}applySettings(t){this._options.applySettings(t)}saveSettings(){return this._options.saveSettings()}onSettingChange(t){this._options.onSettingChange(t)}_getTraces(){const t=this._is3D()?"scatter3d":"scattergl",e=[{name:"",type:t,x:this._coordinates(this._options.x,0)[0],y:this._coordinates(this._options.y,0)[0],z:this._coordinates(this._options.z,0)[0],hovertemplate:this._options.hovertemplate(),marker:{color:this._colors(0)[0],coloraxis:"coloraxis",line:{color:"black",width:this._options.markerOutline.value?.5:0},opacity:1,size:this._sizes(0)[0],sizemode:"area",symbol:this._symbols(0)[0]},line:{color:"black",width:.5,dash:"solid"},mode:this._options.joinPoints.value?"lines+markers":"markers",showlegend:!1},{name:"selected",type:t,x:[],y:[],z:[],hoverinfo:"none",marker:{color:[],line:{color:[],width:2},opacity:1,size:[],sizemode:"area"},mode:"markers",showlegend:!1}],r=this._legendNames().slice(2),n=this._showlegend().slice(2);o()(r.length===n.length,"legendNames.length === showlegend.length");const i=r.length;this._data.maxSymbols>0&&(r.length=this._data.maxSymbols,r.fill("",i),n.length=this._data.maxSymbols,n.fill(!1,i));for(let i=0;i{t&&Object.keys(t).length>1&&(this._options.remove(),this._options=new D(this._root,this._getCurrentProperties(),(t=>this.positionSettingsModal(t)),{}))};"atom"!==this._target?t(this._data.structure):t(this._data.atom)}_getCurrentProperties(){const t=this._data[this._target],e=Object.keys(t);if(e.length<2){if("structure"===this._target&&!this._indexer.hasEnvironments()&&Object.keys(this._data.atom).length>=2)throw Error("could not find enough structure properties to display, but there are atom properties. Please provide the environment list to display them");let t="we need at least two properties to plot in the map";throw 0===e.length?t+=", we have none":t+=`, we have only one: '${e[0]}'`,Error(t)}return t}_restyle(t,e){c().restyle(this._plot,t,e).catch((t=>setTimeout((()=>{throw t}))))}_relayout(t){c().relayout(this._plot,t).catch((t=>setTimeout((()=>{throw t}))))}_react(t,e){return new Promise(((r,n)=>{c().react(this._plot,t,e).then((()=>{r()})).catch((t=>{setTimeout((()=>{n(t)}))}))}))}_connectSettings(){const t=t=>{"log"===t.scale.value&&(0,s.GI)(this._coordinates(t,0)[0]).min<0&&t.min.value<=0&&(0,s.R4)("This property contains negative values. Note that taking the log will discard them.")};this._options.x.property.onchange.push((()=>{t(this._options.x);const e=this._coordinates(this._options.x);this._restyle({x:e},[0,1]),this._relayout({"scene.xaxis.title":this._title(this._options.x.property.value),"xaxis.title":this._title(this._options.x.property.value)}),this._is3D()?this._relayout({"scene.xaxis.autorange":!0}):this._relayout({"xaxis.autorange":!0}),this._setScaleStep(this._getBounds().x,"x")})),this._options.x.scale.onchange.push((()=>{t(this._options.x),this._options.setLogLabel(this._options.x,"x"),this._is3D()?this._relayout({"scene.xaxis.type":this._options.x.scale.value}):this._relayout({"xaxis.type":this._options.x.scale.value})}));const e=(e,r,n)=>(i,o)=>{if("JS"===o)return;const a=r.min.value,l=r.max.value;if(a>l)return(0,s.R4)(`The inserted min and max values in ${e} are such that min > max! 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t=this._colors(0)[0],{min:e,max:r}=(0,s.GI)(t);this._options.color.min.value=e,this._options.color.max.value=r,this._relayout({"coloraxis.cmax":r,"coloraxis.cmin":e,"coloraxis.colorscale":this._options.colorScale()})},this._options.color.property.enable(),this._options.hasColors()?(this._options.color.mode.enable(),this._options.color.min.enable(),this._options.color.max.enable(),this._colorReset.disabled=!1):(this._options.color.min.disable(),this._options.color.max.disable(),this._colorReset.disabled=!0),this._options.palette.onchange.push((()=>{this._relayout({"coloraxis.colorscale":this._options.colorScale()})})),this._options.symbol.onchange.push((()=>{this._restyle({"marker.symbol":this._symbols()},[0,1]),this._restyle({name:this._legendNames(),showlegend:this._showlegend()}),this._relayout({"coloraxis.colorbar.len":this._colorbarLen()})})),""===this._options.size.property.value?this._options.size.mode.disable():this._options.size.mode.enable(),this._options.size.property.onchange.push((()=>{""!==this._options.size.property.value?this._options.size.mode.enable():this._options.size.mode.disable(),this._restyle({"marker.size":this._sizes(0)},0)})),this._options.size.factor.onchange.push((()=>{this._restyle({"marker.size":this._sizes(0)},0)})),this._options.size.mode.onchange.push((()=>{this._restyle({"marker.size":this._sizes(0)},0)})),this._options.markerOutline.onchange.push((()=>{const 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=/[ \xA0\u1680\u2000-\u200A\u2028\u2029\u202F\u205F\u3000]/,ht=new Uint16Array('ᵁ<Õıʊҝջאٵ۞ޢߖࠏ੊ઑඡ๭༉༦჊ረዡᐕᒝᓃᓟᔥ\0\0\0\0\0\0ᕫᛍᦍᰒᷝ὾⁠↰⊍⏀⏻⑂⠤⤒ⴈ⹈⿎〖㊺㘹㞬㣾㨨㩱㫠㬮ࠀEMabcfglmnoprstu\\bfms„‹•˜¦³¹ÈÏlig耻Æ䃆P耻&䀦cute耻Á䃁reve;䄂Āiyx}rc耻Â䃂;䐐r;쀀𝔄rave耻À䃀pha;䎑acr;䄀d;橓Āgp¡on;䄄f;쀀𝔸plyFunction;恡ing耻Å䃅Ācs¾Ãr;쀀𝒜ign;扔ilde耻Ã䃃ml耻Ä䃄ЀaceforsuåûþėĜĢħĪĀcrêòkslash;或Ŷöø;櫧ed;挆y;䐑ƀcrtąċĔause;戵noullis;愬a;䎒r;쀀𝔅pf;쀀𝔹eve;䋘còēmpeq;扎܀HOacdefhilorsuōőŖƀƞƢƵƷƺǜȕɳɸɾcy;䐧PY耻©䂩ƀcpyŝŢźute;䄆Ā;iŧŨ拒talDifferentialD;慅leys;愭ȀaeioƉƎƔƘron;䄌dil耻Ç䃇rc;䄈nint;戰ot;䄊ĀdnƧƭilla;䂸terDot;䂷òſi;䎧rcleȀDMPTLJNjǑǖot;抙inus;抖lus;投imes;抗oĀcsǢǸkwiseContourIntegral;戲eCurlyĀDQȃȏoubleQuote;思uote;怙ȀlnpuȞȨɇɕonĀ;eȥȦ户;橴ƀgitȯȶȺruent;扡nt;戯ourIntegral;戮ĀfrɌɎ;愂oduct;成nterClockwiseContourIntegral;戳oss;樯cr;쀀𝒞pĀ;Cʄʅ拓ap;才րDJSZacefiosʠʬʰʴʸˋ˗ˡ˦̳ҍĀ;oŹʥtrahd;椑cy;䐂cy;䐅cy;䐏ƀgrsʿ˄ˇger;怡r;憡hv;櫤Āayː˕ron;䄎;䐔lĀ;t˝˞戇a;䎔r;쀀𝔇Āaf˫̧Ācm˰̢riticalȀADGT̖̜̀̆cute;䂴oŴ̋̍;䋙bleAcute;䋝rave;䁠ilde;䋜ond;拄ferentialD;慆Ѱ̽\0\0\0͔͂\0Ѕf;쀀𝔻ƀ;DE͈͉͍䂨ot;惜qual;扐blèCDLRUVͣͲ΂ϏϢϸontourIntegraìȹoɴ͹\0\0ͻ»͉nArrow;懓Āeo·ΤftƀARTΐΖΡrrow;懐ightArrow;懔eåˊngĀLRΫτeftĀARγιrrow;柸ightArrow;柺ightArrow;柹ightĀATϘϞrrow;懒ee;抨pɁϩ\0\0ϯrrow;懑ownArrow;懕erticalBar;戥ǹABLRTaВЪаўѿͼrrowƀ;BUНОТ憓ar;椓pArrow;懵reve;䌑eft˒к\0ц\0ѐightVector;楐eeVector;楞ectorĀ;Bљњ憽ar;楖ightǔѧ\0ѱeeVector;楟ectorĀ;BѺѻ懁ar;楗eeĀ;A҆҇护rrow;憧ĀctҒҗr;쀀𝒟rok;䄐ࠀNTacdfglmopqstuxҽӀӄӋӞӢӧӮӵԡԯԶՒ՝ՠեG;䅊H耻Ð䃐cute耻É䃉ƀaiyӒӗӜron;䄚rc耻Ê䃊;䐭ot;䄖r;쀀𝔈rave耻È䃈ement;戈ĀapӺӾcr;䄒tyɓԆ\0\0ԒmallSquare;旻erySmallSquare;斫ĀgpԦԪon;䄘f;쀀𝔼silon;䎕uĀaiԼՉlĀ;TՂՃ橵ilde;扂librium;懌Āci՗՚r;愰m;橳a;䎗ml耻Ë䃋Āipժկsts;戃onentialE;慇ʀcfiosօֈ֍ֲ׌y;䐤r;쀀𝔉lledɓ֗\0\0֣mallSquare;旼erySmallSquare;斪Ͱֺ\0ֿ\0\0ׄf;쀀𝔽All;戀riertrf;愱cò׋؀JTabcdfgorstר׬ׯ׺؀ؒؖ؛؝أ٬ٲcy;䐃耻>䀾mmaĀ;d׷׸䎓;䏜reve;䄞ƀeiy؇،ؐdil;䄢rc;䄜;䐓ot;䄠r;쀀𝔊;拙pf;쀀𝔾eater̀EFGLSTصلَٖٛ٦qualĀ;Lؾؿ扥ess;招ullEqual;执reater;檢ess;扷lantEqual;橾ilde;扳cr;쀀𝒢;扫ЀAacfiosuڅڋږڛڞڪھۊRDcy;䐪Āctڐڔek;䋇;䁞irc;䄤r;愌lbertSpace;愋ǰگ\0ڲf;愍izontalLine;攀Āctۃۅòکrok;䄦mpńېۘownHumðįqual;扏܀EJOacdfgmnostuۺ۾܃܇܎ܚܞܡܨ݄ݸދޏޕcy;䐕lig;䄲cy;䐁cute耻Í䃍Āiyܓܘrc耻Î䃎;䐘ot;䄰r;愑rave耻Ì䃌ƀ;apܠܯܿĀcgܴܷr;䄪inaryI;慈lieóϝǴ݉\0ݢĀ;eݍݎ戬Āgrݓݘral;戫section;拂isibleĀCTݬݲomma;恣imes;恢ƀgptݿރވon;䄮f;쀀𝕀a;䎙cr;愐ilde;䄨ǫޚ\0ޞcy;䐆l耻Ï䃏ʀcfosuެ޷޼߂ߐĀiyޱ޵rc;䄴;䐙r;쀀𝔍pf;쀀𝕁ǣ߇\0ߌr;쀀𝒥rcy;䐈kcy;䐄΀HJacfosߤߨ߽߬߱ࠂࠈcy;䐥cy;䐌ppa;䎚Āey߶߻dil;䄶;䐚r;쀀𝔎pf;쀀𝕂cr;쀀𝒦րJTaceflmostࠥࠩࠬࡐࡣ঳সে্਷ੇcy;䐉耻<䀼ʀcmnpr࠷࠼ࡁࡄࡍute;䄹bda;䎛g;柪lacetrf;愒r;憞ƀaeyࡗ࡜ࡡron;䄽dil;䄻;䐛Āfsࡨ॰tԀACDFRTUVarࡾࢩࢱࣦ࣠ࣼयज़ΐ४Ānrࢃ࢏gleBracket;柨rowƀ;BR࢙࢚࢞憐ar;懤ightArrow;懆eiling;挈oǵࢷ\0ࣃbleBracket;柦nǔࣈ\0࣒eeVector;楡ectorĀ;Bࣛࣜ懃ar;楙loor;挊ightĀAV࣯ࣵrrow;憔ector;楎Āerँगeƀ;AVउऊऐ抣rrow;憤ector;楚iangleƀ;BEतथऩ抲ar;槏qual;抴pƀDTVषूौownVector;楑eeVector;楠ectorĀ;Bॖॗ憿ar;楘ectorĀ;B॥०憼ar;楒ightáΜs̀EFGLSTॾঋকঝঢভqualGreater;拚ullEqual;扦reater;扶ess;檡lantEqual;橽ilde;扲r;쀀𝔏Ā;eঽা拘ftarrow;懚idot;䄿ƀnpw৔ਖਛgȀLRlr৞৷ਂਐeftĀAR০৬rrow;柵ightArrow;柷ightArrow;柶eftĀarγਊightáοightáϊf;쀀𝕃erĀLRਢਬeftArrow;憙ightArrow;憘ƀchtਾੀੂòࡌ;憰rok;䅁;扪Ѐacefiosuਗ਼੝੠੷੼અઋ઎p;椅y;䐜Ādl੥੯iumSpace;恟lintrf;愳r;쀀𝔐nusPlus;戓pf;쀀𝕄cò੶;䎜ҀJacefostuણધભીଔଙඑ඗ඞcy;䐊cute;䅃ƀaey઴હાron;䅇dil;䅅;䐝ƀgswે૰଎ativeƀMTV૓૟૨ediumSpace;怋hiĀcn૦૘ë૙eryThiî૙tedĀGL૸ଆreaterGreateòٳessLesóੈLine;䀊r;쀀𝔑ȀBnptଢନଷ଺reak;恠BreakingSpace;䂠f;愕ڀ;CDEGHLNPRSTV୕ୖ୪୼஡௫ఄ౞಄ದ೘ൡඅ櫬Āou୛୤ngruent;扢pCap;扭oubleVerticalBar;戦ƀlqxஃஊ஛ement;戉ualĀ;Tஒஓ扠ilde;쀀≂̸ists;戄reater΀;EFGLSTஶஷ஽௉௓௘௥扯qual;扱ullEqual;쀀≧̸reater;쀀≫̸ess;批lantEqual;쀀⩾̸ilde;扵umpń௲௽ownHump;쀀≎̸qual;쀀≏̸eĀfsఊధtTriangleƀ;BEచఛడ拪ar;쀀⧏̸qual;括s̀;EGLSTవశ఼ౄోౘ扮qual;扰reater;扸ess;쀀≪̸lantEqual;쀀⩽̸ilde;扴estedĀGL౨౹reaterGreater;쀀⪢̸essLess;쀀⪡̸recedesƀ;ESಒಓಛ技qual;쀀⪯̸lantEqual;拠ĀeiಫಹverseElement;戌ghtTriangleƀ;BEೋೌ೒拫ar;쀀⧐̸qual;拭ĀquೝഌuareSuĀbp೨೹setĀ;E೰ೳ쀀⊏̸qual;拢ersetĀ;Eഃആ쀀⊐̸qual;拣ƀbcpഓതൎsetĀ;Eഛഞ쀀⊂⃒qual;抈ceedsȀ;ESTലള഻െ抁qual;쀀⪰̸lantEqual;拡ilde;쀀≿̸ersetĀ;E൘൛쀀⊃⃒qual;抉ildeȀ;EFT൮൯൵ൿ扁qual;扄ullEqual;扇ilde;扉erticalBar;戤cr;쀀𝒩ilde耻Ñ䃑;䎝܀Eacdfgmoprstuvලෂ෉෕ෛ෠෧෼ขภยา฿ไlig;䅒cute耻Ó䃓Āiy෎ීrc耻Ô䃔;䐞blac;䅐r;쀀𝔒rave耻Ò䃒ƀaei෮ෲ෶cr;䅌ga;䎩cron;䎟pf;쀀𝕆enCurlyĀDQฎบoubleQuote;怜uote;怘;橔Āclวฬr;쀀𝒪ash耻Ø䃘iŬื฼de耻Õ䃕es;樷ml耻Ö䃖erĀBP๋๠Āar๐๓r;怾acĀek๚๜;揞et;掴arenthesis;揜Ҁacfhilors๿ງຊຏຒດຝະ໼rtialD;戂y;䐟r;쀀𝔓i;䎦;䎠usMinus;䂱Āipຢອncareplanåڝf;愙Ȁ;eio຺ູ໠໤檻cedesȀ;EST່້໏໚扺qual;檯lantEqual;扼ilde;找me;怳Ādp໩໮uct;戏ortionĀ;aȥ໹l;戝Āci༁༆r;쀀𝒫;䎨ȀUfos༑༖༛༟OT耻"䀢r;쀀𝔔pf;愚cr;쀀𝒬؀BEacefhiorsu༾གྷཇའཱིྦྷྪྭ႖ႩႴႾarr;椐G耻®䂮ƀcnrཎནབute;䅔g;柫rĀ;tཛྷཝ憠l;椖ƀaeyཧཬཱron;䅘dil;䅖;䐠Ā;vླྀཹ愜erseĀEUྂྙĀlq྇ྎement;戋uilibrium;懋pEquilibrium;楯r»ཹo;䎡ghtЀACDFTUVa࿁࿫࿳ဢဨၛႇϘĀnr࿆࿒gleBracket;柩rowƀ;BL࿜࿝࿡憒ar;懥eftArrow;懄eiling;按oǵ࿹\0စbleBracket;柧nǔည\0နeeVector;楝ectorĀ;Bဝသ懂ar;楕loor;挋Āerိ၃eƀ;AVဵံြ抢rrow;憦ector;楛iangleƀ;BEၐၑၕ抳ar;槐qual;抵pƀDTVၣၮၸownVector;楏eeVector;楜ectorĀ;Bႂႃ憾ar;楔ectorĀ;B႑႒懀ar;楓Āpuႛ႞f;愝ndImplies;楰ightarrow;懛ĀchႹႼr;愛;憱leDelayed;槴ڀHOacfhimoqstuფჱჷჽᄙᄞᅑᅖᅡᅧᆵᆻᆿĀCcჩხHcy;䐩y;䐨FTcy;䐬cute;䅚ʀ;aeiyᄈᄉᄎᄓᄗ檼ron;䅠dil;䅞rc;䅜;䐡r;쀀𝔖ortȀDLRUᄪᄴᄾᅉownArrow»ОeftArrow»࢚ightArrow»࿝pArrow;憑gma;䎣allCircle;战pf;쀀𝕊ɲᅭ\0\0ᅰt;戚areȀ;ISUᅻᅼᆉᆯ斡ntersection;抓uĀbpᆏᆞsetĀ;Eᆗᆘ抏qual;抑ersetĀ;Eᆨᆩ抐qual;抒nion;抔cr;쀀𝒮ar;拆ȀbcmpᇈᇛሉላĀ;sᇍᇎ拐etĀ;Eᇍᇕqual;抆ĀchᇠህeedsȀ;ESTᇭᇮᇴᇿ扻qual;檰lantEqual;扽ilde;承Tháྌ;我ƀ;esሒሓሣ拑rsetĀ;Eሜም抃qual;抇et»ሓրHRSacfhiorsሾቄ቉ቕ቞ቱቶኟዂወዑORN耻Þ䃞ADE;愢ĀHc቎ቒcy;䐋y;䐦Ābuቚቜ;䀉;䎤ƀaeyብቪቯron;䅤dil;䅢;䐢r;쀀𝔗Āeiቻ኉Dzኀ\0ኇefore;戴a;䎘Ācn኎ኘkSpace;쀀  Space;怉ldeȀ;EFTካኬኲኼ戼qual;扃ullEqual;扅ilde;扈pf;쀀𝕋ipleDot;惛Āctዖዛr;쀀𝒯rok;䅦ૡዷጎጚጦ\0ጬጱ\0\0\0\0\0ጸጽ፷ᎅ\0᏿ᐄᐊᐐĀcrዻጁute耻Ú䃚rĀ;oጇገ憟cir;楉rǣጓ\0጖y;䐎ve;䅬Āiyጞጣrc耻Û䃛;䐣blac;䅰r;쀀𝔘rave耻Ù䃙acr;䅪Ādiፁ፩erĀBPፈ፝Āarፍፐr;䁟acĀekፗፙ;揟et;掵arenthesis;揝onĀ;P፰፱拃lus;抎Āgp፻፿on;䅲f;쀀𝕌ЀADETadps᎕ᎮᎸᏄϨᏒᏗᏳrrowƀ;BDᅐᎠᎤar;椒ownArrow;懅ownArrow;憕quilibrium;楮eeĀ;AᏋᏌ报rrow;憥ownáϳerĀLRᏞᏨeftArrow;憖ightArrow;憗iĀ;lᏹᏺ䏒on;䎥ing;䅮cr;쀀𝒰ilde;䅨ml耻Ü䃜ҀDbcdefosvᐧᐬᐰᐳᐾᒅᒊᒐᒖash;披ar;櫫y;䐒ashĀ;lᐻᐼ抩;櫦Āerᑃᑅ;拁ƀbtyᑌᑐᑺar;怖Ā;iᑏᑕcalȀBLSTᑡᑥᑪᑴar;戣ine;䁼eparator;杘ilde;所ThinSpace;怊r;쀀𝔙pf;쀀𝕍cr;쀀𝒱dash;抪ʀcefosᒧᒬᒱᒶᒼirc;䅴dge;拀r;쀀𝔚pf;쀀𝕎cr;쀀𝒲Ȁfiosᓋᓐᓒᓘr;쀀𝔛;䎞pf;쀀𝕏cr;쀀𝒳ҀAIUacfosuᓱᓵᓹᓽᔄᔏᔔᔚᔠcy;䐯cy;䐇cy;䐮cute耻Ý䃝Āiyᔉᔍrc;䅶;䐫r;쀀𝔜pf;쀀𝕐cr;쀀𝒴ml;䅸ЀHacdefosᔵᔹᔿᕋᕏᕝᕠᕤcy;䐖cute;䅹Āayᕄᕉron;䅽;䐗ot;䅻Dzᕔ\0ᕛoWidtè૙a;䎖r;愨pf;愤cr;쀀𝒵௡ᖃᖊᖐ\0ᖰᖶᖿ\0\0\0\0ᗆᗛᗫᙟ᙭\0ᚕ᚛ᚲᚹ\0ᚾcute耻á䃡reve;䄃̀;Ediuyᖜᖝᖡᖣᖨᖭ戾;쀀∾̳;房rc耻â䃢te肻´̆;䐰lig耻æ䃦Ā;r²ᖺ;쀀𝔞rave耻à䃠ĀepᗊᗖĀfpᗏᗔsym;愵èᗓha;䎱ĀapᗟcĀclᗤᗧr;䄁g;樿ɤᗰ\0\0ᘊʀ;adsvᗺᗻᗿᘁᘇ戧nd;橕;橜lope;橘;橚΀;elmrszᘘᘙᘛᘞᘿᙏᙙ戠;榤e»ᘙsdĀ;aᘥᘦ戡ѡᘰᘲᘴᘶᘸᘺᘼᘾ;榨;榩;榪;榫;榬;榭;榮;榯tĀ;vᙅᙆ戟bĀ;dᙌᙍ抾;榝Āptᙔᙗh;戢»¹arr;捼Āgpᙣᙧon;䄅f;쀀𝕒΀;Eaeiop዁ᙻᙽᚂᚄᚇᚊ;橰cir;橯;扊d;手s;䀧roxĀ;e዁ᚒñᚃing耻å䃥ƀctyᚡᚦᚨr;쀀𝒶;䀪mpĀ;e዁ᚯñʈilde耻ã䃣ml耻ä䃤Āciᛂᛈoninôɲnt;樑ࠀNabcdefiklnoprsu᛭ᛱᜰ᜼ᝃᝈ᝸᝽០៦ᠹᡐᜍ᤽᥈ᥰot;櫭Ācrᛶ᜞kȀcepsᜀᜅᜍᜓong;扌psilon;䏶rime;怵imĀ;e᜚᜛戽q;拍Ŷᜢᜦee;抽edĀ;gᜬᜭ挅e»ᜭrkĀ;t፜᜷brk;掶Āoyᜁᝁ;䐱quo;怞ʀcmprtᝓ᝛ᝡᝤᝨausĀ;eĊĉptyv;榰séᜌnoõēƀahwᝯ᝱ᝳ;䎲;愶een;扬r;쀀𝔟g΀costuvwឍឝឳេ៕៛៞ƀaiuបពរðݠrc;旯p»፱ƀdptឤឨឭot;樀lus;樁imes;樂ɱឹ\0\0ើcup;樆ar;昅riangleĀdu៍្own;施p;斳plus;樄eåᑄåᒭarow;植ƀako៭ᠦᠵĀcn៲ᠣkƀlst៺֫᠂ozenge;槫riangleȀ;dlr᠒᠓᠘᠝斴own;斾eft;旂ight;斸k;搣Ʊᠫ\0ᠳƲᠯ\0ᠱ;斒;斑4;斓ck;斈ĀeoᠾᡍĀ;qᡃᡆ쀀=⃥uiv;쀀≡⃥t;挐Ȁptwxᡙᡞᡧᡬf;쀀𝕓Ā;tᏋᡣom»Ꮜtie;拈؀DHUVbdhmptuvᢅᢖᢪᢻᣗᣛᣬ᣿ᤅᤊᤐᤡȀLRlrᢎᢐᢒᢔ;敗;敔;敖;敓ʀ;DUduᢡᢢᢤᢦᢨ敐;敦;敩;敤;敧ȀLRlrᢳᢵᢷᢹ;敝;敚;敜;教΀;HLRhlrᣊᣋᣍᣏᣑᣓᣕ救;敬;散;敠;敫;敢;敟ox;槉ȀLRlrᣤᣦᣨᣪ;敕;敒;攐;攌ʀ;DUduڽ᣷᣹᣻᣽;敥;敨;攬;攴inus;抟lus;択imes;抠ȀLRlrᤙᤛᤝ᤟;敛;敘;攘;攔΀;HLRhlrᤰᤱᤳᤵᤷ᤻᤹攂;敪;敡;敞;攼;攤;攜Āevģ᥂bar耻¦䂦Ȁceioᥑᥖᥚᥠr;쀀𝒷mi;恏mĀ;e᜚᜜lƀ;bhᥨᥩᥫ䁜;槅sub;柈Ŭᥴ᥾lĀ;e᥹᥺怢t»᥺pƀ;Eeįᦅᦇ;檮Ā;qۜۛೡᦧ\0᧨ᨑᨕᨲ\0ᨷᩐ\0\0᪴\0\0᫁\0\0ᬡᬮ᭍᭒\0᯽\0ᰌƀcpr᦭ᦲ᧝ute;䄇̀;abcdsᦿᧀᧄ᧊᧕᧙戩nd;橄rcup;橉Āau᧏᧒p;橋p;橇ot;橀;쀀∩︀Āeo᧢᧥t;恁îړȀaeiu᧰᧻ᨁᨅǰ᧵\0᧸s;橍on;䄍dil耻ç䃧rc;䄉psĀ;sᨌᨍ橌m;橐ot;䄋ƀdmnᨛᨠᨦil肻¸ƭptyv;榲t脀¢;eᨭᨮ䂢räƲr;쀀𝔠ƀceiᨽᩀᩍy;䑇ckĀ;mᩇᩈ朓ark»ᩈ;䏇r΀;Ecefms᩟᩠ᩢᩫ᪤᪪᪮旋;槃ƀ;elᩩᩪᩭ䋆q;扗eɡᩴ\0\0᪈rrowĀlr᩼᪁eft;憺ight;憻ʀRSacd᪒᪔᪖᪚᪟»ཇ;擈st;抛irc;抚ash;抝nint;樐id;櫯cir;槂ubsĀ;u᪻᪼晣it»᪼ˬ᫇᫔᫺\0ᬊonĀ;eᫍᫎ䀺Ā;qÇÆɭ᫙\0\0᫢aĀ;t᫞᫟䀬;䁀ƀ;fl᫨᫩᫫戁îᅠeĀmx᫱᫶ent»᫩eóɍǧ᫾\0ᬇĀ;dኻᬂot;橭nôɆƀfryᬐᬔᬗ;쀀𝕔oäɔ脀©;sŕᬝr;愗Āaoᬥᬩrr;憵ss;朗Ācuᬲᬷr;쀀𝒸Ābpᬼ᭄Ā;eᭁᭂ櫏;櫑Ā;eᭉᭊ櫐;櫒dot;拯΀delprvw᭠᭬᭷ᮂᮬᯔ᯹arrĀlr᭨᭪;椸;椵ɰ᭲\0\0᭵r;拞c;拟arrĀ;p᭿ᮀ憶;椽̀;bcdosᮏᮐᮖᮡᮥᮨ截rcap;橈Āauᮛᮞp;橆p;橊ot;抍r;橅;쀀∪︀Ȁalrv᮵ᮿᯞᯣrrĀ;mᮼᮽ憷;椼yƀevwᯇᯔᯘqɰᯎ\0\0ᯒreã᭳uã᭵ee;拎edge;拏en耻¤䂤earrowĀlrᯮ᯳eft»ᮀight»ᮽeäᯝĀciᰁᰇoninôǷnt;戱lcty;挭ঀAHabcdefhijlorstuwz᰸᰻᰿ᱝᱩᱵᲊᲞᲬᲷ᳻᳿ᴍᵻᶑᶫᶻ᷆᷍rò΁ar;楥Ȁglrs᱈ᱍ᱒᱔ger;怠eth;愸òᄳhĀ;vᱚᱛ怐»ऊūᱡᱧarow;椏aã̕Āayᱮᱳron;䄏;䐴ƀ;ao̲ᱼᲄĀgrʿᲁr;懊tseq;橷ƀglmᲑᲔᲘ耻°䂰ta;䎴ptyv;榱ĀirᲣᲨsht;楿;쀀𝔡arĀlrᲳᲵ»ࣜ»သʀaegsv᳂͸᳖᳜᳠mƀ;oș᳊᳔ndĀ;ș᳑uit;晦amma;䏝in;拲ƀ;io᳧᳨᳸䃷de脀÷;o᳧ᳰntimes;拇nø᳷cy;䑒cɯᴆ\0\0ᴊrn;挞op;挍ʀlptuwᴘᴝᴢᵉᵕlar;䀤f;쀀𝕕ʀ;emps̋ᴭᴷᴽᵂqĀ;d͒ᴳot;扑inus;戸lus;戔quare;抡blebarwedgåúnƀadhᄮᵝᵧownarrowóᲃarpoonĀlrᵲᵶefôᲴighôᲶŢᵿᶅkaro÷གɯᶊ\0\0ᶎrn;挟op;挌ƀcotᶘᶣᶦĀryᶝᶡ;쀀𝒹;䑕l;槶rok;䄑Ādrᶰᶴot;拱iĀ;fᶺ᠖斿Āah᷀᷃ròЩaòྦangle;榦Āci᷒ᷕy;䑟grarr;柿ऀDacdefglmnopqrstuxḁḉḙḸոḼṉṡṾấắẽỡἪἷὄ὎὚ĀDoḆᴴoôᲉĀcsḎḔute耻é䃩ter;橮ȀaioyḢḧḱḶron;䄛rĀ;cḭḮ扖耻ê䃪lon;払;䑍ot;䄗ĀDrṁṅot;扒;쀀𝔢ƀ;rsṐṑṗ檚ave耻è䃨Ā;dṜṝ檖ot;檘Ȁ;ilsṪṫṲṴ檙nters;揧;愓Ā;dṹṺ檕ot;檗ƀapsẅẉẗcr;䄓tyƀ;svẒẓẕ戅et»ẓpĀ1;ẝẤijạả;怄;怅怃ĀgsẪẬ;䅋p;怂ĀgpẴẸon;䄙f;쀀𝕖ƀalsỄỎỒrĀ;sỊị拕l;槣us;橱iƀ;lvỚớở䎵on»ớ;䏵ȀcsuvỪỳἋἣĀioữḱrc»Ḯɩỹ\0\0ỻíՈantĀglἂἆtr»ṝess»Ṻƀaeiἒ἖Ἒls;䀽st;扟vĀ;DȵἠD;橸parsl;槥ĀDaἯἳot;打rr;楱ƀcdiἾὁỸr;愯oô͒ĀahὉὋ;䎷耻ð䃰Āmrὓὗl耻ë䃫o;悬ƀcipὡὤὧl;䀡sôծĀeoὬὴctatioîՙnentialåչৡᾒ\0ᾞ\0ᾡᾧ\0\0ῆῌ\0ΐ\0ῦῪ \0 ⁚llingdotseñṄy;䑄male;晀ƀilrᾭᾳ῁lig;耀ffiɩᾹ\0\0᾽g;耀ffig;耀ffl;쀀𝔣lig;耀filig;쀀fjƀaltῙ῜ῡt;晭ig;耀flns;斱of;䆒ǰ΅\0ῳf;쀀𝕗ĀakֿῷĀ;vῼ´拔;櫙artint;樍Āao‌⁕Ācs‑⁒ႉ‸⁅⁈\0⁐β•‥‧‪‬\0‮耻½䂽;慓耻¼䂼;慕;慙;慛Ƴ‴\0‶;慔;慖ʴ‾⁁\0\0⁃耻¾䂾;慗;慜5;慘ƶ⁌\0⁎;慚;慝8;慞l;恄wn;挢cr;쀀𝒻ࢀEabcdefgijlnorstv₂₉₟₥₰₴⃰⃵⃺⃿℃ℒℸ̗ℾ⅒↞Ā;lٍ₇;檌ƀcmpₐₕ₝ute;䇵maĀ;dₜ᳚䎳;檆reve;䄟Āiy₪₮rc;䄝;䐳ot;䄡Ȁ;lqsؾق₽⃉ƀ;qsؾٌ⃄lanô٥Ȁ;cdl٥⃒⃥⃕c;檩otĀ;o⃜⃝檀Ā;l⃢⃣檂;檄Ā;e⃪⃭쀀⋛︀s;檔r;쀀𝔤Ā;gٳ؛mel;愷cy;䑓Ȁ;Eajٚℌℎℐ;檒;檥;檤ȀEaesℛℝ℩ℴ;扩pĀ;p℣ℤ檊rox»ℤĀ;q℮ℯ檈Ā;q℮ℛim;拧pf;쀀𝕘Āci⅃ⅆr;愊mƀ;el٫ⅎ⅐;檎;檐茀>;cdlqr׮ⅠⅪⅮⅳⅹĀciⅥⅧ;檧r;橺ot;拗Par;榕uest;橼ʀadelsↄⅪ←ٖ↛ǰ↉\0↎proø₞r;楸qĀlqؿ↖lesó₈ií٫Āen↣↭rtneqq;쀀≩︀Å↪ԀAabcefkosy⇄⇇⇱⇵⇺∘∝∯≨≽ròΠȀilmr⇐⇔⇗⇛rsðᒄf»․ilôکĀdr⇠⇤cy;䑊ƀ;cwࣴ⇫⇯ir;楈;憭ar;意irc;䄥ƀalr∁∎∓rtsĀ;u∉∊晥it»∊lip;怦con;抹r;쀀𝔥sĀew∣∩arow;椥arow;椦ʀamopr∺∾≃≞≣rr;懿tht;戻kĀlr≉≓eftarrow;憩ightarrow;憪f;쀀𝕙bar;怕ƀclt≯≴≸r;쀀𝒽asè⇴rok;䄧Ābp⊂⊇ull;恃hen»ᱛૡ⊣\0⊪\0⊸⋅⋎\0⋕⋳\0\0⋸⌢⍧⍢⍿\0⎆⎪⎴cute耻í䃭ƀ;iyݱ⊰⊵rc耻î䃮;䐸Ācx⊼⊿y;䐵cl耻¡䂡ĀfrΟ⋉;쀀𝔦rave耻ì䃬Ȁ;inoܾ⋝⋩⋮Āin⋢⋦nt;樌t;戭fin;槜ta;愩lig;䄳ƀaop⋾⌚⌝ƀcgt⌅⌈⌗r;䄫ƀelpܟ⌏⌓inåގarôܠh;䄱f;抷ed;䆵ʀ;cfotӴ⌬⌱⌽⍁are;愅inĀ;t⌸⌹戞ie;槝doô⌙ʀ;celpݗ⍌⍐⍛⍡al;抺Āgr⍕⍙eróᕣã⍍arhk;樗rod;樼Ȁcgpt⍯⍲⍶⍻y;䑑on;䄯f;쀀𝕚a;䎹uest耻¿䂿Āci⎊⎏r;쀀𝒾nʀ;EdsvӴ⎛⎝⎡ӳ;拹ot;拵Ā;v⎦⎧拴;拳Ā;iݷ⎮lde;䄩ǫ⎸\0⎼cy;䑖l耻ï䃯̀cfmosu⏌⏗⏜⏡⏧⏵Āiy⏑⏕rc;䄵;䐹r;쀀𝔧ath;䈷pf;쀀𝕛ǣ⏬\0⏱r;쀀𝒿rcy;䑘kcy;䑔Ѐacfghjos␋␖␢␧␭␱␵␻ppaĀ;v␓␔䎺;䏰Āey␛␠dil;䄷;䐺r;쀀𝔨reen;䄸cy;䑅cy;䑜pf;쀀𝕜cr;쀀𝓀஀ABEHabcdefghjlmnoprstuv⑰⒁⒆⒍⒑┎┽╚▀♎♞♥♹♽⚚⚲⛘❝❨➋⟀⠁⠒ƀart⑷⑺⑼rò৆òΕail;椛arr;椎Ā;gঔ⒋;檋ar;楢ॣ⒥\0⒪\0⒱\0\0\0\0\0⒵Ⓔ\0ⓆⓈⓍ\0⓹ute;䄺mptyv;榴raîࡌbda;䎻gƀ;dlࢎⓁⓃ;榑åࢎ;檅uo耻«䂫rЀ;bfhlpst࢙ⓞⓦⓩ⓫⓮⓱⓵Ā;f࢝ⓣs;椟s;椝ë≒p;憫l;椹im;楳l;憢ƀ;ae⓿─┄檫il;椙Ā;s┉┊檭;쀀⪭︀ƀabr┕┙┝rr;椌rk;杲Āak┢┬cĀek┨┪;䁻;䁛Āes┱┳;榋lĀdu┹┻;榏;榍Ȁaeuy╆╋╖╘ron;䄾Ādi═╔il;䄼ìࢰâ┩;䐻Ȁcqrs╣╦╭╽a;椶uoĀ;rนᝆĀdu╲╷har;楧shar;楋h;憲ʀ;fgqs▋▌উ◳◿扤tʀahlrt▘▤▷◂◨rrowĀ;t࢙□aé⓶arpoonĀdu▯▴own»њp»०eftarrows;懇ightƀahs◍◖◞rrowĀ;sࣴࢧarpoonó྘quigarro÷⇰hreetimes;拋ƀ;qs▋ও◺lanôবʀ;cdgsব☊☍☝☨c;檨otĀ;o☔☕橿Ā;r☚☛檁;檃Ā;e☢☥쀀⋚︀s;檓ʀadegs☳☹☽♉♋pproøⓆot;拖qĀgq♃♅ôউgtò⒌ôছiíলƀilr♕࣡♚sht;楼;쀀𝔩Ā;Eজ♣;檑š♩♶rĀdu▲♮Ā;l॥♳;楪lk;斄cy;䑙ʀ;achtੈ⚈⚋⚑⚖rò◁orneòᴈard;楫ri;旺Āio⚟⚤dot;䅀ustĀ;a⚬⚭掰che»⚭ȀEaes⚻⚽⛉⛔;扨pĀ;p⛃⛄檉rox»⛄Ā;q⛎⛏檇Ā;q⛎⚻im;拦Ѐa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di㩀㩑Ābg㩅㩉ar;機eĀ;qᗺ㩏;扙erp;愘r;쀀𝔴pf;쀀𝕨Ā;eᑹ㩦atèᑹcr;쀀𝓌ૣណ㪇\0㪋\0㪐㪛\0\0㪝㪨㪫㪯\0\0㫃㫎\0㫘ៜ៟tré៑r;쀀𝔵ĀAa㪔㪗ròσrò৶;䎾ĀAa㪡㪤ròθrò৫að✓is;拻ƀdptឤ㪵㪾Āfl㪺ឩ;쀀𝕩imåឲĀAa㫇㫊ròώròਁĀcq㫒ីr;쀀𝓍Āpt៖㫜ré។Ѐacefiosu㫰㫽㬈㬌㬑㬕㬛㬡cĀuy㫶㫻te耻ý䃽;䑏Āiy㬂㬆rc;䅷;䑋n耻¥䂥r;쀀𝔶cy;䑗pf;쀀𝕪cr;쀀𝓎Ācm㬦㬩y;䑎l耻ÿ䃿Ԁacdefhiosw㭂㭈㭔㭘㭤㭩㭭㭴㭺㮀cute;䅺Āay㭍㭒ron;䅾;䐷ot;䅼Āet㭝㭡træᕟa;䎶r;쀀𝔷cy;䐶grarr;懝pf;쀀𝕫cr;쀀𝓏Ājn㮅㮇;怍j;怌'.split("").map((t=>t.charCodeAt(0)))),dt=new 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a=n;for(s.push(t.bMarks[f]),t.bMarks[f]=i;i=o,l.push(t.bsCount[f]),t.bsCount[f]=t.sCount[f]+1+(e?1:0),c.push(t.sCount[f]),t.sCount[f]=a-n,u.push(t.tShift[f]),t.tShift[f]=i-t.bMarks[f];continue}if(p)break;let n=!1;for(let e=0,i=h.length;e";const v=[e,0];g.map=v,t.md.block.tokenize(t,e,f),t.push("blockquote_close","blockquote",-1).markup=">",t.lineMax=a,t.parentType=d,v[1]=t.line;for(let r=0;r=4)return!1;let o=t.bMarks[e]+t.tShift[e];const a=t.src.charCodeAt(o++);if(42!==a&&45!==a&&95!==a)return!1;let s=1;for(;o=4)return!1;if(t.listIndent>=0&&t.sCount[l]-t.listIndent>=4&&t.sCount[l]=t.blkIndent&&(f=!0),(d=Pe(t,l))>=0){if(u=!0,a=t.bMarks[l]+t.tShift[l],h=Number(t.src.slice(a,d-1)),f&&1!==h)return!1}else{if(!((d=Re(t,l))>=0))return!1;u=!1}if(f&&t.skipSpaces(d)>=t.eMarks[l])return!1;if(n)return!0;const p=t.src.charCodeAt(d-1),m=t.tokens.length;u?(s=t.push("ordered_list_open","ol",1),1!==h&&(s.attrs=[["start",h]])):s=t.push("bullet_list_open","ul",1);const g=[l,0];s.map=g,s.markup=String.fromCharCode(p);let v=!1;const b=t.md.block.ruler.getRules("list"),y=t.parentType;for(t.parentType="list";l=i?1:n-e,f>4&&(f=1);const m=e+f;s=t.push("list_item_open","li",1),s.markup=String.fromCharCode(p);const g=[l,0];s.map=g,u&&(s.info=t.src.slice(a,d-1));const y=t.tight,x=t.tShift[l],_=t.sCount[l],w=t.listIndent;if(t.listIndent=t.blkIndent,t.blkIndent=m,t.tight=!0,t.tShift[l]=h-t.bMarks[l],t.sCount[l]=n,h>=i&&t.isEmpty(l+1)?t.line=Math.min(t.line+2,r):t.md.block.tokenize(t,l,r,!0),t.tight&&!v||(c=!1),v=t.line-l>1&&t.isEmpty(t.line-1),t.blkIndent=t.listIndent,t.listIndent=w,t.tShift[l]=x,t.sCount[l]=_,t.tight=y,s=t.push("list_item_close","li",-1),s.markup=String.fromCharCode(p),l=t.line,g[1]=l,l>=r)break;if(t.sCount[l]=4)break;let k=!1;for(let e=0,n=b.length;e=4)return!1;if(91!==t.src.charCodeAt(i))return!1;function s(e){const r=t.lineMax;if(e>=r||t.isEmpty(e))return null;let n=!1;if(t.sCount[e]-t.blkIndent>3&&(n=!0),t.sCount[e]<0&&(n=!0),!n){const n=t.md.block.ruler.getRules("reference"),i=t.parentType;t.parentType="reference";let o=!1;for(let i=0,a=n.length;i=4)return!1;if(!t.md.options.html)return!1;if(60!==t.src.charCodeAt(i))return!1;let a=t.src.slice(i,o),s=0;for(;s=4)return!1;let a=t.src.charCodeAt(i);if(35!==a||i>=o)return!1;let s=1;for(a=t.src.charCodeAt(++i);35===a&&i6||ii&&Jt(t.src.charCodeAt(l-1))&&(o=l),t.line=e+1;const c=t.push("heading_open","h"+String(s),1);c.markup="########".slice(0,s),c.map=[e,t.line];const u=t.push("inline","",0);return u.content=t.src.slice(i,o).trim(),u.map=[e,t.line],u.children=[],t.push("heading_close","h"+String(s),-1).markup="########".slice(0,s),!0},["paragraph","reference","blockquote"]],["lheading",function(t,e,r){const n=t.md.block.ruler.getRules("paragraph");if(t.sCount[e]-t.blkIndent>=4)return!1;const i=t.parentType;t.parentType="paragraph";let o,a=0,s=e+1;for(;s3)continue;if(t.sCount[s]>=t.blkIndent){let e=t.bMarks[s]+t.tShift[s];const r=t.eMarks[s];if(e=r))){a=61===o?1:2;break}}if(t.sCount[s]<0)continue;let e=!1;for(let i=0,o=n.length;i3)continue;if(t.sCount[o]<0)continue;let e=!1;for(let i=0,a=n.length;i=r))&&!(t.sCount[a]=o){t.line=r;break}const e=t.line;let l=!1;for(let o=0;o=t.line)throw new Error("block rule didn't increment state.line");break}if(!l)throw new Error("none of the block rules matched");t.tight=!s,t.isEmpty(t.line-1)&&(s=!0),a=t.line,a0&&(this.level++,this._prev_delimiters.push(this.delimiters),this.delimiters=[],i={delimiters:this.delimiters}),this.pendingLevel=this.level,this.tokens.push(n),this.tokens_meta.push(i),n},qe.prototype.scanDelims=function(t,e){const r=this.posMax,n=this.src.charCodeAt(t),i=t>0?this.src.charCodeAt(t-1):32;let o=t;for(;o?@[]^_`{|}~-".split("").forEach((function(t){$e[t.charCodeAt(0)]=1}));const Ke={tokenize:function(t,e){const r=t.pos,n=t.src.charCodeAt(r);if(e)return!1;if(126!==n)return!1;const i=t.scanDelims(t.pos,!0);let o=i.length;const a=String.fromCharCode(n);if(o<2)return!1;let s;o%2&&(s=t.push("text","",0),s.content=a,o--);for(let e=0;e=0;r--){const n=e[r];if(95!==n.marker&&42!==n.marker)continue;if(-1===n.end)continue;const i=e[n.end],o=r>0&&e[r-1].end===n.end+1&&e[r-1].marker===n.marker&&e[r-1].token===n.token-1&&e[n.end+1].token===i.token+1,a=String.fromCharCode(n.marker),s=t.tokens[n.token];s.type=o?"strong_open":"em_open",s.tag=o?"strong":"em",s.nesting=1,s.markup=o?a+a:a,s.content="";const l=t.tokens[i.token];l.type=o?"strong_close":"em_close",l.tag=o?"strong":"em",l.nesting=-1,l.markup=o?a+a:a,l.content="",o&&(t.tokens[e[r-1].token].content="",t.tokens[e[n.end+1].token].content="",r--)}}const tr={tokenize:function(t,e){const r=t.pos,n=t.src.charCodeAt(r);if(e)return!1;if(95!==n&&42!==n)return!1;const i=t.scanDelims(t.pos,42===n);for(let e=0;e\x00-\x20]*)$/,nr=/^&#((?:x[a-f0-9]{1,6}|[0-9]{1,7}));/i,ir=/^&([a-z][a-z0-9]{1,31});/i;function or(t){const e={},r=t.length;if(!r)return;let n=0,i=-2;const o=[];for(let a=0;as;l-=o[l]+1){const e=t[l];if(e.marker===r.marker&&e.open&&e.end<0){let n=!1;if((e.close||r.open)&&(e.length+r.length)%3==0&&(e.length%3==0&&r.length%3==0||(n=!0)),!n){const n=l>0&&!t[l-1].open?o[l-1]+1:0;o[a]=a-l+n,o[l]=n,r.open=!1,e.end=a,e.close=!1,c=-1,i=-2;break}}}-1!==c&&(e[r.marker][(r.open?3:0)+(r.length||0)%3]=c)}}const ar=[["text",function(t,e){let r=t.pos;for(;r0)return!1;const r=t.pos;if(r+3>t.posMax)return!1;if(58!==t.src.charCodeAt(r))return!1;if(47!==t.src.charCodeAt(r+1))return!1;if(47!==t.src.charCodeAt(r+2))return!1;const n=t.pending.match(Xe);if(!n)return!1;const i=n[1],o=t.md.linkify.matchAtStart(t.src.slice(r-i.length));if(!o)return!1;let a=o.url;if(a.length<=i.length)return!1;a=a.replace(/\*+$/,"");const s=t.md.normalizeLink(a);if(!t.md.validateLink(s))return!1;if(!e){t.pending=t.pending.slice(0,-i.length);const e=t.push("link_open","a",1);e.attrs=[["href",s]],e.markup="linkify",e.info="auto",t.push("text","",0).content=t.md.normalizeLinkText(a);const r=t.push("link_close","a",-1);r.markup="linkify",r.info="auto"}return t.pos+=a.length-i.length,!0}],["newline",function(t,e){let r=t.pos;if(10!==t.src.charCodeAt(r))return!1;const n=t.pending.length-1,i=t.posMax;if(!e)if(n>=0&&32===t.pending.charCodeAt(n))if(n>=1&&32===t.pending.charCodeAt(n-1)){let e=n-1;for(;e>=1&&32===t.pending.charCodeAt(e-1);)e--;t.pending=t.pending.slice(0,e),t.push("hardbreak","br",0)}else t.pending=t.pending.slice(0,-1),t.push("softbreak","br",0);else t.push("softbreak","br",0);for(r++;r=n)return!1;let i=t.src.charCodeAt(r);if(10===i){for(e||t.push("hardbreak","br",0),r++;r=55296&&i<=56319&&r+1=56320&&e<=57343&&(o+=t.src[r+1],r++)}const a="\\"+o;if(!e){const e=t.push("text_special","",0);i<256&&0!==$e[i]?e.content=o:e.content=a,e.markup=a,e.info="escape"}return t.pos=r+1,!0}],["backticks",function(t,e){let r=t.pos;if(96!==t.src.charCodeAt(r))return!1;const n=r;r++;const i=t.posMax;for(;r=h)return!1;if(l=p,i=t.md.helpers.parseLinkDestination(t.src,p,t.posMax),i.ok){for(a=t.md.normalizeLink(i.str),t.md.validateLink(a)?p=i.pos:a="",l=p;p=h||41!==t.src.charCodeAt(p))&&(c=!0),p++}if(c){if(void 0===t.env.references)return!1;if(p=0?n=t.src.slice(l,p++):p=f+1):p=f+1,n||(n=t.src.slice(d,f)),o=t.env.references[ee(n)],!o)return t.pos=u,!1;a=o.href,s=o.title}if(!e){t.pos=d,t.posMax=f;const e=[["href",a]];t.push("link_open","a",1).attrs=e,s&&e.push(["title",s]),t.linkLevel++,t.md.inline.tokenize(t),t.linkLevel--,t.push("link_close","a",-1)}return t.pos=p,t.posMax=h,!0}],["image",function(t,e){let r,n,i,o,a,s,l,c,u="";const h=t.pos,d=t.posMax;if(33!==t.src.charCodeAt(t.pos))return!1;if(91!==t.src.charCodeAt(t.pos+1))return!1;const f=t.pos+2,p=t.md.helpers.parseLinkLabel(t,t.pos+1,!1);if(p<0)return!1;if(o=p+1,o=d)return!1;for(c=o,s=t.md.helpers.parseLinkDestination(t.src,o,t.posMax),s.ok&&(u=t.md.normalizeLink(s.str),t.md.validateLink(u)?o=s.pos:u=""),c=o;o=d||41!==t.src.charCodeAt(o))return t.pos=h,!1;o++}else{if(void 0===t.env.references)return!1;if(o=0?i=t.src.slice(c,o++):o=p+1):o=p+1,i||(i=t.src.slice(f,p)),a=t.env.references[ee(i)],!a)return t.pos=h,!1;u=a.href,l=a.title}if(!e){n=t.src.slice(f,p);const e=[];t.md.inline.parse(n,t.md,t.env,e);const r=t.push("image","img",0),i=[["src",u],["alt",""]];r.attrs=i,r.children=e,r.content=n,l&&i.push(["title",l])}return t.pos=o,t.posMax=d,!0}],["autolink",function(t,e){let r=t.pos;if(60!==t.src.charCodeAt(r))return!1;const n=t.pos,i=t.posMax;for(;;){if(++r>=i)return!1;const e=t.src.charCodeAt(r);if(60===e)return!1;if(62===e)break}const o=t.src.slice(n+1,r);if(rr.test(o)){const r=t.md.normalizeLink(o);if(!t.md.validateLink(r))return!1;if(!e){const e=t.push("link_open","a",1);e.attrs=[["href",r]],e.markup="autolink",e.info="auto",t.push("text","",0).content=t.md.normalizeLinkText(o);const n=t.push("link_close","a",-1);n.markup="autolink",n.info="auto"}return t.pos+=o.length+2,!0}if(er.test(o)){const r=t.md.normalizeLink("mailto:"+o);if(!t.md.validateLink(r))return!1;if(!e){const e=t.push("link_open","a",1);e.attrs=[["href",r]],e.markup="autolink",e.info="auto",t.push("text","",0).content=t.md.normalizeLinkText(o);const n=t.push("link_close","a",-1);n.markup="autolink",n.info="auto"}return t.pos+=o.length+2,!0}return!1}],["html_inline",function(t,e){if(!t.md.options.html)return!1;const r=t.posMax,n=t.pos;if(60!==t.src.charCodeAt(n)||n+2>=r)return!1;const i=t.src.charCodeAt(n+1);if(33!==i&&63!==i&&47!==i&&!function(t){const e=32|t;return e>=97&&e<=122}(i))return!1;const o=t.src.slice(n).match(Be);if(!o)return!1;if(!e){const e=t.push("html_inline","",0);e.content=o[0],a=e.content,/^\s]/i.test(a)&&t.linkLevel++,function(t){return/^<\/a\s*>/i.test(t)}(e.content)&&t.linkLevel--}var a;return t.pos+=o[0].length,!0}],["entity",function(t,e){const r=t.pos,n=t.posMax;if(38!==t.src.charCodeAt(r))return!1;if(r+1>=n)return!1;if(35===t.src.charCodeAt(r+1)){const n=t.src.slice(r).match(nr);if(n){if(!e){const e="x"===n[1][0].toLowerCase()?parseInt(n[1].slice(1),16):parseInt(n[1],10),r=t.push("text_special","",0);r.content=Pt(e)?jt(e):jt(65533),r.markup=n[0],r.info="entity"}return t.pos+=n[0].length,!0}}else{const n=t.src.slice(r).match(ir);if(n){const r=Tt(n[0]);if(r!==n[0]){if(!e){const e=t.push("text_special","",0);e.content=r,e.markup=n[0],e.info="entity"}return t.pos+=n[0].length,!0}}}return!1}]],sr=[["balance_pairs",function(t){const e=t.tokens_meta,r=t.tokens_meta.length;or(t.delimiters);for(let t=0;t0&&n++,"text"===i[e].type&&e+1=t.pos)throw new Error("inline rule didn't increment state.pos");break}}else t.pos=t.posMax;a||t.pos++,o[e]=t.pos},lr.prototype.tokenize=function(t){const e=this.ruler.getRules(""),r=e.length,n=t.posMax,i=t.md.options.maxNesting;for(;t.pos=t.pos)throw new Error("inline rule didn't increment state.pos");break}if(a){if(t.pos>=n)break}else t.pending+=t.src[t.pos++]}t.pending&&t.pushPending()},lr.prototype.parse=function(t,e,r,n){const i=new this.State(t,e,r,n);this.tokenize(i);const o=this.ruler2.getRules(""),a=o.length;for(let t=0;t=3&&":"===t[e-3]||e>=3&&"/"===t[e-3]?0:n.match(r.re.no_http)[0].length:0}},"mailto:":{validate:function(t,e,r){const n=t.slice(e);return r.re.mailto||(r.re.mailto=new RegExp("^"+r.re.src_email_name+"@"+r.re.src_host_strict,"i")),r.re.mailto.test(n)?n.match(r.re.mailto)[0].length:0}}},gr="biz|com|edu|gov|net|org|pro|web|xxx|aero|asia|coop|info|museum|name|shop|рф".split("|");function vr(t){const e=t.re=function(t){const 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e=!0;for(const r of t)e="string"==typeof r&&e;return e}return!1}var on=__webpack_require__(79352),an=function(t,e,r,n){return new(r||(r=Promise))((function(i,o){function a(t){try{l(n.next(t))}catch(t){o(t)}}function s(t){try{l(n.throw(t))}catch(t){o(t)}}function l(t){var e;t.done?i(t.value):(e=t.value,e instanceof r?e:new r((function(t){t(e)}))).then(a,s)}l((n=n.apply(t,e||[])).next())}))};class sn{constructor(t,e,r,n,i,o,a=9){if(this._target=n,this._structures=r,void 0===i)this._properties={};else{const t=y(i,(t=>Object.values(t.values).every((t=>"number"==typeof t)))),e=y(t,(t=>"atom"===t.target));this._properties=Object.fromEntries(Object.entries(e).map((([t,e])=>[t,e.values])))}if(this._resolvedStructures=new Array(r.length),this._indexer=e,this._calculatedEnvironments=function(t,e){if(void 0===e)return;const r=Array.from({length:t.length}).map(((e,r)=>Array.from({length:t[r].size})));for(let t=0;t{if(""!==Qr(e))throw Error(`got custom data for this structure, but no custom loadStructure callback\nthe object was ${JSON.stringify(e)}`);return e},this._cellsData=new Map,this.onselect=()=>{},this.onremove=()=>{},this.oncreate=()=>{},this.activeChanged=()=>{},this.delayChanged=()=>{},this._onSettingChangeCallbacks=[],a>9)throw Error("chemiscope only supports up to 9 structure viewers in the grid");this._maxViewers=a;const l=(0,s.V6)(t),c=document.createElement("div");c.style.setProperty("height","100%"),l.appendChild(c),this._shadow=c.attachShadow({mode:"open"}),this._shadow.adoptedStyleSheets=[v.A,b.A],this._root=document.createElement("div"),this._root.id="grid-root",this._root.className="chsp-structure-viewer-grid",this._shadow.appendChild(this._root),this._setupGrid(1),this._active=(0,s.o)(this._cellsData),this.setActive(this._active)}_getById(t){return(0,s.VT)(t,this._shadow)}get active(){return this._active}pinned(){const t=[];for(const e of this._cellsData.values())t.push(e.current);return t}show(t){this._showInViewer(this.active,t).catch((t=>{throw t}))}addViewer(){const t=this._setupGrid(this._cellsData.size+1);if(0===t.length)return{guid:void 0,color:""};o()(1===t.length,"newGUIDs.length === 1");const e=t[0],r=this._cellsData.get(e);o()(void 0!==r,"newData !== undefined");for(const t of this._onSettingChangeCallbacks)r.viewer.onSettingChange(((r,n)=>{let i=0;for(const t of this._cellsData.keys()){if(e===t)break;i+=1}r.unshift(i.toString()),t(r,n)}));return{guid:e,color:r.color}}removeViewer(t){o()(this._cellsData.size>1,"this._cellsData.size > 1"),this._active===t&&this.setActive((0,s.o)(this._cellsData,t));const e=this._cellsData.get(t);o()(void 0!==e,"data !== undefined"),e.viewer.remove(),this._getById(`gi-${t}`).remove(),this._cellsData.delete(t)}remove(){for(const t of this._cellsData.values())t.viewer.remove();this._shadow.host.remove()}setActive(t){const e=(t,e)=>{const r=this._getById(`chsp-activate-${t}`);r.classList.toggle("chsp-active-pin",e),o()(null!==r.parentElement,"button.parentElement !== null");const n=r.parentElement.querySelector(".chsp-tooltip");o()(null!==n,"tooltip !== null"),n.innerHTML=e?"Active viewer":"Choose as active",this._getById(`gi-${t}`).classList.toggle("chsp-structure-viewer-cell-active",e)},r=this._cellsData.get(this._active);o()(void 0!==r,"current !== undefined"),e(this._active,!1),this._active=t;const n=this._cellsData.get(this._active);o()(void 0!==n,"newData !== undefined"),n.viewer._options.playbackDelay.onchange.push((t=>{this.delayChanged(t)})),this.delayChanged(n.viewer._options.playbackDelay.value),e(this._active,!0)}set positionSettingsModal(t){this._positionSettingsModal=t;for(const e of this._cellsData.values())e.viewer.positionSettingsModal=t}applySettings(t){if(0!==t.length){o()(t.length===this._cellsData.size,"settings.length === this._cellsData.size");for(const[e,r]of(0,s.HL)(this._cellsData.values()))r.viewer.applySettings(t[e])}}saveSettings(){const t=[];for(const e of this._cellsData.values())t.push(e.viewer.saveSettings());return t}onSettingChange(t){for(const e of this._cellsData.keys()){const r=this._cellsData.get(e);o()(void 0!==r,"data !== undefined"),r.viewer.onSettingChange(((r,n)=>{(r=JSON.parse(JSON.stringify(r))).unshift(this._getCurrentPositionInGrid(e).toString()),t(r,n)}))}this._onSettingChangeCallbacks.push(t)}switchTarget(t){return an(this,void 0,void 0,(function*(){this._target=t,this._updateEnvironments("atom"===this._target);const e=Array.from(this._cellsData.entries()).map((([t,e])=>this._refreshCell(t,e,"atom"===this._target)));yield Promise.all(e)}))}_updateEnvironments(t){if(this._environments=t?this._calculatedEnvironments:void 0,t){o()(void 0!==this._environments,"this._environments !== undefined");for(const t of this._cellsData.values())t.viewer.environments=this._environments[t.current.structure]}}_refreshCell(t,e,r){return an(this,void 0,void 0,(function*(){e.current.atom=r?this._indexer.fromEnvironment(e.current.environment,this._target).atom:void 0,this._cellsData.set(t,e);const n=this._properties?Object.keys(this._properties):[];e.viewer.refreshOptions(r,n),yield this._loadViewer(e.viewer,e.current.structure,e.current.atom)}))}_duplicate(t){return an(this,void 0,void 0,(function*(){const e=this._cellsData.get(t);o()(void 0!==e,"data !== undefined");const r=this.addViewer().guid;if(void 0===r)return;const n=this._cellsData.get(r);return o()(void 0!==n,"newData !== undefined"),yield this._showInViewer(r,e.current),n.viewer.applySettings(e.viewer.saveSettings()),this.setActive(r),n}))}_structure(t){if(void 0===this._resolvedStructures[t]){const e=this.loadStructure(t,this._structures[t]),r=Qr(e);if(""!==r)throw Error(`got invalid object as structure: ${r}\n the object was ${JSON.stringify(e)}`);this._resolvedStructures[t]=e}return this._resolvedStructures[t]}_propertiesForStructure(t){const e={};if(void 0!==this._environments){const r=this._environments[t];for(const t in this._properties){const n=this._properties[t];e[t]=[];for(const i of r)void 0!==i?e[t].push(n[i.index]):e[t].push(void 0)}return e}}_showInViewer(t,e){return an(this,void 0,void 0,(function*(){const r=this._cellsData.get(t);o()(void 0!==r,"data !== undefined");const n=r.viewer;r.current.structure!==e.structure&&(yield this._loadViewer(n,e.structure,e.atom),r.current=e),n.highlight("atom"===this._target?e.atom:void 0),r.current=e}))}_loadViewer(t,e,r){return new Promise((n=>{const i={trajectory:!0};void 0!==this._environments&&(i.environments=this._environments[e],"atom"===this._target&&(i.highlight=r)),t.load(this._structure(e),this._propertiesForStructure(e),i,(()=>{n()}))}))}_getNextColor(){const t=[];for(const e of this._cellsData.values())t.push(e.color);return(0,s.Lz)(t)}_setupCell(t,e,r){const n=`gi-${t}`;let i=this._root.querySelector(`#${n}`),a="";if(null===i){i=document.createElement("div"),i.id=n,i.classList.add("chsp-structure-viewer-cell","grid-item"),i.style.gridColumn=`${e}`,i.style.gridRow=`${r}`,a=this._getNextColor();const l=document.createElement("template");l.innerHTML=`\n
\n WILL BE FILLED LATER\n `;const c=l.content.firstChild;c.onclick=()=>{this.setActive(t);const e=this._cellsData.get(this._active);o()(void 0!==e,"data !== undefined"),this.activeChanged(t,e.current)},i.appendChild(c),l.innerHTML='\n \n\n Remove viewer\n ';const u=l.content.firstChild;u.onclick=()=>{1!==this._cellsData.size?(this.onremove(t),this.removeViewer(t),this._setupGrid(this._cellsData.size)):(0,s.R4)("can not remove the last viewer from the grid")},i.appendChild(u),l.innerHTML='\n \n\n Duplicate viewer\n ';const h=l.content.firstChild;h.onclick=()=>an(this,void 0,void 0,(function*(){const e=yield this._duplicate(t);void 0!==e&&this.oncreate(this.active,e.color,e.current)})),i.appendChild(h),l.innerHTML=`\n ${I}\n Download PNG\n `;const d=l.content.firstChild;return d.onclick=()=>{const e=this._cellsData.get(t);o()(void 0!==e,"data !== undefined");const r=e.viewer,n=e.current.structure;if(void 0!==e.current.atom){const t=e.current.atom;ln(r.exportPNG(),`chemiscope-structure-${n+1}-atom-${t+1}.png`)}else ln(r.exportPNG(),`chemiscope-structure-${n+1}.png`)},i.appendChild(d),this._root.appendChild(i),a}return i.style.gridColumn=`${e}`,i.style.gridRow=`${r}`,""}_setupGrid(t){const e=[];if(t<1)return(0,s.R4)("Cannot delete last molecular viewer."),e;if(t>this._maxViewers)return(0,s.R4)(`Viewer grid cannot contain more than ${this._maxViewers} viewers.`),e;const r=this.bestGridArrangement(t);if(this._cellsData.size>t){(0,s.R4)(`Eliminating last ${this._cellsData.size-t} viewers.`);let e=0;for(const r of this._cellsData.keys())e>=t&&this.removeViewer(r),e+=1}let n=1,i=1;const a=this._cellsData.keys();for(let l=0;l=this._cellsData.size?(0,s.Nl)():a.next().value;let c=this._setupCell(t,i,n);if(""===c&&(c=this._getNextColor()),i++,i>r.columns&&(n++,i=1),!this._cellsData.has(t)){const r=this._properties?Object.keys(this._properties):[],n=new on.MoleculeViewer(this._getById(`gi-${t}`),r);n.onselect=e=>{if("atom"!==this._target||this._active!==t)return;const r=this._cellsData.get(this._active);o()(void 0!==r,"data !== undefined");const i=n.natoms();o()(void 0!==i,"natoms !== undefined");const a=this._indexer.fromStructureAtom(this._target,r.current.structure,e%i);void 0!==a&&(n.highlight(e),this.onselect(a))};const i={atom:void 0,structure:-1,environment:-1};this._cellsData.set(t,{color:c,current:i,viewer:n}),void 0!==this._positionSettingsModal&&(n.positionSettingsModal=this._positionSettingsModal),e.push(t)}}for(const t of this._cellsData.values())t.viewer.resize();return e}bestGridArrangement(t){switch(t){case 1:case 2:return{rows:t,columns:1};case 3:case 4:return{rows:2,columns:2};case 5:case 6:return{rows:3,columns:2};case 8:case 7:case 9:return{rows:3,columns:3};default:throw Error("reached unreachable code: too many viewer in the grid")}}_getCurrentPositionInGrid(t){let e=0;for(const r of this._cellsData.keys()){if(t===r)break;e+=1}return e}}function ln(t,e){const r=document.createElement("a");r.download=e,r.href=t,document.body.appendChild(r),r.click(),document.body.removeChild(r),r.remove()}var cn=__webpack_require__(59838);class un{constructor(t,e){this._containerElement=(0,s.V6)(t);const r=document.createElement("div");this._containerElement.appendChild(r),this._shadow=r.attachShadow({mode:"open"}),this._shadow.adoptedStyleSheets=[v.A,b.A],this._toggleContainer=this._createToggleElement("atom"===e),this._shadow.appendChild(this._toggleContainer),this._containerElement.style.setProperty("height",`calc(100% - ${this._toggleContainer.offsetHeight}px)`),this.onchange=()=>{}}_createToggleElement(t){const e=document.createElement("div");return e.innerHTML=`\n
\n \x3c!-- Spinner --\x3e\n \n\n \x3c!-- Buttons --\x3e\n
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\n
\n `,e.querySelector("#structure-btn").onclick=()=>this._select("structure"),e.querySelector("#atom-btn").onclick=()=>this._select("atom"),e.firstElementChild}_select(t){const e="atom"===t;this._toggleContainer.querySelector("#structure-btn").classList.toggle("active",!e),this._toggleContainer.querySelector("#atom-btn").classList.toggle("active",e),this.onchange(t)}loader(t){this._toggleContainer.querySelector("#chsp-target-spinner").style.display=t?"inline-block":"none",this._toggleContainer.querySelectorAll(".btn-outline-secondary").forEach((e=>{t?e.setAttribute("disabled","true"):e.removeAttribute("disabled")}))}remove(){this._shadow.host.remove(),this._containerElement.style.setProperty("height","100%")}}var hn=__webpack_require__(85072),dn=__webpack_require__.n(hn),fn=__webpack_require__(97825),pn=__webpack_require__.n(fn),mn=__webpack_require__(77659),gn=__webpack_require__.n(mn),vn=__webpack_require__(55056),bn=__webpack_require__.n(vn),yn=__webpack_require__(10540),xn=__webpack_require__.n(yn),_n=__webpack_require__(41113),wn=__webpack_require__.n(_n),kn=__webpack_require__(5018),An={};An.styleTagTransform=wn(),An.setAttributes=bn(),An.insert=gn().bind(null,"head"),An.domAPI=pn(),An.insertStyleElement=xn(),dn()(kn.A,An),kn.A&&kn.A.locals&&kn.A.locals;function Mn(t,e){if("object"!=typeof t||null===t)throw Error("the configuration must be a JavaScript object");for(const r of e)if(!(r in t)||!("string"==typeof t[r]||t[r]instanceof HTMLElement))throw Error(`missing "${r}" key in chemiscope configuration`);if("settings"in t){if("object"!=typeof t.settings||null===t.settings)throw Error('"settings" must be an object in chemiscope configuration');Tn(t.settings)}if("loadStructure"in t&&void 0!==t.loadStructure&&!((r=t.loadStructure)&&r.constructor&&r.call&&r.apply))throw Error('"loadStructure" should be a function in chemiscope config');var r;if("maxStructureViewers"in t&&"number"!=typeof t.maxStructureViewers)throw Error('"maxStructureViewers" should be a number in chemiscope config')}function Tn(t){const e=(t,e)=>{if("object"!=typeof e||null===e)throw Error(`"settings.${t}" must be an object`)},r=(t,e)=>{if(!(Array.isArray(e)&&e.length>0))throw Error(`"settings.${t}" must be an array containing at least one element`)};for(const n in t)if("map"===n)e(n,t.map);else if("structure"===n){r(n,t.structure);for(const r of t.structure)e("structure entry",r)}else if("pinned"===n){r(n,t.pinned);for(const e of t.pinned)if(!(Number.isInteger(e)&&e>=0))throw Error('"settings.pinned" must be an array of number')}else{if("target"!==n)throw Error(`invalid key "${n}" in settings`);if(!["atom","structure"].includes(t.target))throw Error('"settings.target" should be either "atom" or "structure"')}}class Sn{static load(t,e){return new Promise((r=>{r(new Sn(t,e))}))}constructor(t,e){var r;this._target="structure",Mn(t,["meta","map","info","structure"]),$r(e),this._dataset=e,this._pinned=[],this._target=Jr(e),this._indexer=new a(e.structures,e.environments),this.meta=new Zr(t.meta,e.meta),this.structure=new sn(t.structure,this._indexer,e.structures,this._target,e.properties,e.environments,t.maxStructureViewers),void 0!==t.loadStructure&&(this.structure.loadStructure=t.loadStructure),this.structure.activeChanged=(t,e)=>{this.map.setActive(t),this.info.show(e)},this.structure.onselect=t=>{this.map.select(t),this.info.show(t)},this.structure.onremove=t=>{this.map.removeMarker(t);const e=this._pinned.indexOf(t);o()(e>-1,"index > -1"),this._pinned.splice(e,1)},this.structure.oncreate=(t,e,r)=>{this.map.addMarker(t,e,r),this.info.show(r),this._pinned.push(t)},this.map=new P(t.map,zn(e.settings),this._indexer,this._target,e.properties),this.map.onselect=t=>{this.info.show(t),this.structure.show(t)},this.map.activeChanged=(t,e)=>{this.info.show(e),this.structure.setActive(t)};const n="atom"===this._target?"structure":"atom",i=Object.values(e.properties).filter((t=>t.target===n));void 0!==e.environments&&i.length>1&&(this._toggle=new un(t.map,this._target),this._toggle.onchange=t=>this._switchTarget(t)),this.info=new x(t.info,e.properties,this._indexer,this._target,e.parameters),this.info.onchange=t=>{this.map.select(t),this.structure.show(t)},this.structure.delayChanged=t=>{this.info.playbackDelay=t};let l={environment:0,structure:0,atom:0};if(void 0!==e.environments&&(l=this._indexer.fromEnvironment(0,this._target)),e.settings&&e.settings.pinned){if(!Array.isArray(e.settings.pinned)||"number"!=typeof e.settings.pinned[0])throw Error("settings.pinned must be an array of numbers");l=this._indexer.fromEnvironment(e.settings.pinned[0],this._target)}const c=this.structure.active;this.map.addMarker(c,(0,s.Lz)([]),l),this._pinned.push(c),this.structure.show(l),this.info.show(l),void 0!==e.settings&&(delete e.settings.map,this.applySettings(e.settings)),void 0!==this._toggle&&(null===(r=e.settings)||void 0===r?void 0:r.target)&&this._switchTarget(this._target,!0)}_switchTarget(t,e=!1){(e||this._target!==t)&&(o()(void 0!==this._toggle,"this._toggle !== undefined"),this._toggle.loader(!0),this._target=t,setTimeout((()=>{return t=this,e=void 0,n=function*(){var t;try{this.info.switchTarget(this._target),yield this.map.switchTarget(this._target),yield this.structure.switchTarget(this._target)}finally{null===(t=this._toggle)||void 0===t||t.loader(!1)}},new((r=void 0)||(r=Promise))((function(i,o){function a(t){try{l(n.next(t))}catch(t){o(t)}}function s(t){try{l(n.throw(t))}catch(t){o(t)}}function l(t){var e;t.done?i(t.value):(e=t.value,e instanceof r?e:new r((function(t){t(e)}))).then(a,s)}l((n=n.apply(t,e||[])).next())}));var t,e,r,n}),0))}remove(){var t;this.map.remove(),this.meta.remove(),this.info.remove(),this.structure.remove(),null===(t=this._toggle)||void 0===t||t.remove()}saveSettings(){return{target:this._target,map:this.map.saveSettings(),pinned:this.structure.pinned().map((t=>"atom"===this._target?t.environment:t.structure)),structure:this.structure.saveSettings()}}applySettings(t){if(Tn(t),void 0!==t.map&&this.map.applySettings(t.map),void 0!==t.pinned){if(!Array.isArray(t.pinned))throw Error("settings.pinned must be an array");for(const t of this._pinned.slice(1))this.map.removeMarker(t),this.structure.removeViewer(t);if(this._pinned=[this._pinned[0]],o()(t.pinned.length>0,"settings.pinned.length > 0"),"number"!=typeof t.pinned[0])throw Error("settings.pinned must be an array of numbers");const e=this._indexer.fromEnvironment(t.pinned[0],this._target);this.map.select(e),this.info.show(e),this.structure.show(e);for(const e of t.pinned.slice(1)){if("number"!=typeof e)throw Error("settings.pinned must be an array of numbers");const{guid:t,color:r}=this.structure.addViewer();if(void 0===t)throw Error("too many environments in 'pinned' setting");const n=this._indexer.fromEnvironment(e,this._target);this.map.addMarker(t,r,n),this.map.setActive(t),this._pinned.push(t),this.info.show(n),this.structure.setActive(t),this.structure.show(n)}}void 0!==t.structure&&this.structure.applySettings(t.structure)}onSettingChange(t){this.map.onSettingChange(((e,r)=>{(e=JSON.parse(JSON.stringify(e))).unshift("map"),t(e,r)})),this.structure.onSettingChange(((e,r)=>{(e=JSON.parse(JSON.stringify(e))).unshift("structure"),t(e,r)}))}dataset(t=!1){const e=JSON.parse(JSON.stringify(this._dataset,((t,e)=>"number"==typeof e&&isNaN(e)?"***NaN***":e)),((t,e)=>"***NaN***"===e?NaN:e));if(t){e.structures=[];for(let t=0;t{r(new Cn(t,e))}))}constructor(t,e){Mn(t,["meta","info","structure"]),$r(e),this._target=Jr(e),this._indexer=new a(e.structures,e.environments),this.meta=new Zr(t.meta,e.meta),this.structure=new sn(t.structure,this._indexer,e.structures,this._target,e.properties,e.environments,1),void 0!==t.loadStructure&&(this.structure.loadStructure=t.loadStructure),this.structure.activeChanged=(t,e)=>{this.info.show(e)},this.structure.onselect=t=>{this.info.show(t)},this.structure.oncreate=(t,e,r)=>{this.info.show(r)},this.info=new x(t.info,e.properties,this._indexer,this._target),this.info.onchange=t=>{this.structure.show(t)},this.structure.delayChanged=t=>{this.info.playbackDelay=t};let r={environment:0,structure:0,atom:0};if(void 0!==e.environments&&(r=this._indexer.fromEnvironment(0,this._target)),e.settings&&e.settings.pinned){if(!Array.isArray(e.settings.pinned)||"number"!=typeof e.settings.pinned[0])throw Error("settings.pinned must be an array of numbers");r=this._indexer.fromEnvironment(e.settings.pinned[0],this._target)}this.structure.show(r),this.info.show(r),void 0!==e.settings&&this.applySettings(e.settings)}remove(){this.meta.remove(),this.info.remove(),this.structure.remove()}applySettings(t){Tn(t),void 0!==t.structure&&this.structure.applySettings(t.structure)}saveSettings(){return{target:this._target,pinned:this.structure.pinned().map((t=>t.environment)),structure:this.structure.saveSettings()}}onSettingChange(t){this.structure.onSettingChange(((e,r)=>{(e=JSON.parse(JSON.stringify(e))).unshift("structure"),t(e,r)}))}}class En{static load(t,e){return new Promise((r=>{r(new En(t,e))}))}constructor(t,e){let r;this._target="structure",Mn(t,["meta","map","info"]),$r(e);for(const t in e.properties){const n=e.properties[t];"atom"===n.target?(0,s.R4)("unsupported per-atom property in a map-only viewer"):(o()("structure"===n.target,"property.target === 'structure'"),r=n.values.length)}this._indexer=new a(new Array(r).fill({size:1,data:0})),this.meta=new Zr(t.meta,e.meta),this.map=new P(t.map,zn(e.settings),this._indexer,this._target,e.properties),this.map.onselect=t=>{this.info.show(t)},this.map.activeChanged=(t,e)=>{this.info.show(e)},this.info=new x(t.info,e.properties,this._indexer,this._target),this.info.onchange=t=>{this.map.select(t)};let n={environment:0,structure:0,atom:0};if(void 0!==e.environments&&(n=this._indexer.fromEnvironment(0,this._target)),e.settings&&e.settings.pinned){if(!Array.isArray(e.settings.pinned)||"number"!=typeof e.settings.pinned[0])throw Error("settings.pinned must be an array of numbers");n=this._indexer.fromEnvironment(e.settings.pinned[0],this._target)}this.map.addMarker("map-0","red",n),this.info.show(n)}remove(){this.meta.remove(),this.info.remove(),this.map.remove()}saveSettings(){return{target:this._target,map:this.map.saveSettings()}}applySettings(t){Tn(t),void 0!==t.map&&this.map.applySettings(zn(t))}onSettingChange(t){this.map.onSettingChange(((e,r)=>{(e=JSON.parse(JSON.stringify(e))).unshift("map"),t(e,r)}))}}function Ln(){return"v0.8.2"}function zn(t){if(void 0===t)return{};if("map"in t){const e=t.map;if("object"==typeof e){if(null===e)throw Error("invalid settings for map, should not be null");return e}throw Error(`invalid type '${typeof e}' for map, should be an object`)}return{}}})(),__webpack_exports__})())); \ No newline at end of file diff --git a/_static/cookbook-icon.png b/_static/cookbook-icon.png new file mode 100644 index 00000000..d1143962 Binary files /dev/null and b/_static/cookbook-icon.png differ diff --git a/_static/cookbook-icon.svg b/_static/cookbook-icon.svg new file mode 100644 index 00000000..6852f0fe --- /dev/null +++ b/_static/cookbook-icon.svg @@ -0,0 +1,283 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/_static/daily-recipe.js b/_static/daily-recipe.js new file mode 100644 index 00000000..844a5096 --- /dev/null +++ b/_static/daily-recipe.js @@ -0,0 +1,34 @@ +(function() { + // Calculate days since Unix epoch (January 1, 1970) + var millisecondsPerDay = 1000 * 60 * 60 * 24; + var today = new Date(); + var utcMidnight = Date.UTC(today.getFullYear(), today.getMonth(), today.getDate()); + var epoch = Date.UTC(1970, 0, 1); + var daysSinceEpoch = Math.floor((utcMidnight - epoch) / millisecondsPerDay); + + // Calculate index based on the day of the year + var index = daysSinceEpoch % examplesData.length; + + // Get the example + var example = examplesData[index]; + + // Build the HTML code + var html = ''; + html += '
'; + html += '
'; + html += '
'; + html += ' '; + html += '

' + example.title + '

'; + html += ' ' + example.html + ''; + html += ' '; + html += ' ' + example.html; + html += '
'; + html += '
'; + html += '
'; + + // Insert the HTML into the page + var container = document.getElementById('daily-thumbnail'); + if (container) { + container.innerHTML = html; + } +})(); diff --git a/_static/debug.css b/_static/debug.css new file mode 100644 index 00000000..74d4aec3 --- /dev/null +++ b/_static/debug.css @@ -0,0 +1,69 @@ +/* + This CSS file should be overridden by the theme authors. It's + meant for debugging and developing the skeleton that this theme provides. +*/ +body { + font-family: -apple-system, "Segoe UI", Roboto, Helvetica, Arial, sans-serif, + "Apple Color Emoji", "Segoe UI Emoji"; + background: lavender; +} +.sb-announcement { + background: rgb(131, 131, 131); +} +.sb-announcement__inner { + background: black; + color: white; +} +.sb-header { + background: lightskyblue; +} +.sb-header__inner { + background: royalblue; + color: white; +} +.sb-header-secondary { + background: lightcyan; +} +.sb-header-secondary__inner { + background: cornflowerblue; + color: white; +} +.sb-sidebar-primary { + background: lightgreen; +} +.sb-main { + background: blanchedalmond; +} +.sb-main__inner { + background: antiquewhite; +} +.sb-header-article { + background: lightsteelblue; +} +.sb-article-container { + background: snow; +} +.sb-article-main { + background: white; +} +.sb-footer-article { + background: lightpink; +} +.sb-sidebar-secondary { + background: lightgoldenrodyellow; +} +.sb-footer-content { + background: plum; +} +.sb-footer-content__inner { + background: palevioletred; +} +.sb-footer { + background: pink; +} +.sb-footer__inner { + background: salmon; +} +.sb-article { + background: white; +} diff --git a/_static/design-tabs.js b/_static/design-tabs.js new file mode 100644 index 00000000..b25bd6a4 --- /dev/null +++ b/_static/design-tabs.js @@ -0,0 +1,101 @@ +// @ts-check + +// Extra JS capability for selected tabs to be synced +// The selection is stored in local storage so that it persists across page loads. + +/** + * @type {Record} + */ +let sd_id_to_elements = {}; +const storageKeyPrefix = "sphinx-design-tab-id-"; + +/** + * Create a key for a tab element. + * @param {HTMLElement} el - The tab element. + * @returns {[string, string, string] | null} - The key. + * + */ +function create_key(el) { + let syncId = el.getAttribute("data-sync-id"); + let syncGroup = el.getAttribute("data-sync-group"); + if (!syncId || !syncGroup) return null; + return [syncGroup, syncId, syncGroup + "--" + syncId]; +} + +/** + * Initialize the tab selection. + * + */ +function ready() { + // Find all tabs with sync data + + /** @type {string[]} */ + let groups = []; + + document.querySelectorAll(".sd-tab-label").forEach((label) => { + if (label instanceof HTMLElement) { + let data = create_key(label); + if (data) { + let [group, id, key] = data; + + // add click event listener + // @ts-ignore + label.onclick = onSDLabelClick; + + // store map of key to elements + if (!sd_id_to_elements[key]) { + sd_id_to_elements[key] = []; + } + sd_id_to_elements[key].push(label); + + if (groups.indexOf(group) === -1) { + groups.push(group); + // Check if a specific tab has been selected via URL parameter + const tabParam = new URLSearchParams(window.location.search).get( + group + ); + if (tabParam) { + console.log( + "sphinx-design: Selecting tab id for group '" + + group + + "' from URL parameter: " + + tabParam + ); + window.sessionStorage.setItem(storageKeyPrefix + group, tabParam); + } + } + + // Check is a specific tab has been selected previously + let previousId = window.sessionStorage.getItem( + storageKeyPrefix + group + ); + if (previousId === id) { + // console.log( + // "sphinx-design: Selecting tab from session storage: " + id + // ); + // @ts-ignore + label.previousElementSibling.checked = true; + } + } + } + }); +} + +/** + * Activate other tabs with the same sync id. + * + * @this {HTMLElement} - The element that was clicked. + */ +function onSDLabelClick() { + let data = create_key(this); + if (!data) return; + let [group, id, key] = data; + for (const label of sd_id_to_elements[key]) { + if (label === this) continue; + // @ts-ignore + label.previousElementSibling.checked = true; + } + window.sessionStorage.setItem(storageKeyPrefix + group, id); +} + +document.addEventListener("DOMContentLoaded", ready, false); diff --git a/_static/doctools.js b/_static/doctools.js new file mode 100644 index 00000000..4d67807d --- /dev/null +++ b/_static/doctools.js @@ -0,0 +1,156 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Base JavaScript utilities for all Sphinx HTML documentation. + * + * :copyright: Copyright 2007-2024 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } + }, + + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; + }, + + addTranslations: (catalog) => { + Object.assign(Documentation.TRANSLATIONS, catalog.messages); + Documentation.PLURAL_EXPR = new Function( + "n", + `return (${catalog.plural_expr})` + ); + Documentation.LOCALE = catalog.locale; + }, + + /** + * helper function to focus on search bar + */ + focusSearchBar: () => { + document.querySelectorAll("input[name=q]")[0]?.focus(); + }, + + /** + * Initialise the domain index toggle buttons + */ + initDomainIndexTable: () => { + const toggler = (el) => { + const idNumber = el.id.substr(7); + const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`); + if (el.src.substr(-9) === "minus.png") { + el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`; + toggledRows.forEach((el) => (el.style.display = "none")); + } else { + el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`; + toggledRows.forEach((el) => (el.style.display = "")); + } + }; + + const togglerElements = document.querySelectorAll("img.toggler"); + togglerElements.forEach((el) => + el.addEventListener("click", (event) => toggler(event.currentTarget)) + ); + togglerElements.forEach((el) => (el.style.display = "")); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler); + }, + + initOnKeyListeners: () => { + // only install a listener if it is really needed + if ( + !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS + ) + return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.altKey || event.ctrlKey || event.metaKey) return; + + if (!event.shiftKey) { + switch (event.key) { + case "ArrowLeft": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const prevLink = document.querySelector('link[rel="prev"]'); + if (prevLink && prevLink.href) { + window.location.href = prevLink.href; + event.preventDefault(); + } + break; + case "ArrowRight": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const nextLink = document.querySelector('link[rel="next"]'); + if (nextLink && nextLink.href) { + window.location.href = nextLink.href; + event.preventDefault(); + } + break; + } + } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case "/": + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break; + Documentation.focusSearchBar(); + event.preventDefault(); + } + }); + }, +}; + +// quick alias for translations +const _ = Documentation.gettext; + +_ready(Documentation.init); diff --git a/_static/documentation_options.js b/_static/documentation_options.js new file mode 100644 index 00000000..7e4c114f --- /dev/null +++ b/_static/documentation_options.js @@ -0,0 +1,13 @@ +const DOCUMENTATION_OPTIONS = { + VERSION: '', + LANGUAGE: 'en', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: false, + SHOW_SEARCH_SUMMARY: true, + ENABLE_SEARCH_SHORTCUTS: true, +}; \ No newline at end of file diff --git a/_static/file.png b/_static/file.png new file mode 100644 index 00000000..a858a410 Binary files /dev/null and b/_static/file.png differ diff --git a/_static/jupyterlite_badge_logo.svg b/_static/jupyterlite_badge_logo.svg new file mode 100644 index 00000000..5de36d7f --- /dev/null +++ b/_static/jupyterlite_badge_logo.svg @@ -0,0 +1,3 @@ + + +launchlaunchlitelite \ No newline at end of file diff --git a/_static/language_data.js b/_static/language_data.js new file mode 100644 index 00000000..367b8ed8 --- /dev/null +++ b/_static/language_data.js @@ -0,0 +1,199 @@ +/* + * language_data.js + * ~~~~~~~~~~~~~~~~ + * + * This script contains the language-specific data used by searchtools.js, + * namely the list of stopwords, stemmer, scorer and splitter. + * + * :copyright: Copyright 2007-2024 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; + + +/* Non-minified version is copied as a separate JS file, if available */ + +/** + * Porter Stemmer + */ +var Stemmer = function() { + + var step2list = { + ational: 'ate', + tional: 'tion', + enci: 'ence', + anci: 'ance', + izer: 'ize', + bli: 'ble', + alli: 'al', + entli: 'ent', + eli: 'e', + ousli: 'ous', + ization: 'ize', + ation: 'ate', + ator: 'ate', + alism: 'al', + iveness: 'ive', + fulness: 'ful', + ousness: 'ous', + aliti: 'al', + iviti: 'ive', + biliti: 'ble', + logi: 'log' + }; + + var step3list = { + icate: 'ic', + ative: '', + alize: 'al', + iciti: 'ic', + ical: 'ic', + ful: '', + ness: '' + }; + + var c = "[^aeiou]"; // consonant + var v = "[aeiouy]"; // vowel + var C = c + "[^aeiouy]*"; // consonant sequence + var V = v + "[aeiou]*"; // vowel sequence + + var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0 + var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1 + var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1 + var s_v = "^(" + C + ")?" + v; // vowel in stem + + this.stemWord = function (w) { + var stem; + var suffix; + var firstch; + var origword = w; + + if (w.length < 3) + return w; + + var re; + var re2; + var re3; + var re4; + + firstch = w.substr(0,1); + if (firstch == "y") + w = firstch.toUpperCase() + w.substr(1); + + // Step 1a + re = /^(.+?)(ss|i)es$/; + re2 = /^(.+?)([^s])s$/; + + if (re.test(w)) + w = w.replace(re,"$1$2"); + else if (re2.test(w)) + w = w.replace(re2,"$1$2"); + + // Step 1b + re = /^(.+?)eed$/; + re2 = /^(.+?)(ed|ing)$/; + if (re.test(w)) { + var fp = re.exec(w); + re = new RegExp(mgr0); + if (re.test(fp[1])) { + re = /.$/; + w = w.replace(re,""); + } + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1]; + re2 = new RegExp(s_v); + if (re2.test(stem)) { + w = stem; + re2 = /(at|bl|iz)$/; + re3 = new RegExp("([^aeiouylsz])\\1$"); + re4 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re2.test(w)) + w = w + "e"; + else if (re3.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + else if (re4.test(w)) + w = w + "e"; + } + } + + // Step 1c + re = /^(.+?)y$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(s_v); + if (re.test(stem)) + w = stem + "i"; + } + + // Step 2 + re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step2list[suffix]; + } + + // Step 3 + re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step3list[suffix]; + } + + // Step 4 + re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/; + re2 = /^(.+?)(s|t)(ion)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + if (re.test(stem)) + w = stem; + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1] + fp[2]; + re2 = new RegExp(mgr1); + if (re2.test(stem)) + w = stem; + } + + // Step 5 + re = /^(.+?)e$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + re2 = new RegExp(meq1); + re3 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re.test(stem) || (re2.test(stem) && !(re3.test(stem)))) + w = stem; + } + re = /ll$/; + re2 = new RegExp(mgr1); + if (re.test(w) && re2.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + + // and turn initial Y back to y + if (firstch == "y") + w = firstch.toLowerCase() + w.substr(1); + return w; + } +} + diff --git a/_static/minus.png b/_static/minus.png new file mode 100644 index 00000000..d96755fd Binary files /dev/null and b/_static/minus.png differ diff --git a/_static/no_image.png b/_static/no_image.png new file mode 100644 index 00000000..8c2d48d5 Binary files /dev/null and b/_static/no_image.png differ diff --git a/_static/plus.png b/_static/plus.png new file mode 100644 index 00000000..7107cec9 Binary files /dev/null and b/_static/plus.png differ diff --git a/_static/pygments.css b/_static/pygments.css new file mode 100644 index 00000000..02b4b128 --- /dev/null +++ b/_static/pygments.css @@ -0,0 +1,258 @@ +.highlight pre { line-height: 125%; } +.highlight td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; } +.highlight span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; } +.highlight td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } +.highlight span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } +.highlight .hll { background-color: #ffffcc } +.highlight { background: #f8f8f8; } +.highlight .c { color: #8f5902; font-style: italic } /* Comment */ +.highlight .err { color: #a40000; border: 1px solid #ef2929 } /* Error */ +.highlight .g { color: #000000 } /* Generic */ +.highlight .k { color: #204a87; font-weight: bold } /* Keyword */ +.highlight .l { color: #000000 } /* Literal */ +.highlight .n { color: #000000 } /* Name */ +.highlight .o { color: #ce5c00; font-weight: bold } /* Operator */ +.highlight .x { color: #000000 } /* Other */ +.highlight .p { color: #000000; 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false,\n nestedClass: \"active\",\n\n // Offset & reflow\n offset: 0,\n reflow: false,\n\n // Event support\n events: true,\n };\n\n //\n // Methods\n //\n\n /**\n * Merge two or more objects together.\n * @param {Object} objects The objects to merge together\n * @returns {Object} Merged values of defaults and options\n */\n var extend = function () {\n var merged = {};\n Array.prototype.forEach.call(arguments, function (obj) {\n for (var key in obj) {\n if (!obj.hasOwnProperty(key)) return;\n merged[key] = obj[key];\n }\n });\n return merged;\n };\n\n /**\n * Emit a custom event\n * @param {String} type The event type\n * @param {Node} elem The element to attach the event to\n * @param {Object} detail Any details to pass along with the event\n */\n var emitEvent = function (type, elem, detail) {\n // Make sure events are enabled\n if (!detail.settings.events) return;\n\n // Create a new event\n var event = new CustomEvent(type, {\n bubbles: true,\n cancelable: true,\n detail: detail,\n });\n\n // Dispatch the event\n elem.dispatchEvent(event);\n };\n\n /**\n * Get an element's distance from the top of the Document.\n * @param {Node} elem The element\n * @return {Number} Distance from the top in pixels\n */\n var getOffsetTop = function (elem) {\n var location = 0;\n if (elem.offsetParent) {\n while (elem) {\n location += elem.offsetTop;\n elem = elem.offsetParent;\n }\n }\n return location >= 0 ? location : 0;\n };\n\n /**\n * Sort content from first to last in the DOM\n * @param {Array} contents The content areas\n */\n var sortContents = function (contents) {\n if (contents) {\n contents.sort(function (item1, item2) {\n var offset1 = getOffsetTop(item1.content);\n var offset2 = getOffsetTop(item2.content);\n if (offset1 < offset2) return -1;\n return 1;\n });\n }\n };\n\n /**\n * Get the offset to use for calculating position\n * @param {Object} settings The settings for this instantiation\n * @return {Float} The number of pixels to offset the calculations\n */\n var getOffset = function (settings) {\n // if the offset is a function run it\n if (typeof settings.offset === \"function\") {\n return parseFloat(settings.offset());\n }\n\n // Otherwise, return it as-is\n return parseFloat(settings.offset);\n };\n\n /**\n * Get the document element's height\n * @private\n * @returns {Number}\n */\n var getDocumentHeight = function () {\n return Math.max(\n document.body.scrollHeight,\n document.documentElement.scrollHeight,\n document.body.offsetHeight,\n document.documentElement.offsetHeight,\n document.body.clientHeight,\n document.documentElement.clientHeight,\n );\n };\n\n /**\n * Determine if an element is in view\n * @param {Node} elem The element\n * @param {Object} settings The settings for this instantiation\n * @param {Boolean} bottom If true, check if element is above bottom of viewport instead\n * @return {Boolean} Returns true if element is in the viewport\n */\n var isInView = function (elem, settings, bottom) {\n var bounds = elem.getBoundingClientRect();\n var offset = getOffset(settings);\n if (bottom) {\n return (\n parseInt(bounds.bottom, 10) <\n (window.innerHeight || document.documentElement.clientHeight)\n );\n }\n return parseInt(bounds.top, 10) <= offset;\n };\n\n /**\n * Check if at the bottom of the viewport\n * @return {Boolean} If true, page is at the bottom of the viewport\n */\n var isAtBottom = function () {\n if (\n Math.ceil(window.innerHeight + window.pageYOffset) >=\n getDocumentHeight()\n )\n return true;\n return false;\n };\n\n /**\n * Check if the last item should be used (even if not at the top of the page)\n * @param {Object} item The last item\n * @param {Object} settings The settings for this instantiation\n * @return {Boolean} If true, use the last item\n */\n var useLastItem = function (item, settings) {\n if (isAtBottom() && isInView(item.content, settings, true)) return true;\n return false;\n };\n\n /**\n * Get the active content\n * @param {Array} contents The content areas\n * @param {Object} settings The settings for this instantiation\n * @return {Object} The content area and matching navigation link\n */\n var getActive = function (contents, settings) {\n var last = contents[contents.length - 1];\n if (useLastItem(last, settings)) return last;\n for (var i = contents.length - 1; i >= 0; i--) {\n if (isInView(contents[i].content, settings)) return contents[i];\n }\n };\n\n /**\n * Deactivate parent navs in a nested navigation\n * @param {Node} nav The starting navigation element\n * @param {Object} settings The settings for this instantiation\n */\n var deactivateNested = function (nav, settings) {\n // If nesting isn't activated, bail\n if (!settings.nested || !nav.parentNode) return;\n\n // Get the parent navigation\n var li = nav.parentNode.closest(\"li\");\n if (!li) return;\n\n // Remove the active class\n li.classList.remove(settings.nestedClass);\n\n // Apply recursively to any parent navigation elements\n deactivateNested(li, settings);\n };\n\n /**\n * Deactivate a nav and content area\n * @param {Object} items The nav item and content to deactivate\n * @param {Object} settings The settings for this instantiation\n */\n var deactivate = function (items, settings) {\n // Make sure there are items to deactivate\n if (!items) return;\n\n // Get the parent list item\n var li = items.nav.closest(\"li\");\n if (!li) return;\n\n // Remove the active class from the nav and content\n li.classList.remove(settings.navClass);\n items.content.classList.remove(settings.contentClass);\n\n // Deactivate any parent navs in a nested navigation\n deactivateNested(li, settings);\n\n // Emit a custom event\n emitEvent(\"gumshoeDeactivate\", li, {\n link: items.nav,\n content: items.content,\n settings: settings,\n });\n };\n\n /**\n * Activate parent navs in a nested navigation\n * @param {Node} nav The starting navigation element\n * @param {Object} settings The settings for this instantiation\n */\n var activateNested = function (nav, settings) {\n // If nesting isn't activated, bail\n if (!settings.nested) return;\n\n // Get the parent navigation\n var li = nav.parentNode.closest(\"li\");\n if (!li) return;\n\n // Add the active class\n li.classList.add(settings.nestedClass);\n\n // Apply recursively to any parent navigation elements\n activateNested(li, settings);\n };\n\n /**\n * Activate a nav and content area\n * @param {Object} items The nav item and content to activate\n * @param {Object} settings The settings for this instantiation\n */\n var activate = function (items, settings) {\n // Make sure there are items to activate\n if (!items) return;\n\n // Get the parent list item\n var li = items.nav.closest(\"li\");\n if (!li) return;\n\n // Add the active class to the nav and content\n li.classList.add(settings.navClass);\n items.content.classList.add(settings.contentClass);\n\n // Activate any parent navs in a nested navigation\n activateNested(li, settings);\n\n // Emit a custom event\n emitEvent(\"gumshoeActivate\", li, {\n link: items.nav,\n content: items.content,\n settings: settings,\n });\n };\n\n /**\n * Create the Constructor object\n * @param {String} selector The selector to use for navigation items\n * @param {Object} options User options and settings\n */\n var Constructor = function (selector, options) {\n //\n // Variables\n //\n\n var publicAPIs = {};\n var navItems, contents, current, timeout, settings;\n\n //\n // Methods\n //\n\n /**\n * Set variables from DOM elements\n */\n publicAPIs.setup = function () {\n // Get all nav items\n navItems = document.querySelectorAll(selector);\n\n // Create contents array\n contents = [];\n\n // Loop through each item, get it's matching content, and push to the array\n Array.prototype.forEach.call(navItems, function (item) {\n // Get the content for the nav item\n var content = document.getElementById(\n decodeURIComponent(item.hash.substr(1)),\n );\n if (!content) return;\n\n // Push to the contents array\n 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window.cancelAnimationFrame(timeout);\n }\n\n // Setup debounce callback\n timeout = window.requestAnimationFrame(publicAPIs.detect);\n };\n\n /**\n * Update content sorting on resize\n * Debounced for performance\n */\n var resizeHandler = function (event) {\n // If there's a timer, cancel it\n if (timeout) {\n window.cancelAnimationFrame(timeout);\n }\n\n // Setup debounce callback\n timeout = window.requestAnimationFrame(function () {\n sortContents(contents);\n publicAPIs.detect();\n });\n };\n\n /**\n * Destroy the current instantiation\n */\n publicAPIs.destroy = function () {\n // Undo DOM changes\n if (current) {\n deactivate(current, settings);\n }\n\n // Remove event listeners\n window.removeEventListener(\"scroll\", scrollHandler, false);\n if (settings.reflow) {\n window.removeEventListener(\"resize\", resizeHandler, false);\n }\n\n // Reset variables\n contents = null;\n navItems = null;\n current = null;\n timeout = null;\n settings = null;\n };\n\n /**\n * Initialize the current instantiation\n */\n var init = function () {\n // Merge user options into defaults\n settings = extend(defaults, options || {});\n\n // Setup variables based on the current DOM\n publicAPIs.setup();\n\n // Find the currently active content\n publicAPIs.detect();\n\n // Setup event listeners\n window.addEventListener(\"scroll\", scrollHandler, false);\n if (settings.reflow) {\n window.addEventListener(\"resize\", resizeHandler, false);\n }\n };\n\n //\n // Initialize and return the public APIs\n //\n\n init();\n return publicAPIs;\n };\n\n //\n // Return the Constructor\n //\n\n return Constructor;\n },\n);\n","// The module cache\nvar __webpack_module_cache__ = {};\n\n// The require function\nfunction __webpack_require__(moduleId) {\n\t// Check if module is in cache\n\tvar cachedModule = __webpack_module_cache__[moduleId];\n\tif (cachedModule !== undefined) {\n\t\treturn cachedModule.exports;\n\t}\n\t// Create a new module (and put it into the cache)\n\tvar module = __webpack_module_cache__[moduleId] = {\n\t\t// no module.id needed\n\t\t// no module.loaded needed\n\t\texports: {}\n\t};\n\n\t// Execute the module function\n\t__webpack_modules__[moduleId].call(module.exports, module, module.exports, __webpack_require__);\n\n\t// Return the exports of the module\n\treturn module.exports;\n}\n\n","// getDefaultExport function for compatibility with non-harmony modules\n__webpack_require__.n = (module) => {\n\tvar getter = module && module.__esModule ?\n\t\t() => (module['default']) :\n\t\t() => (module);\n\t__webpack_require__.d(getter, { a: getter });\n\treturn getter;\n};","// define getter functions for harmony exports\n__webpack_require__.d = (exports, definition) => {\n\tfor(var key in definition) {\n\t\tif(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {\n\t\t\tObject.defineProperty(exports, key, { enumerable: true, get: definition[key] });\n\t\t}\n\t}\n};","__webpack_require__.g = (function() {\n\tif (typeof 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Resetting to auto.`);\n mode = \"auto\";\n }\n\n document.body.dataset.theme = mode;\n localStorage.setItem(\"theme\", mode);\n console.log(`Changed to ${mode} mode.`);\n}\n\nfunction cycleThemeOnce() {\n const currentTheme = localStorage.getItem(\"theme\") || \"auto\";\n const prefersDark = window.matchMedia(\"(prefers-color-scheme: dark)\").matches;\n\n if (prefersDark) {\n // Auto (dark) -> Light -> Dark\n if (currentTheme === \"auto\") {\n setTheme(\"light\");\n } else if (currentTheme == \"light\") {\n setTheme(\"dark\");\n } else {\n setTheme(\"auto\");\n }\n } else {\n // Auto (light) -> Dark -> Light\n if (currentTheme === \"auto\") {\n setTheme(\"dark\");\n } else if (currentTheme == \"dark\") {\n setTheme(\"light\");\n } else {\n setTheme(\"auto\");\n }\n }\n}\n\n////////////////////////////////////////////////////////////////////////////////\n// Setup\n////////////////////////////////////////////////////////////////////////////////\nfunction setupScrollHandler() {\n // Taken 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\ No newline at end of file diff --git a/_static/searchtools.js b/_static/searchtools.js new file mode 100644 index 00000000..b08d58c9 --- /dev/null +++ b/_static/searchtools.js @@ -0,0 +1,620 @@ +/* + * searchtools.js + * ~~~~~~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for the full-text search. + * + * :copyright: Copyright 2007-2024 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +/** + * Simple result scoring code. + */ +if (typeof Scorer === "undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms, highlightTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + const contentRoot = document.documentElement.dataset.content_root; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = contentRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = contentRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) { + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + // highlight search terms in the description + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + } + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms, anchor) + ); + // highlight search terms in the summary + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + "Search finished, found ${resultCount} page(s) matching the search query." + ).replace('${resultCount}', resultCount); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms, + highlightTerms, +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms, highlightTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms, highlightTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; +// Helper function used by query() to order search results. +// Each input is an array of [docname, title, anchor, descr, score, filename]. +// Order the results by score (in opposite order of appearance, since the +// `_displayNextItem` function uses pop() to retrieve items) and then alphabetically. +const _orderResultsByScoreThenName = (a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString, anchor) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + for (const removalQuery of [".headerlink", "script", "style"]) { + htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() }); + } + if (anchor) { + const anchorContent = htmlElement.querySelector(`[role="main"] ${anchor}`); + if (anchorContent) return anchorContent.textContent; + + console.warn( + `Anchored content block not found. Sphinx search tries to obtain it via DOM query '[role=main] ${anchor}'. Check your theme or template.` + ); + } + + // if anchor not specified or not found, fall back to main content + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent) return docContent.textContent; + + console.warn( + "Content block not found. Sphinx search tries to obtain it via DOM query '[role=main]'. Check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + _parseQuery: (query) => { + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + return [query, searchTerms, excludedTerms, highlightTerms, objectTerms]; + }, + + /** + * execute search (requires search index to be loaded) + */ + _performSearch: (query, searchTerms, excludedTerms, highlightTerms, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // Collect multiple result groups to be sorted separately and then ordered. + // Each is an array of [docname, title, anchor, descr, score, filename]. + const normalResults = []; + const nonMainIndexResults = []; + + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase().trim(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + const score = Math.round(Scorer.title * queryLower.length / title.length); + const boost = titles[file] === title ? 1 : 0; // add a boost for document titles + normalResults.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score + boost, + filenames[file], + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id, isMain] of foundEntries) { + const score = Math.round(100 * queryLower.length / entry.length); + const result = [ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]; + if (isMain) { + normalResults.push(result); + } else { + nonMainIndexResults.push(result); + } + } + } + } + + // lookup as object + objectTerms.forEach((term) => + normalResults.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + normalResults.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) { + normalResults.forEach((item) => (item[4] = Scorer.score(item))); + nonMainIndexResults.forEach((item) => (item[4] = Scorer.score(item))); + } + + // Sort each group of results by score and then alphabetically by name. + normalResults.sort(_orderResultsByScoreThenName); + nonMainIndexResults.sort(_orderResultsByScoreThenName); + + // Combine the result groups in (reverse) order. + // Non-main index entries are typically arbitrary cross-references, + // so display them after other results. + let results = [...nonMainIndexResults, ...normalResults]; + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + return results.reverse(); + }, + + query: (query) => { + const [searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms] = Search._parseQuery(query); + const results = Search._performSearch(searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms, highlightTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + if (!terms.hasOwnProperty(word)) { + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + } + if (!titleTerms.hasOwnProperty(word)) { + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: titleTerms[term], score: Scorer.partialTitle }); + }); + } + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (!fileMap.has(file)) fileMap.set(file, [word]); + else if (fileMap.get(file).indexOf(word) === -1) fileMap.get(file).push(word); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords, anchor) => { + const text = Search.htmlToText(htmlText, anchor); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/_static/sg_gallery-binder.css b/_static/sg_gallery-binder.css new file mode 100644 index 00000000..420005d2 --- /dev/null +++ b/_static/sg_gallery-binder.css @@ -0,0 +1,11 @@ +/* CSS for binder integration */ + +div.binder-badge { + margin: 1em auto; + vertical-align: middle; +} + +div.lite-badge { + margin: 1em auto; + vertical-align: middle; +} diff --git a/_static/sg_gallery-dataframe.css b/_static/sg_gallery-dataframe.css new file mode 100644 index 00000000..fac74c43 --- /dev/null +++ b/_static/sg_gallery-dataframe.css @@ -0,0 +1,47 @@ +/* Pandas dataframe css */ +/* Taken from: https://github.com/spatialaudio/nbsphinx/blob/fb3ba670fc1ba5f54d4c487573dbc1b4ecf7e9ff/src/nbsphinx.py#L587-L619 */ +html[data-theme="light"] { + --sg-text-color: #000; + --sg-tr-odd-color: #f5f5f5; + --sg-tr-hover-color: rgba(66, 165, 245, 0.2); +} +html[data-theme="dark"] { + --sg-text-color: #fff; + --sg-tr-odd-color: #373737; + --sg-tr-hover-color: rgba(30, 81, 122, 0.2); +} + +table.dataframe { + border: none !important; + border-collapse: collapse; + border-spacing: 0; + border-color: transparent; + color: var(--sg-text-color); + font-size: 12px; + table-layout: fixed; + width: auto; +} +table.dataframe thead { + border-bottom: 1px solid var(--sg-text-color); + vertical-align: bottom; +} +table.dataframe tr, +table.dataframe th, +table.dataframe td { + text-align: right; + vertical-align: middle; + padding: 0.5em 0.5em; + line-height: normal; + white-space: normal; + max-width: none; + border: none; +} +table.dataframe th { + font-weight: bold; +} +table.dataframe tbody tr:nth-child(odd) { + background: var(--sg-tr-odd-color); +} +table.dataframe tbody tr:hover { + background: var(--sg-tr-hover-color); +} diff --git a/_static/sg_gallery-rendered-html.css b/_static/sg_gallery-rendered-html.css new file mode 100644 index 00000000..93dc2ffb --- /dev/null +++ b/_static/sg_gallery-rendered-html.css @@ -0,0 +1,224 @@ +/* Adapted from notebook/static/style/style.min.css */ +html[data-theme="light"] { + --sg-text-color: #000; + --sg-background-color: #ffffff; + --sg-code-background-color: #eff0f1; + --sg-tr-hover-color: rgba(66, 165, 245, 0.2); + --sg-tr-odd-color: #f5f5f5; +} +html[data-theme="dark"] { + --sg-text-color: #fff; + --sg-background-color: #121212; + --sg-code-background-color: #2f2f30; + --sg-tr-hover-color: rgba(66, 165, 245, 0.2); + --sg-tr-odd-color: #1f1f1f; +} + +.rendered_html { + color: var(--sg-text-color); + /* any extras will just be numbers: */ +} +.rendered_html em { + font-style: italic; +} +.rendered_html strong { + font-weight: bold; +} +.rendered_html u { + text-decoration: underline; +} +.rendered_html :link { + text-decoration: underline; +} +.rendered_html :visited { + text-decoration: underline; +} +.rendered_html h1 { + font-size: 185.7%; + margin: 1.08em 0 0 0; + font-weight: bold; + line-height: 1.0; +} +.rendered_html h2 { + font-size: 157.1%; + margin: 1.27em 0 0 0; + font-weight: bold; + line-height: 1.0; +} +.rendered_html h3 { + font-size: 128.6%; + margin: 1.55em 0 0 0; + font-weight: bold; + line-height: 1.0; +} +.rendered_html h4 { + font-size: 100%; + margin: 2em 0 0 0; + font-weight: bold; + line-height: 1.0; +} +.rendered_html h5 { + font-size: 100%; + margin: 2em 0 0 0; + font-weight: bold; + line-height: 1.0; + font-style: italic; +} +.rendered_html h6 { + font-size: 100%; + margin: 2em 0 0 0; + font-weight: bold; + line-height: 1.0; + font-style: italic; +} +.rendered_html h1:first-child { + margin-top: 0.538em; +} +.rendered_html h2:first-child { + margin-top: 0.636em; +} +.rendered_html h3:first-child { + margin-top: 0.777em; +} +.rendered_html h4:first-child { + margin-top: 1em; +} +.rendered_html h5:first-child { + margin-top: 1em; +} +.rendered_html h6:first-child { + margin-top: 1em; +} +.rendered_html ul:not(.list-inline), +.rendered_html ol:not(.list-inline) { + padding-left: 2em; +} +.rendered_html ul { + list-style: disc; +} +.rendered_html ul ul { + list-style: square; + margin-top: 0; +} +.rendered_html ul ul ul { + list-style: circle; +} +.rendered_html ol { + list-style: decimal; +} +.rendered_html ol ol { + list-style: upper-alpha; + margin-top: 0; +} +.rendered_html ol ol ol { + list-style: lower-alpha; +} +.rendered_html ol ol ol ol { + list-style: lower-roman; +} +.rendered_html ol ol ol ol ol { + list-style: decimal; +} +.rendered_html * + ul { + margin-top: 1em; +} +.rendered_html * + ol { + margin-top: 1em; +} +.rendered_html hr { + color: var(--sg-text-color); + background-color: var(--sg-text-color); +} +.rendered_html pre { + margin: 1em 2em; + padding: 0px; + background-color: var(--sg-background-color); +} +.rendered_html code { + background-color: var(--sg-code-background-color); +} +.rendered_html p code { + padding: 1px 5px; +} +.rendered_html pre code { + background-color: var(--sg-background-color); +} +.rendered_html pre, +.rendered_html code { + border: 0; + color: var(--sg-text-color); + font-size: 100%; +} +.rendered_html blockquote { + margin: 1em 2em; +} +.rendered_html table { + margin-left: auto; + margin-right: auto; + border: none; + border-collapse: collapse; + border-spacing: 0; + color: var(--sg-text-color); + font-size: 12px; + table-layout: fixed; +} +.rendered_html thead { + border-bottom: 1px solid var(--sg-text-color); + vertical-align: bottom; +} +.rendered_html tr, +.rendered_html th, +.rendered_html td { + text-align: right; + vertical-align: middle; + padding: 0.5em 0.5em; + line-height: normal; + white-space: normal; + max-width: none; + border: none; +} +.rendered_html th { + font-weight: bold; +} +.rendered_html tbody tr:nth-child(odd) { + background: var(--sg-tr-odd-color); +} +.rendered_html tbody tr:hover { + color: var(--sg-text-color); + background: var(--sg-tr-hover-color); +} +.rendered_html * + table { + margin-top: 1em; +} +.rendered_html p { + text-align: left; +} +.rendered_html * + p { + margin-top: 1em; +} +.rendered_html img { + display: block; + margin-left: auto; + margin-right: auto; +} +.rendered_html * + img { + margin-top: 1em; +} +.rendered_html img, +.rendered_html svg { + max-width: 100%; + height: auto; +} +.rendered_html img.unconfined, +.rendered_html svg.unconfined { + max-width: none; +} +.rendered_html .alert { + margin-bottom: initial; +} +.rendered_html * + .alert { + margin-top: 1em; +} +[dir="rtl"] .rendered_html p { + text-align: right; +} diff --git a/_static/sg_gallery.css b/_static/sg_gallery.css new file mode 100644 index 00000000..9bcd33c8 --- /dev/null +++ b/_static/sg_gallery.css @@ -0,0 +1,367 @@ +/* +Sphinx-Gallery has compatible CSS to fix default sphinx themes +Tested for Sphinx 1.3.1 for all themes: default, alabaster, sphinxdoc, +scrolls, agogo, traditional, nature, haiku, pyramid +Tested for Read the Docs theme 0.1.7 */ + +/* Define light colors */ +:root, html[data-theme="light"], body[data-theme="light"]{ + --sg-tooltip-foreground: black; + --sg-tooltip-background: rgba(250, 250, 250, 0.9); + --sg-tooltip-border: #ccc transparent; + --sg-thumb-box-shadow-color: #6c757d40; + --sg-thumb-hover-border: #0069d9; + --sg-script-out: #888; + --sg-script-pre: #fafae2; + --sg-pytb-foreground: #000; + --sg-pytb-background: #ffe4e4; + --sg-pytb-border-color: #f66; + --sg-download-a-background-color: #ffc; + --sg-download-a-background-image: linear-gradient(to bottom, #ffc, #d5d57e); + --sg-download-a-border-color: 1px solid #c2c22d; + --sg-download-a-color: #000; + --sg-download-a-hover-background-color: #d5d57e; + --sg-download-a-hover-box-shadow-1: rgba(255, 255, 255, 0.1); + --sg-download-a-hover-box-shadow-2: rgba(0, 0, 0, 0.25); +} +@media(prefers-color-scheme: light) { + :root[data-theme="auto"], html[data-theme="auto"], body[data-theme="auto"] { + --sg-tooltip-foreground: black; + --sg-tooltip-background: rgba(250, 250, 250, 0.9); + --sg-tooltip-border: #ccc transparent; + --sg-thumb-box-shadow-color: #6c757d40; + --sg-thumb-hover-border: #0069d9; + --sg-script-out: #888; + --sg-script-pre: #fafae2; + --sg-pytb-foreground: #000; + --sg-pytb-background: #ffe4e4; + --sg-pytb-border-color: #f66; + --sg-download-a-background-color: #ffc; + --sg-download-a-background-image: linear-gradient(to bottom, #ffc, #d5d57e); + --sg-download-a-border-color: 1px solid #c2c22d; + --sg-download-a-color: #000; + --sg-download-a-hover-background-color: #d5d57e; + --sg-download-a-hover-box-shadow-1: rgba(255, 255, 255, 0.1); + --sg-download-a-hover-box-shadow-2: rgba(0, 0, 0, 0.25); + } +} + +html[data-theme="dark"], body[data-theme="dark"] { + --sg-tooltip-foreground: white; + --sg-tooltip-background: rgba(10, 10, 10, 0.9); + --sg-tooltip-border: #333 transparent; + --sg-thumb-box-shadow-color: #79848d40; + --sg-thumb-hover-border: #003975; + --sg-script-out: rgb(179, 179, 179); + --sg-script-pre: #2e2e22; + --sg-pytb-foreground: #fff; + --sg-pytb-background: #1b1717; + --sg-pytb-border-color: #622; + --sg-download-a-background-color: #443; + --sg-download-a-background-image: linear-gradient(to bottom, #443, #221); + --sg-download-a-border-color: 1px solid #3a3a0d; + --sg-download-a-color: #fff; + --sg-download-a-hover-background-color: #616135; + --sg-download-a-hover-box-shadow-1: rgba(0, 0, 0, 0.1); + --sg-download-a-hover-box-shadow-2: rgba(255, 255, 255, 0.25); +} +@media(prefers-color-scheme: dark){ + html[data-theme="auto"], body[data-theme="auto"] { + --sg-tooltip-foreground: white; + --sg-tooltip-background: rgba(10, 10, 10, 0.9); + --sg-tooltip-border: #333 transparent; + --sg-thumb-box-shadow-color: #79848d40; + --sg-thumb-hover-border: #003975; + --sg-script-out: rgb(179, 179, 179); + --sg-script-pre: #2e2e22; + --sg-pytb-foreground: #fff; + --sg-pytb-background: #1b1717; + --sg-pytb-border-color: #622; + --sg-download-a-background-color: #443; + --sg-download-a-background-image: linear-gradient(to bottom, #443, #221); + --sg-download-a-border-color: 1px solid #3a3a0d; + --sg-download-a-color: #fff; + --sg-download-a-hover-background-color: #616135; + --sg-download-a-hover-box-shadow-1: rgba(0, 0, 0, 0.1); + --sg-download-a-hover-box-shadow-2: rgba(255, 255, 255, 0.25); + } +} + +.sphx-glr-thumbnails { + width: 100%; + margin: 0px 0px 20px 0px; + + /* align thumbnails on a grid */ + justify-content: space-between; + display: grid; + /* each grid column should be at least 160px (this will determine + the actual number of columns) and then take as much of the + remaining width as possible */ + grid-template-columns: repeat(auto-fill, minmax(160px, 1fr)); + gap: 15px; +} +.sphx-glr-thumbnails .toctree-wrapper { + /* hide empty toctree divs added to the DOM + by sphinx even though the toctree is hidden + (they would fill grid places with empty divs) */ + display: none; +} +.sphx-glr-thumbcontainer { + background: transparent; + -moz-border-radius: 5px; + -webkit-border-radius: 5px; + border-radius: 5px; + box-shadow: 0 0 10px var(--sg-thumb-box-shadow-color); + + /* useful to absolutely position link in div */ + position: relative; + + /* thumbnail width should include padding and borders + and take all available space */ + box-sizing: border-box; + width: 100%; + padding: 10px; + border: 1px solid transparent; + + /* align content in thumbnail */ + display: flex; + flex-direction: column; + align-items: center; + gap: 7px; +} +.sphx-glr-thumbcontainer p { + position: absolute; + top: 0; + left: 0; +} +.sphx-glr-thumbcontainer p, +.sphx-glr-thumbcontainer p a { + /* link should cover the whole thumbnail div */ + width: 100%; + height: 100%; +} +.sphx-glr-thumbcontainer p a span { + /* text within link should be masked + (we are just interested in the href) */ + display: none; +} +.sphx-glr-thumbcontainer:hover { + border: 1px solid; + border-color: var(--sg-thumb-hover-border); + cursor: pointer; +} +.sphx-glr-thumbcontainer a.internal { + bottom: 0; + display: block; + left: 0; + box-sizing: border-box; + padding: 150px 10px 0; + position: absolute; + right: 0; + top: 0; +} +/* Next one is to avoid Sphinx traditional theme to cover all the +thumbnail with its default link Background color */ +.sphx-glr-thumbcontainer a.internal:hover { + background-color: transparent; +} + +.sphx-glr-thumbcontainer p { + margin: 0 0 0.1em 0; +} +.sphx-glr-thumbcontainer .figure { + margin: 10px; + width: 160px; +} +.sphx-glr-thumbcontainer img { + display: inline; + max-height: 112px; + max-width: 160px; +} + +.sphx-glr-thumbcontainer[tooltip]::before { + content: ""; + position: absolute; + pointer-events: none; + top: 0; + left: 0; + width: 100%; + height: 100%; + z-index: 97; + background-color: var(--sg-tooltip-background); + backdrop-filter: blur(3px); + opacity: 0; + transition: opacity 0.3s; +} + +.sphx-glr-thumbcontainer[tooltip]:hover::before { + opacity: 1; +} + +.sphx-glr-thumbcontainer[tooltip]:hover::after { + -webkit-border-radius: 4px; + -moz-border-radius: 4px; + border-radius: 4px; + color: var(--sg-tooltip-foreground); + content: attr(tooltip); + padding: 10px 10px 5px; + z-index: 98; + width: 100%; + max-height: 100%; + position: absolute; + pointer-events: none; + top: 0; + box-sizing: border-box; + overflow: hidden; + display: -webkit-box; + -webkit-box-orient: vertical; + -webkit-line-clamp: 6; +} + +.sphx-glr-script-out { + color: var(--sg-script-out); + display: flex; + gap: 0.5em; +} +.sphx-glr-script-out::before { + content: "Out:"; + /* These numbers come from the pre style in the pydata sphinx theme. This + * turns out to match perfectly on the rtd theme, but be a bit too low for + * the pydata sphinx theme. As I could not find a dimension to use that was + * scaled the same way, I just picked one option that worked pretty close for + * both. */ + line-height: 1.4; + padding-top: 10px; +} +.sphx-glr-script-out .highlight { + background-color: transparent; + /* These options make the div expand... */ + flex-grow: 1; + /* ... but also keep it from overflowing its flex container. */ + overflow: auto; +} +.sphx-glr-script-out .highlight pre { + background-color: var(--sg-script-pre); + border: 0; + max-height: 30em; + overflow: auto; + padding-left: 1ex; + /* This margin is necessary in the pydata sphinx theme because pre has a box + * shadow which would be clipped by the overflow:auto in the parent div + * above. */ + margin: 2px; + word-break: break-word; +} +.sphx-glr-script-out + p { + margin-top: 1.8em; +} +blockquote.sphx-glr-script-out { + margin-left: 0pt; +} +.sphx-glr-script-out.highlight-pytb .highlight pre { + color: var(--sg-pytb-foreground); + background-color: var(--sg-pytb-background); + border: 1px solid var(--sg-pytb-border-color); + margin-top: 10px; + padding: 7px; +} + +div.sphx-glr-footer { + text-align: center; +} + +div.sphx-glr-download { + margin: 1em auto; + vertical-align: middle; +} + +div.sphx-glr-download a { + background-color: var(--sg-download-a-background-color); + background-image: var(--sg-download-a-background-image); + border-radius: 4px; + border: 1px solid var(--sg-download-a-border-color); + color: var(--sg-download-a-color); + display: inline-block; + font-weight: bold; + padding: 1ex; + text-align: center; +} + +div.sphx-glr-download code.download { + display: inline-block; + white-space: normal; + word-break: normal; + overflow-wrap: break-word; + /* border and background are given by the enclosing 'a' */ + border: none; + background: none; +} + +div.sphx-glr-download a:hover { + box-shadow: inset 0 1px 0 var(--sg-download-a-hover-box-shadow-1), 0 1px 5px var(--sg-download-a-hover-box-shadow-2); + text-decoration: none; + background-image: none; + background-color: var(--sg-download-a-hover-background-color); +} + +div.sphx-glr-sidebar-item img { + max-height: 20px; +} + +.sphx-glr-example-title:target::before { + display: block; + content: ""; + margin-top: -50px; + height: 50px; + visibility: hidden; +} + +ul.sphx-glr-horizontal { + list-style: none; + padding: 0; +} +ul.sphx-glr-horizontal li { + display: inline; +} +ul.sphx-glr-horizontal img { + height: auto !important; +} + +.sphx-glr-single-img { + margin: auto; + display: block; + max-width: 100%; +} + +.sphx-glr-multi-img { + max-width: 42%; + height: auto; +} + +div.sphx-glr-animation { + margin: auto; + display: block; + max-width: 100%; +} +div.sphx-glr-animation .animation { + display: block; +} + +p.sphx-glr-signature a.reference.external { + -moz-border-radius: 5px; + -webkit-border-radius: 5px; + border-radius: 5px; + padding: 3px; + font-size: 75%; + text-align: right; + margin-left: auto; + display: table; +} + +.sphx-glr-clear { + clear: both; +} + +a.sphx-glr-backref-instance { + text-decoration: none; +} diff --git a/_static/skeleton.css b/_static/skeleton.css new file mode 100644 index 00000000..467c878c --- /dev/null +++ b/_static/skeleton.css @@ -0,0 +1,296 @@ +/* Some sane resets. */ +html { + height: 100%; +} + +body { + margin: 0; + min-height: 100%; +} + +/* All the flexbox magic! */ +body, +.sb-announcement, +.sb-content, +.sb-main, +.sb-container, +.sb-container__inner, +.sb-article-container, +.sb-footer-content, +.sb-header, +.sb-header-secondary, +.sb-footer { + display: flex; +} + +/* These order things vertically */ +body, +.sb-main, +.sb-article-container { + flex-direction: column; +} + +/* Put elements in the center */ +.sb-header, +.sb-header-secondary, +.sb-container, +.sb-content, +.sb-footer, +.sb-footer-content { + justify-content: center; +} +/* Put elements at the ends */ +.sb-article-container { + justify-content: space-between; +} + +/* These elements grow. */ +.sb-main, +.sb-content, +.sb-container, +article { + flex-grow: 1; +} + +/* Because padding making this wider is not fun */ +article { + box-sizing: border-box; +} + +/* The announcements element should never be wider than the page. */ +.sb-announcement { + max-width: 100%; +} + +.sb-sidebar-primary, +.sb-sidebar-secondary { + flex-shrink: 0; + width: 17rem; +} + +.sb-announcement__inner { + justify-content: center; + + box-sizing: border-box; + height: 3rem; + + overflow-x: auto; + white-space: nowrap; +} + +/* Sidebars, with checkbox-based toggle */ +.sb-sidebar-primary, +.sb-sidebar-secondary { + position: fixed; + height: 100%; + top: 0; +} + +.sb-sidebar-primary { + left: -17rem; + transition: left 250ms ease-in-out; +} +.sb-sidebar-secondary { + right: -17rem; + transition: right 250ms ease-in-out; +} + +.sb-sidebar-toggle { + display: none; +} +.sb-sidebar-overlay { + position: fixed; + top: 0; + width: 0; + height: 0; + + transition: width 0ms ease 250ms, height 0ms ease 250ms, opacity 250ms ease; + + opacity: 0; + background-color: rgba(0, 0, 0, 0.54); +} + +#sb-sidebar-toggle--primary:checked + ~ .sb-sidebar-overlay[for="sb-sidebar-toggle--primary"], +#sb-sidebar-toggle--secondary:checked + ~ .sb-sidebar-overlay[for="sb-sidebar-toggle--secondary"] { + width: 100%; + height: 100%; + opacity: 1; + transition: width 0ms ease, height 0ms ease, opacity 250ms ease; +} + +#sb-sidebar-toggle--primary:checked ~ .sb-container .sb-sidebar-primary { + left: 0; +} +#sb-sidebar-toggle--secondary:checked ~ .sb-container .sb-sidebar-secondary { + right: 0; +} + +/* Full-width mode */ +.drop-secondary-sidebar-for-full-width-content + .hide-when-secondary-sidebar-shown { + display: none !important; +} +.drop-secondary-sidebar-for-full-width-content .sb-sidebar-secondary { + display: none !important; +} + +/* Mobile views */ +.sb-page-width { + width: 100%; +} + +.sb-article-container, +.sb-footer-content__inner, +.drop-secondary-sidebar-for-full-width-content .sb-article, +.drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 100vw; +} + +.sb-article, +.match-content-width { + padding: 0 1rem; + box-sizing: border-box; +} + +@media (min-width: 32rem) { + .sb-article, + .match-content-width { + padding: 0 2rem; + } +} + +/* Tablet views */ +@media (min-width: 42rem) { + .sb-article-container { + width: auto; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 42rem; + } + .sb-article, + .match-content-width { + width: 42rem; + } +} +@media (min-width: 46rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 46rem; + } + .sb-article, + .match-content-width { + width: 46rem; + } +} +@media (min-width: 50rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 50rem; + } + .sb-article, + .match-content-width { + width: 50rem; + } +} + +/* Tablet views */ +@media (min-width: 59rem) { + .sb-sidebar-secondary { + position: static; + } + .hide-when-secondary-sidebar-shown { + display: none !important; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 59rem; + } + .sb-article, + .match-content-width { + width: 42rem; + } +} +@media (min-width: 63rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 63rem; + } + .sb-article, + .match-content-width { + width: 46rem; + } +} +@media (min-width: 67rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 67rem; + } + .sb-article, + .match-content-width { + width: 50rem; + } +} + +/* Desktop views */ +@media (min-width: 76rem) { + .sb-sidebar-primary { + position: static; + } + .hide-when-primary-sidebar-shown { + display: none !important; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 59rem; + } + .sb-article, + .match-content-width { + width: 42rem; + } +} + +/* Full desktop views */ +@media (min-width: 80rem) { + .sb-article, + .match-content-width { + width: 46rem; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 63rem; + } +} + +@media (min-width: 84rem) { + .sb-article, + .match-content-width { + width: 50rem; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 67rem; + } +} + +@media (min-width: 88rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 67rem; + } + .sb-page-width { + width: 88rem; + } +} diff --git a/_static/sphinx-design.min.css b/_static/sphinx-design.min.css new file mode 100644 index 00000000..860c36da --- /dev/null +++ b/_static/sphinx-design.min.css @@ -0,0 +1 @@ +.sd-bg-primary{background-color:var(--sd-color-primary) !important}.sd-bg-text-primary{color:var(--sd-color-primary-text) !important}button.sd-bg-primary:focus,button.sd-bg-primary:hover{background-color:var(--sd-color-primary-highlight) !important}a.sd-bg-primary:focus,a.sd-bg-primary:hover{background-color:var(--sd-color-primary-highlight) !important}.sd-bg-secondary{background-color:var(--sd-color-secondary) !important}.sd-bg-text-secondary{color:var(--sd-color-secondary-text) !important}button.sd-bg-secondary:focus,button.sd-bg-secondary:hover{background-color:var(--sd-color-secondary-highlight) !important}a.sd-bg-secondary:focus,a.sd-bg-secondary:hover{background-color:var(--sd-color-secondary-highlight) !important}.sd-bg-success{background-color:var(--sd-color-success) !important}.sd-bg-text-success{color:var(--sd-color-success-text) !important}button.sd-bg-success:focus,button.sd-bg-success:hover{background-color:var(--sd-color-success-highlight) !important}a.sd-bg-success:focus,a.sd-bg-success:hover{background-color:var(--sd-color-success-highlight) !important}.sd-bg-info{background-color:var(--sd-color-info) !important}.sd-bg-text-info{color:var(--sd-color-info-text) !important}button.sd-bg-info:focus,button.sd-bg-info:hover{background-color:var(--sd-color-info-highlight) !important}a.sd-bg-info:focus,a.sd-bg-info:hover{background-color:var(--sd-color-info-highlight) !important}.sd-bg-warning{background-color:var(--sd-color-warning) !important}.sd-bg-text-warning{color:var(--sd-color-warning-text) !important}button.sd-bg-warning:focus,button.sd-bg-warning:hover{background-color:var(--sd-color-warning-highlight) !important}a.sd-bg-warning:focus,a.sd-bg-warning:hover{background-color:var(--sd-color-warning-highlight) !important}.sd-bg-danger{background-color:var(--sd-color-danger) !important}.sd-bg-text-danger{color:var(--sd-color-danger-text) !important}button.sd-bg-danger:focus,button.sd-bg-danger:hover{background-color:var(--sd-color-danger-highlight) !important}a.sd-bg-danger:focus,a.sd-bg-danger:hover{background-color:var(--sd-color-danger-highlight) !important}.sd-bg-light{background-color:var(--sd-color-light) !important}.sd-bg-text-light{color:var(--sd-color-light-text) !important}button.sd-bg-light:focus,button.sd-bg-light:hover{background-color:var(--sd-color-light-highlight) !important}a.sd-bg-light:focus,a.sd-bg-light:hover{background-color:var(--sd-color-light-highlight) !important}.sd-bg-muted{background-color:var(--sd-color-muted) !important}.sd-bg-text-muted{color:var(--sd-color-muted-text) !important}button.sd-bg-muted:focus,button.sd-bg-muted:hover{background-color:var(--sd-color-muted-highlight) !important}a.sd-bg-muted:focus,a.sd-bg-muted:hover{background-color:var(--sd-color-muted-highlight) !important}.sd-bg-dark{background-color:var(--sd-color-dark) !important}.sd-bg-text-dark{color:var(--sd-color-dark-text) !important}button.sd-bg-dark:focus,button.sd-bg-dark:hover{background-color:var(--sd-color-dark-highlight) !important}a.sd-bg-dark:focus,a.sd-bg-dark:hover{background-color:var(--sd-color-dark-highlight) !important}.sd-bg-black{background-color:var(--sd-color-black) 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utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + const rest = document.createTextNode(val.substr(pos + text.length)); + parent.insertBefore( + span, + parent.insertBefore( + rest, + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + /* There may be more occurrences of search term in this node. So call this + * function recursively on the remaining fragment. + */ + _highlight(rest, addItems, text, className); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

' + + '' + + _("Hide Search Matches") + + "

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highlightSearchWords() when we are on the search page. + * It will highlight words from the *previous* search query. + */ + if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords(); + SphinxHighlight.initEscapeListener(); +}); diff --git a/_static/styles/furo-extensions.css b/_static/styles/furo-extensions.css new file mode 100644 index 00000000..82295876 --- /dev/null +++ b/_static/styles/furo-extensions.css @@ -0,0 +1,2 @@ +#furo-sidebar-ad-placement{padding:var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)}#furo-sidebar-ad-placement .ethical-sidebar{background:var(--color-background-secondary);border:none;box-shadow:none}#furo-sidebar-ad-placement .ethical-sidebar:hover{background:var(--color-background-hover)}#furo-sidebar-ad-placement .ethical-sidebar a{color:var(--color-foreground-primary)}#furo-sidebar-ad-placement .ethical-callout 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Remove the inheritance of text transform in Firefox.\n */\n\nbutton,\nselect { /* 1 */\n text-transform: none;\n}\n\n/**\n * Correct the inability to style clickable types in iOS and Safari.\n */\n\nbutton,\n[type=\"button\"],\n[type=\"reset\"],\n[type=\"submit\"] {\n -webkit-appearance: button;\n}\n\n/**\n * Remove the inner border and padding in Firefox.\n */\n\nbutton::-moz-focus-inner,\n[type=\"button\"]::-moz-focus-inner,\n[type=\"reset\"]::-moz-focus-inner,\n[type=\"submit\"]::-moz-focus-inner {\n border-style: none;\n padding: 0;\n}\n\n/**\n * Restore the focus styles unset by the previous rule.\n */\n\nbutton:-moz-focusring,\n[type=\"button\"]:-moz-focusring,\n[type=\"reset\"]:-moz-focusring,\n[type=\"submit\"]:-moz-focusring {\n outline: 1px dotted ButtonText;\n}\n\n/**\n * Correct the padding in Firefox.\n */\n\nfieldset {\n padding: 0.35em 0.75em 0.625em;\n}\n\n/**\n * 1. Correct the text wrapping in Edge and IE.\n * 2. Correct the color inheritance from `fieldset` elements in IE.\n * 3. Remove the padding so developers are not caught out when they zero out\n * `fieldset` elements in all browsers.\n */\n\nlegend {\n box-sizing: border-box; /* 1 */\n color: inherit; /* 2 */\n display: table; /* 1 */\n max-width: 100%; /* 1 */\n padding: 0; /* 3 */\n white-space: normal; /* 1 */\n}\n\n/**\n * Add the correct vertical alignment in Chrome, Firefox, and Opera.\n */\n\nprogress {\n vertical-align: baseline;\n}\n\n/**\n * Remove the default vertical scrollbar in IE 10+.\n */\n\ntextarea {\n overflow: auto;\n}\n\n/**\n * 1. Add the correct box sizing in IE 10.\n * 2. Remove the padding in IE 10.\n */\n\n[type=\"checkbox\"],\n[type=\"radio\"] {\n box-sizing: border-box; /* 1 */\n padding: 0; /* 2 */\n}\n\n/**\n * Correct the cursor style of increment and decrement buttons in Chrome.\n */\n\n[type=\"number\"]::-webkit-inner-spin-button,\n[type=\"number\"]::-webkit-outer-spin-button {\n height: auto;\n}\n\n/**\n * 1. Correct the odd appearance in Chrome and Safari.\n * 2. Correct the outline style in Safari.\n */\n\n[type=\"search\"] {\n -webkit-appearance: textfield; /* 1 */\n outline-offset: -2px; /* 2 */\n}\n\n/**\n * Remove the inner padding in Chrome and Safari on macOS.\n */\n\n[type=\"search\"]::-webkit-search-decoration {\n -webkit-appearance: none;\n}\n\n/**\n * 1. Correct the inability to style clickable types in iOS and Safari.\n * 2. Change font properties to `inherit` in Safari.\n */\n\n::-webkit-file-upload-button {\n -webkit-appearance: button; /* 1 */\n font: inherit; /* 2 */\n}\n\n/* Interactive\n ========================================================================== */\n\n/*\n * Add the correct display in Edge, IE 10+, and Firefox.\n */\n\ndetails {\n display: block;\n}\n\n/*\n * Add the correct display in all browsers.\n */\n\nsummary {\n display: list-item;\n}\n\n/* Misc\n ========================================================================== */\n\n/**\n * Add the correct display in IE 10+.\n */\n\ntemplate {\n display: none;\n}\n\n/**\n * Add the correct display in IE 10.\n */\n\n[hidden] {\n display: none;\n}\n","// This file contains styles for managing print media.\n\n////////////////////////////////////////////////////////////////////////////////\n// Hide elements not relevant to print media.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n // Hide icon container.\n .content-icon-container\n display: none !important\n\n // Hide showing header links if hovering over when printing.\n .headerlink\n display: none !important\n\n // Hide mobile header.\n .mobile-header\n display: none !important\n\n // Hide navigation links.\n .related-pages\n display: none !important\n\n////////////////////////////////////////////////////////////////////////////////\n// Tweaks related to decolorization.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n // Apply a border around code which no longer have a color background.\n .highlight\n border: 0.1pt solid var(--color-foreground-border)\n\n////////////////////////////////////////////////////////////////////////////////\n// Avoid page break in some relevant cases.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n ul, ol, dl, a, table, pre, blockquote, p\n page-break-inside: avoid\n\n h1, h2, h3, h4, h5, h6, img, figure, caption\n page-break-inside: avoid\n page-break-after: avoid\n\n ul, ol, dl\n page-break-before: avoid\n",".visually-hidden\n position: absolute !important\n width: 1px !important\n height: 1px !important\n padding: 0 !important\n margin: -1px !important\n overflow: hidden !important\n clip: rect(0,0,0,0) !important\n white-space: nowrap !important\n border: 0 !important\n color: var(--color-foreground-primary)\n background: var(--color-background-primary)\n\n:-moz-focusring\n outline: auto\n","// This file serves as the \"skeleton\" of the theming logic.\n//\n// This contains the bulk of the logic for handling dark mode, color scheme\n// toggling and the handling of color-scheme-specific hiding of elements.\n\nbody\n @include fonts\n @include spacing\n @include icons\n @include admonitions\n @include default-admonition(#651fff, \"abstract\")\n @include default-topic(#14B8A6, \"pencil\")\n\n @include colors\n\n.only-light\n display: block !important\nhtml body .only-dark\n display: none !important\n\n// Ignore dark-mode hints if print media.\n@media not print\n // Enable dark-mode, if requested.\n body[data-theme=\"dark\"]\n @include colors-dark\n\n html & .only-light\n display: none !important\n .only-dark\n display: block !important\n\n // Enable dark mode, unless explicitly told to avoid.\n @media (prefers-color-scheme: dark)\n body:not([data-theme=\"light\"])\n @include colors-dark\n\n html & .only-light\n display: none !important\n .only-dark\n display: block !important\n\n//\n// Theme toggle presentation\n//\nbody[data-theme=\"auto\"]\n .theme-toggle svg.theme-icon-when-auto-light\n display: block\n\n @media (prefers-color-scheme: dark)\n .theme-toggle svg.theme-icon-when-auto-dark\n display: block\n .theme-toggle svg.theme-icon-when-auto-light\n display: none\n\nbody[data-theme=\"dark\"]\n .theme-toggle svg.theme-icon-when-dark\n display: block\n\nbody[data-theme=\"light\"]\n .theme-toggle svg.theme-icon-when-light\n display: block\n","// Fonts used by this theme.\n//\n// There are basically two things here -- using the system font stack and\n// defining sizes for various elements in %ages. We could have also used `em`\n// but %age is easier to reason about for me.\n\n@mixin fonts {\n // These are adapted from https://systemfontstack.com/\n --font-stack: -apple-system, BlinkMacSystemFont, Segoe UI, Helvetica, Arial,\n sans-serif, Apple Color Emoji, Segoe UI Emoji;\n --font-stack--monospace: \"SFMono-Regular\", Menlo, Consolas, Monaco,\n Liberation Mono, Lucida Console, monospace;\n --font-stack--headings: var(--font-stack);\n\n --font-size--normal: 100%;\n --font-size--small: 87.5%;\n --font-size--small--2: 81.25%;\n --font-size--small--3: 75%;\n --font-size--small--4: 62.5%;\n\n // Sidebar\n --sidebar-caption-font-size: var(--font-size--small--2);\n --sidebar-item-font-size: var(--font-size--small);\n --sidebar-search-input-font-size: var(--font-size--small);\n\n // Table of Contents\n --toc-font-size: var(--font-size--small--3);\n --toc-font-size--mobile: var(--font-size--normal);\n --toc-title-font-size: var(--font-size--small--4);\n\n // Admonitions\n //\n // These aren't defined in terms of %ages, since nesting these is permitted.\n --admonition-font-size: 0.8125rem;\n --admonition-title-font-size: 0.8125rem;\n\n // Code\n --code-font-size: var(--font-size--small--2);\n\n // API\n --api-font-size: var(--font-size--small);\n}\n","// Spacing for various elements on the page\n//\n// If the user wants to tweak things in a certain way, they are permitted to.\n// They also have to deal with the consequences though!\n\n@mixin spacing {\n // Header!\n --header-height: calc(\n var(--sidebar-item-line-height) + 4 * #{var(--sidebar-item-spacing-vertical)}\n );\n --header-padding: 0.5rem;\n\n // Sidebar\n --sidebar-tree-space-above: 1.5rem;\n --sidebar-caption-space-above: 1rem;\n\n --sidebar-item-line-height: 1rem;\n --sidebar-item-spacing-vertical: 0.5rem;\n --sidebar-item-spacing-horizontal: 1rem;\n --sidebar-item-height: calc(\n var(--sidebar-item-line-height) + 2 *#{var(--sidebar-item-spacing-vertical)}\n );\n\n --sidebar-expander-width: var(--sidebar-item-height); // be square\n\n --sidebar-search-space-above: 0.5rem;\n --sidebar-search-input-spacing-vertical: 0.5rem;\n --sidebar-search-input-spacing-horizontal: 0.5rem;\n --sidebar-search-input-height: 1rem;\n --sidebar-search-icon-size: var(--sidebar-search-input-height);\n\n // Table of Contents\n --toc-title-padding: 0.25rem 0;\n --toc-spacing-vertical: 1.5rem;\n --toc-spacing-horizontal: 1.5rem;\n --toc-item-spacing-vertical: 0.4rem;\n --toc-item-spacing-horizontal: 1rem;\n}\n","// Expose theme icons as CSS variables.\n\n$icons: (\n // Adapted from tabler-icons\n // url: https://tablericons.com/\n \"search\":\n url('data:image/svg+xml;charset=utf-8,'),\n // Factored out from mkdocs-material on 24-Aug-2020.\n // url: https://squidfunk.github.io/mkdocs-material/reference/admonitions/\n \"pencil\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"abstract\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"info\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"flame\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"question\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"warning\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"failure\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"spark\":\n url('data:image/svg+xml;charset=utf-8,')\n);\n\n@mixin icons {\n @each $name, $glyph in $icons {\n --icon-#{$name}: #{$glyph};\n }\n}\n","// Admonitions\n\n// Structure of these is:\n// admonition-class: color \"icon-name\";\n//\n// The colors are translated into CSS variables below. The icons are\n// used directly in the main declarations to set the `mask-image` in\n// the title.\n\n// prettier-ignore\n$admonitions: (\n // Each of these has an reST directives for it.\n \"caution\": #ff9100 \"spark\",\n \"warning\": #ff9100 \"warning\",\n \"danger\": #ff5252 \"spark\",\n \"attention\": #ff5252 \"warning\",\n \"error\": #ff5252 \"failure\",\n \"hint\": #00c852 \"question\",\n \"tip\": #00c852 \"info\",\n \"important\": #00bfa5 \"flame\",\n \"note\": #00b0ff \"pencil\",\n \"seealso\": #448aff \"info\",\n \"admonition-todo\": #808080 \"pencil\"\n);\n\n@mixin default-admonition($color, $icon-name) {\n --color-admonition-title: #{$color};\n --color-admonition-title-background: #{rgba($color, 0.2)};\n\n --icon-admonition-default: var(--icon-#{$icon-name});\n}\n\n@mixin default-topic($color, $icon-name) {\n --color-topic-title: #{$color};\n --color-topic-title-background: #{rgba($color, 0.2)};\n\n --icon-topic-default: var(--icon-#{$icon-name});\n}\n\n@mixin admonitions {\n @each $name, $values in $admonitions {\n --color-admonition-title--#{$name}: #{nth($values, 1)};\n --color-admonition-title-background--#{$name}: #{rgba(\n nth($values, 1),\n 0.2\n )};\n }\n}\n","// Colors used throughout this theme.\n//\n// The aim is to give the user more control. Thus, instead of hard-coding colors\n// in various parts of the stylesheet, the approach taken is to define all\n// colors as CSS variables and reusing them in all the places.\n//\n// `colors-dark` depends on `colors` being included at a lower specificity.\n\n@mixin colors {\n --color-problematic: #b30000;\n\n // Base Colors\n --color-foreground-primary: black; // for main text and headings\n --color-foreground-secondary: #5a5c63; // for secondary text\n --color-foreground-muted: #6b6f76; // for muted text\n --color-foreground-border: #878787; // for content borders\n\n --color-background-primary: white; // for content\n --color-background-secondary: #f8f9fb; // for navigation + ToC\n --color-background-hover: #efeff4ff; // for navigation-item hover\n --color-background-hover--transparent: #efeff400;\n --color-background-border: #eeebee; // for UI borders\n --color-background-item: #ccc; // for \"background\" items (eg: copybutton)\n\n // Announcements\n --color-announcement-background: #000000dd;\n --color-announcement-text: #eeebee;\n\n // Brand colors\n --color-brand-primary: #0a4bff;\n --color-brand-content: #2757dd;\n --color-brand-visited: #872ee0;\n\n // API documentation\n --color-api-background: var(--color-background-hover--transparent);\n --color-api-background-hover: var(--color-background-hover);\n --color-api-overall: var(--color-foreground-secondary);\n --color-api-name: var(--color-problematic);\n --color-api-pre-name: var(--color-problematic);\n --color-api-paren: var(--color-foreground-secondary);\n --color-api-keyword: var(--color-foreground-primary);\n\n --color-api-added: #21632c;\n --color-api-added-border: #38a84d;\n --color-api-changed: #046172;\n --color-api-changed-border: #06a1bc;\n --color-api-deprecated: #605706;\n --color-api-deprecated-border: #f0d90f;\n --color-api-removed: #b30000;\n --color-api-removed-border: #ff5c5c;\n\n --color-highlight-on-target: #ffffcc;\n\n // Inline code background\n --color-inline-code-background: var(--color-background-secondary);\n\n // Highlighted text (search)\n --color-highlighted-background: #ddeeff;\n --color-highlighted-text: var(--color-foreground-primary);\n\n // GUI Labels\n --color-guilabel-background: #ddeeff80;\n --color-guilabel-border: #bedaf580;\n --color-guilabel-text: var(--color-foreground-primary);\n\n // Admonitions!\n --color-admonition-background: transparent;\n\n //////////////////////////////////////////////////////////////////////////////\n // Everything below this should be one of:\n // - var(...)\n // - *-gradient(...)\n // - special literal values (eg: transparent, none)\n //////////////////////////////////////////////////////////////////////////////\n\n // Tables\n --color-table-header-background: var(--color-background-secondary);\n --color-table-border: var(--color-background-border);\n\n // Cards\n --color-card-border: var(--color-background-secondary);\n --color-card-background: transparent;\n --color-card-marginals-background: var(--color-background-secondary);\n\n // Header\n --color-header-background: var(--color-background-primary);\n --color-header-border: var(--color-background-border);\n --color-header-text: var(--color-foreground-primary);\n\n // Sidebar (left)\n --color-sidebar-background: var(--color-background-secondary);\n --color-sidebar-background-border: var(--color-background-border);\n\n --color-sidebar-brand-text: var(--color-foreground-primary);\n --color-sidebar-caption-text: var(--color-foreground-muted);\n --color-sidebar-link-text: var(--color-foreground-secondary);\n --color-sidebar-link-text--top-level: var(--color-brand-primary);\n\n --color-sidebar-item-background: var(--color-sidebar-background);\n --color-sidebar-item-background--current: var(\n --color-sidebar-item-background\n );\n --color-sidebar-item-background--hover: linear-gradient(\n 90deg,\n var(--color-background-hover--transparent) 0%,\n var(--color-background-hover) var(--sidebar-item-spacing-horizontal),\n var(--color-background-hover) 100%\n );\n\n --color-sidebar-item-expander-background: transparent;\n --color-sidebar-item-expander-background--hover: var(\n --color-background-hover\n );\n\n --color-sidebar-search-text: var(--color-foreground-primary);\n --color-sidebar-search-background: var(--color-background-secondary);\n --color-sidebar-search-background--focus: var(--color-background-primary);\n --color-sidebar-search-border: var(--color-background-border);\n --color-sidebar-search-icon: var(--color-foreground-muted);\n\n // Table of Contents (right)\n --color-toc-background: var(--color-background-primary);\n --color-toc-title-text: var(--color-foreground-muted);\n --color-toc-item-text: var(--color-foreground-secondary);\n --color-toc-item-text--hover: var(--color-foreground-primary);\n --color-toc-item-text--active: var(--color-brand-primary);\n\n // Actual page contents\n --color-content-foreground: var(--color-foreground-primary);\n --color-content-background: transparent;\n\n // Links\n --color-link: var(--color-brand-content);\n --color-link-underline: var(--color-background-border);\n --color-link--hover: var(--color-brand-content);\n --color-link-underline--hover: var(--color-foreground-border);\n\n --color-link--visited: var(--color-brand-visited);\n --color-link-underline--visited: var(--color-background-border);\n --color-link--visited--hover: var(--color-brand-visited);\n --color-link-underline--visited--hover: var(--color-foreground-border);\n}\n\n@mixin colors-dark {\n --color-problematic: #ee5151;\n\n // Base Colors\n --color-foreground-primary: #cfd0d0; // for main text and headings\n --color-foreground-secondary: #9ca0a5; // for secondary text\n --color-foreground-muted: #81868d; // for muted text\n --color-foreground-border: #666666; // for content borders\n\n --color-background-primary: #131416; // for content\n --color-background-secondary: #1a1c1e; // for navigation + ToC\n --color-background-hover: #1e2124ff; // for navigation-item hover\n --color-background-hover--transparent: #1e212400;\n --color-background-border: #303335; // for UI borders\n --color-background-item: #444; // for \"background\" items (eg: copybutton)\n\n // Announcements\n --color-announcement-background: #000000dd;\n --color-announcement-text: #eeebee;\n\n // Brand colors\n --color-brand-primary: #3d94ff;\n --color-brand-content: #5ca5ff;\n --color-brand-visited: #b27aeb;\n\n // Highlighted text (search)\n --color-highlighted-background: #083563;\n\n // GUI Labels\n --color-guilabel-background: #08356380;\n --color-guilabel-border: #13395f80;\n\n // API documentation\n --color-api-keyword: var(--color-foreground-secondary);\n --color-highlight-on-target: #333300;\n\n --color-api-added: #3db854;\n --color-api-added-border: #267334;\n --color-api-changed: #09b0ce;\n --color-api-changed-border: #056d80;\n --color-api-deprecated: #b1a10b;\n --color-api-deprecated-border: #6e6407;\n --color-api-removed: #ff7575;\n --color-api-removed-border: #b03b3b;\n\n // Admonitions\n --color-admonition-background: #18181a;\n\n // Cards\n --color-card-border: var(--color-background-secondary);\n --color-card-background: #18181a;\n --color-card-marginals-background: var(--color-background-hover);\n}\n","// This file contains the styling for making the content throughout the page,\n// including fonts, paragraphs, headings and spacing among these elements.\n\nbody\n font-family: var(--font-stack)\npre,\ncode,\nkbd,\nsamp\n font-family: var(--font-stack--monospace)\n\n// Make fonts look slightly nicer.\nbody\n -webkit-font-smoothing: antialiased\n -moz-osx-font-smoothing: grayscale\n\n// Line height from Bootstrap 4.1\narticle\n line-height: 1.5\n\n//\n// Headings\n//\nh1,\nh2,\nh3,\nh4,\nh5,\nh6\n line-height: 1.25\n font-family: var(--font-stack--headings)\n font-weight: bold\n\n border-radius: 0.5rem\n margin-top: 0.5rem\n margin-bottom: 0.5rem\n margin-left: -0.5rem\n margin-right: -0.5rem\n padding-left: 0.5rem\n padding-right: 0.5rem\n\n + p\n margin-top: 0\n\nh1\n font-size: 2.5em\n margin-top: 1.75rem\n margin-bottom: 1rem\nh2\n font-size: 2em\n margin-top: 1.75rem\nh3\n font-size: 1.5em\nh4\n font-size: 1.25em\nh5\n font-size: 1.125em\nh6\n font-size: 1em\n\nsmall\n opacity: 75%\n font-size: 80%\n\n// Paragraph\np\n margin-top: 0.5rem\n margin-bottom: 0.75rem\n\n// Horizontal rules\nhr.docutils\n height: 1px\n padding: 0\n margin: 2rem 0\n background-color: var(--color-background-border)\n border: 0\n\n.centered\n text-align: center\n\n// Links\na\n text-decoration: underline\n\n color: var(--color-link)\n text-decoration-color: var(--color-link-underline)\n\n &:visited\n color: var(--color-link--visited)\n text-decoration-color: var(--color-link-underline--visited)\n &:hover\n color: var(--color-link--visited--hover)\n text-decoration-color: var(--color-link-underline--visited--hover)\n\n &:hover\n color: var(--color-link--hover)\n text-decoration-color: var(--color-link-underline--hover)\n &.muted-link\n color: inherit\n &:hover\n color: var(--color-link--hover)\n text-decoration-color: var(--color-link-underline--hover)\n &:visited\n color: var(--color-link--visited--hover)\n text-decoration-color: var(--color-link-underline--visited--hover)\n","// This file contains the styles for the overall layouting of the documentation\n// skeleton, including the responsive changes as well as sidebar toggles.\n//\n// This is implemented as a mobile-last design, which isn't ideal, but it is\n// reasonably good-enough and I got pretty tired by the time I'd finished this\n// to move the rules around to fix this. Shouldn't take more than 3-4 hours,\n// if you know what you're doing tho.\n\n// HACK: Not all browsers account for the scrollbar width in media queries.\n// This results in horizontal scrollbars in the breakpoint where we go\n// from displaying everything to hiding the ToC. We accomodate for this by\n// adding a bit of padding to the TOC drawer, disabling the horizontal\n// scrollbar and allowing the scrollbars to cover the padding.\n// https://www.456bereastreet.com/archive/201301/media_query_width_and_vertical_scrollbars/\n\n// HACK: Always having the scrollbar visible, prevents certain browsers from\n// causing the content to stutter horizontally between taller-than-viewport and\n// not-taller-than-viewport pages.\n\nhtml\n overflow-x: hidden\n overflow-y: scroll\n scroll-behavior: smooth\n\n.sidebar-scroll, .toc-scroll, article[role=main] *\n // Override Firefox scrollbar style\n scrollbar-width: thin\n scrollbar-color: var(--color-foreground-border) transparent\n\n // Override Chrome scrollbar styles\n &::-webkit-scrollbar\n width: 0.25rem\n height: 0.25rem\n &::-webkit-scrollbar-thumb\n background-color: var(--color-foreground-border)\n border-radius: 0.125rem\n\n//\n// Overalls\n//\nhtml,\nbody\n height: 100%\n color: var(--color-foreground-primary)\n background: var(--color-background-primary)\n\n.skip-to-content\n position: fixed\n padding: 1rem\n border-radius: 1rem\n left: 0.25rem\n top: 0.25rem\n z-index: 40\n background: var(--color-background-primary)\n color: var(--color-foreground-primary)\n\n transform: translateY(-200%)\n transition: transform 300ms ease-in-out\n\n &:focus-within\n transform: translateY(0%)\n\narticle\n color: var(--color-content-foreground)\n background: var(--color-content-background)\n overflow-wrap: break-word\n\n.page\n display: flex\n // fill the viewport for pages with little content.\n min-height: 100%\n\n.mobile-header\n width: 100%\n height: var(--header-height)\n background-color: var(--color-header-background)\n color: var(--color-header-text)\n border-bottom: 1px solid var(--color-header-border)\n\n // Looks like sub-script/super-script have this, and we need this to\n // be \"on top\" of those.\n z-index: 10\n\n // We don't show the header on large screens.\n display: none\n\n // Add shadow when scrolled\n &.scrolled\n border-bottom: none\n box-shadow: 0 0 0.2rem rgba(0, 0, 0, 0.1), 0 0.2rem 0.4rem rgba(0, 0, 0, 0.2)\n\n .header-center\n a\n color: var(--color-header-text)\n text-decoration: none\n\n.main\n display: flex\n flex: 1\n\n// Sidebar (left) also covers the entire left portion of screen.\n.sidebar-drawer\n box-sizing: border-box\n\n border-right: 1px solid var(--color-sidebar-background-border)\n background: var(--color-sidebar-background)\n\n display: flex\n justify-content: flex-end\n // These next two lines took me two days to figure out.\n width: calc((100% - #{$full-width}) / 2 + #{$sidebar-width})\n min-width: $sidebar-width\n\n// Scroll-along sidebars\n.sidebar-container,\n.toc-drawer\n box-sizing: border-box\n width: $sidebar-width\n\n.toc-drawer\n background: var(--color-toc-background)\n // See HACK described on top of this document\n padding-right: 1rem\n\n.sidebar-sticky,\n.toc-sticky\n position: sticky\n top: 0\n height: min(100%, 100vh)\n height: 100vh\n\n display: flex\n flex-direction: column\n\n.sidebar-scroll,\n.toc-scroll\n flex-grow: 1\n flex-shrink: 1\n\n overflow: auto\n scroll-behavior: smooth\n\n// Central items.\n.content\n padding: 0 $content-padding\n width: $content-width\n\n display: flex\n flex-direction: column\n justify-content: space-between\n\n.icon\n display: inline-block\n height: 1rem\n width: 1rem\n svg\n width: 100%\n height: 100%\n\n//\n// Accommodate announcement banner\n//\n.announcement\n background-color: var(--color-announcement-background)\n color: var(--color-announcement-text)\n\n height: var(--header-height)\n display: flex\n align-items: center\n overflow-x: auto\n & + .page\n min-height: calc(100% - var(--header-height))\n\n.announcement-content\n box-sizing: border-box\n padding: 0.5rem\n min-width: 100%\n white-space: nowrap\n text-align: center\n\n a\n color: var(--color-announcement-text)\n text-decoration-color: var(--color-announcement-text)\n\n &:hover\n color: var(--color-announcement-text)\n text-decoration-color: var(--color-link--hover)\n\n////////////////////////////////////////////////////////////////////////////////\n// Toggles for theme\n////////////////////////////////////////////////////////////////////////////////\n.no-js .theme-toggle-container // don't show theme toggle if there's no JS\n display: none\n\n.theme-toggle-container\n display: flex\n\n.theme-toggle\n display: flex\n cursor: pointer\n border: none\n padding: 0\n background: transparent\n\n.theme-toggle svg\n height: 1.25rem\n width: 1.25rem\n color: var(--color-foreground-primary)\n display: none\n\n.theme-toggle-header\n display: flex\n align-items: center\n justify-content: center\n\n////////////////////////////////////////////////////////////////////////////////\n// Toggles for elements\n////////////////////////////////////////////////////////////////////////////////\n.toc-overlay-icon, .nav-overlay-icon\n display: none\n cursor: pointer\n\n .icon\n color: var(--color-foreground-secondary)\n height: 1.5rem\n width: 1.5rem\n\n.toc-header-icon, .nav-overlay-icon\n // for when we set display: flex\n justify-content: center\n align-items: center\n\n.toc-content-icon\n height: 1.5rem\n width: 1.5rem\n\n.content-icon-container\n float: right\n display: flex\n margin-top: 1.5rem\n margin-left: 1rem\n margin-bottom: 1rem\n gap: 0.5rem\n\n .edit-this-page, .view-this-page\n svg\n color: inherit\n height: 1.25rem\n width: 1.25rem\n\n.sidebar-toggle\n position: absolute\n display: none\n// \n.sidebar-toggle[name=\"__toc\"]\n left: 20px\n.sidebar-toggle:checked\n left: 40px\n// \n\n.overlay\n position: fixed\n top: 0\n width: 0\n height: 0\n\n transition: width 0ms, height 0ms, opacity 250ms ease-out\n\n opacity: 0\n background-color: rgba(0, 0, 0, 0.54)\n.sidebar-overlay\n z-index: 20\n.toc-overlay\n z-index: 40\n\n// Keep things on top and smooth.\n.sidebar-drawer\n z-index: 30\n transition: left 250ms ease-in-out\n.toc-drawer\n z-index: 50\n transition: right 250ms ease-in-out\n\n// Show the Sidebar\n#__navigation:checked\n & ~ .sidebar-overlay\n width: 100%\n height: 100%\n opacity: 1\n & ~ .page\n .sidebar-drawer\n top: 0\n left: 0\n // Show the toc sidebar\n#__toc:checked\n & ~ .toc-overlay\n width: 100%\n height: 100%\n opacity: 1\n & ~ .page\n .toc-drawer\n top: 0\n right: 0\n\n////////////////////////////////////////////////////////////////////////////////\n// Back to top\n////////////////////////////////////////////////////////////////////////////////\n.back-to-top\n text-decoration: none\n\n display: none\n position: fixed\n left: 0\n top: 1rem\n padding: 0.5rem\n padding-right: 0.75rem\n border-radius: 1rem\n font-size: 0.8125rem\n\n background: var(--color-background-primary)\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), #6b728080 0px 0px 1px 0px\n\n z-index: 10\n\n margin-left: 50%\n transform: translateX(-50%)\n svg\n height: 1rem\n width: 1rem\n fill: currentColor\n display: inline-block\n\n span\n margin-left: 0.25rem\n\n .show-back-to-top &\n display: flex\n align-items: center\n\n////////////////////////////////////////////////////////////////////////////////\n// Responsive layouting\n////////////////////////////////////////////////////////////////////////////////\n// Make things a bit bigger on bigger screens.\n@media (min-width: $full-width + $sidebar-width)\n html\n font-size: 110%\n\n@media (max-width: $full-width)\n // Collapse \"toc\" into the icon.\n .toc-content-icon\n display: flex\n .toc-drawer\n position: fixed\n height: 100vh\n top: 0\n right: -$sidebar-width\n border-left: 1px solid var(--color-background-muted)\n .toc-tree\n border-left: none\n font-size: var(--toc-font-size--mobile)\n\n // Accomodate for a changed content width.\n .sidebar-drawer\n width: calc((100% - #{$full-width - $sidebar-width}) / 2 + #{$sidebar-width})\n\n@media (max-width: $content-padded-width + $sidebar-width)\n // Center the page\n .content\n margin-left: auto\n margin-right: auto\n padding: 0 $content-padding--small\n\n@media (max-width: $content-padded-width--small + $sidebar-width)\n // Collapse \"navigation\".\n .nav-overlay-icon\n display: flex\n .sidebar-drawer\n position: fixed\n height: 100vh\n width: $sidebar-width\n\n top: 0\n left: -$sidebar-width\n\n // Swap which icon is visible.\n .toc-header-icon, .theme-toggle-header\n display: flex\n .toc-content-icon, .theme-toggle-content\n display: none\n\n // Show the header.\n .mobile-header\n position: sticky\n top: 0\n display: flex\n justify-content: space-between\n align-items: center\n\n .header-left,\n .header-right\n display: flex\n height: var(--header-height)\n padding: 0 var(--header-padding)\n label\n height: 100%\n width: 100%\n user-select: none\n\n .nav-overlay-icon .icon,\n .theme-toggle svg\n height: 1.5rem\n width: 1.5rem\n\n // Add a scroll margin for the content\n :target\n scroll-margin-top: calc(var(--header-height) + 2.5rem)\n\n // Show back-to-top below the header\n .back-to-top\n top: calc(var(--header-height) + 0.5rem)\n\n // Accommodate for the header.\n .page\n flex-direction: column\n justify-content: center\n\n@media (max-width: $content-width + 2* $content-padding--small)\n // Content should respect window limits.\n .content\n width: 100%\n overflow-x: auto\n\n@media (max-width: $content-width)\n article[role=main] aside.sidebar\n float: none\n width: 100%\n margin: 1rem 0\n","// Overall Layout Variables\n//\n// Because CSS variables can't be used in media queries. The fact that this\n// makes the layout non-user-configurable is a good thing.\n$content-padding: 3em;\n$content-padding--small: 1em;\n$content-width: 46em;\n$sidebar-width: 15em;\n$content-padded-width: $content-width + 2 * $content-padding;\n$content-padded-width--small: $content-width + 2 * $content-padding--small;\n$full-width: $content-padded-width + 2 * $sidebar-width;\n","//\n// The design here is strongly inspired by mkdocs-material.\n.admonition, .topic\n margin: 1rem auto\n padding: 0 0.5rem 0.5rem 0.5rem\n\n background: var(--color-admonition-background)\n\n border-radius: 0.2rem\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), 0 0 0.0625rem rgba(0, 0, 0, 0.1)\n\n font-size: var(--admonition-font-size)\n\n overflow: hidden\n page-break-inside: avoid\n\n // First element should have no margin, since the title has it.\n > :nth-child(2)\n margin-top: 0\n\n // Last item should have no margin, since we'll control that w/ padding\n > :last-child\n margin-bottom: 0\n\n.admonition p.admonition-title,\np.topic-title\n position: relative\n margin: 0 -0.5rem 0.5rem\n padding-left: 2rem\n padding-right: .5rem\n padding-top: .4rem\n padding-bottom: .4rem\n\n font-weight: 500\n font-size: var(--admonition-title-font-size)\n line-height: 1.3\n\n // Our fancy icon\n &::before\n content: \"\"\n position: absolute\n left: 0.5rem\n width: 1rem\n height: 1rem\n\n// Default styles\np.admonition-title\n background-color: var(--color-admonition-title-background)\n &::before\n background-color: var(--color-admonition-title)\n mask-image: var(--icon-admonition-default)\n mask-repeat: no-repeat\n\np.topic-title\n background-color: var(--color-topic-title-background)\n &::before\n background-color: var(--color-topic-title)\n mask-image: var(--icon-topic-default)\n mask-repeat: no-repeat\n\n//\n// Variants\n//\n.admonition\n border-left: 0.2rem solid var(--color-admonition-title)\n\n @each $type, $value in $admonitions\n &.#{$type}\n border-left-color: var(--color-admonition-title--#{$type})\n > .admonition-title\n background-color: var(--color-admonition-title-background--#{$type})\n &::before\n background-color: var(--color-admonition-title--#{$type})\n mask-image: var(--icon-#{nth($value, 2)})\n\n.admonition-todo > .admonition-title\n text-transform: uppercase\n","// This file stylizes the API documentation (stuff generated by autodoc). It's\n// deeply nested due to how autodoc structures the HTML without enough classes\n// to select the relevant items.\n\n// API docs!\ndl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)\n // Tweak the spacing of all the things!\n dd\n margin-left: 2rem\n > :first-child\n margin-top: 0.125rem\n > :last-child\n margin-bottom: 0.75rem\n\n // This is used for the arguments\n .field-list\n margin-bottom: 0.75rem\n\n // \"Headings\" (like \"Parameters\" and \"Return\")\n > dt\n text-transform: uppercase\n font-size: var(--font-size--small)\n\n dd:empty\n margin-bottom: 0.5rem\n dd > ul\n margin-left: -1.2rem\n > li\n > p:nth-child(2)\n margin-top: 0\n // When the last-empty-paragraph follows a paragraph, it doesn't need\n // to augument the existing spacing.\n > p + p:last-child:empty\n margin-top: 0\n margin-bottom: 0\n\n // Colorize the elements\n > dt\n color: var(--color-api-overall)\n\n.sig:not(.sig-inline)\n font-weight: bold\n\n font-size: var(--api-font-size)\n font-family: var(--font-stack--monospace)\n\n margin-left: -0.25rem\n margin-right: -0.25rem\n padding-top: 0.25rem\n padding-bottom: 0.25rem\n padding-right: 0.5rem\n\n // These are intentionally em, to properly match the font size.\n padding-left: 3em\n text-indent: -2.5em\n\n border-radius: 0.25rem\n\n background: var(--color-api-background)\n transition: background 100ms ease-out\n\n &:hover\n background: var(--color-api-background-hover)\n\n // adjust the size of the [source] link on the right.\n a.reference\n .viewcode-link\n font-weight: normal\n width: 4.25rem\n\nem.property\n font-style: normal\n &:first-child\n color: var(--color-api-keyword)\n.sig-name\n color: var(--color-api-name)\n.sig-prename\n font-weight: normal\n color: var(--color-api-pre-name)\n.sig-paren\n color: var(--color-api-paren)\n.sig-param\n font-style: normal\n\ndiv.versionadded,\ndiv.versionchanged,\ndiv.deprecated,\ndiv.versionremoved\n border-left: 0.1875rem solid\n border-radius: 0.125rem\n\n padding-left: 0.75rem\n\n p\n margin-top: 0.125rem\n margin-bottom: 0.125rem\n\ndiv.versionadded\n border-color: var(--color-api-added-border)\n .versionmodified\n color: var(--color-api-added)\n\ndiv.versionchanged\n border-color: var(--color-api-changed-border)\n .versionmodified\n color: var(--color-api-changed)\n\ndiv.deprecated\n border-color: var(--color-api-deprecated-border)\n .versionmodified\n color: var(--color-api-deprecated)\n\ndiv.versionremoved\n border-color: var(--color-api-removed-border)\n .versionmodified\n color: var(--color-api-removed)\n\n// Align the [docs] and [source] to the right.\n.viewcode-link, .viewcode-back\n float: right\n text-align: right\n",".line-block\n margin-top: 0.5rem\n margin-bottom: 0.75rem\n .line-block\n margin-top: 0rem\n margin-bottom: 0rem\n padding-left: 1rem\n","// Captions\narticle p.caption,\ntable > caption,\n.code-block-caption\n font-size: var(--font-size--small)\n text-align: center\n\n// Caption above a TOCTree\n.toctree-wrapper.compound\n .caption, :not(.caption) > .caption-text\n font-size: var(--font-size--small)\n text-transform: uppercase\n\n text-align: initial\n margin-bottom: 0\n\n > ul\n margin-top: 0\n margin-bottom: 0\n","// Inline code\ncode.literal, .sig-inline\n background: var(--color-inline-code-background)\n border-radius: 0.2em\n // Make the font smaller, and use padding to recover.\n font-size: var(--font-size--small--2)\n padding: 0.1em 0.2em\n\n pre.literal-block &\n font-size: inherit\n padding: 0\n\n p &\n border: 1px solid var(--color-background-border)\n\n.sig-inline\n font-family: var(--font-stack--monospace)\n\n// Code and Literal Blocks\n$code-spacing-vertical: 0.625rem\n$code-spacing-horizontal: 0.875rem\n\n// Wraps every literal block + line numbers.\ndiv[class*=\" highlight-\"],\ndiv[class^=\"highlight-\"]\n margin: 1em 0\n display: flex\n\n .table-wrapper\n margin: 0\n padding: 0\n\npre\n margin: 0\n padding: 0\n overflow: auto\n\n // Needed to have more specificity than pygments' \"pre\" selector. :(\n article[role=\"main\"] .highlight &\n line-height: 1.5\n\n &.literal-block,\n .highlight &\n font-size: var(--code-font-size)\n padding: $code-spacing-vertical $code-spacing-horizontal\n\n // Make it look like all the other blocks.\n &.literal-block\n margin-top: 1rem\n margin-bottom: 1rem\n\n border-radius: 0.2rem\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n\n// All code is always contained in this.\n.highlight\n width: 100%\n border-radius: 0.2rem\n\n // Make line numbers and prompts un-selectable.\n .gp, span.linenos\n user-select: none\n pointer-events: none\n\n // Expand the line-highlighting.\n .hll\n display: block\n margin-left: -$code-spacing-horizontal\n margin-right: -$code-spacing-horizontal\n padding-left: $code-spacing-horizontal\n padding-right: $code-spacing-horizontal\n\n/* Make code block captions be nicely integrated */\n.code-block-caption\n display: flex\n padding: $code-spacing-vertical $code-spacing-horizontal\n\n border-radius: 0.25rem\n border-bottom-left-radius: 0\n border-bottom-right-radius: 0\n font-weight: 300\n border-bottom: 1px solid\n\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n border-color: var(--color-background-border)\n\n + div[class]\n margin-top: 0\n pre\n border-top-left-radius: 0\n border-top-right-radius: 0\n\n// When `html_codeblock_linenos_style` is table.\n.highlighttable\n width: 100%\n display: block\n tbody\n display: block\n\n tr\n display: flex\n\n // Line numbers\n td.linenos\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n padding: $code-spacing-vertical $code-spacing-horizontal\n padding-right: 0\n border-top-left-radius: 0.2rem\n border-bottom-left-radius: 0.2rem\n\n .linenodiv\n padding-right: $code-spacing-horizontal\n font-size: var(--code-font-size)\n box-shadow: -0.0625rem 0 var(--color-foreground-border) inset\n\n // Actual code\n td.code\n padding: 0\n display: block\n flex: 1\n overflow: hidden\n\n .highlight\n border-top-left-radius: 0\n border-bottom-left-radius: 0\n\n// When `html_codeblock_linenos_style` is inline.\n.highlight\n span.linenos\n display: inline-block\n padding-left: 0\n padding-right: $code-spacing-horizontal\n margin-right: $code-spacing-horizontal\n box-shadow: -0.0625rem 0 var(--color-foreground-border) inset\n","// Inline Footnote Reference\n.footnote-reference\n font-size: var(--font-size--small--4)\n vertical-align: super\n\n// Definition list, listing the content of each note.\n// docutils <= 0.17\ndl.footnote.brackets\n font-size: var(--font-size--small)\n color: var(--color-foreground-secondary)\n\n display: grid\n grid-template-columns: max-content auto\n dt\n margin: 0\n > .fn-backref\n margin-left: 0.25rem\n\n &:after\n content: \":\"\n\n .brackets\n &:before\n content: \"[\"\n &:after\n content: \"]\"\n\n dd\n margin: 0\n padding: 0 1rem\n\n// docutils >= 0.18\naside.footnote\n font-size: var(--font-size--small)\n color: var(--color-foreground-secondary)\n\naside.footnote > span,\ndiv.citation > span\n float: left\n font-weight: 500\n padding-right: 0.25rem\n\naside.footnote > *:not(span),\ndiv.citation > p\n margin-left: 2rem\n","//\n// Figures\n//\nimg\n box-sizing: border-box\n max-width: 100%\n height: auto\n\narticle\n figure, .figure\n border-radius: 0.2rem\n\n margin: 0\n :last-child\n margin-bottom: 0\n\n .align-left\n float: left\n clear: left\n margin: 0 1rem 1rem\n\n .align-right\n float: right\n clear: right\n margin: 0 1rem 1rem\n\n .align-default,\n .align-center\n display: block\n text-align: center\n margin-left: auto\n margin-right: auto\n\n // WELL, table needs to be stylised like a table.\n table.align-default\n display: table\n text-align: initial\n",".genindex-jumpbox, .domainindex-jumpbox\n border-top: 1px solid var(--color-background-border)\n border-bottom: 1px solid var(--color-background-border)\n padding: 0.25rem\n\n.genindex-section, .domainindex-section\n h2\n margin-top: 0.75rem\n margin-bottom: 0.5rem\n ul\n margin-top: 0\n margin-bottom: 0\n","ul,\nol\n padding-left: 1.2rem\n\n // Space lists out like paragraphs\n margin-top: 1rem\n margin-bottom: 1rem\n // reduce margins within li.\n li\n > p:first-child\n margin-top: 0.25rem\n margin-bottom: 0.25rem\n\n > p:last-child\n margin-top: 0.25rem\n\n > ul,\n > ol\n margin-top: 0.5rem\n margin-bottom: 0.5rem\n\nol\n &.arabic\n list-style: decimal\n &.loweralpha\n list-style: lower-alpha\n &.upperalpha\n list-style: upper-alpha\n &.lowerroman\n list-style: lower-roman\n &.upperroman\n list-style: upper-roman\n\n// Don't space lists out when they're \"simple\" or in a `.. toctree::`\n.simple,\n.toctree-wrapper\n li\n > ul,\n > ol\n margin-top: 0\n margin-bottom: 0\n\n// Definition Lists\n.field-list,\n.option-list,\ndl:not([class]),\ndl.simple,\ndl.footnote,\ndl.glossary\n dt\n font-weight: 500\n margin-top: 0.25rem\n + dt\n margin-top: 0\n\n .classifier::before\n content: \":\"\n margin-left: 0.2rem\n margin-right: 0.2rem\n\n dd\n > p:first-child,\n ul\n margin-top: 0.125rem\n\n ul\n margin-bottom: 0.125rem\n",".math-wrapper\n width: 100%\n overflow-x: auto\n\ndiv.math\n position: relative\n text-align: center\n\n .headerlink,\n &:focus .headerlink\n display: none\n\n &:hover .headerlink\n display: inline-block\n\n span.eqno\n position: absolute\n right: 0.5rem\n top: 50%\n transform: translate(0, -50%)\n z-index: 1\n","// Abbreviations\nabbr[title]\n cursor: help\n\n// \"Problematic\" content, as identified by Sphinx\n.problematic\n color: var(--color-problematic)\n\n// Keyboard / Mouse \"instructions\"\nkbd:not(.compound)\n margin: 0 0.2rem\n padding: 0 0.2rem\n border-radius: 0.2rem\n border: 1px solid var(--color-foreground-border)\n color: var(--color-foreground-primary)\n vertical-align: text-bottom\n\n font-size: var(--font-size--small--3)\n display: inline-block\n\n box-shadow: 0 0.0625rem 0 rgba(0, 0, 0, 0.2), inset 0 0 0 0.125rem var(--color-background-primary)\n\n background-color: var(--color-background-secondary)\n\n// Blockquote\nblockquote\n border-left: 4px solid var(--color-background-border)\n background: var(--color-background-secondary)\n\n margin-left: 0\n margin-right: 0\n padding: 0.5rem 1rem\n\n .attribution\n font-weight: 600\n text-align: right\n\n &.pull-quote,\n &.highlights\n font-size: 1.25em\n\n &.epigraph,\n &.pull-quote\n border-left-width: 0\n border-radius: 0.5rem\n\n &.highlights\n border-left-width: 0\n background: transparent\n\n// Center align embedded-in-text images\np .reference img\n vertical-align: middle\n","p.rubric\n line-height: 1.25\n font-weight: bold\n font-size: 1.125em\n\n // For Numpy-style documentation that's got rubrics within it.\n // https://github.com/pradyunsg/furo/discussions/505\n dd &\n line-height: inherit\n font-weight: inherit\n\n font-size: var(--font-size--small)\n text-transform: uppercase\n","article .sidebar\n float: right\n clear: right\n width: 30%\n\n margin-left: 1rem\n margin-right: 0\n\n border-radius: 0.2rem\n background-color: var(--color-background-secondary)\n border: var(--color-background-border) 1px solid\n\n > *\n padding-left: 1rem\n padding-right: 1rem\n\n > ul, > ol // lists need additional padding, because bullets.\n padding-left: 2.2rem\n\n .sidebar-title\n margin: 0\n padding: 0.5rem 1rem\n border-bottom: var(--color-background-border) 1px solid\n\n font-weight: 500\n\n// TODO: subtitle\n// TODO: dedicated variables?\n","[role=main] .table-wrapper.container\n width: 100%\n overflow-x: auto\n margin-top: 1rem\n margin-bottom: 0.5rem\n padding: 0.2rem 0.2rem 0.75rem\n\ntable.docutils\n border-radius: 0.2rem\n border-spacing: 0\n border-collapse: collapse\n\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), 0 0 0.0625rem rgba(0, 0, 0, 0.1)\n\n th\n background: var(--color-table-header-background)\n\n td,\n th\n // Space things out properly\n padding: 0 0.25rem\n\n // Get the borders looking just-right.\n border-left: 1px solid var(--color-table-border)\n border-right: 1px solid var(--color-table-border)\n border-bottom: 1px solid var(--color-table-border)\n\n p\n margin: 0.25rem\n\n &:first-child\n border-left: none\n &:last-child\n border-right: none\n\n // MyST-parser tables set these classes for control of column alignment\n &.text-left\n text-align: left\n &.text-right\n text-align: right\n &.text-center\n text-align: center\n",":target\n scroll-margin-top: 2.5rem\n\n@media (max-width: $full-width - $sidebar-width)\n :target\n scroll-margin-top: calc(2.5rem + var(--header-height))\n\n // When a heading is selected\n section > span:target\n scroll-margin-top: calc(2.8rem + var(--header-height))\n\n// Permalinks\n.headerlink\n font-weight: 100\n user-select: none\n\nh1,\nh2,\nh3,\nh4,\nh5,\nh6,\ndl dt,\np.caption,\nfigcaption p,\ntable > caption,\n.code-block-caption\n > .headerlink\n margin-left: 0.5rem\n visibility: hidden\n &:hover > .headerlink\n visibility: visible\n\n // Don't change to link-like, if someone adds the contents directive.\n > .toc-backref\n color: inherit\n text-decoration-line: none\n\n// Figure and table captions are special.\nfigure:hover > figcaption > p > .headerlink,\ntable:hover > caption > .headerlink\n visibility: visible\n\n:target >, // Regular section[id] style anchors\nspan:target ~ // Non-regular span[id] style \"extra\" anchors\n h1,\n h2,\n h3,\n h4,\n h5,\n h6\n &:nth-of-type(1)\n background-color: var(--color-highlight-on-target)\n // .headerlink\n // visibility: visible\n code.literal\n background-color: transparent\n\ntable:target > caption,\nfigure:target\n background-color: var(--color-highlight-on-target)\n\n// Inline page contents\n.this-will-duplicate-information-and-it-is-still-useful-here li :target\n background-color: var(--color-highlight-on-target)\n\n// Code block permalinks\n.literal-block-wrapper:target .code-block-caption\n background-color: var(--color-highlight-on-target)\n\n// When a definition list item is selected\n//\n// There isn't really an alternative to !important here, due to the\n// high-specificity of API documentation's selector.\ndt:target\n background-color: var(--color-highlight-on-target) !important\n\n// When a footnote reference is selected\n.footnote > dt:target + dd,\n.footnote-reference:target\n background-color: var(--color-highlight-on-target)\n",".guilabel\n background-color: var(--color-guilabel-background)\n border: 1px solid var(--color-guilabel-border)\n color: var(--color-guilabel-text)\n\n padding: 0 0.3em\n border-radius: 0.5em\n font-size: 0.9em\n","// This file contains the styles used for stylizing the footer that's shown\n// below the content.\n\nfooter\n font-size: var(--font-size--small)\n display: flex\n flex-direction: column\n\n margin-top: 2rem\n\n// Bottom of page information\n.bottom-of-page\n display: flex\n align-items: center\n justify-content: space-between\n\n margin-top: 1rem\n padding-top: 1rem\n padding-bottom: 1rem\n\n color: var(--color-foreground-secondary)\n border-top: 1px solid var(--color-background-border)\n\n line-height: 1.5\n\n @media (max-width: $content-width)\n text-align: center\n flex-direction: column-reverse\n gap: 0.25rem\n\n .left-details\n font-size: var(--font-size--small)\n\n .right-details\n display: flex\n flex-direction: column\n gap: 0.25rem\n text-align: right\n\n .icons\n display: flex\n justify-content: flex-end\n gap: 0.25rem\n font-size: 1rem\n\n a\n text-decoration: none\n\n svg,\n img\n font-size: 1.125rem\n height: 1em\n width: 1em\n\n// Next/Prev page information\n.related-pages\n a\n display: flex\n align-items: center\n\n text-decoration: none\n &:hover .page-info .title\n text-decoration: underline\n color: var(--color-link)\n text-decoration-color: var(--color-link-underline)\n\n svg.furo-related-icon,\n svg.furo-related-icon > use\n flex-shrink: 0\n\n color: var(--color-foreground-border)\n\n width: 0.75rem\n height: 0.75rem\n margin: 0 0.5rem\n\n &.next-page\n max-width: 50%\n\n float: right\n clear: right\n text-align: right\n\n &.prev-page\n max-width: 50%\n\n float: left\n clear: left\n\n svg\n transform: rotate(180deg)\n\n.page-info\n display: flex\n flex-direction: column\n overflow-wrap: anywhere\n\n .next-page &\n align-items: flex-end\n\n .context\n display: flex\n align-items: center\n\n padding-bottom: 0.1rem\n\n color: var(--color-foreground-muted)\n font-size: var(--font-size--small)\n text-decoration: none\n","// This file contains the styles for the contents of the left sidebar, which\n// contains the navigation tree, logo, search etc.\n\n////////////////////////////////////////////////////////////////////////////////\n// Brand on top of the scrollable tree.\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-brand\n display: flex\n flex-direction: column\n flex-shrink: 0\n\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n text-decoration: none\n\n.sidebar-brand-text\n color: var(--color-sidebar-brand-text)\n overflow-wrap: break-word\n margin: var(--sidebar-item-spacing-vertical) 0\n font-size: 1.5rem\n\n.sidebar-logo-container\n margin: var(--sidebar-item-spacing-vertical) 0\n\n.sidebar-logo\n margin: 0 auto\n display: block\n max-width: 100%\n\n////////////////////////////////////////////////////////////////////////////////\n// Search\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-search-container\n display: flex\n align-items: center\n margin-top: var(--sidebar-search-space-above)\n\n position: relative\n\n background: var(--color-sidebar-search-background)\n &:hover,\n &:focus-within\n background: var(--color-sidebar-search-background--focus)\n\n &::before\n content: \"\"\n position: absolute\n left: var(--sidebar-item-spacing-horizontal)\n width: var(--sidebar-search-icon-size)\n height: var(--sidebar-search-icon-size)\n\n background-color: var(--color-sidebar-search-icon)\n mask-image: var(--icon-search)\n\n.sidebar-search\n box-sizing: border-box\n\n border: none\n border-top: 1px solid var(--color-sidebar-search-border)\n border-bottom: 1px solid var(--color-sidebar-search-border)\n\n padding-top: var(--sidebar-search-input-spacing-vertical)\n padding-bottom: var(--sidebar-search-input-spacing-vertical)\n padding-right: var(--sidebar-search-input-spacing-horizontal)\n padding-left: calc(var(--sidebar-item-spacing-horizontal) + var(--sidebar-search-input-spacing-horizontal) + var(--sidebar-search-icon-size))\n\n width: 100%\n\n color: var(--color-sidebar-search-foreground)\n background: transparent\n z-index: 10\n\n &:focus\n outline: none\n\n &::placeholder\n font-size: var(--sidebar-search-input-font-size)\n\n//\n// Hide Search Matches link\n//\n#searchbox .highlight-link\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal) 0\n margin: 0\n text-align: center\n\n a\n color: var(--color-sidebar-search-icon)\n font-size: var(--font-size--small--2)\n\n////////////////////////////////////////////////////////////////////////////////\n// Structure/Skeleton of the navigation tree (left)\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-tree\n font-size: var(--sidebar-item-font-size)\n margin-top: var(--sidebar-tree-space-above)\n margin-bottom: var(--sidebar-item-spacing-vertical)\n\n ul\n padding: 0\n margin-top: 0\n margin-bottom: 0\n\n display: flex\n flex-direction: column\n\n list-style: none\n\n li\n position: relative\n margin: 0\n\n > ul\n margin-left: var(--sidebar-item-spacing-horizontal)\n\n .icon\n color: var(--color-sidebar-link-text)\n\n .reference\n box-sizing: border-box\n color: var(--color-sidebar-link-text)\n\n // Fill the parent.\n display: inline-block\n line-height: var(--sidebar-item-line-height)\n text-decoration: none\n\n // Don't allow long words to cause wrapping.\n overflow-wrap: anywhere\n\n height: 100%\n width: 100%\n\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n\n &:hover\n color: var(--color-sidebar-link-text)\n background: var(--color-sidebar-item-background--hover)\n\n // Add a nice little \"external-link\" arrow here.\n &.external::after\n content: url('data:image/svg+xml,')\n margin: 0 0.25rem\n vertical-align: middle\n color: var(--color-sidebar-link-text)\n\n // Make the current page reference bold.\n .current-page > .reference\n font-weight: bold\n\n label\n position: absolute\n top: 0\n right: 0\n height: var(--sidebar-item-height)\n width: var(--sidebar-expander-width)\n\n cursor: pointer\n user-select: none\n\n display: flex\n justify-content: center\n align-items: center\n\n .caption, :not(.caption) > .caption-text\n font-size: var(--sidebar-caption-font-size)\n color: var(--color-sidebar-caption-text)\n\n font-weight: bold\n text-transform: uppercase\n\n margin: var(--sidebar-caption-space-above) 0 0 0\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n\n // If it has children, add a bit more padding to wrap the content to avoid\n // overlapping with the