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--git a/.nojekyll b/.nojekyll new file mode 100644 index 00000000..e69de29b diff --git a/.readthedocs.yml b/.readthedocs.yml new file mode 100644 index 00000000..3b1193ae --- /dev/null +++ b/.readthedocs.yml @@ -0,0 +1,28 @@ +# .readthedocs.yml +# Read the Docs configuration file +# See https://docs.readthedocs.io/en/stable/config-file/v2.html for details + +# Required +version: 2 + +# Set the version of Python and other tools we need +build: + os: ubuntu-22.04 + apt_packages: + - cmake + tools: + python: "3.10" + rust: "1.64" + +# Build documentation in the docs/ directory with Sphinx +sphinx: + configuration: docs/src/conf.py + +# Declare the Python requirements required to build the docs +python: + install: + - method: pip + path: . + - requirements: docs/requirements.txt + - requirements: docs/requirements-rascal.txt + diff --git a/CONDUCT.md b/CONDUCT.md new file mode 100644 index 00000000..3f5562bc --- /dev/null +++ b/CONDUCT.md @@ -0,0 +1,44 @@ + +# Code of Conduct + +## Our Pledge + +In the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to making participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, gender identity and expression, level of experience, nationality, personal appearance, race, religion, or sexual identity and orientation. + +## Our Standards + +Examples of behavior that contributes to creating a positive environment include: + +* Using welcoming and inclusive language +* Being respectful of differing viewpoints and experiences +* Gracefully accepting constructive criticism +* Focusing on what is best for the community +* Showing empathy towards other community members + +Examples of unacceptable behavior by participants include: + +* The use of sexualized language or imagery and unwelcome sexual attention or advances +* Trolling, insulting/derogatory comments, and personal or political attacks +* Public or private harassment +* Publishing others' private information, such as a physical or electronic address, without explicit permission +* Other conduct which could reasonably be considered inappropriate in a professional setting + +## Our Responsibilities + +Project maintainers are responsible for clarifying the standards of acceptable behavior and are expected to take appropriate and fair corrective action in response to any instances of unacceptable behavior. + +Project maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, or to ban temporarily or permanently any contributor for other behaviors that they deem inappropriate, threatening, offensive, or harmful. + +## Scope + +This Code of Conduct applies both within project spaces and in public spaces when an individual is representing the project or its community. Examples of representing a project or community include using an official project e-mail address, posting via an official social media account, or acting as an appointed representative at an online or offline event. Representation of a project may be further defined and clarified by project maintainers. + +## Enforcement + +Instances of abusive, harassing, or otherwise unacceptable behavior may be reported by contacting the project team. The project team will review and investigate all complaints, and will respond in a way that it deems appropriate to the circumstances. The project team is obligated to maintain confidentiality with regard to the reporter of an incident. Further details of specific enforcement policies may be posted separately. + +Project maintainers who do not follow or enforce the Code of Conduct in good faith may face temporary or permanent repercussions as determined by other members of the project's leadership. + +## Attribution + +This Code of Conduct is adapted from the [Contributor Covenant, version 1.4](http://contributor-covenant.org/version/1/4). diff --git a/CONTRIBUTING.rst b/CONTRIBUTING.rst new file mode 100644 index 00000000..4522c39c --- /dev/null +++ b/CONTRIBUTING.rst @@ -0,0 +1,73 @@ +Contributing +============ + +Contributions are welcome, and they are greatly appreciated! Every little bit +helps, and credit will always be given. You can contribute in the ways listed below. + +Requirements for new contributions +---------------------------------- + +All code included in this repository is executed in each pull request. +This ensures that the code in this repository stays executable for a longer time frame. +Because of that we do not want to have examples with heavy calculations that take more +than 30 seconds to execute. If heavy calculations are needed, it might be a better option +to put your example in an external repository and link to it on the `Wiki page `_. +If you feel unsure if a contribution is suitable, feel free to contact one of the `support`_ before. + +Adding an sphinx-gallery examples +--------------------------------- + +To visualize examples on our readthedocs page we use `sphinx-gallery`. +When building the doc the examples are run and compiled automatically into HTML files +and moved to the documentation folder `docs/src `_. +You will find all the examples Python scripts in the `examples/` folder of the repository. +Each example is put into one of the example category folders, e.g. `examples/sample_selection `_. +If you do not know where to put your example, just put in the `examples/uncategorized `_ +folder and when doing a pull request, we will figure out where to put it. + +Converting a Jupyter notebook to a sphinx-gallery compatible Python script +-------------------------------------------------------------------------- + +Often it is more convenient to work in a Jupyter notebook and convert in later to +sphinx-gallery example. To convert your Jupyter notebook you can just use the +`ipynb_to_gallery.py `_ file that is root folder of the repository + +.. code-block:: bash + + python ipynb_to_gallery.py + +Building the cookbook locally +----------------------------- + +When you add a new example, you can build the doc and check if your code runs with + +.. code-block:: bash + + tox + +To visualize the generated cookbook open in a browser the file +``docs/build/html/index.html``. + +When you generate the examples locally all the notebook will be automatically generated +in the folder ``docs/src/examples/`` + +Known issues +------------ + +Sometimes the doc preview from readthedocs is not correcty rendered. If something works in your local build but not in the readthedocs PR preview. It could that the issue is fixed once you merge with the main branch. + +Chemiscope widgets are not currently integrated into our sphinx gallery. + +Support +------- + +If you still have problems adding your example to the repository, please feel free to contact one of the people + +`@agoscinski (Alexander Goscinski) `_ + +`@davidetisi (Davide Tisi) `_ + +Code of Conduct +--------------- + +Please note that the COSMO cookbook project is released with a `Contributor Code of Conduct `_. By contributing to this project you agree to abide by its terms. diff --git a/LICENSE b/LICENSE new file mode 100755 index 00000000..d627fbeb --- /dev/null +++ b/LICENSE @@ -0,0 +1,28 @@ +BSD 3-Clause License + +Copyright (c) 2023, cosmo software cookbook developers + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: + +1. Redistributions of source code must retain the above copyright notice, this + list of conditions and the following disclaimer. + +2. Redistributions in binary form must reproduce the above copyright notice, + this list of conditions and the following disclaimer in the documentation + and/or other materials provided with the distribution. + +3. Neither the name of the copyright holder nor the names of its + contributors may be used to endorse or promote products derived from + this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE +DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE +FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR +SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, +OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/README.rst b/README.rst new file mode 100644 index 00000000..ce4497e7 --- /dev/null +++ b/README.rst @@ -0,0 +1,16 @@ +COSMO Software Cookbook +======================= + +`COSMO Software Cookbook `_ + +.. marker-intro-start + +The COSMO cookbook contains recipes for atomic-scale modelling for materials and molecules, with a particular focus on machine learning and statistical sampling methods. +Rather than focusing on the usage of a specific package (see the `COSMO github page `_ for a list of available tools, and their documentations) this cookbook provides concrete examples of the solution of modeling problems using a combination of the various tools. + +.. marker-intro-end + +Contributors +------------ + +If you want contribute an example, recipe or tutorial that combines multiple software tools together, check out the `contributing guidelines `_ first. diff --git a/docs/requirements-rascal.txt b/docs/requirements-rascal.txt new file mode 100644 index 00000000..450b6599 --- /dev/null +++ b/docs/requirements-rascal.txt @@ -0,0 +1,6 @@ +# rascal needs to be in a separate requirements file because we need to specify +# the packages index-url for it te use the prebuilt from +# from https://github.com/Luthaf/nightly-wheels +# extra-url does not work here because there is another rascal package on pypi +--index-url https://luthaf.fr/nightly-wheels/ +rascal diff --git a/docs/requirements.txt b/docs/requirements.txt new file mode 100644 index 00000000..f4c54e99 --- /dev/null +++ b/docs/requirements.txt @@ -0,0 +1,26 @@ +--extra-index-url https://luthaf.fr/nightly-wheels/ +# Sphinx +sphinx +sphinx_rtd_theme +sphinx-gallery +sphinx-toggleprompt +furo + +# Jupyter widgets +ipywidgets +jupyter_sphinx + +# Scientific libraries +matplotlib +numpy +ase +scipy + +# COSMO stack and friends +scikit-learn +skmatter +chemiscope +equisolve @ git+https://github.com/lab-cosmo/equisolve.git@71b3dfd + +metatensor +rascaline diff --git a/docs/src/conf.py b/docs/src/conf.py new file mode 100644 index 00000000..ddbb71f2 --- /dev/null +++ b/docs/src/conf.py @@ -0,0 +1,75 @@ +# Sphinx documentation build configuration file +import os + +# Add any Sphinx extension module names here, as strings. +extensions = [ + 'sphinx.ext.autodoc', # import the modules you are documenting + 'sphinx.ext.intersphinx', # generate links to the documentation of objects in external projects + "sphinx.ext.viewcode", # add links to highlighted source code + "sphinx_gallery.gen_gallery", # provides a source parser for *.ipynb files +] + +examples_root = os.path.join(os.getcwd(), '../../examples/') +examples_subdirs = [] +for path in os.listdir(examples_root): + # ignores files and hidden directories + if os.path.isdir(os.path.join(examples_root, path)) and path[0] != ".": + examples_subdirs.append(path) + +sphinx_gallery_conf = { + "filename_pattern": "/*", + "examples_dirs": [f"../../examples/{subdir}" for subdir in examples_subdirs], + "gallery_dirs": [f"{subdir}" for subdir in examples_subdirs], + "min_reported_time": 60, + # Make the code snippet for own functions clickable + "reference_url": {"cosmo-software-cookbook": None}, +} + +templates_path = ["_templates"] +exclude_patterns = ["_build"] + +project = "cosmo-software-cookbook" +copyright = "BSD 3-Clause License, Copyright (c) 2023, COSMO software cookbook team" + +htmlhelp_basename = "COSMO software-cookbook" +html_theme = "furo" + +# We create the index.rst here because sphinx is not able to automatically +# include all subdirectories using regex expression +root_index_rst_content = r""" +COSMO Software Cookbook +======================= + +.. include:: ../../README.rst + :start-after: marker-intro-start + :end-before: marker-intro-end + +.. toctree:: + :caption: Table of Contents + +""" +root_index_rst_content += ''.join([f" {subdir}/index\n" for subdir in examples_subdirs]) +print("Creating index.rst including all examples") +print(root_index_rst_content) + +with open('index.rst', 'w') as f: + f.write(root_index_rst_content) + +# Configuration for intersphinx: refer to the Python standard library +# and other packages used by the cookbook + +intersphinx_mapping = { + "ase": ("https://wiki.fysik.dtu.dk/ase/", None), + "chemiscope": ('https://chemiscope.org/docs/', None), + "metatensor": ("https://lab-cosmo.github.io/metatensor/latest/", None), + "equisolve": ("https://lab-cosmo.github.io/equisolve/latest/", None), + "matplotlib": ("https://matplotlib.org/stable/", None), + "numpy": ("https://numpy.org/doc/stable/", None), + "python": ("https://docs.python.org/3", None), + "rascaline": ("https://luthaf.fr/rascaline/latest/", None), + "rascal": ("https://lab-cosmo.github.io/librascal/", None), + "scipy": ("https://docs.scipy.org/doc/scipy/", None), + "sklearn": ('http://scikit-learn.org/stable', + (None, './_intersphinx/sklearn-objects.inv')), + "skmatter": ("https://scikit-matter.readthedocs.io/en/latest/", None), +} diff --git a/examples/README.rst b/examples/README.rst new file mode 100644 index 00000000..ce68152a --- /dev/null +++ b/examples/README.rst @@ -0,0 +1,3 @@ +Examples +======== + diff --git a/examples/lode_linear/README.rst b/examples/lode_linear/README.rst new file mode 100644 index 00000000..3634a913 --- /dev/null +++ b/examples/lode_linear/README.rst @@ -0,0 +1,3 @@ +LODE Tutorial +============= + diff --git a/examples/lode_linear/dataset/charge-charge.xyz b/examples/lode_linear/dataset/charge-charge.xyz new file mode 100644 index 00000000..a988fbef --- /dev/null +++ b/examples/lode_linear/dataset/charge-charge.xyz @@ -0,0 +1,2834 @@ +23 +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=-13961.0350892859 label=CC chargeA=1 energyA=-7738.76386157005 chargeB=-1 energyB=-6220.47808514827 distance=5.690705127008064 pbc="T T T" +C -23.00700000 -14.39400000 -25.47600000 -0.69902091 -0.75330680 0.65287932 +C -23.86700000 -15.59000000 -25.01000000 0.54022160 0.53450759 2.35559299 +C -22.00600000 -15.99600000 -27.05600000 -0.00837973 1.27218157 0.31933751 +N -22.00900000 -14.81000000 -26.46800000 -0.50291940 -0.34870639 -0.02343831 +N -22.97400000 -16.87300000 -26.85700000 -0.57339954 -1.76724206 -1.26909466 +N -21.03500000 -16.32600000 -27.87900000 1.83030176 -0.47050530 -1.21950425 +H -23.65000000 -13.61700000 -25.89000000 0.06849366 0.32652106 0.12670392 +H -22.47300000 -13.98600000 -24.61600000 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Properties=species:S:1:pos:R:3:forces:R:3 energy=-8843.07650806844 label=CC chargeA=1 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 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0.0 30.0 0.0 0.0 0.0 30.0" Properties=species:S:1:pos:R:3:forces:R:3 energy=-8842.13744870909 label=CC chargeA=1 energyA=-2617.69985845671 chargeB=-1 energyB=-6220.46984312555 distance=4.665954893108933 pbc="T T T" +C 9.12400000 -6.69000000 22.74000000 0.77549461 0.23142476 0.59885428 +N 7.96000000 -6.55600000 21.83900000 0.37855809 -0.21657085 0.14426968 +H 8.24600000 -6.67200000 20.86300000 0.25290152 0.24767983 -1.47168891 +H 7.55700000 -5.63000000 21.88900000 -0.26059053 0.77137473 -0.12133384 +H 7.23800000 -7.23200000 22.05200000 -0.52241703 -0.38716676 0.08604644 +H 9.98100000 -6.18400000 22.28300000 -0.09167839 0.09512682 -0.11153279 +H 9.39500000 -7.74000000 22.88700000 -0.21128831 -0.03423650 -0.08854748 +H 8.91513100 -6.21360700 23.70924000 -0.08267146 -0.16960697 -0.15964246 +C 7.90849076 -4.94799126 16.62444389 -0.29396286 -0.68311190 -0.66481105 +C 8.46849076 -4.74099126 18.01844389 0.71623630 1.31116537 1.44129558 +O 8.66949076 -5.77099126 18.71244389 -0.53109846 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0.58891342 0.62579320 +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=-8841.0230520496 label=CC chargeA=1 energyA=-2617.69985845671 chargeB=-1 energyB=-6220.46984312555 distance=6.160151893959503 pbc="T T T" +C 9.12400000 -6.69000000 22.74000000 0.99880688 0.20228146 0.66702899 +N 7.96000000 -6.55600000 21.83900000 0.81818717 -0.03614648 -0.28081085 +H 8.24600000 -6.67200000 20.86300000 0.07257315 -0.18551308 -0.71544014 +H 7.55700000 -5.63000000 21.88900000 -0.49434497 1.04597750 0.09905022 +H 7.23800000 -7.23200000 22.05200000 -0.90496499 -0.75132394 0.19113609 +H 9.98100000 -6.18400000 22.28300000 -0.06926411 0.08845546 -0.04905032 +H 9.39500000 -7.74000000 22.88700000 -0.23833029 -0.05701763 -0.09523325 +H 8.91513100 -6.21360700 23.70924000 -0.13992636 -0.15052965 -0.17053214 +C 7.79596304 -4.47096504 15.20677556 -0.32087668 -0.61165770 -0.61125505 +C 8.35596304 -4.26396504 16.60077556 0.50465262 0.33998271 0.84611657 +O 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13.99863945 0.28283702 0.58583985 0.61871965 +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=-12894.1967352065 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=4.05795004937235 pbc="T T T" +C 34.44500000 12.62500000 24.95900000 0.09596403 0.15255510 0.05400508 +C 33.70500000 11.92700000 26.09800000 2.83373346 0.95364648 1.97596119 +O 32.60000000 11.42900000 25.81100000 -0.92649065 -0.50553497 -2.94148067 +O 34.21200000 11.87200000 27.24800000 -0.07613523 0.25968668 -0.56152555 +H 33.75000000 13.28700000 24.44000000 -0.16357722 0.13194912 -0.20479328 +H 34.76300000 11.86300000 24.24500000 0.11998623 -0.14168116 -0.24527435 +H 35.32079000 13.21299000 25.27085000 -0.12216062 -0.22743281 0.16978040 +C 30.51697621 11.41297253 28.35997957 0.08565697 -0.61685292 -0.42877017 +C 30.16897621 9.79197253 26.50897957 0.60343895 2.15410928 1.48065485 +N 30.79097621 10.81897253 27.04797957 -3.66416739 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label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=5.05035266446833 pbc="T T T" +C 34.44500000 12.62500000 24.95900000 0.20038562 0.23237943 -0.02834430 +C 33.70500000 11.92700000 26.09800000 1.33488111 0.29192980 1.80396066 +O 32.60000000 11.42900000 25.81100000 -3.00238466 -1.16610089 -1.12786282 +O 34.21200000 11.87200000 27.24800000 0.49679178 0.34079941 -0.09646774 +H 33.75000000 13.28700000 24.44000000 -0.16098506 0.14067625 -0.20369900 +H 34.76300000 11.86300000 24.24500000 0.12560099 -0.13991843 -0.24131018 +H 35.32079000 13.21299000 25.27085000 -0.07673916 -0.18123972 0.14586673 +C 29.68902379 10.96702747 28.70002043 0.22849011 -0.27031880 -0.16653350 +C 29.34102379 9.34602747 26.84902043 0.30266235 1.19197852 0.63871736 +N 29.96302379 10.37302747 27.38802043 -0.04348732 0.62218610 0.72842417 +N 28.33102379 8.75302747 27.45902043 -1.17921075 -1.00027194 0.23783424 +N 29.71402379 8.92402747 25.66402043 -0.07657454 -1.04100162 -1.40966930 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energyB=-6669.20926086133 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 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Properties=species:S:1:pos:R:3:forces:R:3 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 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chargeB=-1 energyB=-6220.48400518575 distance=7.448111902988495 pbc="T T T" +C 3.69000000 1.17800000 9.65700000 0.37754720 0.04359837 0.51512072 +C 5.89300000 2.10500000 10.26700000 -0.47367109 -0.45303108 -0.03487791 +N 6.46800000 0.95000000 9.98900000 1.38861066 -0.85680080 -0.27239639 +N 4.58400000 2.24900000 10.11300000 -1.55122778 -0.09896012 -0.43428794 +N 6.62900000 3.10900000 10.69900000 0.54284081 1.52685641 0.53011787 +H 5.91600000 0.16800000 9.69300000 -0.04442488 -0.38195291 -0.18311568 +H 7.49000000 0.89000000 9.89100000 -0.39197710 -0.20464706 0.00900612 +H 4.18700000 3.12900000 10.38500000 -0.31420362 0.36755733 0.08382543 +H 6.22600000 4.01600000 10.92500000 0.22365429 -0.23011075 -0.11440689 +H 7.61200000 2.96300000 10.84200000 0.44973989 0.16517788 0.14117202 +H 3.74200000 0.36200000 10.38300000 -0.14643947 -0.30690576 0.16358271 +H 4.02000000 0.78400000 8.69500000 -0.11741531 0.06036758 -0.37152548 +H 2.63834300 1.49675000 9.60785000 0.35787965 0.24533246 -0.07406850 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energy=-12894.4095196711 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=4.484376426240713 pbc="T T T" +C 25.65400000 -5.20500000 -2.23100000 0.00273026 -0.06174100 -0.08231323 +C 25.43700000 -3.85300000 -1.56500000 -1.81793911 -0.07845036 -0.05356085 +O 26.43300000 -3.22700000 -1.14000000 2.62227439 1.03002551 0.59781226 +O 24.27400000 -3.40300000 -1.47500000 -0.84403718 -0.04452061 -0.24893233 +H 26.34900000 -5.06000000 -3.05900000 0.34135003 -0.12680825 -0.16074181 +H 24.71500000 -5.57700000 -2.64500000 -0.14454553 -0.09783094 0.06523007 +H 26.07672000 -5.94638300 -1.53698600 0.05243828 0.09605397 -0.02907044 +C 25.00884500 1.16864491 1.76872301 -0.33555583 -0.18236146 -0.49605107 +C 25.43784500 0.02864491 -0.37827699 0.58372835 -1.17442642 1.04663712 +N 25.97684500 -1.00435509 0.24572301 -0.09256694 1.41052472 0.51007664 +N 24.97484500 1.06564491 0.30772301 -0.37042039 1.35013080 0.82855842 +N 25.35484500 0.01564491 -1.69327699 -0.08450647 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24.55546501 2.76006527 0.19583096 -0.04177162 0.04485904 -0.03642289 +H 24.96546501 1.73406527 -1.78716904 -0.06617361 -0.09678583 -0.16746794 +H 25.73846501 0.17106527 -1.80416904 -0.06245884 -0.35846910 -0.26344718 +H 24.75946501 3.11306527 2.46683096 -0.02424537 0.06059665 -0.06240015 +H 25.95946501 1.82306527 2.55483096 0.17943472 -0.02496715 0.12363763 +H 24.20350501 1.42583437 2.61276196 0.09688298 0.00835993 0.12068609 +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=-12893.1076496113 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=5.733418286779269 pbc="T T T" +C 25.65400000 -5.20500000 -2.23100000 -0.03777314 -0.18073865 -0.15283819 +C 25.43700000 -3.85300000 -1.56500000 -0.88773952 0.66251515 0.38374356 +O 26.43300000 -3.22700000 -1.14000000 2.17605209 0.63439949 0.47262313 +O 24.27400000 -3.40300000 -1.47500000 -1.38753233 -0.10665508 -0.29504592 +H 26.34900000 -5.06000000 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25.94962002 2.05142037 2.65610795 0.17985177 -0.02221663 0.12393525 +H 24.19366002 1.65418947 2.71403895 0.09548503 0.01067252 0.11929501 +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=-12892.9073116316 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=5.983274680706614 pbc="T T T" +C 25.65400000 -5.20500000 -2.23100000 -0.04697711 -0.17864904 -0.15518480 +C 25.43700000 -3.85300000 -1.56500000 -0.72530526 0.60405922 0.37206550 +O 26.43300000 -3.22700000 -1.14000000 2.04035619 0.53956199 0.42669274 +O 24.27400000 -3.40300000 -1.47500000 -1.40770419 -0.07921543 -0.27002536 +H 26.34900000 -5.06000000 -3.05900000 0.33105578 -0.11695696 -0.16402126 +H 24.71500000 -5.57700000 -2.64500000 -0.16596953 -0.14771955 0.03273865 +H 26.07672000 -5.94638300 -1.53698600 0.04320332 0.08795534 -0.02080123 +C 24.94977502 2.53877546 2.37638494 -0.32482020 -0.19427369 -0.37457700 +C 25.37877502 1.39877546 0.22938494 0.12605606 -0.32510601 0.47145518 +N 25.91777502 0.36577546 0.85338494 0.32746196 -0.53348284 -0.15948086 +N 24.91577502 2.43577546 0.91538494 -0.17445264 0.95928571 0.79830500 +N 25.29577502 1.38577546 -1.08561506 -0.07873289 0.18322050 -1.03749556 +H 26.07877502 0.39377546 1.84338494 -0.00779484 -0.22572562 0.30856380 +H 26.18977502 -0.46422454 0.31838494 -0.04256240 -0.33638276 0.12095249 +H 24.53577502 3.21677546 0.39838494 -0.03501628 0.06578787 -0.05124595 +H 24.94577502 2.19077546 -1.58461506 -0.05847545 -0.07583416 -0.18883457 +H 25.71877502 0.62777546 -1.60161506 -0.04742696 -0.27470674 -0.29907204 +H 24.73977502 3.56977546 2.66938494 -0.02180874 0.05983711 -0.06255187 +H 25.93977502 2.27977546 2.75738494 0.17887311 -0.01804756 0.13047981 +H 24.18381502 1.88254456 2.81531594 0.09004007 0.00639264 0.12203734 +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=-12892.7385235753 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=6.233142590610293 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 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0.0 0.0 30.0" Properties=species:S:1:pos:R:3:forces:R:3 energy=-12892.3722607997 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=6.982803051457227 pbc="T T T" +C 25.65400000 -5.20500000 -2.23100000 -0.07341265 -0.14803780 -0.14575823 +C 25.43700000 -3.85300000 -1.56500000 -0.29297357 0.26850244 0.24610376 +O 26.43300000 -3.22700000 -1.14000000 1.60027063 0.38605706 0.35292650 +O 24.27400000 -3.40300000 -1.47500000 -1.38161765 0.04465404 -0.16637260 +H 26.34900000 -5.06000000 -3.05900000 0.32322971 -0.11028653 -0.16679780 +H 24.71500000 -5.57700000 -2.64500000 -0.18161418 -0.16426097 0.01648803 +H 26.07672000 -5.94638300 -1.53698600 0.03489391 0.08968838 -0.01660099 +C 24.91039504 3.45219582 2.78149289 -0.28820582 -0.18681857 -0.42121584 +C 25.33939504 2.31219582 0.63449289 -0.20388508 -0.09139960 0.45013052 +N 25.87839504 1.27919582 1.25849289 0.57970589 -1.04478346 -0.05138096 +N 24.87639504 3.34919582 1.32049289 -0.18424074 1.01861396 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energyB=-6220.48400518575 distance=4.40539507967846 pbc="T T T" +C 32.59000000 -10.26800000 58.76100000 -0.87100741 0.22908970 0.86816072 +C 31.01900000 -11.54600000 60.23100000 0.18443116 0.90051754 -0.85458082 +N 29.86200000 -11.49700000 60.84900000 -1.25285790 -0.33649210 0.95389649 +N 31.29100000 -10.55900000 59.39400000 1.42094902 -0.91036104 -0.56976584 +N 31.82000000 -12.58200000 60.45800000 0.58348227 -0.68449169 0.26050929 +H 29.30600000 -10.65300000 60.75300000 -0.44451662 0.67564855 -0.06876312 +H 29.60200000 -12.19700000 61.53200000 -0.08655168 0.11454391 -0.06068137 +H 30.57700000 -9.82700000 59.36500000 -1.13455971 1.30397346 0.04296863 +H 32.67200000 -12.69900000 59.93600000 0.13836881 -0.19653967 0.02032466 +H 31.49700000 -13.30000000 61.09500000 0.32825666 -0.09280612 -0.15195979 +H 32.42700000 -9.97000000 57.72400000 0.01358948 0.01721160 -0.12458035 +H 33.27200000 -11.11900000 58.79900000 0.09502809 -0.07214661 -0.02615546 +H 32.99285000 -9.42516400 59.34181000 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8.15666886 16.72549281 22.55812966 -0.11680591 0.18210251 -1.26840912 +N 5.91666886 16.70949281 23.19112966 -0.43434197 0.01216932 -0.26831748 +N 7.63266886 16.58349281 24.72412966 -0.08919987 -0.11582051 1.30018792 +H 9.11566886 16.70649281 22.90212966 0.70177637 0.17135634 0.06539813 +H 5.60666886 16.72649281 22.22812966 -0.09476899 0.02359951 0.16112187 +H 5.23566886 16.67849281 23.93312966 -0.20022341 0.00745750 -0.02026001 +H 8.63966886 16.52749281 24.85512966 0.48526670 0.10605556 0.64255380 +H 6.97166886 16.47749281 25.48512966 0.36461892 0.02660435 0.09258376 +H 6.92266886 16.94249281 20.82512966 -0.11906271 0.23433519 -0.00143067 +H 8.26366886 15.81049281 20.68712966 0.05569782 -0.17197901 -0.20355794 +H 8.60995986 17.55310281 20.67227966 -0.19630050 0.00668215 0.07898108 +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=-12893.0896501194 label=CC chargeA=-1 energyA=-6220.48891391419 chargeB=1 energyB=-6669.20926086133 distance=5.496444811251947 pbc="T T T" +C 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 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20.60719448 -0.11472301 0.23436341 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 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11.25200000 16.92500000 24.47100000 -0.98509251 -0.86818306 0.34591765 +O 12.41100000 18.73500000 23.94100000 0.26454304 1.23176054 -0.69412000 +H 13.24200000 18.68100000 26.32900000 0.09825999 0.17334000 0.06188686 +H 13.90100000 17.18800000 25.64900000 0.26194532 -0.18634940 0.09387513 +H 12.47004000 17.11600000 26.73359000 0.17371919 -0.08685246 0.03241141 +C 6.85975494 16.55260882 20.55729173 0.61783355 -0.22130036 0.45552224 +C 6.11675494 16.45660882 22.93929173 -0.28356764 0.16168982 -0.77976292 +N 7.05375494 16.50360882 22.01329173 0.36629609 0.17819733 -1.38439953 +N 4.81375494 16.48760882 22.64629173 -0.26694977 0.01236471 -0.26285313 +N 6.52975494 16.36160882 24.17929173 0.23442561 -0.10523413 1.45146182 +H 8.01275494 16.48460882 22.35729173 0.15921619 0.06282215 -0.21722171 +H 4.50375494 16.50460882 21.68329173 -0.13920475 -0.01489227 0.06483187 +H 4.13275494 16.45660882 23.38829173 -0.27045244 -0.03830225 0.07291924 +H 7.53675494 16.30560882 24.31029173 0.01014500 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12.47004000 17.11600000 26.73359000 0.17139489 -0.08603439 0.03199290 +C 6.63917215 16.50823202 20.44832414 0.62928346 -0.23076605 0.44868090 +C 5.89617215 16.41223202 22.83032414 -0.35358521 0.21491756 -0.77655509 +N 6.83317215 16.45923202 21.90432414 0.42730570 0.17333066 -1.41507016 +N 4.59317215 16.44323202 22.53732414 -0.24885732 0.01007956 -0.26579087 +N 6.30917215 16.31723202 24.07032414 0.28102862 -0.10445439 1.48792934 +H 7.79217215 16.44023202 22.24832414 0.10759492 0.04630070 -0.23998216 +H 4.28317215 16.46023202 21.57432414 -0.14595726 -0.02196272 0.04750568 +H 3.91217215 16.41223202 23.27932414 -0.28573770 -0.04903540 0.09395175 +H 7.31617215 16.26123202 24.20132414 -0.03970395 -0.02142110 0.69643279 +H 5.64817215 16.21123202 24.83132414 0.32055445 -0.01705460 0.18072457 +H 5.59917215 16.67623202 20.17132414 -0.12215852 0.23214034 0.03270120 +H 6.94017215 15.54423202 20.03332414 0.02732817 -0.15908053 -0.22313365 +H 7.28646315 17.28684202 20.01847414 -0.20315733 0.02004071 0.04954034 diff --git a/examples/lode_linear/lode_tutorial.py b/examples/lode_linear/lode_tutorial.py new file mode 100644 index 00000000..4e6c0e30 --- /dev/null +++ b/examples/lode_linear/lode_tutorial.py @@ -0,0 +1,373 @@ +""" +LODE Tutorial +============= + +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 numpy as np +import matplotlib.pyplot as plt +import ase.io + +from equisolve.numpy.models.linear_model import Ridge +from equisolve.utils.convert import ase_to_tensormap +import metatensor +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 +# structures of the charge-charge structures. +# + +frames = ase.io.read("dataset/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 #justmetatensorthings +# + +y = ase_to_tensormap(frames, energy="energy", forces="forces") + + +# %% Step 1: Compute short-range (SR) 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 part. These will be used to +# create SOAP features. +# + +SR_HYPERS = { + "cutoff": 3., + "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., + # 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., + "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. +# + +samples_names_to_sum = ['center', 'species_center'] + +ps_sr = metatensor.sum_over_samples(ps_sr, samples_names=samples_names_to_sum) +ps_lr = metatensor.sum_over_samples(ps_lr, samples_names=samples_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, samples_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 + +samples_train = metatensor.Labels(["structure"], np.reshape(idx_train, (-1, 1))) +samples_test = metatensor.Labels(["structure"], np.reshape(idx_test, (-1, 1))) + + +# %% +# +# That we use as input to the ``slice`` function + +X_sr_train = metatensor.slice(X_sr, axis="samples", labels=samples_train) +X_sr_test = metatensor.slice(X_sr, axis="samples", labels=samples_test) + +X_lr_train = metatensor.slice(X_lr, axis="samples", labels=samples_train) +X_lr_test = metatensor.slice(X_lr, axis="samples", labels=samples_test) + +y_train = metatensor.slice(y, axis="samples", labels=samples_train) +y_test = metatensor.slice(y, axis="samples", labels=samples_test) + + +# %% +# +# 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("$E - E_\mathrm{monomer}$ in eV") +plt.axvline(r_cut, c="red", label="$r_\mathrm{train}$") + +plt.legend() +plt.tight_layout() +plt.show() diff --git a/examples/mlp_models/README.rst b/examples/mlp_models/README.rst new file mode 100644 index 00000000..572a37d4 --- /dev/null +++ b/examples/mlp_models/README.rst @@ -0,0 +1,3 @@ +Machine Learning Potentials +=========================== + diff --git a/examples/mlp_models/linear_model.py b/examples/mlp_models/linear_model.py new file mode 100644 index 00000000..3f4b7647 --- /dev/null +++ b/examples/mlp_models/linear_model.py @@ -0,0 +1,20 @@ +#!/usr/bin/env python +# coding: utf-8 + +""" +MLP with Linear Model +===================== +""" +# %% +# + + +import numpy as np +import matplotlib.pyplot as plt + +# %% +# Explanation + +X = np.random.rand(10000)*400 +Y = 0.1*X+10.1 +Y_p = Y + np.random.randn(10000)*1.5 diff --git a/examples/roy_gch/README.rst b/examples/roy_gch/README.rst new file mode 100644 index 00000000..7326467d --- /dev/null +++ b/examples/roy_gch/README.rst @@ -0,0 +1,11 @@ +Generalized Convex Hull analysis of the polymorphs of ROY +========================================================= + +This is an example of the construction of a generalized convex hull +based on SOAP figures, for a dataset containing known (and hypothetical) +polymorphs of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecabonitrile +(ROY). + +It showcases the use of ``rascaline`` to compute descriptors for a +database of atomic structures, and ``scikit-matter`` to compute the +convex hull. The structures are visualized using ``chemiscope`` widgets. diff --git a/examples/roy_gch/roy_gch.py b/examples/roy_gch/roy_gch.py new file mode 100644 index 00000000..121c020c --- /dev/null +++ b/examples/roy_gch/roy_gch.py @@ -0,0 +1,266 @@ +""" +Generalized Convex Hull construction for the polymorphs of ROY +============================================================== + +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. +""" +import matplotlib.tri as mtri +import numpy as np +from matplotlib import pyplot as plt +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 +# + +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") + +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``. +# This runs only in a notebook, and +# requires having the ``chemiscope`` package installed. +# + +import chemiscope +if chemiscope.jupyter._is_running_in_notebook(): + 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}}], + }, + ) + + + +# %% +# 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 +# + +from rascaline import SoapPowerSpectrum +from metatensor import mean_over_samples +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, + samples_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") + + +# %% +# 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 = mtri.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) + + +# %% +# 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 ``chemiscope``. This runs only in a notebook, and +# requires having the ``chemiscope`` package installed. +# + +import chemiscope +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}) + +# shows chemiscope if not run in terminal +if chemiscope.jupyter._is_running_in_notebook(): + chemiscope.show( + frames=structures, + properties=structure_properties, + settings={ + "map": { + "x": {"property": "pca_1"}, + "y": {"property": "pca_2"}, + "z": {"property": "energy"}, + "symbol": "type", + "symbol": "type", + "color": {"property": "hull_energy"}, + "size": {"factor": 35, "mode": "linear", + "property": "", "reverse": True}, + }, + "structure": [ + { + "bonds": True, + "unitCell": True, + "keepOrientation": True, + } + ], + }, + ) diff --git a/examples/sample_selection/README.rst b/examples/sample_selection/README.rst new file mode 100644 index 00000000..e7462e30 --- /dev/null +++ b/examples/sample_selection/README.rst @@ -0,0 +1,3 @@ +Sample Selection +================ + diff --git a/examples/sample_selection/dataset/input-fps.xyz b/examples/sample_selection/dataset/input-fps.xyz new file mode 100755 index 00000000..94414eca --- /dev/null +++ b/examples/sample_selection/dataset/input-fps.xyz @@ -0,0 +1,21000 @@ +40 +Lattice="7.77345020413335 0.0 0.0 0.0 8.037141181957962 0.0 0.0 0.06848409629841481 8.036838017400001" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.075045239035 pbc="T T T" +Ba 3.90123036 0.13396764 8.02872953 -0.01778406 -0.22361167 -0.10579164 +Ba 3.87825049 0.05835063 4.01542001 0.04901063 0.11108374 -0.05085102 +Ba 3.88220018 4.05428027 0.00212759 0.18164047 0.00436008 -0.27661959 +Ba 3.86373979 4.07895009 3.99807978 0.20534964 0.04347067 0.17126658 +Ba 0.00873036 0.12886670 8.02188112 0.00341031 -0.26996069 -0.02343895 +Ba 7.75912995 0.06117861 3.99750998 0.20647372 0.01524150 -0.03002097 +Ba 0.00144975 4.06557043 0.01162131 -0.02495590 0.01200988 -0.20849641 +Ba 7.74926622 4.10588043 4.00892996 0.22716828 -0.04697971 -0.00722943 +Ti 1.95243028 2.14688003 2.04345039 -0.08341019 -0.52217331 -0.12731691 +Ti 1.91425020 2.12886972 6.06698044 0.52843420 0.19241879 0.05825786 +Ti 1.94607004 6.15453048 2.04565027 -0.10324470 -0.12206621 0.06024069 +Ti 1.94553989 6.17001985 6.08354022 0.11433104 -0.06445447 -0.15279938 +Ti 5.84590041 2.11760988 2.04187004 -0.07081898 0.10397207 0.11480181 +Ti 5.83860036 2.14715987 6.05982031 -0.41242860 0.24951039 -0.11325967 +Ti 5.83034029 6.15982031 2.04468015 0.07300287 -0.31499176 -0.15875174 +Ti 5.83913051 6.17473989 6.06197978 -0.15886435 -0.36628681 0.30190922 +O 1.93391004 2.02894979 3.88722027 -0.00362526 -0.02727786 0.28611313 +O 1.96907013 2.02930038 7.93148056 -0.13299314 0.21653291 -0.06932645 +O 1.96671011 6.05991049 3.92438980 -0.01654659 -0.05013831 -0.09582939 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1.95718996 5.90986035 -0.33734236 0.15530980 0.08686935 +O 0.02994722 6.00302982 1.93829037 -0.16284313 0.00073431 0.02465071 +O 0.01850003 6.07656044 5.94724054 0.09331433 -0.06125345 -0.09053317 +O 3.86695022 1.95506004 1.91919023 0.44120516 0.18857011 -0.02095938 +O 3.91631008 2.04054001 5.91016041 -0.07227602 -0.02438691 0.13251054 +O 3.93054015 6.02787998 1.90629019 -0.37682551 -0.05104874 0.08989785 +O 3.91141047 5.99073999 5.94634038 -0.23261336 0.14069411 0.05526149 +40 +Lattice="7.955584598 0.0 0.0 0.0 7.955584598 0.0 0.0 0.0 7.955584598" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.216246470478 stress="0.00019373125680708432 -0.0 -0.0 -0.0 0.00019373125680708432 -0.0 -0.0 -0.0 0.00019373125680708432" pbc="T T T" +Ba 1.98910859 1.98910859 1.98910859 -0.00453491 -0.00453491 -0.00453491 +Ba 5.96647601 5.96647601 1.98910859 0.00453491 0.00453491 -0.00453491 +Ba 5.96647601 1.98910859 5.96647601 0.00453491 -0.00453491 0.00453491 +Ba 1.98910859 5.96647601 5.96647601 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7.822880117988445 0.0 0.0 0.0 8.2061230149687" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.08938359747 pbc="T T T" +Ba 1.95381985 1.96532966 0.01370960 0.06276269 -0.05351263 -0.00350107 +Ba 1.95140024 1.94349991 4.08534972 0.06444059 0.10582481 0.21506687 +Ba 1.92914023 5.86598040 0.01635764 0.20014418 0.00088857 -0.00757833 +Ba 1.96987006 5.85131015 4.10554997 -0.09754045 0.13932757 0.09485391 +Ba 5.88465987 1.93656023 0.00882108 -0.23405523 0.18750644 0.03899695 +Ba 5.86584976 1.95853001 4.12502972 -0.03546143 0.00345428 -0.03728228 +Ba 5.86704040 5.88633006 8.19448805 -0.08687115 -0.16465268 0.16207900 +Ba 5.87833038 5.86741042 4.11488970 -0.07704593 0.02948155 0.02803994 +Ti 7.82243500 0.00256825 2.14045030 -0.12370014 0.00007045 -0.20980665 +Ti 7.81008814 0.00725494 6.24370034 0.11660827 -0.03570362 -0.26678435 +Ti 7.81932071 3.91504015 2.14948025 0.01892332 -0.04325058 -0.38726881 +Ti 7.81718975 3.91554003 6.24657994 -0.12637152 -0.01300207 -0.21624237 +Ti 3.90574031 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-0.02173078465181779 7.9280181425316245 0.0 -0.02173078465181779 0.02167528830283467 7.927986430332206" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.027044221835 pbc="T T T" +Ba 3.96700508 0.02230715 0.06908978 0.39614426 0.24270365 -0.39642066 +Ba 4.01822266 0.04875989 4.03410968 -0.14840999 -0.02099949 -0.04981924 +Ba 4.02607222 4.01122695 0.02138036 -0.14536169 -0.15335550 0.18321681 +Ba 3.98828000 4.00249024 3.97802983 0.02081591 0.09365783 0.10874249 +Ba 0.04063443 0.02748734 0.04148986 -0.06614163 0.20530464 -0.11809411 +Ba 0.04333948 0.05967998 3.99475008 -0.01495894 -0.09032003 0.17656794 +Ba 0.02900715 4.01440689 0.03625973 0.02734445 -0.13521406 0.11298713 +Ba 0.01589574 3.98097985 3.95962010 0.04388873 0.21602023 0.19895942 +O 2.00729977 4.04093018 2.00085030 -0.04108391 -0.02251926 0.03506599 +O 1.95500001 4.01951018 5.91904952 -0.00041806 0.57458911 0.14606309 +O 1.98662262 0.08817973 1.96976997 -0.00608194 -0.18557246 0.12601851 +O 1.93423249 0.10154008 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0.30977576 -0.02507366 -0.30444947 +O -0.00797562 6.02128965 1.97653973 -0.13196881 0.05741453 -0.01147201 +O 7.86723378 6.00524010 5.93079017 0.56219022 0.05950767 0.10388285 +O 3.96179001 2.01107987 2.00659021 -0.38177591 0.17632060 -0.11452233 +O 3.91141994 2.05791006 5.96077009 0.08321221 -0.02576323 0.09301120 +O 3.94839002 6.02552957 1.95288005 0.11779921 0.08228790 0.31143130 +O 3.91153014 6.02625974 5.93927001 -0.13074805 -0.06741201 -0.05475036 +Ti 2.07554997 2.02268970 2.06645967 -0.01168181 0.31799687 -0.44722565 +Ti 2.03913961 2.01389987 6.01776959 -0.19659452 0.15680027 0.38403848 +Ti 2.04830999 6.00848981 2.03019994 -0.31537408 -0.60467333 0.35658244 +Ti 2.04749023 5.95648022 6.00819013 0.03324822 -0.17335277 -0.21116882 +Ti 6.02449020 1.95700977 2.06006015 -0.16382144 0.50696344 -0.27503862 +Ti 5.98750981 2.02793014 6.03121002 0.27981804 -0.34087969 0.17231585 +Ti 5.98884965 5.97386960 2.06583019 0.34818496 -0.51274225 -0.19758311 +Ti 6.02902980 5.97363018 6.01101965 -0.39309262 0.19249489 0.13544289 +40 +Lattice="7.9172800401866334 0.0 0.0 -0.02170126459015156 7.9172483710664725 0.0 -0.02170126459015156 0.021645843629870255 7.9172167019463116" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.073906034442 pbc="T T T" +Ba 4.00627592 0.06274682 0.02662027 0.00748937 -0.21938760 0.10057050 +Ba 4.00085258 0.06736972 4.01671010 -0.10912379 -0.19635772 -0.21452411 +Ba 4.00602257 3.99467631 0.02529017 -0.15220699 -0.00859237 0.05324857 +Ba 3.96664993 3.98407032 4.00302983 -0.00362963 0.16630358 -0.07951831 +Ba 0.05544392 0.03010625 0.04641030 -0.14375295 -0.02629776 -0.08141604 +Ba 0.05556189 0.04692018 3.97131004 -0.13968855 -0.05796861 0.11203068 +Ba 0.02107817 3.99052687 0.04690988 0.12838289 0.02601339 -0.08313945 +Ba 0.00735674 4.00702014 4.00399020 0.17687878 -0.00691884 -0.11051913 +O 2.03659995 3.99135976 1.99801033 -0.07943423 0.05597266 -0.02300443 +O 1.98831008 4.00508041 5.96607033 -0.02035594 0.03553110 0.05359979 +O 1.99897307 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2.01590022 -0.24003999 -0.06366437 0.04300247 +O 0.03022501 2.02943006 5.99864994 -0.09744532 0.01947354 -0.02575268 +O 0.01059886 5.94723037 1.98518988 -0.09250264 0.14887844 0.07153246 +O -0.00582870 5.98683023 5.94807040 -0.20937804 0.10737390 0.08404139 +O 3.99877034 2.01633013 2.03580980 0.12983274 -0.04555378 0.02147360 +O 4.00015982 2.05435999 5.97955029 -0.12592209 -0.12085625 -0.00472414 +O 3.97435978 5.98426978 1.99053009 0.04921914 0.05736748 0.09228769 +O 3.92608021 5.99357021 5.96637040 0.28519550 0.03823153 -0.11375897 +Ti 2.00594978 2.02145023 1.98601011 -0.09789835 0.05608270 0.13052951 +Ti 1.98509012 2.01677983 5.96074992 0.00147890 0.33870119 -0.16253280 +Ti 2.01274993 5.97234003 2.05789981 0.07120182 0.04228719 0.02331399 +Ti 2.00114003 5.99617975 6.02172010 0.02091181 -0.31528590 0.03552185 +Ti 5.96309027 1.99609039 1.97990985 0.01340265 0.06918684 -0.18766945 +Ti 5.96623976 2.02917037 5.92576979 -0.07773936 -0.16879369 0.17239581 +Ti 5.96087976 5.95986002 2.02690999 -0.01569633 -0.11495968 -0.03918284 +Ti 5.95895032 5.98347014 5.98310990 0.15555894 0.08563496 0.05699981 +40 +Lattice="7.942739814034939 0.0 0.0 0.0 7.942739814034939 0.0 0.0 0.0 7.942739814034939" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.025091668984 pbc="T T T" +Ba 3.97650965 3.97712998 0.00982279 -0.02525697 -0.04663904 -0.11590636 +Ba 3.97953028 7.93681691 3.92888975 0.16034196 0.07814302 0.35162381 +Ba 7.91615149 3.99331014 4.00051976 0.14936130 -0.05683655 -0.07799956 +Ba 0.00203096 0.07122175 3.99988990 -0.15094432 -0.48435470 -0.08592601 +Ba 0.01179576 4.02783961 7.89936848 0.15273587 -0.41212264 0.22162909 +Ba 4.01412965 0.00355438 0.04585344 -0.15956626 -0.02123371 -0.34194772 +Ba 3.98641028 3.97160025 4.00788983 -0.06122105 -0.03608338 -0.13639394 +Ba 0.01628738 7.92347390 0.04958414 -0.01241046 0.21052218 -0.29121677 +Ti 5.91572005 2.01925018 2.02279979 0.18873723 -0.22201836 0.40295074 +Ti 1.92420974 6.01107979 2.02293005 0.23696649 -0.31432456 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-0.34512715 -0.08130060 +Ti 6.01744007 1.97276020 1.99354998 0.01437067 0.14783200 0.04176294 +Ti 5.96127977 2.00389014 5.95324033 0.10217667 -0.13484510 -0.16199390 +Ti 6.00670971 5.95480983 1.98248970 0.17522145 -0.16091532 -0.06228446 +Ti 5.98537985 5.96562029 5.95198964 0.07610928 0.02316153 0.00706051 +40 +Lattice="7.81511973422794 0.0 0.0 0.0 7.81511973422794 0.0 0.0 0.0 8.197990265127501" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.882254625198 pbc="T T T" +Ba 1.94155005 1.97695020 0.04908677 0.03043312 -0.29002918 -0.19417408 +Ba 1.99134956 1.96737980 4.10127949 -0.35342795 -0.10371547 0.02328751 +Ba 1.99746958 5.86131948 0.02789138 -0.49135787 0.05758166 -0.13692847 +Ba 1.94263010 5.84742967 4.05337984 -0.09092166 -0.00720269 0.44966512 +Ba 5.86357961 1.94173996 8.17596413 -0.01990368 0.17388396 0.26187920 +Ba 5.90621969 1.93196012 4.09552991 -0.21727596 0.24237815 0.03828681 +Ba 5.80986004 5.91742970 8.19492908 0.49553437 -0.53915545 0.07807180 +Ba 5.81531969 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5.85935029 4.00833002 5.95008054 -0.13781704 0.04324287 0.02600054 +O 5.82285043 7.98786015 1.91838990 -0.10696149 0.10602561 0.08873031 +O 5.82541994 8.02619017 5.99428039 -0.02570229 0.08298235 -0.10481256 +O 0.00695365 1.95596970 1.93019008 0.04382497 0.20842005 0.07919563 +O 0.00910033 2.02969016 5.96537035 0.19035419 -0.13150396 -0.08827163 +O 0.00424837 6.00396026 1.90993039 -0.05392349 0.03988064 0.03725811 +O 0.00193023 6.08814029 5.92558024 0.20415639 -0.24900337 0.06306530 +O 3.88059019 1.97510988 1.96511969 -0.01677233 0.03476954 -0.12369449 +O 3.90835979 2.00338997 5.90943006 -0.20994574 0.17492320 0.26331542 +O 3.88568033 5.98686048 1.92458015 -0.10069366 0.14629988 -0.03429286 +O 3.87980972 6.01178981 5.93236011 -0.02162838 0.18298593 0.02389403 +40 +Lattice="7.761519903971019 0.0 0.0 0.0 8.024798420633621 0.0 0.0 0.06837899035398468 8.024511244397173" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.044042356996 pbc="T T T" +Ba 3.86802019 0.08258180 8.02127624 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0.0216790889689057 7.929376567737363" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.82928916313 pbc="T T T" +Ba 4.04327221 0.02271309 0.06346010 -0.13824359 0.21870883 -0.26697204 +Ba 4.00282651 0.06086004 4.03060968 -0.26597908 0.12328620 -0.30516809 +Ba 4.00242607 3.96257350 0.02730027 0.21512832 0.13523771 0.01866724 +Ba 3.92745005 4.02872010 3.95328020 0.34425297 -0.23286584 0.20216481 +Ba 0.07464061 0.02661358 0.04805003 -0.24785383 -0.08371486 -0.30559309 +Ba 0.06329993 0.02203988 4.02052026 0.05651542 0.16972418 -0.10387103 +Ba 0.00441670 4.00297321 0.08713027 -0.01954321 0.09843803 -0.55428588 +Ba -0.01308358 4.05506011 3.98518034 0.33515101 -0.24242006 0.15114050 +O 2.05125970 3.94538961 2.05166013 -0.07683202 0.12795712 -0.12892565 +O 2.05496037 4.00774039 6.02197991 -0.20535812 0.19981842 0.09546660 +O 2.00773976 7.91548022 2.05215969 0.20285953 0.17033584 -0.08244242 +O 2.03025620 0.03978993 5.98461004 0.12776172 -0.23067141 0.37407057 +O 6.00383973 4.02688998 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7.979719775709101 0.0 0.0 0.0 7.979719775709101" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29604.754642865097 pbc="T T T" +Ba 3.92761967 4.07325993 3.96603963 -0.38307483 -0.64318022 0.54543177 +Ba 4.08657010 0.12639078 3.95813013 -1.09948830 -0.09316572 -0.36214168 +Ba 0.07717985 4.00580975 4.08401021 0.97297357 0.43584492 0.71276893 +Ba 3.95461027 3.86072967 0.01677337 0.51849972 0.52351311 -0.38475145 +Ba 0.03953472 0.08119046 4.00952990 0.83665291 -1.70678081 0.20345011 +Ba 0.01844831 4.11282976 7.95545425 0.81698937 -1.16121097 -0.92748253 +Ba 3.91755964 7.82622667 0.03891151 0.65316845 1.68852418 -0.26557850 +Ba 7.85672038 7.87977458 7.88624773 1.17064872 0.46332899 0.34886296 +Ti 1.90308018 5.72743988 1.83882987 1.34637745 5.58648241 1.49930538 +Ti 6.03213989 2.31125003 2.21703028 -2.84989559 -18.33207044 -5.27681746 +Ti 6.07021991 6.01529949 5.80431012 -0.80658694 -0.56791889 1.41481302 +Ti 1.93928018 1.86109967 6.03823002 -0.02211586 0.26395022 -0.92930493 +Ti 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5.98104017 6.04508017 0.20395482 0.75761668 -0.51340996 +Ti 5.93896957 2.00852009 2.01622969 0.11576058 0.28108200 0.24612733 +Ti 5.95667988 2.05092013 5.97846951 -0.20386123 -0.01806174 -0.03773042 +Ti 5.95942952 5.96560987 2.03995959 -0.45519350 -0.12204178 0.03604430 +Ti 6.00701999 6.03057962 6.02019006 -0.26330565 0.03870153 0.10174652 +40 +Lattice="7.979540774 0.0 0.0 0.0 7.979540774 0.0 0.0 0.0 7.979540774" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.29608630342 stress="-0.00013588732704951885 -0.0 -0.0 -0.0 -0.00013588732704951885 -0.0 -0.0 -0.0 -0.00013588732704951885" pbc="T T T" +Ba 3.98977039 3.98977039 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.98977039 3.98977039 0.00000000 0.00000000 0.00000000 +Ba 3.98977039 0.00000000 3.98977039 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 3.98977039 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.98977039 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.98977039 0.00000000 0.00000000 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1.94358982 0.62993287 -0.06942261 0.13204517 +O 5.81478947 4.17923976 5.95552005 0.19392134 0.44985255 0.29960037 +O 5.92871007 0.10153967 2.02808015 -0.00613799 -0.44698731 -0.35320118 +O 5.66310012 0.23345014 6.04038973 0.88162922 -0.02389686 -0.05414949 +O 0.01810384 2.13279974 2.04269967 -0.17365334 0.17147150 -0.65340139 +O 7.77305111 2.17361964 6.00835949 -0.03674158 -0.26283591 0.10350644 +O 0.01405206 6.13189009 1.88271005 -0.21187716 -0.22648693 0.01975224 +O 7.72978968 6.26634981 6.06361001 0.23198164 -0.19241930 0.00249628 +O 3.89558996 2.14145983 1.93784973 -0.39266196 -0.78244120 0.23743958 +O 3.88589019 2.23824991 5.98388956 -0.49978080 -0.06041193 0.12009160 +O 3.95456991 6.25109962 2.07290969 -0.71687781 -0.42625702 -0.28173994 +O 3.85748010 6.21780022 5.79928951 -0.01858111 -0.24189916 0.82748950 +40 +Lattice="7.972839942823297 0.0 0.0 0.0 7.972839942823297 0.0 0.0 0.0 7.972839942823297" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.68595156593 pbc="T T T" 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5.89660000 5.95653025 7.88655867 0.60443370 0.04725816 0.43892331 +O 1.94976997 6.04269034 7.96174016 -0.03495183 -0.33945195 -0.57959376 +O 5.97367983 1.95684028 7.86430009 -0.05174294 0.23420899 -0.16106162 +O 1.94892006 2.01639979 0.00543030 0.26077594 -0.01525384 -1.25483975 +O 6.01011969 7.91694874 5.94059972 0.05533374 0.29264939 -0.14085043 +O 6.05010029 7.97247957 1.96598991 -0.42935520 -0.09281554 0.04950659 +O 1.90826974 7.96516848 5.99208034 0.11535049 0.32196614 -0.27533969 +O 1.95098024 0.03278990 1.97258983 0.20755976 -0.20659380 0.13594837 +O 7.93742060 5.86080993 5.93191969 0.03718227 0.65387704 0.30671050 +O 0.01930623 2.01692998 5.91261026 -0.49685643 -0.13399073 0.17017129 +O 0.00652976 5.98270030 2.00397970 -0.58237492 -0.08370149 -0.25288034 +O 7.96401959 2.02719980 1.93307962 -0.57395790 0.06294832 0.22433826 +40 +Lattice="7.979600181660014 0.0 0.0 0.0 7.979600181660014 0.0 0.0 0.0 7.979600181660014" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29604.984526132623 pbc="T T T" +Ba 3.94192967 3.96752982 3.83779030 0.11262949 0.73865197 0.23704877 +Ba 3.96893024 7.83503217 4.06450032 -0.36125876 0.16037796 -0.15182827 +Ba 0.01840974 4.11313040 3.80452973 0.56573551 0.27290717 1.33928069 +Ba 4.04704016 3.96049022 0.28711878 -0.48344067 -0.48491186 -0.66627593 +Ba 7.82292153 7.72703147 4.06460006 2.36348350 -0.14448134 0.85816662 +Ba 7.94141141 3.84697004 0.31139432 0.56097023 1.45302501 -2.00170460 +Ba 3.94158974 0.20750073 7.82261112 0.64899812 -0.50223852 0.22994841 +Ba 7.92193799 0.24203883 7.78568233 1.05823032 -1.81562075 0.08594144 +Ti 1.92201039 6.13914051 1.65312020 0.51884990 -1.87394031 0.34519965 +Ti 6.31342056 1.90498990 2.39912026 -2.14400744 1.82759823 -28.11357274 +Ti 6.02628024 5.88633002 6.28087975 0.09136518 0.49381070 -1.49463755 +Ti 2.09017966 2.12870039 5.76746988 -0.17557524 -0.94519949 0.04814879 +Ti 2.27607004 5.77017018 6.02519022 -4.87404463 0.21321799 -1.30135949 +Ti 6.16682015 2.15803020 6.06246054 -1.26272610 0.70205489 -2.96497842 +Ti 5.94631028 6.18569031 1.99281976 -0.79929684 -0.48520779 -1.94851336 +Ti 2.06043012 1.73950975 1.94831993 -0.24723497 2.31648270 0.80043944 +O 6.07604023 5.89836006 3.69900032 -0.67748260 0.14631788 2.15135489 +O 1.83276973 5.87194041 4.22970996 0.61108052 1.18036441 -0.64235156 +O 6.23201029 1.76311979 3.76794008 -1.44773523 -2.18379527 27.12142414 +O 1.84644038 2.20875971 3.95810033 -0.10076436 -0.30080519 -0.99533677 +O 5.90616012 4.02899030 5.81700006 -0.57631560 -1.65557189 0.07018623 +O 5.96299004 3.66738993 2.09720969 0.15422762 1.94246407 -0.28365027 +O 2.18532044 3.99984002 6.21549012 -0.27686384 -0.83892988 -0.00440816 +O 1.92889040 4.37483016 1.96076012 0.55653071 -1.88178886 -0.04216686 +O 3.93829018 5.94829002 6.09461993 4.16030151 0.71110980 -0.90061553 +O 3.95780987 1.97414032 5.59685007 1.34618668 0.26384121 0.85764931 +O 3.91949024 6.14772018 1.90814025 1.26413686 -0.30541646 0.39754500 +O 3.83937984 1.96181024 2.22869994 1.18077450 -0.34171889 -0.37922666 +O 5.81965009 5.85125010 0.06128413 0.42015322 -0.23345565 0.57694681 +O 2.13340037 6.16698054 7.80415511 -1.08776021 0.62131171 2.26806266 +O 6.01846023 2.03298029 7.73747039 -0.62479247 -0.07100718 1.82367910 +O 2.05315033 2.08167022 0.15577696 0.18532357 -0.02037059 -0.66422316 +O 6.04038019 7.81803402 6.01913052 -0.51394064 0.80518441 -0.56704523 +O 6.05965970 7.96330504 1.88107025 -0.43105933 0.66003278 0.23747403 +O 1.94536029 0.33536185 6.01583973 -0.08435275 -1.46582988 -0.17499622 +O 2.11058988 7.96166683 1.94341008 -0.59645505 0.21270145 0.81728350 +O 7.75952440 5.71939040 6.12604998 1.61324408 0.61189504 -0.05794598 +O 0.02205482 2.20051998 5.81213011 -1.04336729 -0.15231395 0.78357094 +O 0.03167343 6.08800005 1.75371982 -1.02243568 0.48957584 0.28402797 +O 0.03600715 1.84821983 1.72694986 1.41868844 -0.12032146 2.02145761 +40 +Lattice="7.8399000445407205 0.0 0.0 0.0 7.8399000445407205 0.0 0.0 0.0 8.223992427522859" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.901900428 pbc="T T T" +Ba 1.97216998 1.94923984 0.00046412 -0.11294162 0.11173989 -0.09320712 +Ba 2.02722019 1.96565972 4.14020966 -0.57815368 0.02332248 -0.10680285 +Ba 1.89100976 5.85810032 0.03176022 0.37324550 0.04133511 -0.32844454 +Ba 1.99249021 5.86924003 4.12043979 -0.20508919 0.05651773 0.01964863 +Ba 5.87457038 1.94538025 0.03655197 0.25991436 -0.01304758 -0.18112188 +Ba 5.80653024 1.99318012 4.11664998 0.77778467 -0.38861787 -0.03824799 +Ba 5.83745002 5.88028018 8.22385288 0.45980915 0.07256193 0.04656859 +Ba 5.88866966 5.90422010 4.12248992 0.16389420 -0.00764132 -0.10726128 +Ti 0.08424365 0.04498064 2.16023036 -0.91452083 -0.26476140 0.32225281 +Ti 0.04719855 7.81824154 6.24668967 -0.45948699 -0.12254520 -0.27205511 +Ti 0.02354871 3.95068008 2.12492964 -0.25600063 -0.00862785 0.26324523 +Ti 7.81718001 3.88338002 6.21788039 0.18920337 0.20430166 -0.06155478 +Ti 3.93340015 7.80828957 2.11837000 0.49829805 -0.01582745 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0.42847486 +O 0.01904939 3.87490980 8.04291034 -0.07426811 0.26992598 0.36433715 +O 3.88492997 1.98029995 1.93364000 0.15750167 -0.29017342 0.16869548 +O 5.84462980 7.82301996 1.99760967 0.00975836 0.12134450 -0.15255589 +O 3.90476022 7.82720960 3.92506007 0.04916926 0.20362494 0.57251551 +O 3.88977973 1.99364973 6.09406014 0.12110333 -0.42915080 -0.07197546 +O 5.87363038 7.83688639 6.11957980 -0.07830012 0.26169639 -0.25881084 +O 3.93881988 0.00942513 8.07016967 -0.30373084 -0.11912050 0.29114787 +O 3.84131974 5.86733023 1.96306001 0.22489362 0.25124023 -0.11110919 +O 5.89221016 3.91649968 1.93492026 0.02182558 -0.05615418 0.14688610 +O 3.95825969 3.92601027 3.93748004 -0.16842551 -0.04501127 0.18654408 +O 3.93169027 5.88752974 6.04515014 0.14514469 0.03745326 0.18270105 +O 5.89965022 3.87910963 6.04026040 -0.19740287 0.22134499 0.10478274 +O 3.96250030 3.94232039 8.07695981 -0.22893231 -0.02749615 -0.08280521 +40 +Lattice="7.955129969191328 0.0 0.0 0.0 7.955129969191328 0.0 0.0 0.0 7.955129969191328" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29607.815848854727 pbc="T T T" +Ba 1.82734029 1.95367969 6.23859032 0.93115458 0.38118173 -2.46065474 +Ba 1.97779009 6.07244982 1.89539006 0.45673231 -1.54103465 -0.10088340 +Ba 5.73206969 1.86750017 1.83772969 0.96156944 0.34616279 2.05862059 +Ba 6.00047021 6.00252979 2.21740975 -1.17409606 0.26556976 -0.83219333 +Ba 6.15474007 2.03721014 5.94473021 -2.17520470 -0.82957621 -2.38246441 +Ba 2.04918977 5.99069972 5.99367017 -1.02879993 -1.04546968 0.20172798 +Ba 2.13435023 1.96785016 1.86292995 -0.70699012 0.65017928 0.80262205 +Ba 6.02427037 5.93202030 5.99567009 -0.39352251 1.16506043 -0.74696795 +Ti 0.03573444 4.12883974 0.12419310 -1.00627218 1.38737241 -0.26332364 +Ti 3.91909955 7.85176578 0.03244738 0.91774062 -0.94293229 -1.51390385 +Ti 3.96271037 3.73777987 4.04045029 0.19670199 1.42224351 0.50748434 +Ti 0.32105870 7.82129286 3.87723966 -2.93970937 1.68273097 1.14049071 +Ti 0.06600371 3.93018980 3.88154020 0.95040854 -0.99352851 0.88742783 +Ti 3.89672018 7.83630101 4.22073024 1.93287745 0.23432443 -2.48907623 +Ti 4.26241989 3.96359975 7.89358590 -3.07172420 1.05948014 0.39906401 +Ti 7.83244516 0.16713092 0.01146414 0.49914368 -3.76833683 -0.69605779 +O 4.21402009 4.11616005 1.78392994 -1.77420799 -0.80153781 1.65349778 +O 7.88399122 4.26988976 1.97134007 0.35887715 -1.44295529 -1.14013153 +O 3.88152986 7.74233581 1.77080000 0.21769685 1.43534765 1.35654874 +O 0.00813253 0.05243147 1.85646004 -0.13445893 -0.49993275 2.11430503 +O 3.83413956 1.88170008 4.00448992 -0.26053297 2.71326408 -0.75608328 +O 3.92242002 2.15433034 7.85839638 0.46302508 -1.93320038 0.18422854 +O 0.31817099 1.96226964 3.81740038 -1.40318109 0.69354762 0.30829198 +O 7.44299620 1.85327958 7.87411254 2.68211620 3.65675250 1.23141649 +O 1.96071998 4.26844988 3.90818034 0.06448121 -2.23209344 -0.21752073 +O 2.02979994 0.13135988 3.77118982 -0.56434763 -0.92946253 0.06740970 +O 1.80138031 3.84138987 7.78783518 -0.40345417 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7.955180241026122 0.0 0.0 0.0 7.955180241026122" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29611.880556394604 pbc="T T T" +Ba 3.83359022 3.99531028 3.97566019 1.13397117 -0.38853123 -0.46550645 +Ba 4.07942995 7.94998233 3.96248005 -0.65261412 0.63486682 0.14528507 +Ba 0.03518258 3.88632988 3.99210992 -0.26429938 0.09156187 -0.32644140 +Ba 4.02287021 4.05058049 0.07825272 -0.32897034 -0.29392620 -0.59040628 +Ba 7.92157517 7.87332700 4.11482971 0.94582889 0.79470305 -0.95303287 +Ba 7.82778519 4.10358029 0.00438808 0.91842633 -0.93978680 0.43646225 +Ba 3.95084003 0.06725389 7.82803419 0.92337956 -0.34970088 0.93818732 +Ba 7.94945649 7.85809443 7.82479404 0.07711741 0.92202690 1.58733430 +Ti 6.00581980 1.97831013 1.98767020 -0.26586209 0.53727597 1.16182701 +Ti 1.91509986 6.07548014 1.94563025 1.30687965 -0.79539339 0.60725806 +Ti 5.84226050 5.92261021 5.99769041 0.34401309 0.00815734 -0.54570276 +Ti 2.03316985 1.80239007 5.96968022 0.47635651 0.90532502 0.46127648 +Ti 1.93332995 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5.86320002 1.95564975 -0.00968817 0.25237280 0.24598592 +O 5.84311970 3.86267990 2.00481007 0.45556991 0.23126199 -0.10184551 +O 3.90517981 3.93207036 3.95099978 -0.00920044 -0.26153956 0.13648084 +O 3.86161014 5.86773029 6.01910013 0.31431685 0.32519621 0.24343693 +O 5.86056972 3.92798017 6.05377000 0.24895992 -0.16806170 -0.19470244 +O 3.94006972 3.93957971 8.06355041 -0.13092546 -0.08036240 -0.00514581 +40 +Lattice="7.912359750503362 0.0 0.0 -0.021687778076129715 7.91232810106436 0.0 -0.021687778076129715 0.02163239155787619 7.912296451625358" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.940552974273 pbc="T T T" +Ba 4.01452878 0.03104019 0.04373003 -0.02895088 0.07782524 -0.10110169 +Ba 3.99227923 0.03782029 4.00169019 0.10450917 -0.16854275 -0.06932465 +Ba 3.97915895 4.01298983 0.00842983 0.00574976 -0.22388729 0.29129442 +Ba 3.97112949 3.98974015 3.99892956 0.06688313 0.27994994 -0.22347952 +Ba 0.04152802 0.02272984 0.03782978 0.05258832 0.29723007 -0.06225669 +Ba 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2.01270018 2.06116972 5.96506946 -0.35970299 -0.06707854 0.34991428 +Ti 2.00202008 5.96554974 1.99491003 0.00588963 -0.32701244 -0.01261615 +Ti 1.96834033 6.02628977 5.94512953 0.07533409 -0.01970365 -0.06542403 +Ti 5.94573957 1.97082956 1.99782969 0.02060482 0.09851747 -0.40389125 +Ti 5.93768004 2.00347991 5.92363956 0.17421512 -0.05992033 0.49975072 +Ti 5.95992010 5.92167967 2.01076957 -0.10186274 0.04557023 0.27568911 +Ti 5.93918972 5.93677961 5.99433966 -0.23833638 0.26731991 -0.41953179 +40 +Lattice="7.961126154 0.0 0.0 0.0 7.961126154 0.0 0.0 0.0 7.961126154" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.641838239153 stress="0.0014075356241007595 -0.0 -0.0 -0.0 0.0014075356241007595 -0.0 -0.0 -0.0 0.0014075356241007595" pbc="T T T" +Ba 3.98056308 3.98056308 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.98056308 0.00000000 3.98056308 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.98056308 3.98056308 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 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1.93643002 0.00443010 -0.13020066 0.10790303 0.06137249 +Ba 1.94907983 1.97682000 4.11399018 0.01459512 -0.10657043 -0.08673308 +Ba 1.96090986 5.89385024 0.05730232 -0.05173240 -0.12635069 -0.27954165 +Ba 1.97092964 5.86458013 4.10299010 -0.11828463 -0.02492890 0.06516178 +Ba 5.86425989 1.92046038 8.19663457 0.01900251 0.21523065 0.04786237 +Ba 5.90542032 1.96063973 4.11385002 -0.28898402 0.05950355 0.02845851 +Ba 5.85456035 5.88645970 0.01008399 0.03437899 -0.08104888 -0.08168318 +Ba 5.89267029 5.89481017 4.14462032 -0.19776077 -0.36346888 -0.11776989 +Ti 7.77734226 7.80104226 2.15260035 0.53059059 0.58381037 -0.48703764 +Ti 0.01057648 7.82142712 6.22797009 -0.23900589 -0.03284996 -0.10372087 +Ti 7.82401564 3.91138026 2.13532000 -0.13283065 -0.46867765 -0.46160069 +Ti 7.81954014 3.90346983 6.26753010 0.07824253 0.13017084 -0.13363257 +Ti 3.90261012 0.01007772 2.15970980 -0.24836445 -0.17740046 -0.27546028 +Ti 3.89580994 0.01531977 6.20808007 0.22301492 0.11501162 0.07061226 +Ti 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energy=-29615.214851070716 stress="3.397183176237971e-05 -0.0 -0.0 -0.0 3.397183176237971e-05 -0.0 -0.0 -0.0 3.397183176237971e-05" pbc="T T T" +Ba 3.97761387 3.97761387 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.97761387 0.00000000 3.97761387 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.97761387 3.97761387 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 3.97761387 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.97761387 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.97761387 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.97761387 3.97761387 3.97761387 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 5.96642080 1.98880693 1.98880693 0.00000000 0.00000000 0.00000000 +Ti 1.98880693 5.96642080 1.98880693 0.00000000 0.00000000 0.00000000 +Ti 1.98880693 1.98880693 5.96642080 0.00000000 0.00000000 0.00000000 +Ti 5.96642080 5.96642080 5.96642080 0.00000000 0.00000000 0.00000000 +Ti 1.98880693 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7.920249782679913 0.0 0.0 0.0 7.920249782679913" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.96230453002 pbc="T T T" +Ba 3.96637001 3.99155957 0.06501099 0.22413643 -0.12113495 -0.40867582 +Ba 3.95371028 7.90501360 3.96656960 0.19602502 0.20275360 0.00234613 +Ba 7.90707603 3.96721985 3.96637001 0.13917639 0.01346872 -0.06092589 +Ba 0.06276640 0.00225806 3.96202021 -0.32669080 0.11479667 0.06300411 +Ba 0.01219164 3.98492953 7.91312789 -0.07152320 -0.00856537 0.28530092 +Ba 3.95181972 0.02677282 7.90645746 0.21104772 -0.16935085 0.13000063 +Ba 3.94120975 3.95585984 3.99298997 0.33170368 -0.02512636 -0.13964407 +Ba 7.91735176 0.01279912 7.90337094 0.15947113 -0.06854047 0.25777417 +Ti 5.97562966 2.00356024 2.05733003 0.05749655 0.07012324 -0.52373114 +Ti 2.05138984 5.92200957 2.01789985 -0.32322932 0.19961968 -0.54699037 +Ti 2.06664028 1.99773965 5.95830966 -0.20162488 -0.51676474 -0.24742600 +Ti 5.97663949 6.01889007 6.00294977 -0.07654894 -0.16623082 -0.09157884 +Ti 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0.62488425 -0.32480592 0.58246902 +Ti 6.05316036 6.11447006 2.01637992 -1.15269985 -0.32577188 0.24101521 +Ti 5.94662016 5.93862980 6.02959993 0.07489778 0.22966302 -0.44099176 +40 +Lattice="7.790819916820346 0.0 0.0 0.0 8.055100110038726 0.0 0.0 0.06863712346718724 8.05479626806197" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.55070799487 pbc="T T T" +Ba 3.85090957 8.11162017 8.00395883 0.20326267 0.26867745 0.43249915 +Ba 3.90424007 0.08560709 4.02112964 -0.13992663 0.04602043 -0.15826348 +Ba 3.94606976 4.07163986 7.93984584 -0.20691107 0.01176794 0.67269829 +Ba 3.88723973 4.15084991 4.07312012 0.04453433 -0.35055295 -0.40405040 +Ba 7.73914964 0.14553563 8.01700066 0.36620659 -0.38157845 0.53602976 +Ba 7.78292003 0.08822402 4.00492006 0.13810038 -0.02042561 -0.24376115 +Ba 0.05699141 4.07731937 8.03680415 -0.54765757 0.24763400 0.25545324 +Ba 0.02064489 4.14819012 4.02671020 -0.23086527 -0.40557327 -0.24877351 +Ti 2.00257027 2.03196036 1.99663990 -0.66187600 0.12612624 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3.86032011 2.05265979 6.09923970 0.39928384 0.48773364 0.11678902 +O 3.90353968 6.21038977 2.13782981 -0.27009464 -0.37314626 -0.12904238 +O 3.90141980 6.09491969 6.11773978 0.14708356 -0.09913814 -0.27349287 +40 +Lattice="7.790280156067825 0.0 0.0 0.0 8.054526458961647 0.0 0.0 0.06863236817495755 8.054238218595872" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.632825556702 pbc="T T T" +Ba 3.89402996 0.14531755 8.01241532 0.33974377 0.00594928 0.18933449 +Ba 3.90024972 8.08816800 4.04854004 0.17729607 0.23185128 -0.37815194 +Ba 3.82782972 4.15999480 8.03961586 0.48531655 -0.32274184 -0.16482340 +Ba 3.87608973 4.09941992 4.04031039 0.07947048 0.04805083 -0.27382249 +Ba 0.00561991 0.05175005 0.00334748 -0.38851091 0.08386681 -0.23538038 +Ba 0.02235031 8.07672408 3.95469989 -0.37892558 0.36458577 0.29134430 +Ba 0.01363455 4.02929026 0.03683868 -0.25516759 0.15199282 -0.49330317 +Ba 0.06154945 4.07600000 4.01894009 -0.47017686 0.21710806 -0.08346032 +Ti 1.98186986 2.11928028 1.89376024 -0.00269426 0.26876050 0.10015372 +Ti 1.89678988 2.06952999 5.91234977 -0.38111925 0.00605803 0.66001118 +Ti 1.93208997 6.20886030 2.04669980 0.01021011 -0.33223487 0.63940867 +Ti 1.96268007 6.16067975 6.14128974 -0.16846382 -0.79829282 -0.66206909 +Ti 5.86519988 1.99841019 1.94335004 -0.18756917 -0.32795861 -0.22896625 +Ti 5.77271990 2.07926005 5.95669049 0.94074196 -0.07163376 0.03541489 +Ti 5.78255981 5.97411033 1.88629014 0.35536888 0.39508085 0.26485756 +Ti 5.86878029 6.08952021 5.92464984 -0.01177848 -0.50476771 0.21880499 +O 1.95188040 2.12468985 4.07830982 0.03331867 -0.31083017 -0.22244259 +O 1.89328036 2.01874515 0.00885989 0.22867263 0.28693923 0.62996424 +O 1.96166967 6.08372035 4.01340977 0.02139749 0.52175499 -0.22376671 +O 1.97542029 6.18601997 8.05373029 -0.09892037 -0.00316246 -0.15876305 +O 5.86787973 2.12441018 4.02796981 -0.42405564 -0.20086358 0.48511729 +O 5.88189990 2.06809502 0.03028004 -0.31981464 0.23513535 0.08975593 +O 5.89277046 6.13964989 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2.06932019 5.93954996 2.11771008 -1.92646641 1.09506240 -1.63452433 +Ti 6.01009043 1.89652035 2.16457028 0.06537133 2.59457733 -1.18235187 +Ti 6.21894050 5.82111035 5.81782036 -1.46037348 2.19285481 1.08365056 +Ti 2.08554990 1.95997014 5.99011031 -0.11046333 2.84754792 1.17806173 +Ti 1.94478975 5.78449995 6.04782037 -0.48585108 2.18017901 0.62768779 +Ti 6.03267030 1.91181006 6.04089009 -0.17057881 -0.46184443 0.14523288 +Ti 6.00468983 6.07004036 2.00597972 0.43207491 -1.97265036 -0.66490116 +Ti 2.17812044 1.96818035 1.97629002 -1.00020052 0.93188014 -1.14643742 +O 5.82412983 5.95627999 4.05943008 0.48364147 0.00795011 -0.12755011 +O 1.89602961 6.14001986 3.92850000 0.23040992 -0.38617224 1.13666465 +O 6.00844024 1.95183015 3.99446975 -0.44910976 -0.31369284 0.37766163 +O 1.98467020 2.10034009 3.89509979 0.04759523 -0.03973923 0.50075525 +O 6.03713010 4.00023023 6.00616047 -0.36801922 0.53442256 -0.68851237 +O 5.78387036 3.91426041 2.16247005 0.16287681 0.71358089 -0.14100624 +O 1.81915015 4.05433990 6.06273983 0.39882027 -1.42850235 -1.20535553 +O 1.94818028 4.20874995 1.98339027 0.33062793 -2.17771641 0.36531828 +O 3.68368028 6.00211003 5.97561057 2.78773120 0.15820152 -0.24289006 +O 3.97919041 2.01819010 5.91518984 -0.29213671 0.33223692 -0.21726747 +O 3.82179041 6.19633988 1.93408991 1.35137851 -0.18274579 0.37496454 +O 3.99453040 2.00129011 1.89665042 -0.69517564 -0.31139273 0.24724268 +O 5.94405046 5.87093019 0.15611290 -0.19215602 0.83460554 -1.33427167 +O 1.82982047 5.96009983 7.93573153 0.17312035 0.71718223 -0.10520414 +O 5.82581034 2.12808995 7.80162717 0.34918435 -0.91100870 0.84359772 +O 1.87094972 2.24490012 7.93245431 0.93597000 -0.70173556 0.09847531 +O 5.99825030 7.88031640 5.94828044 -0.22144706 0.40430751 0.35520741 +O 5.93069979 0.00485479 2.01744002 -0.16623185 -0.47324213 0.05081708 +O 1.98512982 0.28657697 6.03384011 -0.36431349 -3.73866553 -0.18991608 +O 1.85330044 0.23288224 1.88833967 0.33452700 -1.56923528 0.14264660 +O 0.03620584 6.09619989 5.94915979 -1.42171258 -0.41240109 -0.61179194 +O 7.90229062 2.02214001 5.96883988 0.18115170 -0.35463920 -0.13567917 +O 7.78924682 5.93530003 2.00326027 0.74906725 0.60985256 0.61072365 +O 7.80473123 2.00029027 1.87398038 0.32401196 0.20268829 0.42265285 +40 +Lattice="7.9202598370468715 0.0 0.0 0.0 7.9202598370468715 0.0 0.0 0.0 7.9202598370468715" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.05954087279 pbc="T T T" +Ba 3.98864998 3.96615011 0.00055917 -0.20385326 0.02431647 0.10689233 +Ba 3.99015958 0.01917257 3.98058953 -0.12876779 -0.13517086 -0.09075223 +Ba 0.01133231 3.98053964 3.97278016 -0.05920993 -0.10354038 -0.11213352 +Ba 0.01530669 0.00516955 3.97243959 -0.08432936 0.02215545 -0.00970463 +Ba 0.00007841 3.98805992 0.01074700 0.10151178 -0.19717327 0.06908246 +Ba 3.93846959 0.01809859 7.90992231 0.24107306 -0.08164152 0.15015294 +Ba 3.96230007 3.96608991 3.98139978 0.08621989 0.02994384 -0.17778484 +Ba 0.02555551 7.91293518 0.01394916 -0.20120939 0.16055279 -0.02002349 +Ti 5.89761952 1.99331001 2.00671030 0.16283670 -0.34255553 0.10786858 +Ti 1.98346988 5.93538966 1.99057990 -0.07824407 -0.20354678 0.11813293 +Ti 2.01571959 2.03995004 5.94628001 -0.17573747 -0.32443620 0.05195377 +Ti 5.94001984 5.94075959 5.93736972 -0.13109952 0.15225944 -0.16528080 +Ti 1.97843972 5.96892958 5.94693977 -0.02147617 0.27750251 0.00998796 +Ti 5.97020949 1.98490028 5.97061976 0.15153542 -0.04768445 0.01269919 +Ti 5.92365975 5.94036992 1.96811012 0.10511750 0.29168034 0.13652738 +Ti 1.94296013 1.96478995 1.99310963 -0.10539723 0.29121446 0.00201215 +O 2.01077022 1.95775992 3.95825995 -0.06197516 0.17152575 0.00705074 +O 5.93431963 1.97570961 3.95487958 0.11112025 0.06739813 0.09636006 +O 2.01577979 5.91370002 3.95819975 -0.11307712 0.19789010 0.20572399 +O 5.98068958 5.96265990 3.97688998 -0.13361689 -0.05109913 0.11745802 +O 2.00344002 3.96433003 1.99516018 -0.06218856 -0.17616839 -0.04071625 +O 2.00189003 3.95616979 5.93273954 -0.08040637 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4.10932020 0.07377678 0.00712221 0.07210659 +Ti 0.00278477 0.00141392 2.13937016 -0.02012120 -0.14588311 -0.09188069 +Ti 7.82408670 7.80331091 6.27753001 -0.02975795 0.14380463 -0.45857862 +Ti 0.00765362 3.90862012 2.13242037 -0.11959049 0.19746869 0.22135090 +Ti 7.81328035 3.88785999 6.23516969 0.05205353 0.04402731 -0.27642264 +Ti 3.92127021 7.82282467 2.15114027 -0.01203302 0.07255550 -0.23071409 +Ti 3.90647968 0.00151021 6.23713007 0.01713255 -0.09924715 -0.06057828 +Ti 3.92571003 3.91625965 2.15635985 0.07893904 -0.01937506 -0.40216013 +Ti 3.90025015 3.90600994 6.25352006 0.02480857 0.11354326 -0.38945631 +O 7.82560005 1.96965019 1.95331970 0.04621892 -0.24920829 0.07694438 +O 1.96422000 7.82446014 1.98273008 -0.11813448 -0.04533189 -0.08713057 +O 0.00781020 0.00166992 3.96168032 -0.02641783 0.02670013 -0.00126395 +O 0.02187968 1.95848996 6.06235022 0.01869063 0.00160617 0.20464953 +O 1.97719029 7.82468170 6.07970005 -0.29335593 -0.00598167 0.04292997 +O 7.81566975 7.82337035 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0.04491254 0.12033688 0.05248341 +O 3.94391008 3.92003009 3.96635031 -0.16669156 0.02234109 0.16574617 +O 3.94288996 5.87752029 6.07283011 -0.04952125 0.02641731 0.01153217 +O 5.88522010 3.91181983 6.04789008 -0.04676117 -0.04300324 0.21050907 +O 3.91411999 3.91787008 8.06843026 -0.01079760 -0.06663374 0.13366317 +40 +Lattice="7.913980091115341 0.0 0.0 0.0 7.913980091115341 0.0 0.0 0.0 7.913980091115341" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29613.801585944122 pbc="T T T" +Ba 3.83643006 3.93805981 7.83684728 0.60751105 0.13056756 0.53100479 +Ba 4.04859041 7.88412618 3.97559977 -0.59320775 0.28537008 0.05726567 +Ba 7.90369983 4.02176993 3.83654006 0.25493053 -0.21723096 1.17448250 +Ba 7.87432630 0.03212601 4.06108975 0.57628012 -0.66973638 -0.80141260 +Ba 7.88470153 3.93181014 0.09761024 0.58665015 0.42316964 -0.78054064 +Ba 4.00860028 0.05243566 7.88320262 -0.50479317 -0.32921536 0.14689509 +Ba 4.04455982 3.98105013 3.96924010 -0.55094113 -0.25942765 -0.09338144 +Ba 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-0.00351804 +O 3.96195999 5.98377029 5.97767027 0.00149792 0.29644280 0.23226497 +Ti 1.92014993 2.07991988 2.13184995 0.21404100 -0.10193576 -1.48609763 +Ti 2.03336003 2.06621968 5.97449028 -0.61261058 0.56515367 1.09795515 +Ti 2.14311030 6.00489021 2.02850975 -0.81573056 0.27195175 0.02961731 +Ti 1.93423968 6.03240986 5.90673975 -0.03948957 -0.36746566 0.22762028 +Ti 5.94648965 1.91866964 2.03700986 -0.04824958 0.48368493 -0.18345361 +Ti 6.01571013 2.08028002 6.08933966 0.44020217 0.71064931 -0.15425950 +Ti 6.04239026 5.91043013 1.96409026 0.26676404 -0.00221115 0.03323537 +Ti 5.87237040 6.06731981 5.97112982 0.45316156 -0.60631755 0.03043003 +40 +Lattice="7.934269803638032 0.0 0.0 0.0 7.934269803638032 0.0 0.0 0.0 7.934269803638032" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.904096114566 pbc="T T T" +Ba 4.00973003 3.99809998 0.00972265 -0.23101336 -0.06198775 0.09112838 +Ba 3.96383028 0.07329202 3.98066997 0.11461515 -0.55115067 0.03840431 +Ba 7.92410124 3.93441953 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0.00047876 -0.00344656 0.06479360 0.22424622 +O 1.97731005 2.01702033 7.91786979 0.09349868 -0.14920806 0.38403000 +O 5.95114006 0.00510864 5.94120021 -0.11381528 -0.15673651 0.14081649 +O 5.98408981 7.91257012 1.96888971 -0.13459211 -0.09317009 0.14455848 +O 1.98059004 0.00885234 5.97622037 0.08114144 0.02970473 -0.07233130 +O 1.99775968 0.01380007 1.97844037 0.02550611 -0.10668150 0.00046897 +O 7.91602608 5.97150012 5.95075008 -0.09539410 -0.10344011 -0.00713764 +O 0.01042972 1.98151982 5.96138985 -0.27875181 0.04979250 -0.00597216 +O 0.03518979 5.93873030 2.02775997 -0.11237778 -0.02889174 -0.07843587 +O 0.00828004 1.98236003 1.99989032 0.18087531 0.02872514 -0.07109486 +40 +Lattice="7.985959298 0.0 0.0 0.0 7.985959298 0.0 0.0 0.0 7.985959298" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.30605628236 stress="0.00026902018125343936 -0.0 -0.0 -0.0 0.00026902018125343936 -0.0 -0.0 -0.0 0.00026902018125343936" pbc="T T T" +Ba -0.00082789 3.99215176 0.00082789 -0.01188107 -0.01188107 0.01188107 +Ba 3.99380754 3.99380754 3.99380754 0.01188107 0.01188107 0.01188107 +Ba 0.00082789 -0.00082789 3.99215176 0.01188107 -0.01188107 -0.01188107 +Ba 3.99215176 0.00082789 -0.00082789 -0.01188107 0.01188107 -0.01188107 +Ba 3.99723222 3.98872708 -0.00425257 -0.01055566 0.01055566 0.01055566 +Ba -0.00425257 3.99723222 3.98872708 0.01055566 -0.01055566 0.01055566 +Ba 3.98872708 -0.00425257 3.99723222 0.01055566 0.01055566 -0.01055566 +Ba 0.00425257 0.00425257 0.00425257 -0.01055566 -0.01055566 -0.01055566 +Ti 5.92713416 1.93415451 2.05882513 0.01749456 0.01749456 -0.01749456 +Ti 6.05180478 6.05180478 6.05180478 -0.01749456 -0.01749456 -0.01749456 +Ti 2.05882513 5.92713416 1.93415451 -0.01749456 0.01749456 0.01749456 +Ti 1.93415451 2.05882513 5.92713416 0.01749456 -0.01749456 0.01749456 +Ti 5.93359829 2.05236101 6.04534066 -0.02424756 0.02424756 0.02424756 +Ti 6.04534066 5.93359829 2.05236101 0.02424756 -0.02424756 0.02424756 +Ti 2.05236101 6.04534066 5.93359829 0.02424756 0.02424756 -0.02424756 +Ti 1.94061864 1.94061864 1.94061864 -0.02424756 -0.02424756 -0.02424756 +O 2.02225632 2.00366275 4.03475374 -0.00504373 -0.02954429 0.00972957 +O 5.96370298 5.99664240 -0.04177409 0.00504373 -0.02954429 -0.00972957 +O 6.01523596 1.98931690 3.95120555 -0.00504373 0.02954429 -0.00972957 +O 1.97072333 5.98229655 0.04177409 0.00504373 0.02954429 0.00972957 +O 2.00366275 4.03475374 2.02225632 -0.02954429 0.00972957 -0.00504373 +O 5.99664240 -0.04177409 5.96370298 -0.02954429 -0.00972957 0.00504373 +O 1.98931690 3.95120555 6.01523596 0.02954429 -0.00972957 -0.00504373 +O 5.98229655 0.04177409 1.97072333 0.02954429 0.00972957 0.00504373 +O 4.03475374 2.02225632 2.00366275 0.00972957 -0.00504373 -0.02954429 +O -0.04177409 5.96370298 5.99664240 -0.00972957 0.00504373 -0.02954429 +O 3.95120555 6.01523596 1.98931690 -0.00972957 -0.00504373 0.02954429 +O 0.04177409 1.97072333 5.98229655 0.00972957 0.00504373 0.02954429 +O 1.97362173 5.98402735 4.03820731 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energy=-29614.90618554068 pbc="T T T" +Ba 3.90869996 0.08556495 8.00054128 -0.25385761 0.21488972 0.18142912 +Ba 3.93592019 0.08287630 4.04221977 -0.30710310 0.12719556 -0.34625509 +Ba 3.86461982 4.10230197 8.02849726 -0.10851341 0.05545484 0.05117807 +Ba 3.88464981 4.16810992 4.02142992 0.00578961 -0.67821639 -0.25389567 +Ba 0.00282010 8.02603103 0.01157126 0.07322090 0.43570686 -0.35928210 +Ba 0.03272976 0.07449223 3.98918003 -0.30591037 0.01131851 0.22465554 +Ba 7.74392031 4.06018019 0.00701446 0.35924250 -0.07758561 -0.12436272 +Ba 7.76786157 4.11945976 4.01822017 0.04274536 -0.19924430 -0.16550628 +Ti 1.86947022 2.11898029 2.06445972 1.06498513 0.12481086 0.01113930 +Ti 1.92248040 2.15644028 6.08127996 0.00063840 0.11806403 -0.21879394 +Ti 1.93050982 6.15625050 2.07725982 0.20013236 -0.12492090 -0.87349759 +Ti 1.95954997 6.18703979 6.09218003 -0.09977372 -0.29479318 -0.07983738 +Ti 5.79821028 2.10968004 2.04397008 -0.54607300 0.40482071 0.18144841 +Ti 5.82825994 2.18969968 6.09215047 0.07671529 -0.59718653 -0.37525893 +Ti 5.81516974 6.13875983 2.00549980 0.07148952 -0.45959497 0.59284394 +Ti 5.86738974 6.17072041 6.06200982 -0.06928917 -0.14370358 -0.50392336 +O 1.93014039 2.03393020 3.91801032 -0.06145811 0.04265126 -0.17826358 +O 1.94176999 2.03688018 7.91444047 -0.04865401 0.22321084 0.30121656 +O 1.98163009 6.09631995 3.87993980 -0.14606206 -0.08166081 0.47265644 +O 1.91917966 6.09725013 7.91822030 0.10498843 0.05396026 0.21384071 +O 5.85768973 2.01084990 3.90271989 -0.07093571 0.16835095 0.01809979 +O 5.79082016 2.06396975 7.93436002 0.25257258 -0.12217188 0.17527030 +O 5.89644000 6.03430039 3.89521000 -0.48214612 0.04827066 -0.07745937 +O 5.83189044 6.05974037 7.89601029 0.10244432 0.16774468 0.49148308 +O 1.96667021 4.01406003 1.95282016 -0.25042288 -0.27588528 0.01564516 +O 1.88256041 4.04201989 5.94245983 0.25478655 -0.30756462 0.12945890 +O 1.96473985 8.04036017 1.92803971 -0.19096097 -0.23520452 0.07883002 +O 1.95903977 8.04994041 5.94611989 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energy=-29615.21269293586 stress="0.0003057464858614174 -0.0 -0.0 -0.0 0.0003057464858614174 -0.0 -0.0 -0.0 0.0003057464858614174" pbc="T T T" +Ba 5.96238096 1.99351619 5.97146476 0.02928666 -0.02928666 -0.02928666 +Ba 5.97146476 5.96238096 1.99351619 -0.02928666 0.02928666 -0.02928666 +Ba 1.99351619 5.97146476 5.96238096 -0.02928666 -0.02928666 0.02928666 +Ba 1.98443239 1.98443239 1.98443239 0.02928666 0.02928666 0.02928666 +Ba 1.99351619 5.96238096 1.98443239 -0.02928666 0.02928666 0.02928666 +Ba 1.98443239 1.99351619 5.96238096 0.02928666 -0.02928666 0.02928666 +Ba 5.96238096 1.98443239 1.99351619 0.02928666 0.02928666 -0.02928666 +Ba 5.97146476 5.97146476 5.97146476 -0.02928666 -0.02928666 -0.02928666 +Ti 3.97794857 3.97794857 3.97794857 0.00000000 0.00000000 0.00000000 +Ti 0.00000000 3.97794857 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 3.97794857 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 0.00000000 0.00000000 3.97794857 0.00000000 0.00000000 0.00000000 +Ti 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0.00000000 5.96515332 5.96515332 0.00000000 0.01466712 0.01466712 +O 0.00000000 1.99002770 5.96515332 0.00000000 -0.01466712 0.01466712 +O 0.00000000 5.96515332 1.99002770 0.00000000 0.01466712 -0.01466712 +O 0.00000000 1.99002770 1.99002770 0.00000000 -0.01466712 -0.01466712 +40 +Lattice="7.777959852302938 0.0 0.0 0.0 8.041788250493052 0.0 0.0 0.06852382629878888 8.041500465978519" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.18517215856 pbc="T T T" +Ba 3.88692966 0.10546680 8.02174678 0.06481854 -0.02213514 -0.04379977 +Ba 3.88858014 0.07539099 3.99599999 0.04905356 -0.04237409 0.05360236 +Ba 3.88813991 4.12740629 8.01918472 -0.02695365 -0.11981032 -0.00637634 +Ba 3.89023996 4.08134987 4.01907019 -0.08095118 -0.02514128 -0.10399367 +Ba 7.76958999 0.10387621 8.03764415 0.02261260 -0.04853703 -0.12718013 +Ba 0.00245006 0.06410439 3.99469018 -0.05435801 0.01348055 0.05718802 +Ba 0.00541890 4.13408600 8.03782849 0.04370053 -0.12150699 -0.15685529 +Ba 7.77212560 4.10409030 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0.00000000 +O 0.00000000 0.00000000 1.99946356 0.00000000 0.00000000 -0.29544958 +O 0.00000000 0.00000000 5.95936591 0.00000000 0.00000000 0.29544958 +O 0.00000000 1.99946356 0.00000000 0.00000000 -0.29544958 0.00000000 +O 0.00000000 5.95936591 0.00000000 0.00000000 0.29544958 0.00000000 +O 1.99946356 0.00000000 0.00000000 -0.29544958 0.00000000 0.00000000 +O 5.95936591 0.00000000 0.00000000 0.29544958 0.00000000 0.00000000 +40 +Lattice="8.00504990114136 0.0 0.0 0.0 8.00504990114136 0.0 0.0 0.0 8.00504990114136" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29603.41522018245 pbc="T T T" +Ba 1.85456033 2.06728012 2.19363023 1.10147808 -2.78708225 -1.72573370 +Ba 6.13190024 5.84922992 2.01099021 0.63827225 3.19223875 -3.89249515 +Ba 5.75197017 2.17254973 5.72326966 3.65144651 -0.67368379 3.64339613 +Ba 2.13316969 6.03032016 6.14239006 -1.01796505 0.65092593 -0.99918442 +Ba 6.06755966 1.83276018 1.95056009 -0.27105521 1.37149122 1.19930315 +Ba 1.87523017 6.07561994 1.61761966 0.02836158 0.81537266 3.25482403 +Ba 2.27406977 2.05070967 6.14206986 -2.44141595 -0.33961033 -2.09543005 +Ba 5.93016978 5.97598028 6.20910015 0.28364024 -0.77172098 -1.17011805 +Ti 4.10093023 4.10207975 3.98789012 0.79808096 -0.29433655 -0.22944216 +Ti 7.83230813 3.56825980 7.88649271 2.02843610 2.25401955 -1.06463006 +Ti 4.02758956 0.46833384 7.92598322 1.66602651 -3.86249552 1.88224266 +Ti 7.82590889 7.94129048 3.98909968 1.31651460 0.00950100 2.94453121 +Ti 4.01729027 7.67171562 3.70297999 -0.31945494 7.53070537 3.27045376 +Ti 0.34822928 3.95019034 3.95245016 -3.50913235 1.28414673 3.06343676 +Ti 3.63781007 4.16543012 0.37263427 2.88706860 -3.69182929 -3.67185953 +Ti 7.77925066 7.88873813 7.76376089 0.90809153 -0.36082939 0.78267363 +O 3.90927012 4.13785032 2.03684973 -0.36134361 0.03849019 2.16566796 +O 3.75343021 4.06259004 5.75981992 1.04075171 0.64709550 1.70479463 +O 4.48237006 2.33571026 4.04682970 -2.53919114 -0.73362109 -3.88352020 +O 3.85205003 6.10939965 4.10837012 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0.08622703 0.01072282 0.03143032 -0.10758935 0.13514207 0.14525524 +Ba 0.02588398 0.02886034 4.01751984 0.10740912 0.03889513 -0.25678379 +Ba 7.91574891 4.04127275 0.06722994 0.47679617 -0.32338667 -0.27885028 +Ba -0.01301819 3.97268004 3.99210969 0.30383317 0.17960878 0.08196728 +O 2.03921995 3.95402979 2.03337042 -0.20564737 0.20115977 -0.05395460 +O 1.94602984 4.01676027 5.98853043 0.05815167 -0.15660949 -0.22355382 +O 1.94255980 7.92361998 2.03770002 -0.04560854 -0.14975185 -0.22830136 +O 1.98154690 0.03091998 5.99523001 0.14691772 -0.13524903 -0.08952144 +O 5.90697986 3.95684027 1.94649970 -0.15595618 0.49681375 0.46719130 +O 5.98446989 4.05412981 6.02708020 -0.19316467 -0.13737636 -0.36269241 +O 6.00869664 0.03026994 2.00304968 -0.25105203 -0.27526668 -0.04524473 +O 6.01061658 0.07215005 5.97699011 -0.45058429 0.10633723 0.17944320 +O 2.00571967 1.97884992 3.95100978 -0.27502319 0.23338006 0.55620572 +O 2.00421721 2.02059272 0.00130007 -0.00112409 -0.07859554 -0.12001395 +O 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2.04233996 2.06800012 0.22169106 -0.27667255 -0.11058160 +Ti 2.04073988 2.12847968 6.02501024 -0.16744361 -0.02228118 0.19967033 +Ti 2.11632028 5.98775023 2.02238012 -1.21864428 0.51922323 0.00106649 +Ti 1.99985982 6.08166975 5.98505008 -0.09311456 -0.27700937 0.05578934 +Ti 6.03684027 1.97581007 1.91927993 -0.29348191 0.05713068 0.56261754 +Ti 6.01917976 1.99189033 5.94827978 0.14029482 -0.03911779 -0.33354124 +Ti 6.01842019 5.95393009 2.05390013 0.27443467 0.29504052 -0.24828680 +Ti 5.96479975 5.96644984 6.02838027 0.45382979 0.06639720 0.23114603 +40 +Lattice="7.982289566 0.0 0.0 0.0 7.982289566 0.0 0.0 0.0 7.982289566" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.25813363395 stress="-0.0007308534616987636 -0.0 -0.0 -0.0 -0.0007308534616987636 -0.0 -0.0 -0.0 -0.0007308534616987636" pbc="T T T" +Ba 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.99114478 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.99114478 0.00000000 0.00000000 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5.82892016 6.20849017 6.09513974 0.17628897 0.32928221 -0.01411973 +O 1.93593987 2.03801972 3.92752011 0.04039794 -0.09569697 0.06401507 +O 2.00801994 2.07533001 7.95901980 -0.25761965 -0.03909748 0.05360647 +O 1.91492973 6.03517994 3.92031015 0.17313243 0.18337108 0.12286916 +O 2.02101018 6.13264024 7.95062962 -0.35636467 -0.17877574 -0.26778399 +O 5.92594002 2.06990988 3.92137968 -0.35963408 -0.17324093 -0.04797807 +O 5.84150971 2.09433985 7.92097986 -0.00872298 -0.11593053 0.64051733 +O 5.86783007 6.07243957 3.95128981 0.06460000 -0.00402686 -0.23840734 +O 5.82584020 6.12374025 7.95677005 0.11275521 -0.03865962 -0.13241001 +O 1.90786009 3.96920985 1.99060972 -0.00851935 0.23230791 -0.34574704 +O 1.98084989 4.03188011 5.97027007 -0.19831741 0.28420332 0.16698518 +O 1.98113988 8.00899994 1.97910996 -0.14235787 0.06081147 -0.08588873 +O 1.97851984 8.06966990 5.96389967 -0.01081175 -0.43310053 0.18753806 +O 5.84648006 3.99739019 1.97442960 0.27258244 0.20236664 -0.21148121 +O 5.85946016 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0.51175803 0.07438176 +Ti 3.95980004 3.93093003 6.07983032 -0.25638141 -0.07512198 -0.69486068 +O 7.78920976 1.95291030 1.96906966 0.34130752 -0.23715907 0.06555670 +O 1.94473018 7.81375014 1.84630995 0.37313135 0.06531065 0.65942086 +O 0.03112981 7.79397010 3.97506987 0.03565657 0.23621368 -0.15583122 +O 7.79120457 1.88719025 6.12591026 -0.05543247 0.53289044 -0.12453987 +O 1.94459026 0.01093393 6.04597016 0.25810790 -0.21950433 0.22800363 +O 7.80027032 7.75642048 8.08012985 -0.24821224 0.26760813 -0.79652442 +O 0.01254963 5.86952023 1.96148986 0.17944320 -0.63973058 0.30768032 +O 2.06414983 3.78616020 2.08744032 -1.70442362 0.28654790 0.06782184 +O 7.81285044 3.86359975 4.01219974 0.20153489 0.04547562 -0.04989843 +O 0.02987055 5.76217026 6.06257976 -0.22232766 0.27812317 0.10126316 +O 1.95378029 3.87451023 6.16470976 -0.50791937 -0.20868513 0.13466538 +O 7.81217196 3.91044024 8.17707038 0.21526638 -0.23775325 -0.69252972 +O 4.00311992 1.90494030 1.98047025 -0.60770054 -0.52299735 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0.05652622 0.12627433 +Ba 3.95892991 7.91147413 3.95964999 -0.00256236 0.09488528 0.07664381 +Ba 0.00657343 3.94941040 3.95172037 -0.07065829 0.23903752 0.22165686 +Ba 0.03488321 0.01182868 3.97199992 -0.20524062 -0.10095437 0.04170458 +Ba 7.92101978 3.96489020 7.91691634 0.09390671 0.09414866 0.14603995 +Ba 3.95942026 0.05245433 0.01791730 -0.16201498 -0.26879572 -0.02057422 +Ba 3.99417989 3.97021992 3.95852036 -0.15242759 -0.04466238 0.12330368 +Ba 0.01018731 0.02706290 0.04774884 0.10763615 -0.09512413 -0.17519908 +Ti 5.92909003 1.94735038 2.00008989 -0.24016340 0.33002449 0.06004966 +Ti 1.96541027 5.92320025 2.04548044 -0.02137667 0.33319157 -0.18511557 +Ti 1.95390004 2.02270001 5.98639007 0.15462563 -0.05009846 -0.08354671 +Ti 5.93417022 5.94532001 5.90593015 0.04796959 -0.08912498 -0.39541767 +Ti 1.97543043 5.98401039 6.01546033 0.12549092 -0.08633045 0.09945618 +Ti 5.91962994 1.96703977 5.96289985 -0.07962938 0.08066476 -0.13743318 +Ti 5.91100004 5.92350048 1.90110983 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0.17188699 0.21050779 +O 2.02310006 5.96437012 0.00051016 -0.19049149 -0.00776396 -0.55806360 +O 5.99129043 1.99721036 0.02341259 -0.14185239 -0.06354919 0.11063405 +O 2.02804003 2.01763012 0.03640972 -0.25504418 -0.21177791 -0.44942703 +O 5.93993009 0.03320698 5.96469015 0.09738645 -0.16416956 0.00752716 +O 5.93847012 0.02841039 1.97689991 0.22620000 -0.17401509 0.05280429 +O 1.98735021 0.03506303 5.95627018 -0.05866075 -0.30891650 0.04675885 +O 1.99376045 0.00323998 2.01391009 0.06618945 0.08986674 -0.20258545 +O 7.91076673 6.00882036 5.95414003 0.29761445 -0.24412856 0.06116294 +O 0.01437234 2.04208045 5.97351018 0.28610850 -0.32485940 -0.12665306 +O 0.05534971 5.94610030 1.98905021 -0.49088710 0.05737314 -0.23009342 +O 0.05234026 2.01631037 2.01248973 -0.32094875 -0.14943869 -0.04325161 +40 +Lattice="7.93033007932184 0.0 0.0 0.0 7.93033007932184 0.0 0.0 0.0 7.93033007932184" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.071065982313 pbc="T T T" +Ba 3.98912970 3.96967026 0.03721625 0.04798038 -0.02317490 -0.24354646 +Ba 3.95693018 0.00673126 3.96956003 0.08062928 0.02570795 0.03981533 +Ba 7.91629340 3.96347984 3.97157037 0.27344093 0.16541166 0.06530499 +Ba 0.01811843 0.01520244 3.96660043 0.03562263 -0.10022109 0.07183199 +Ba 7.92680584 3.98525970 0.02027072 -0.01983298 -0.11297144 -0.09487962 +Ba 3.93658968 0.00091992 7.91847027 0.34292217 0.10570525 0.17922389 +Ba 4.01068038 3.99366982 3.96716031 -0.26173702 -0.13080333 0.11654836 +Ba 0.01440148 0.01183998 0.02181792 -0.06286964 0.04915075 -0.12743879 +Ti 5.96416969 2.05506970 2.03502024 -0.14390464 -0.32154910 -0.41173723 +Ti 1.96444030 5.95804985 1.95255036 -0.36544298 0.05422637 0.21312517 +Ti 1.94032020 2.05585005 5.97606042 0.04363239 -0.26249549 -0.14444560 +Ti 5.91939029 6.00883013 5.95888016 0.12504072 -0.14409516 -0.02651424 +Ti 1.95680974 5.98103988 5.93377987 -0.18420669 0.21135856 -0.26684374 +Ti 5.90570967 2.01044018 5.98016040 0.08408690 0.16896004 0.42863504 +Ti 5.92295021 6.02424987 1.99204023 0.25856890 0.03508887 0.04607777 +Ti 2.00296981 1.99971996 2.00083021 -0.17811214 0.11617298 -0.07304221 +O 2.02226034 1.96244979 4.01236002 0.01761514 0.01587656 -0.33002397 +O 5.97980037 1.94157002 3.92794007 0.14979581 -0.03962301 0.18488032 +O 2.03154041 5.91257972 3.99287996 -0.12468693 0.05697513 -0.13783555 +O 5.99953975 5.93103994 3.97692968 0.03968729 0.03529456 -0.22671885 +O 2.00027033 3.92749994 1.94786036 0.24039943 0.30302688 0.39621831 +O 2.03576966 3.92385040 5.91888036 0.02952192 0.04382728 0.39698553 +O 6.00240974 3.92882034 2.02677032 -0.08600289 -0.00851781 -0.32513399 +O 5.98236979 3.90752026 5.91613013 -0.00642262 -0.06540861 0.13314715 +O 4.02000010 1.96543001 1.98492990 -0.04187453 0.04116696 0.06472367 +O 4.04194015 5.94253971 1.99978975 -0.42534094 -0.13930700 -0.06938636 +O 4.05416000 1.90703978 5.97229035 -0.49485405 0.30410288 -0.16266521 +O 4.03162993 5.91001981 5.93479971 -0.26421299 -0.00219984 0.23472758 +O 5.99192981 5.94853028 7.92049806 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energy=-29615.079420965616 pbc="T T T" +Ba 4.00207701 0.05370617 0.03268968 0.02227732 -0.19864009 -0.09071700 +Ba 3.99824380 0.05461038 4.00150009 0.06816534 0.00406209 0.09439137 +Ba 3.96156321 3.98627581 0.03560995 0.24211564 0.20946469 -0.07314788 +Ba 4.00950014 4.01669029 3.96683001 -0.07616790 -0.06786658 0.31796164 +Ba 0.03567573 0.06037565 0.02101015 0.21636116 -0.21984398 0.09213111 +Ba -0.01172707 7.92818004 3.98845988 0.21687769 0.32205407 0.08077969 +Ba 0.03043112 4.01754616 0.07403003 0.18379017 -0.01450231 -0.19490376 +Ba 0.02086513 3.97195020 3.99718029 0.11163241 0.23018084 0.02378142 +O 1.99114998 4.03329030 2.07646013 0.07361197 -0.30013233 -0.18476230 +O 1.98783980 4.04412029 6.03671971 -0.13004717 -0.15712166 -0.23927097 +O 1.99542381 0.06155010 2.00265991 0.07467538 -0.01789848 0.32703275 +O 1.99129342 0.07152977 5.98435996 -0.03150296 0.06149873 0.12614423 +O 5.93651971 4.04200993 2.03542012 0.06047337 -0.19409669 0.09260214 +O 5.93947010 4.03688022 6.01043008 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0.00414513 0.00366999 -0.15595515 +O 3.98703025 2.01463979 2.06333988 -0.10382783 0.20002154 -0.12188032 +O 3.96358006 2.05326987 6.00981036 -0.02675079 0.01719374 -0.06338052 +O 3.94987972 6.00165974 2.04584040 0.00899938 0.07217189 0.07373461 +O 3.92619971 5.99756976 6.03417031 0.01052095 0.03520663 -0.14465155 +Ti 2.02593972 2.04015992 2.00561030 -0.11977664 -0.33951032 -0.10097545 +Ti 2.05512031 2.02040981 5.96276972 -0.09027272 -0.06023683 -0.11779252 +Ti 2.06626015 6.00100039 1.98578015 -0.42577288 0.12226110 -0.33754162 +Ti 2.04287020 5.97778003 5.92371962 0.13434734 -0.06923544 0.36654315 +Ti 5.98500028 2.01555985 1.93895982 0.06017050 -0.09777931 0.42042370 +Ti 6.01770977 2.00107020 5.92516035 -0.03049123 -0.28191349 -0.13881103 +Ti 5.99614013 5.98458027 2.00734028 0.34938361 -0.13110518 -0.16536821 +Ti 6.01925035 5.92943972 5.98356035 -0.29685469 0.38537391 -0.11752821 +40 +Lattice="8.000280909 0.0 0.0 0.0 8.000280909 0.0 0.0 0.0 8.000280909" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.296664273214 stress="0.005767866138682956 -0.0 -0.0 -0.0 0.005767866138682956 -0.0 -0.0 -0.0 0.005767866138682956" pbc="T T T" +Ba 0.00000000 4.00014045 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 4.00014045 4.00014045 4.00014045 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 4.00014045 0.00000000 0.00000000 0.00000000 +Ba 4.00014045 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 4.00014045 4.00014045 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 4.00014045 4.00014045 0.00000000 0.00000000 0.00000000 +Ba 4.00014045 0.00000000 4.00014045 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 2.05854910 5.94173181 1.94159136 0.03635077 -0.03635077 -0.03635077 +Ti 1.94159136 2.05854910 5.94173181 -0.03635077 0.03635077 -0.03635077 +Ti 5.94173181 1.94159136 2.05854910 -0.03635077 -0.03635077 0.03635077 +Ti 6.05868955 6.05868955 6.05868955 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0.26642327 2.00894012 7.88824582 -0.73958348 1.03620214 0.49579148 +O 7.88279678 5.79131979 0.08645214 -0.24435482 1.46101035 -0.38402023 +O 1.99689012 7.81951766 7.72619879 -2.66159648 0.91271385 2.18038033 +O 6.15633006 0.35413300 0.08466461 -2.54922127 -1.21034039 -0.16979668 +40 +Lattice="7.92459009414283 0.0 0.0 -0.021721301448045495 7.924558395782453 0.0 -0.021721301448045495 0.021665829317386497 7.924526697422077" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.06712999169 pbc="T T T" +Ba 3.99702615 0.04622651 0.04127998 0.01856079 -0.07505436 0.07666567 +Ba 3.99301314 0.03439034 3.99116988 -0.03256456 -0.05534377 -0.08963868 +Ba 4.00616320 4.00329688 0.04478978 -0.07172581 -0.17481419 -0.07373307 +Ba 4.01486044 4.00578995 4.02545007 -0.24122758 0.04692829 -0.26262045 +Ba 0.04232999 0.05628678 0.05368038 0.05759477 -0.14689946 -0.12535696 +Ba 0.00780572 0.04782966 4.00958979 0.29114401 -0.08007778 -0.03169039 +Ba 0.03753403 3.99027677 0.00313021 -0.01376646 -0.00735053 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2.01412016 5.97029980 5.93699037 -0.35275767 -0.22579685 -0.29134687 +Ti 5.99066996 2.06246016 1.97295033 0.15026170 0.12456635 0.05368026 +Ti 5.98764990 2.08514033 5.92190036 0.14423452 -0.09406484 0.13715524 +Ti 6.02220983 6.03417992 2.01688980 -0.41930142 -0.15815215 0.04322050 +Ti 5.94551010 6.06775007 6.00176042 0.62132276 -0.15042830 -0.25548512 +40 +Lattice="7.916379909755224 0.0 0.0 -0.021698797332639068 7.916348244235585 0.0 -0.021698797332639068 0.021643382673270782 7.916316578715946" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.485589520595 pbc="T T T" +Ba 4.01337108 0.05906886 0.00370962 -0.42780174 -0.55012480 0.22285448 +Ba 4.00535020 0.08301037 3.89912980 -0.42157504 -0.46275563 0.83516938 +Ba 4.04373990 3.98880972 7.89547988 -0.68708618 0.61151760 0.62661846 +Ba 4.01016020 4.01396006 3.99964012 -0.46451735 0.16954188 0.00166787 +Ba 7.89211858 0.04377916 0.03889001 0.40415891 -0.03752448 0.10430991 +Ba 0.06635430 0.03393990 3.99446993 -0.13700303 0.02120826 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1.95387022 5.99848013 1.96341025 0.59812756 -0.20035013 0.19975852 +Ti 1.92330983 5.95168958 5.93233957 0.73000432 0.30060310 -0.30002177 +Ti 5.98745024 2.07820014 2.12362037 0.37209545 -0.12091435 -0.74474548 +Ti 5.83194958 1.94806989 6.06914966 0.50450932 0.45363464 -0.37998539 +Ti 5.94391965 6.02867954 2.07912002 -0.55189269 -0.16248883 -0.54376724 +Ti 5.93953002 5.91506999 5.98671006 -0.67492332 0.03375447 0.31441712 +40 +Lattice="7.770249740377227 0.0 0.0 0.0 8.033832152070303 0.0 0.0 0.06845590021272337 8.033529112330429" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.97390896073 pbc="T T T" +Ba 3.89363951 0.10161311 8.00398973 -0.19835572 -0.14252730 0.12432646 +Ba 3.86782985 0.09895646 4.00729961 0.14768134 -0.19415274 -0.07883517 +Ba 3.89271019 4.13572863 7.99590323 -0.12953089 -0.06620951 0.13888225 +Ba 3.90351006 4.08052023 4.00362973 -0.00977713 0.00361934 -0.04179842 +Ba 0.01877992 0.13143611 8.01890706 -0.11456861 -0.35426845 0.07292883 +Ba 0.00556972 0.05596212 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3.98978429 0.01744698 0.03498033 0.09778600 0.06159258 0.04245508 +Ba 3.98782223 0.03519983 3.99553972 -0.01261563 0.15836916 -0.00129609 +Ba 4.01203261 3.98896729 0.05145974 0.03750751 0.00758424 -0.05068107 +Ba 3.99401984 4.01277036 3.99396040 -0.03352384 -0.16918553 -0.01117453 +Ba 0.02921459 0.05857737 0.05445989 0.09813747 -0.20348585 -0.27518286 +Ba 0.05407794 0.04677964 3.99463001 -0.02969161 0.04753481 0.10229648 +Ba 0.04475022 4.02770691 0.02917972 -0.17858111 -0.15687432 -0.02603576 +Ba 0.00002219 4.01392018 3.99266002 0.21010875 -0.07304016 0.02895371 +O 1.93558970 4.01712002 2.00662014 0.20634697 -0.12520861 0.04685218 +O 2.00575005 3.98058019 5.96468020 -0.10616008 0.18301575 -0.00940690 +O 1.99782256 0.03135020 1.98855982 0.02220302 0.26417648 0.04584894 +O 1.97754264 0.02880966 5.98153998 -0.02676493 -0.08154305 0.01571510 +O 5.97953989 3.99004975 2.02908004 -0.10060290 -0.12673842 0.04745022 +O 5.92168046 3.95983036 6.00884006 -0.05896362 0.28897425 -0.01159002 +O 5.93377218 0.02050973 2.07254969 0.09372854 -0.05183087 -0.14626183 +O 5.91133209 0.02684997 6.00617036 0.26543323 -0.31748599 -0.12224284 +O 1.97646968 2.02828998 3.99813018 -0.00765597 -0.07008596 -0.09933457 +O 1.98667225 2.03226720 0.03605011 0.08681921 -0.09104122 0.01281206 +O 1.99612041 5.98074993 3.97583986 -0.04962152 -0.02480523 -0.03276537 +O 1.98093028 5.95578991 7.91660985 -0.13241875 0.14061517 0.06658951 +O 5.97958030 2.03955044 4.03116033 -0.18048553 -0.18818650 -0.18808494 +O 5.92556259 1.97704737 0.08629030 0.15633284 0.05584796 -0.11895106 +O 5.93960052 5.96449002 4.00935974 -0.09348480 0.03499477 0.07491475 +O 5.96157228 5.94594711 0.05652972 -0.03609289 0.20650432 0.04116696 +O -0.00796315 2.00268017 1.98080983 0.07355772 -0.03303713 0.22794989 +O 7.89829041 2.03080992 5.98281025 0.09383909 -0.08718585 0.16710551 +O 0.00393997 6.01734999 2.01826017 -0.13053851 -0.10294260 -0.00969923 +O 7.87912465 5.95367015 5.92735031 0.23023612 0.10922689 0.24867041 +O 3.94885042 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energy=-29614.700807484896 pbc="T T T" +Ba 4.00574971 3.95292021 7.91031883 -0.40880257 0.23389557 0.34153660 +Ba 3.90619994 0.04203088 4.00432037 0.73231806 -0.22844020 -0.06717984 +Ba 7.91821038 3.96774036 3.96140983 0.16697618 0.16473135 0.02505797 +Ba 0.04632764 0.01981810 3.95384984 -0.42721527 -0.24973099 0.14270702 +Ba 7.91934307 3.95274016 0.05249398 0.39363487 0.15041313 -0.26251375 +Ba 3.93999026 0.06553181 0.00443557 0.25712831 -0.43767143 0.04792639 +Ba 4.01104036 3.99454973 3.97196019 -0.13294686 -0.10209542 -0.02019704 +Ba 0.02687600 7.88227128 7.92597343 -0.07670989 0.33716084 0.09988890 +Ti 5.95634991 2.04163021 1.90007970 -0.06339286 -0.40571854 0.73831876 +Ti 1.98744989 5.95972022 1.95342003 0.12528729 0.24946566 0.35775255 +Ti 1.98963992 2.02728043 5.99391031 0.48941977 -0.28152320 0.66713391 +Ti 5.96570016 5.88070005 6.00892004 0.02853410 1.18491295 0.13893522 +Ti 2.01035037 5.95844000 5.94804035 -0.13245166 0.33466610 -0.56186832 +Ti 5.98830001 1.94563001 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0.0 0.0 0.0 7.955252515" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.181445967708 stress="-0.001369891161877582 -0.0 -0.0 -0.0 -0.001369891161877582 -0.0 -0.0 -0.0 -0.001369891161877582" pbc="T T T" +Ba 3.97762626 3.97762626 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.97762626 3.97762626 0.00000000 0.00000000 0.00000000 +Ba 3.97762626 0.00000000 3.97762626 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 3.97762626 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.97762626 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.97762626 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.97762626 3.97762626 3.97762626 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 1.95210113 6.00315139 1.95210113 0.01016383 -0.01016383 0.01016383 +Ti 6.00315139 1.95210113 1.95210113 -0.01016383 0.01016383 0.01016383 +Ti 1.95210113 1.95210113 6.00315139 0.01016383 0.01016383 -0.01016383 +Ti 6.00315139 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energy=-29614.87917225569 pbc="T T T" +Ba 1.95066004 1.95890019 0.00240566 0.09117029 0.00732276 -0.04150686 +Ba 1.98652967 1.96164012 4.08136028 -0.28086680 -0.02362844 0.05342675 +Ba 1.90673969 5.86698007 0.04581403 0.35729232 0.09702829 -0.45834156 +Ba 1.96585022 5.84044969 4.16176009 -0.14609677 0.20718721 -0.17921900 +Ba 5.89145002 1.95564985 0.05854924 -0.30215399 -0.02845568 -0.39036956 +Ba 5.90474965 1.94657988 4.09817016 -0.22433389 0.01812679 -0.03793303 +Ba 5.81765971 5.88521001 0.01317438 0.27861759 0.07183071 -0.28922648 +Ba 5.91633017 5.87931994 4.13012013 -0.29866166 -0.02291984 -0.06445061 +Ti 0.01709483 7.79936005 2.10322029 -0.38664249 0.24076916 0.14309732 +Ti 7.80080361 0.00543994 6.22020987 0.31455545 -0.16506302 0.32584285 +Ti 7.79178140 3.90314017 2.10697008 0.28024665 -0.13667933 0.12848060 +Ti 0.00050023 3.88243019 6.26453964 -0.16626759 0.25774846 -0.44507416 +Ti 3.89545975 7.81797751 2.12737005 0.36065353 0.20493261 0.09602556 +Ti 3.89793978 0.02264985 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0.02169494557345022 7.935176303542661" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.17645580808 pbc="T T T" +Ba 4.00587410 0.04124738 0.02315027 0.05617243 -0.00982187 -0.00087675 +Ba 3.97947197 0.06393026 3.99444021 0.07722925 -0.12224721 0.16704380 +Ba 4.01848240 3.99353718 0.04408978 -0.14970120 0.10464750 -0.00431405 +Ba 3.99547973 3.99997980 4.01269999 -0.12717345 0.15013211 -0.04365348 +Ba 0.05693455 0.04511739 0.04513009 -0.11846435 -0.02079637 -0.12157461 +Ba 0.04710914 0.02277017 4.00524959 -0.11493474 0.23190631 0.08540253 +Ba 0.02747974 4.00798725 0.03166002 0.05105157 -0.02941162 0.13655437 +Ba 0.02430167 4.01698026 3.99306027 -0.01717471 -0.04756978 0.03131449 +O 2.03483989 3.95328012 2.00133016 0.01430819 0.25005110 -0.11516382 +O 2.05020013 3.95725012 5.99928965 -0.06205512 0.38524510 -0.24085195 +O 2.05920187 0.01597999 1.97399009 0.07304890 -0.23706008 0.13914913 +O 2.02161025 7.93638960 5.94531970 0.02899536 -0.18555292 0.07352352 +O 5.98790020 3.97599951 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0.0 0.0 7.826310244652992 0.0 0.0 0.0 8.209729009848788" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29613.401546627923 pbc="T T T" +Ba 1.99925991 2.04008038 8.19833468 -0.04130452 -1.10345166 -0.25803103 +Ba 1.81202013 1.97569019 4.05557049 0.99550595 -0.19859484 0.61386271 +Ba 1.99825971 5.84520033 0.03421115 0.01097912 0.82350146 -0.42658818 +Ba 1.92709037 5.82708008 4.24130996 0.46850976 0.25466134 -0.65366930 +Ba 5.81124980 1.86600993 0.03232266 0.67112220 0.25216043 -0.26450507 +Ba 5.86650042 2.00355968 4.13706977 0.32491828 -0.42917677 -0.18898328 +Ba 5.85321995 5.82897013 0.02179158 0.23183817 0.63780970 -0.33441593 +Ba 5.89811010 5.92648048 4.04765026 -0.18586608 -0.34367139 0.41976216 +Ti 0.04940515 7.77195809 2.22149034 -0.51428002 0.09202955 -2.19761520 +Ti 0.02383111 7.80296906 6.29402983 0.06883949 0.68442586 0.46079979 +Ti 0.10327990 3.87897997 1.99784022 -0.31380468 0.52467834 1.19791656 +Ti 0.03268972 3.89913977 6.22385053 -0.82552286 -0.41895612 -1.13239816 +Ti 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2.06760964 6.00085968 0.16636169 -0.03567277 -0.08494539 +O 4.00850953 6.03379992 2.03212993 -0.02162221 -0.15255306 0.00343525 +O 3.99593974 6.00820949 6.00401005 0.10338971 0.14209690 -0.05406439 +Ti 1.96662977 2.00069990 2.04126014 0.11955733 -0.27870398 -0.17809517 +Ti 1.97054001 2.00569961 6.00019015 0.01310028 0.10376330 0.00358797 +Ti 1.99322965 5.95523000 1.97898009 0.08475204 0.08449622 0.06920638 +Ti 1.97711966 5.96889007 5.96165990 -0.14204137 -0.27000388 -0.11583411 +Ti 5.94659025 1.97361986 2.00071020 -0.04401394 -0.04905562 -0.05275672 +Ti 5.95043947 2.03040024 5.96417956 -0.09270447 -0.10422661 -0.09760293 +Ti 5.96455989 5.94329963 1.94384029 -0.16590120 0.08831945 0.10097236 +Ti 5.93565983 5.98542001 5.91427993 0.05817249 -0.10407286 0.18829783 +40 +Lattice="7.955129969191328 0.0 0.0 0.0 7.955129969191328 0.0 0.0 0.0 7.955129969191328" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29602.27037957509 pbc="T T T" +Ba 2.12622009 6.16595998 5.89977020 -0.46336833 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-0.0 9.181576151994517e-07 -0.0 -0.0 -0.0 9.181576151994517e-07" pbc="T T T" +Ba 1.98878317 1.98878317 5.96634952 0.00000000 0.00000000 0.00000000 +Ba 5.96634952 1.98878317 1.98878317 0.00000000 0.00000000 0.00000000 +Ba 1.98878317 5.96634952 1.98878317 0.00000000 0.00000000 0.00000000 +Ba 5.96634952 5.96634952 1.98878317 0.00000000 0.00000000 0.00000000 +Ba 5.96634952 1.98878317 5.96634952 0.00000000 0.00000000 0.00000000 +Ba 1.98878317 5.96634952 5.96634952 0.00000000 0.00000000 0.00000000 +Ba 1.98878317 1.98878317 1.98878317 0.00000000 0.00000000 0.00000000 +Ba 5.96634952 5.96634952 5.96634952 0.00000000 0.00000000 0.00000000 +Ti 0.00000000 3.97756635 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 3.97756635 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 3.97756635 3.97756635 3.97756635 0.00000000 0.00000000 0.00000000 +Ti 0.00000000 0.00000000 3.97756635 0.00000000 0.00000000 0.00000000 +Ti 0.00000000 3.97756635 3.97756635 0.00000000 0.00000000 0.00000000 +Ti 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7.912710065815292" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.084315885397 pbc="T T T" +Ba 3.95530976 3.96112007 0.00320069 0.02705212 0.02430567 0.05526329 +Ba 3.97980989 0.01145919 3.96732996 -0.00953828 -0.05824680 0.00567828 +Ba 7.90911453 3.95809979 3.95613031 0.11609019 0.08833693 0.11475708 +Ba 0.01471527 0.01882592 3.96605997 -0.08939083 -0.14117979 0.03528608 +Ba 0.01247201 3.97524030 0.00891129 0.05402042 -0.04349921 -0.05987251 +Ba 3.95588977 7.91048818 0.01693636 0.07152063 0.04797216 -0.09318038 +Ba 3.97082975 3.96123005 3.96798988 -0.02904652 0.03965824 -0.02503252 +Ba 0.00525325 0.03532709 0.02116492 0.06067032 -0.23678420 -0.15273124 +Ti 5.96239004 2.02067985 1.97756982 -0.12719427 -0.08833591 0.16979977 +Ti 1.96237979 5.92484977 1.98112025 0.09344057 -0.21741737 0.01572255 +Ti 1.97629983 1.96830008 5.89222012 0.04692752 0.09332899 0.11434621 +Ti 5.93878009 5.92346979 5.92738025 0.21465240 0.03806672 -0.13624404 +Ti 1.98993976 5.92881008 5.93169030 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0.0 0.0 0.0 7.954637305210351" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29609.432528191526 stress="-0.0032723137405708458 -0.0 -0.0 -0.0 -0.0032723137405708458 -0.0 -0.0 -0.0 -0.0032723137405708458" pbc="T T T" +Ba 3.97731865 3.97731865 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.97731865 0.00000000 3.97731865 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.97731865 3.97731865 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 3.97731865 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.97731865 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.97731865 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.97731865 3.97731865 3.97731865 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 6.07734290 1.87729440 1.87729440 -0.78861005 0.78861005 0.78861005 +Ti 1.87729440 6.07734290 1.87729440 0.78861005 -0.78861005 0.78861005 +Ti 1.87729440 1.87729440 6.07734290 0.78861005 0.78861005 -0.78861005 +Ti 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3.87390837 6.07734290 1.87729440 0.79353808 -1.39425319 1.39425319 +O 3.87390837 1.87729440 6.07734290 0.79353808 1.39425319 -1.39425319 +O 4.08072894 6.07734290 6.07734290 -0.79353808 -1.39425319 -1.39425319 +O 5.85461306 5.85461306 0.10341028 1.39425242 1.39425242 -0.79352625 +O 2.10002425 5.85461306 -0.10341028 -1.39425242 1.39425242 0.79352625 +O 5.85461306 2.10002425 -0.10341028 1.39425242 -1.39425242 0.79352625 +O 2.10002425 2.10002425 0.10341028 -1.39425242 -1.39425242 -0.79352625 +O 5.85461306 0.10341028 5.85461306 1.39425242 -0.79352625 1.39425242 +O 5.85461306 -0.10341028 2.10002425 1.39425242 0.79352625 -1.39425242 +O 2.10002425 -0.10341028 5.85461306 -1.39425242 0.79352625 1.39425242 +O 2.10002425 0.10341028 2.10002425 -1.39425242 -0.79352625 -1.39425242 +O 0.10341028 5.85461306 5.85461306 -0.79352625 1.39425242 1.39425242 +O -0.10341028 2.10002425 5.85461306 0.79352625 -1.39425242 1.39425242 +O -0.10341028 5.85461306 2.10002425 0.79352625 1.39425242 -1.39425242 +O 0.10341028 2.10002425 2.10002425 -0.79352625 -1.39425242 -1.39425242 +40 +Lattice="7.938300017256853 0.0 0.0 0.0 7.938300017256853 0.0 0.0 0.0 7.938300017256853" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.124951869442 pbc="T T T" +Ba 3.95451020 3.99493996 0.00611487 0.13601444 -0.22018927 0.00014141 +Ba 3.96707017 0.00247357 3.97512040 0.19574914 0.17512992 -0.00088497 +Ba 7.93299803 3.97692002 3.97961983 0.11040497 0.05272433 0.08666032 +Ba 0.01849465 7.91405407 3.96968029 -0.16313418 0.21609762 0.10547282 +Ba 7.93557242 3.96688997 0.00302926 0.11343244 0.07480676 -0.02725626 +Ba 3.98135991 0.03253750 0.02069674 -0.00746417 -0.01883359 -0.02828059 +Ba 3.99505983 4.00828980 3.96228973 -0.05961360 -0.30602478 0.18358962 +Ba 0.04157129 7.93625511 0.02378553 -0.23700583 0.10546280 -0.11101021 +Ti 6.00670999 2.01349979 2.02933987 -0.09770012 -0.11169309 -0.28645689 +Ti 2.02011001 6.00022996 1.98963964 0.06790283 0.13520197 -0.43901304 +Ti 1.99698971 2.02136982 5.94073002 0.29907123 0.12322243 -0.00820722 +Ti 5.95121969 5.99738011 5.93247021 0.19340764 0.10318608 -0.02401153 +Ti 1.99780974 6.00950983 5.93150015 -0.24388713 -0.01163604 0.30611786 +Ti 5.98678962 2.01908994 5.97361998 -0.10669435 0.04923637 0.25989328 +Ti 5.99461996 5.97778997 1.94679028 0.03032153 0.27937273 0.08173691 +Ti 2.01535021 2.04532999 2.00477004 0.20605746 -0.09075531 -0.27861631 +O 1.97806004 1.94498988 3.99860031 -0.08610624 0.07189833 -0.00275519 +O 5.98274982 1.95374027 3.98202990 -0.26620328 0.07209296 -0.04337374 +O 2.03196983 5.93617026 4.01640988 -0.14831023 -0.04089880 -0.08434812 +O 5.95096010 5.93910981 3.98927995 -0.06804425 0.00483419 0.18348086 +O 1.96128006 3.94304967 2.02511987 -0.02015899 0.10598627 0.01301570 +O 1.98986032 3.90446001 5.96998980 -0.07584266 0.21270556 0.09735174 +O 5.96370981 3.94366965 2.01287028 -0.08820941 0.08944379 -0.11260661 +O 5.93590035 3.94357995 5.97660002 0.12835667 -0.19709100 -0.06282593 +O 3.94135008 1.98385976 2.00167966 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5.94229045 1.99923017 -0.13605661 0.06798202 0.10653623 +O 4.00441979 5.97322003 6.00318039 0.00300459 -0.02704569 -0.21609685 +Ti 1.98162976 2.07501003 2.05752998 0.16451872 -0.23786278 -0.06018541 +Ti 1.97890026 2.06048991 6.02730008 -0.06335635 -0.07675360 -0.00980027 +Ti 1.97710990 6.00982004 1.96366986 -0.22065207 0.21683193 -0.09246278 +Ti 1.97141968 5.99863043 5.93954036 -0.05269733 0.21184527 0.15418006 +Ti 5.94412041 2.04310013 2.02070984 -0.17813683 0.15866149 0.18968931 +Ti 5.92880052 2.05116986 5.97673029 0.02911800 -0.05285211 -0.00290663 +Ti 5.92742983 6.01694984 2.04628020 0.22118583 -0.10886925 -0.04914304 +Ti 5.94430016 6.00375052 6.00264035 -0.04402834 0.19760188 0.10809612 +40 +Lattice="7.920910195835939 0.0 0.0 -0.021711214846786307 7.920878512195156 0.0 -0.021711214846786307 0.021655768475415456 7.920846828554372" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.63321848908 pbc="T T T" +Ba 3.97651554 0.02165656 0.06848973 0.40538635 0.20858871 -0.30545271 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3.95695017 0.02433196 0.42331131 0.35666214 -0.13602627 +Ba 3.94501010 0.06944886 4.00853984 0.37907137 -0.48550964 -0.13974511 +Ba 0.04739991 4.00225002 3.98563973 -0.22763570 -0.18268459 -0.16167354 +Ba 0.00161959 0.01261383 4.04288999 0.10724920 0.19329605 -0.58784186 +Ba 0.01591505 3.98945005 0.03182453 -0.21893021 -0.04627780 0.04795647 +Ba 3.98945005 7.93407832 7.90183219 0.22310722 -0.00791257 0.35797289 +Ba 3.94191014 3.96206984 3.96702007 0.63604053 0.37305216 0.14042080 +Ba 0.00460182 7.94036177 7.94951847 -0.13255322 0.27056438 0.31442201 +Ti 6.00618027 1.98329009 2.03818018 0.18251259 0.79953338 -0.06164914 +Ti 1.99840012 5.97221990 1.97082024 -0.38680704 0.01353840 0.04253839 +Ti 1.99176029 1.95879028 5.99800996 -0.42445776 0.59049292 -0.91460593 +Ti 6.08294988 5.97628000 6.02012016 -0.95242994 0.11101458 -0.16833372 +Ti 2.04907976 5.95945970 5.94777975 0.61696783 -0.91089043 0.15171128 +Ti 5.94954968 2.02407961 5.99200015 0.16197384 0.29206575 0.24539534 +Ti 5.94281997 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energy=-29614.250034992503 pbc="T T T" +Ba 3.85688974 0.15859383 8.04967679 0.49624605 -0.62185421 0.51786928 +Ba 4.04396979 0.06158791 4.01533035 -0.77964950 -0.01632496 -0.34942012 +Ba 3.87950971 4.13388523 8.07934345 -0.07193870 0.42313210 0.04645315 +Ba 3.92024988 4.11840031 4.03974990 -0.28961420 -0.04658685 -0.18485820 +Ba 7.80637008 0.00272440 0.02649432 -0.07738943 -0.00863094 -0.37136603 +Ba 7.80902021 0.12454466 4.08354985 0.13554856 -0.49179701 -0.17952394 +Ba 7.76334172 4.11753491 7.99157861 0.48110508 0.31874172 0.06309847 +Ba 0.01545131 4.04304029 4.02911965 -0.00059084 0.72344544 0.12513790 +Ti 1.89208993 1.96833020 2.08007994 0.80433954 -0.00000514 0.47167762 +Ti 1.99288031 2.09331030 6.14566984 -0.55315073 -0.32079089 -0.86707754 +Ti 1.83480009 6.02663027 1.94000032 1.04795722 0.33251871 -0.43169593 +Ti 2.04573996 6.15657996 5.95800973 -0.81428020 -0.35319656 0.14133611 +Ti 5.84754988 2.06083010 2.04743011 -0.24062595 -1.20209511 -0.12042379 +Ti 5.86301995 2.09177963 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0.02172398081036664 7.945796275976648" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29613.593611105982 pbc="T T T" +Ba 4.03263273 0.06142865 0.02645018 -0.16282899 0.21425208 -0.40067943 +Ba 3.99763122 0.11188009 4.02233966 0.03537967 -0.50212411 0.12300800 +Ba 4.09369110 3.86320793 0.01044007 -0.66792092 0.73220236 0.30274251 +Ba 3.97608999 4.03038008 4.12890000 -0.05696845 0.15997455 -0.87762781 +Ba 0.02660671 7.96593983 7.90245956 -0.50731645 0.98636105 0.31778321 +Ba 0.05516413 7.88112969 4.00054973 -0.39209760 0.88499325 -0.10879289 +Ba 7.92597692 4.10688838 0.14879020 0.39261157 -1.31371030 -1.35099644 +Ba 0.00631696 4.04497980 3.97072018 0.08026701 -0.11679879 0.33608278 +O 2.14260031 4.04692018 1.99625982 -0.62691543 0.67302225 0.10991209 +O 1.91593036 4.05288990 6.12472995 0.09233783 0.10099602 -0.97691173 +O 1.85113108 0.09258993 1.88755966 0.24314357 -0.68317553 0.70404826 +O 1.97861127 0.12037024 5.93680957 -0.07994820 -0.79928501 0.35462095 +O 5.79139001 4.00820954 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2.05502114 6.04682536 5.92858728 0.00089963 0.00089963 -0.00089963 +Ti 1.93678307 1.93678307 1.93678307 -0.00089963 -0.00089963 -0.00089963 +O 6.01089230 1.99605175 3.95104229 -0.00073688 -0.00083895 -0.00075051 +O 1.97271613 5.98785596 0.04076192 0.00073688 -0.00083895 0.00075051 +O 2.01908809 1.99575246 4.03256613 -0.00073688 0.00083895 0.00075051 +O 5.96452034 5.98755667 -0.04076192 0.00073688 0.00083895 -0.00075051 +O 1.99605175 3.95104229 6.01089230 -0.00083895 -0.00075051 -0.00073688 +O 5.98785596 0.04076192 1.97271613 -0.00083895 0.00075051 0.00073688 +O 1.99575246 4.03256613 2.01908809 0.00083895 0.00075051 -0.00073688 +O 5.98755667 -0.04076192 5.96452034 0.00083895 -0.00075051 0.00073688 +O 3.95104229 6.01089230 1.99605175 -0.00075051 -0.00073688 -0.00083895 +O 0.04076192 1.97271613 5.98785596 0.00075051 0.00073688 -0.00083895 +O 4.03256613 2.01908809 1.99575246 0.00075051 -0.00073688 0.00083895 +O -0.04076192 5.96452034 5.98755667 -0.00075051 0.00073688 0.00083895 +O 1.97271613 5.98755667 4.03256613 0.00073688 0.00083895 0.00075051 +O 6.01089230 1.99575246 -0.04076192 -0.00073688 0.00083895 -0.00075051 +O 5.96452034 5.98785596 3.95104229 0.00073688 -0.00083895 -0.00075051 +O 2.01908809 1.99605175 0.04076192 -0.00073688 -0.00083895 0.00075051 +O 5.98755667 4.03256613 1.97271613 0.00083895 0.00075051 0.00073688 +O 1.99575246 -0.04076192 6.01089230 0.00083895 -0.00075051 -0.00073688 +O 5.98785596 3.95104229 5.96452034 -0.00083895 -0.00075051 0.00073688 +O 1.99605175 0.04076192 2.01908809 -0.00083895 0.00075051 -0.00073688 +O 4.03256613 1.97271613 5.98755667 0.00075051 0.00073688 0.00083895 +O -0.04076192 6.01089230 1.99575246 -0.00075051 -0.00073688 0.00083895 +O 3.95104229 5.96452034 5.98785596 -0.00075051 0.00073688 -0.00083895 +O 0.04076192 2.01908809 1.99605175 0.00075051 -0.00073688 -0.00083895 +40 +Lattice="7.984075962488268 0.0 0.0 0.0 7.984075962488268 0.0 0.0 0.0 7.984075962488268" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.326871222278 stress="-8.630681582874845e-05 -0.0 -0.0 -0.0 -8.630681582874845e-05 -0.0 -0.0 -0.0 -8.630681582874845e-05" pbc="T T T" +Ba -0.00122635 3.99081163 0.00122635 0.01029110 0.01029110 -0.01029110 +Ba 3.99326434 3.99326434 3.99326434 -0.01029110 -0.01029110 -0.01029110 +Ba 0.00122635 -0.00122635 3.99081163 -0.01029110 0.01029110 0.01029110 +Ba 3.99081163 0.00122635 -0.00122635 0.01029110 -0.01029110 0.01029110 +Ba 3.99227990 3.99179606 -0.00024192 -0.00629997 0.00629997 0.00629997 +Ba -0.00024192 3.99227990 3.99179606 0.00629997 -0.00629997 0.00629997 +Ba 3.99179606 -0.00024192 3.99227990 0.00629997 0.00629997 -0.00629997 +Ba 0.00024192 0.00024192 0.00024192 -0.00629997 -0.00629997 -0.00629997 +Ti 5.92872411 1.93668613 2.05535185 -0.01174711 -0.01174711 0.01174711 +Ti 6.04738983 6.04738983 6.04738983 0.01174711 0.01174711 0.01174711 +Ti 2.05535185 5.92872411 1.93668613 0.01174711 -0.01174711 -0.01174711 +Ti 1.93668613 2.05535185 5.92872411 -0.01174711 0.01174711 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+40 +Lattice="7.931780024872729 0.0 0.0 0.0 7.931780024872729 0.0 0.0 0.0 7.931780024872729" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.92286312574 pbc="T T T" +Ba 3.99107024 3.97563024 0.00113662 -0.18424808 0.18870792 0.04065865 +Ba 3.94315991 0.00699662 3.97250988 0.08926664 -0.00721657 0.06938713 +Ba 0.02016576 3.92656980 3.95393999 -0.16120328 0.38104700 0.10001797 +Ba 7.89905667 0.03754429 3.98045038 0.25582476 -0.21879291 -0.18621163 +Ba 0.05348399 3.97469032 0.01614752 -0.30021897 0.08141090 -0.02163532 +Ba 3.96598995 0.02221295 0.03288437 -0.12778383 -0.26385123 -0.25042905 +Ba 4.02819970 3.99097030 4.01026039 -0.41581680 -0.12052715 -0.22743901 +Ba 0.01793931 0.00914693 7.92058749 0.04551521 -0.07477668 0.24386065 +Ti 5.94816002 1.93257979 1.94722027 0.42012186 -0.03262653 0.11914363 +Ti 1.92108981 5.99099005 2.00971000 0.29734422 0.01265008 -0.22299281 +Ti 2.02885018 1.99912029 5.97968012 0.28901771 -0.34605686 0.05332982 +Ti 5.92299011 5.98746993 5.94406009 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-0.02384441 +40 +Lattice="7.767749907244965 0.0 0.0 0.0 8.031239751848622 0.0 0.0 0.06843387668282815 8.030936809602238" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.294779079166 pbc="T T T" +Ba 3.90201032 0.06640805 0.01580349 -0.14257693 -0.14895352 -0.35199585 +Ba 3.87157006 0.08926154 4.02040015 0.16666688 -0.16917936 -0.24418358 +Ba 3.87855016 4.14811672 8.01423382 0.08012792 -0.00356946 0.04542522 +Ba 3.87785029 4.10445963 4.02828985 0.16682063 0.04793153 -0.36567129 +Ba 0.07012026 0.07083877 7.90929773 -0.55095501 0.25610373 0.86258711 +Ba 0.02489020 0.03568194 4.05923968 -0.19243653 0.32084128 -0.59550374 +Ba 7.72908282 4.04282642 7.96780753 0.30754765 0.59193762 0.30844136 +Ba 7.71159296 4.07817978 4.07150029 0.27144447 0.14359148 -0.69742639 +Ti 1.93273968 2.17098978 2.03336001 -0.26535970 -0.11885259 -0.12743056 +Ti 2.01405016 2.04624981 6.00942961 -0.54761463 -0.24594993 0.09061185 +Ti 1.95745977 6.17020028 1.95631014 -0.07619233 -0.16732328 -0.26478609 +Ti 1.95746987 6.03437030 5.95476019 -0.00862837 0.09596617 0.06388266 +Ti 5.82970019 2.12100975 1.98213015 0.26407158 0.38641341 0.08392826 +Ti 5.86345029 2.06853005 5.98538998 0.21292488 0.25279472 0.07203100 +Ti 5.85846028 6.16267955 1.93489990 -0.16735670 -0.35118750 -0.05201779 +Ti 5.84642959 6.11064961 5.96196011 -0.24198580 -0.15745770 0.31907082 +O 1.91245032 1.98080963 4.03469980 0.49892257 0.60280953 -0.29167983 +O 1.96903993 2.03041992 8.02607964 -0.33977565 0.68780481 0.25239877 +O 1.84883012 6.09674999 4.05613957 0.30483642 -0.01730867 0.07143579 +O 1.90843983 6.08620372 0.02166037 0.28016000 -0.32969307 0.08371383 +O 5.83370990 2.17128029 4.01130023 -0.43578707 -0.66771883 -0.46748363 +O 5.90210028 2.11671962 7.97173956 -0.37966246 -0.12417837 0.70069477 +O 5.75710979 6.09559027 4.00933033 0.43328385 0.03781990 0.04078515 +O 5.74871984 6.14752001 7.95185024 0.19156544 -0.11438272 0.54111566 +O 1.87345000 4.06756981 2.01183014 0.15432404 -1.07301854 0.07725368 +O 1.93683018 4.09306978 5.95902002 0.16680083 0.15708978 0.43933802 +O 1.92479017 8.01988019 2.06064035 0.06907989 0.30398333 -0.26787244 +O 1.89707018 0.13030012 6.07158015 0.42794881 0.05004087 -0.52485240 +O 5.83090031 4.08507987 1.96520033 -0.12172888 -0.77040638 -0.14589339 +O 5.82448958 4.08181975 6.02241030 -0.19552597 0.73148656 -0.11213866 +O 5.73171002 0.03042006 1.88428990 0.41667606 0.09171408 0.69880630 +O 5.87405016 0.07327008 5.94573018 -0.29386964 0.13596842 0.17698574 +O 7.74267095 2.01270012 2.11948028 0.25092887 0.06702172 -0.66545189 +O 7.74215906 2.15505968 5.95829995 0.70053897 -0.32308637 0.29876476 +O 7.71101271 6.07240975 1.98625016 -0.08090593 0.13445224 0.02265142 +O 0.01366969 6.11515024 6.07682028 -0.58388776 -0.17355589 -0.29348885 +O 3.87777028 2.06888970 1.98033036 -0.22222765 0.06469384 0.19153382 +O 3.92679022 2.11109965 6.02481985 -0.85832859 -0.16955860 -0.06773906 +O 3.83213009 6.02944011 2.04014980 0.13926817 0.04898800 -0.10373681 +O 3.84166034 6.14528989 5.97180030 0.20086795 -0.08407147 0.19789678 +40 +Lattice="7.955180241026122 0.0 0.0 0.0 7.955180241026122 0.0 0.0 0.0 7.955180241026122" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29607.22898951048 pbc="T T T" +Ba 3.98228049 3.90715018 4.01893001 0.69947144 0.34661736 -0.04245611 +Ba 4.20105034 7.89111638 4.05831054 -0.61075399 -0.00471129 -0.49047290 +Ba 7.84040847 3.96856020 4.10105054 -0.04488940 -0.26578650 -1.37899627 +Ba 3.75288969 4.02911980 7.73342402 1.84091449 0.94056302 1.09291939 +Ba 7.92165711 7.88244364 3.89251026 -0.92343278 -0.04492669 -0.46510356 +Ba 0.17524228 4.18690046 0.03563443 -0.82019425 -0.63061447 -0.05530083 +Ba 3.91535038 7.91822604 7.89315927 0.30315260 -0.40712930 0.69591406 +Ba 0.08527317 0.09126501 0.21210022 -1.26112661 -3.40844204 -2.55392279 +Ti 5.44868035 1.82821020 1.99629998 4.83697704 2.28549602 0.11838490 +Ti 2.17486991 5.91054061 2.25012034 -0.45338653 0.42969844 -2.77673305 +Ti 6.15195010 5.95052016 6.00115011 -0.64260815 0.39526289 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4.11488970 -0.07704593 0.02948155 0.02803994 +Ti 7.82243500 0.00256825 2.14045030 -0.12370014 0.00007045 -0.20980665 +Ti 7.81008814 0.00725494 6.24370034 0.11660827 -0.03570362 -0.26678435 +Ti 7.81932071 3.91504015 2.14948025 0.01892332 -0.04325058 -0.38726881 +Ti 7.81718975 3.91554003 6.24657994 -0.12637152 -0.01300207 -0.21624237 +Ti 3.90574031 0.00035829 2.14461990 0.16681960 0.04884068 -0.22223639 +Ti 3.89389021 7.80474042 6.23949007 -0.02361970 0.07508932 -0.24942966 +Ti 3.92024002 3.91918002 2.15322037 -0.03170787 -0.11356537 -0.66256377 +Ti 3.89840010 3.89488997 6.26496997 0.18928256 0.02440080 -0.26617037 +O 7.80709980 1.95454034 1.95735971 0.08267099 -0.01436912 0.13254577 +O 1.96855972 0.01707031 1.96095041 -0.23979214 -0.02245576 0.07815459 +O 7.81398003 0.00062974 3.95923003 0.06215333 0.03289547 0.13060973 +O 0.00577485 1.96800977 6.05046034 0.02051046 -0.15602534 0.10645370 +O 1.96506994 0.00958303 6.05516033 -0.18602446 0.01751513 0.06611669 +O 0.00301963 0.00825001 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1.97711016 0.25909444 0.99746667 0.00553636 +Ti 1.96967006 6.06119015 5.96172038 -0.05501518 0.13839914 0.07004585 +Ti 6.06899983 2.00134037 2.04717002 -0.16445881 -0.19687785 0.32535408 +Ti 6.02348016 2.06672046 6.03756001 -0.62306906 0.58733046 -0.19160144 +Ti 5.95170036 5.92205042 1.92910992 -0.30314618 0.24272782 -0.14329092 +Ti 5.91239045 6.06816053 5.92882051 0.19455923 -0.52929990 0.52966628 +40 +Lattice="7.798029956284163 0.0 0.0 0.0 7.798029956284163 0.0 0.0 0.0 8.180071039902435" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.09084676421 pbc="T T T" +Ba 1.97370010 2.00351976 8.06620265 -0.04923483 -0.38286811 0.61648626 +Ba 1.97688013 1.85406974 4.08814996 -0.24904605 0.68208564 0.06668182 +Ba 1.93825025 5.84508977 0.04561458 0.16560013 0.15521930 -0.32567007 +Ba 1.85892011 5.85007973 4.09046987 0.50539686 -0.08217811 0.21325964 +Ba 5.88293985 1.98961978 0.03361497 -0.46941350 0.01970956 -0.18393543 +Ba 5.86671995 1.90597967 4.09900014 -0.24652843 0.37215998 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3.92518985 5.85847977 2.00191961 -0.09265099 -0.17743877 -0.17524048 +O 5.82989999 3.84331989 1.98209000 0.54932853 0.09425690 -0.03813255 +O 3.92181018 3.83891010 3.97861025 -0.26248752 0.26100040 0.04288034 +O 3.90434961 5.85745979 6.08781983 -0.21204376 -0.34809574 -0.36912608 +O 5.78546994 3.94774019 6.05165959 1.07054822 -0.48248576 -0.04966986 +O 3.90219034 3.86667031 8.01450015 0.00861140 0.36126879 0.63676995 +40 +Lattice="7.824509983790174 0.0 0.0 0.0 7.824509983790174 0.0 0.0 0.0 8.207840552406038" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.977830121145 pbc="T T T" +Ba 1.96349036 1.96215002 8.20147218 0.05194091 -0.16246389 0.15036788 +Ba 1.93207965 1.95938014 4.13720965 0.13833409 -0.22501986 -0.02681301 +Ba 1.95047976 5.89202972 8.18534743 0.06791235 -0.19072340 0.21411170 +Ba 1.96941038 5.83546008 4.06176025 -0.12706520 0.34070768 0.42173882 +Ba 5.87653015 1.97687027 0.02837637 -0.16815040 -0.28375337 -0.13759259 +Ba 5.85918008 1.98416976 4.08020027 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0.24514389 +Ba 1.95647026 5.86319998 4.09664986 0.02134144 0.00058081 0.18872231 +Ba 5.87684019 1.93500985 0.00287902 0.20916258 0.19280857 0.17328361 +Ba 5.87769000 1.99962019 4.13537966 0.02717270 -0.24740492 0.01499570 +Ba 5.88770026 5.90150996 8.21650684 0.14255687 -0.14939729 0.31599835 +Ba 5.85477950 5.92745015 4.12648994 0.27399629 -0.31893506 -0.01186564 +Ti 7.84165716 0.01295911 2.16490980 0.02207883 -0.25318347 -0.35727407 +Ti 0.02845353 0.02251659 6.26033006 -0.23383335 -0.29722827 0.13988652 +Ti 7.83651589 3.92481989 2.14811985 0.11515714 0.28314376 0.00234202 +Ti 7.82584964 3.93226029 6.28400956 0.27091226 0.18392284 -0.31134877 +Ti 3.91203969 0.00009966 2.13584970 -0.05003804 -0.30239310 0.04462098 +Ti 3.94039985 0.02134976 6.27721966 0.09511385 -0.11391992 -0.30482125 +Ti 3.92121975 3.90926975 2.15865977 -0.11189647 0.41035269 -0.02367112 +Ti 3.92165996 3.95109984 6.28480994 -0.25946930 -0.08337136 -0.71779081 +O 0.01435977 1.93135007 1.96264967 -0.03340814 0.19773326 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5.95811992 5.95682032 -0.06047055 0.53328819 0.06206412 +Ti 2.00217013 2.11883013 2.14320994 0.09006472 -0.33959850 -1.09933661 +Ti 2.04955042 1.93695984 6.01304027 0.35106408 0.81533975 0.60677572 +Ti 1.94313014 6.10203000 2.14768996 0.27143033 -0.10380546 -0.80176227 +Ti 1.83124995 5.92035984 6.11923014 0.92277869 0.23187031 -0.10632052 +Ti 5.94367047 1.92633982 2.05391005 0.31812285 -0.02415963 -0.19345469 +Ti 5.95727000 2.13734022 6.10179002 0.35956929 -1.24291241 -0.52758163 +Ti 5.85935052 5.84267023 1.90336007 1.67805413 1.70881584 0.72295076 +Ti 5.85987036 6.04151979 5.87860051 0.59840395 1.47040798 0.35760985 +40 +Lattice="7.939680111416239 0.0 0.0 -0.02176266318539191 7.9396483526957935 0.0 -0.02176266318539191 0.021707085424611996 7.939616593975347" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.80318024848 pbc="T T T" +Ba 3.97979880 0.02517514 0.04926016 0.47459325 0.07674177 -0.03466078 +Ba 4.01782431 0.06344995 3.96276024 -0.02011605 -0.00578215 0.22234180 +Ba 3.96444425 4.02124551 0.06232014 0.32847874 -0.06885723 -0.37534224 +Ba 3.99244988 4.04609036 3.97508024 0.05276855 -0.28794427 0.32374688 +Ba 0.04946024 0.02362531 0.08778984 -0.11417549 -0.11221631 -0.22876390 +Ba 0.01973407 0.06521018 4.01224986 0.25099675 -0.05797375 -0.21227722 +Ba -0.03248917 3.98009018 7.92226045 0.30794874 0.51428414 0.46483154 +Ba 0.05750472 4.00033002 4.07720041 -0.06441925 0.14150683 -0.69287554 +O 2.00162035 3.99604973 1.93172973 0.11227982 -0.42295650 0.26473647 +O 2.04134019 3.96533032 5.96499989 -0.17840011 0.21128477 -0.16533993 +O 2.07641452 0.00574039 1.97325981 -0.22350908 -0.02889457 -0.09080802 +O 2.07775394 0.02260983 5.94679976 -0.20426540 0.04003928 0.02936534 +O 6.03253004 3.95150019 2.00243020 -0.10951408 0.09025498 -0.08237172 +O 6.01148989 3.94041004 5.91523000 0.05790304 0.36320637 0.22358750 +O 6.00567011 7.89063036 1.97137970 -0.10380726 0.38779795 0.12617972 +O 5.99091024 7.91845020 5.91247970 -0.01180085 0.38695180 0.16931409 +O 2.13183031 2.01119005 3.91960967 -0.52500821 0.16856358 0.34472914 +O 2.00611977 2.02420001 7.91401033 0.09555094 -0.04020871 0.27935113 +O 2.05433983 5.97590980 3.94254026 -0.25245585 -0.05816864 0.16452232 +O 1.96791006 5.94108001 7.91179992 0.12369140 0.38497642 -0.46908543 +O 5.97508011 2.01080021 3.97990995 0.36551445 -0.14597053 -0.04829509 +O 6.06357419 1.93426487 0.02748003 -0.11740068 0.31265797 -0.50167262 +O 6.01755978 6.00577015 3.89822017 -0.18318519 -0.45259566 0.84281019 +O 6.02486031 5.98309045 7.87596021 -0.28133448 -0.25156727 0.02595734 +O 0.09221224 2.00794034 2.03858036 0.02748998 -0.06097063 -0.11547184 +O 0.08292123 1.97619035 5.92038047 -0.21685404 0.14532209 0.13572674 +O 0.03048202 5.93879021 1.94528991 0.01289125 0.02595683 0.28849320 +O 0.03732047 6.01723981 5.90033993 0.43424261 -0.18839861 0.06709062 +O 4.07517023 2.01791972 2.05811038 -0.19788727 0.03428617 -0.71491297 +O 4.03584023 2.04598967 6.00024016 0.34243752 -0.23485459 0.01001856 +O 3.96017032 5.92360001 1.92770987 0.36116697 0.09317884 0.23751105 +O 4.02744005 6.01768046 5.93760005 -0.17552279 -0.33986410 0.04233167 +Ti 1.98740991 2.07191987 1.99448972 -0.17914316 -0.30201283 0.71430517 +Ti 1.95962976 2.12973027 5.99562006 0.94680720 -0.39939825 -0.16763901 +Ti 2.06616042 5.98827983 2.05534023 -0.16072429 0.42762613 -0.22524586 +Ti 1.94851977 6.13695034 6.01175031 -0.01684253 -0.72226324 0.26048258 +Ti 5.96019003 2.04801984 2.09943006 -0.01883436 -0.13692281 -0.17836411 +Ti 5.95877994 2.07248041 6.05965040 -0.99269985 -0.53970978 -0.17320854 +Ti 6.07866991 5.97039014 2.10065992 -0.09404581 0.48833862 -1.06445291 +Ti 5.91559047 6.03550028 6.03006001 0.14718537 0.56455589 0.30335443 +40 +Lattice="7.924059858580059 0.0 0.0 0.0 7.924059858580059 0.0 0.0 0.0 7.924059858580059" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29613.936324199793 pbc="T T T" +Ba 4.03797967 4.00380003 7.85373858 -0.58973933 -0.57708051 0.82271445 +Ba 3.91099978 7.85170765 3.97866015 0.39543181 0.83838815 -0.21006916 +Ba 7.91738542 3.97314976 4.00589990 -0.04590268 0.12413672 -0.39059402 +Ba 0.01069352 7.91553674 4.02151030 0.08195700 0.01558988 -0.32594286 +Ba 0.03532625 3.97501984 0.01272762 0.07157154 -0.17368959 0.34788054 +Ba 3.97603967 0.06886404 7.88594989 -0.36391446 -0.05376280 0.44213847 +Ba 3.95105986 3.92483994 3.93208966 0.20671155 0.22849420 0.28394055 +Ba 7.91453276 0.04463702 0.01826100 0.44716986 -0.10192110 0.16338872 +Ti 5.90895004 1.99426003 2.01028961 0.88328141 0.67097076 0.07121030 +Ti 2.01825963 5.94555999 1.98711966 -0.15980589 0.32520264 -0.22391815 +Ti 1.96807973 1.99861034 5.91022027 0.35617801 0.53097728 0.91716778 +Ti 5.89231982 5.86761973 6.03497984 0.54441695 0.52295313 -1.43596292 +Ti 2.00200976 5.96942013 5.96127023 -0.62103171 -0.35210024 0.10781535 +Ti 5.96738998 1.91428963 5.93792991 -0.07038832 0.27858340 -0.04500973 +Ti 5.96453019 6.05446985 2.02551965 -0.25612815 -0.81634762 0.90881349 +Ti 1.97528032 2.01120959 2.00437985 -0.80050783 -0.61812611 -0.67273480 +O 1.91676035 2.00037027 3.93839959 0.27315194 -0.00618067 0.69661161 +O 5.92953992 1.99203020 3.89976029 0.00761535 -0.03402289 1.51412419 +O 2.09153975 5.84851958 4.00349020 -0.52174779 0.45839710 -0.45556246 +O 5.98600994 6.06474974 4.02204993 0.28028727 -0.43566006 -0.36413840 +O 2.04734965 3.97109030 2.01444023 -0.08934455 0.30075222 -0.31202239 +O 2.00182989 3.92887962 6.01440977 0.36473232 -0.09989404 -0.36967347 +O 5.89039982 3.99439020 2.16465030 0.18940391 0.28304143 -1.03848168 +O 5.95896988 4.02929965 5.97263967 -0.29754606 -0.32644885 -0.10912533 +O 3.92206018 1.95745990 1.96547985 0.52308400 -0.05723558 -0.18911518 +O 3.99257956 6.12962956 1.99834964 0.48270174 -0.67062855 -0.07114602 +O 3.92721003 1.93151970 5.92089952 0.38864050 0.53566338 0.11076004 +O 4.03673004 6.05053952 5.84089980 0.16760019 -0.76504666 0.92886347 +O 5.96200004 5.96892963 0.01687983 -0.10284978 0.20090574 0.21868955 +O 2.20760029 5.93315012 0.00353968 -0.64018746 0.08417946 0.10269475 +O 6.06776960 2.02767024 0.03831521 -1.00026429 -0.02601339 -0.28624323 +O 1.88025975 1.98280026 7.89436999 0.61007341 -0.08207270 0.08449005 +O 5.95211953 0.10624896 5.97739966 0.20558721 -0.71661916 0.11921383 +O 6.04633977 0.02991016 2.12351016 -0.43403050 -0.42469405 -0.96847748 +O 2.03559985 7.89401341 5.93817001 -0.53067338 0.07858860 0.02718170 +O 1.87209005 0.04651978 1.98790969 0.70652115 -0.71094628 0.13975694 +O 0.10703899 5.82153023 5.99559013 -0.27406623 0.95412096 -0.01465863 +O 7.88742535 2.00992986 5.98729998 0.16113515 -0.10463644 -0.73079905 +O 0.08209009 5.93455981 1.93501025 -0.43478357 -0.00479048 0.20875275 +O 7.92236966 1.94012999 2.01078011 -0.11434056 0.72697299 -0.00253357 +40 +Lattice="7.984075882 0.0 0.0 0.0 7.984075882 0.0 0.0 0.0 7.984075882" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.309613082343 stress="-6.243471783356271e-05 -0.0 -0.0 -0.0 -6.243471783356271e-05 -0.0 -0.0 -0.0 -6.243471783356271e-05" pbc="T T T" +Ba -0.00122660 3.99081135 0.00122660 0.01030292 0.01030292 -0.01030292 +Ba 3.99326454 3.99326454 3.99326454 -0.01030292 -0.01030292 -0.01030292 +Ba 0.00122660 -0.00122660 3.99081135 -0.01030292 0.01030292 0.01030292 +Ba 3.99081135 0.00122660 -0.00122660 0.01030292 -0.01030292 0.01030292 +Ba 3.99228026 3.99179562 -0.00024232 -0.00630229 0.00630229 0.00630229 +Ba -0.00024232 3.99228026 3.99179562 0.00630229 -0.00630229 0.00630229 +Ba 3.99179562 -0.00024232 3.99228026 0.00630229 0.00630229 -0.00630229 +Ba 0.00024232 0.00024232 0.00024232 -0.00630229 -0.00630229 -0.00630229 +Ti 5.92872440 1.93668646 2.05535149 -0.01167487 -0.01167487 0.01167487 +Ti 6.04738943 6.04738943 6.04738943 0.01167487 0.01167487 0.01167487 +Ti 2.05535149 5.92872440 1.93668646 0.01167487 -0.01167487 -0.01167487 +Ti 1.93668646 2.05535149 5.92872440 -0.01167487 0.01167487 -0.01167487 +Ti 5.92876033 2.05531556 6.04735350 0.01178439 -0.01178439 -0.01178439 +Ti 6.04735350 5.92876033 2.05531556 -0.01178439 0.01178439 -0.01178439 +Ti 2.05531556 6.04735350 5.92876033 -0.01178439 -0.01178439 0.01178439 +Ti 1.93672238 1.93672238 1.93672238 0.01178439 0.01178439 0.01178439 +O 2.02013735 1.99870531 4.03417834 -0.00070037 -0.01820932 -0.02383824 +O 5.96393853 5.99074325 -0.04214039 0.00070037 -0.01820932 0.02383824 +O 6.01217529 1.99333263 3.94989755 -0.00070037 0.01820932 0.02383824 +O 1.97190059 5.98537057 0.04214039 0.00070037 0.01820932 -0.02383824 +O 1.99870531 4.03417834 2.02013735 -0.01820932 -0.02383824 -0.00070037 +O 5.99074325 -0.04214039 5.96393853 -0.01820932 0.02383824 0.00070037 +O 1.99333263 3.94989755 6.01217529 0.01820932 0.02383824 -0.00070037 +O 5.98537057 0.04214039 1.97190059 0.01820932 -0.02383824 0.00070037 +O 4.03417834 2.02013735 1.99870531 -0.02383824 -0.00070037 -0.01820932 +O -0.04214039 5.96393853 5.99074325 0.02383824 0.00070037 -0.01820932 +O 3.94989755 6.01217529 1.99333263 0.02383824 -0.00070037 0.01820932 +O 0.04214039 1.97190059 5.98537057 -0.02383824 0.00070037 0.01820932 +O 1.97279572 5.98713313 4.03328799 -0.00195867 0.00502394 0.01012783 +O 6.01128017 1.99509519 -0.04125005 0.00195867 0.00502394 -0.01012783 +O 5.96483366 5.98898070 3.95078789 -0.00195867 -0.00502394 -0.01012783 +O 2.01924223 1.99694276 0.04125005 0.00195867 -0.00502394 0.01012783 +O 5.98713313 4.03328799 1.97279572 0.00502394 0.01012783 -0.00195867 +O 1.99509519 -0.04125005 6.01128017 0.00502394 -0.01012783 0.00195867 +O 5.98898070 3.95078789 5.96483366 -0.00502394 -0.01012783 -0.00195867 +O 1.99694276 0.04125005 2.01924223 -0.00502394 0.01012783 0.00195867 +O 4.03328799 1.97279572 5.98713313 0.01012783 -0.00195867 0.00502394 +O -0.04125005 6.01128017 1.99509519 -0.01012783 0.00195867 0.00502394 +O 3.95078789 5.96483366 5.98898070 -0.01012783 -0.00195867 -0.00502394 +O 0.04125005 2.01924223 1.99694276 0.01012783 0.00195867 -0.00502394 +40 +Lattice="8.033103983 0.0 0.0 0.0 8.033103983 0.0 0.0 0.0 8.033103983" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29613.02988633607 stress="0.01068368201046082 -0.0 -0.0 -0.0 0.01068368201046082 -0.0 -0.0 -0.0 0.01068368201046082" pbc="T T T" +Ba -0.10814445 3.90840755 0.10814445 0.46519818 0.46519818 -0.46519818 +Ba 4.12469644 4.12469644 4.12469644 -0.46519818 -0.46519818 -0.46519818 +Ba 0.10814445 -0.10814445 3.90840755 -0.46519818 0.46519818 0.46519818 +Ba 3.90840755 0.10814445 -0.10814445 0.46519818 -0.46519818 0.46519818 +Ba 4.11473882 3.91836516 -0.09818683 -0.27693841 0.27693841 0.27693841 +Ba -0.09818683 4.11473882 3.91836516 0.27693841 -0.27693841 0.27693841 +Ba 3.91836516 -0.09818683 4.11473882 0.27693841 0.27693841 -0.27693841 +Ba 0.09818683 0.09818683 0.09818683 -0.27693841 -0.27693841 -0.27693841 +Ti 5.95566910 1.93911711 2.07743488 0.14358737 0.14358737 -0.14358737 +Ti 6.09398687 6.09398687 6.09398687 -0.14358737 -0.14358737 -0.14358737 +Ti 2.07743488 5.95566910 1.93911711 -0.14358737 0.14358737 0.14358737 +Ti 1.93911711 2.07743488 5.95566910 0.14358737 -0.14358737 0.14358737 +Ti 6.07692560 1.95617838 5.97273037 -0.99604048 0.99604048 0.99604048 +Ti 5.97273037 6.07692560 1.95617838 0.99604048 -0.99604048 0.99604048 +Ti 1.95617838 5.97273037 6.07692560 0.99604048 0.99604048 -0.99604048 +Ti 2.06037361 2.06037361 2.06037361 -0.99604048 -0.99604048 -0.99604048 +O 1.93643082 1.91881502 4.08376092 0.67404400 0.64242921 -0.07604475 +O 6.09667316 5.93536701 -0.06720893 -0.67404400 0.64242921 0.07604475 +O 5.95298281 2.09773698 3.94934306 0.67404400 -0.64242921 0.07604475 +O 2.08012117 6.11428897 0.06720893 -0.67404400 -0.64242921 -0.07604475 +O 1.91881502 4.08376092 1.93643082 0.64242921 -0.07604475 0.67404400 +O 5.93536701 -0.06720893 6.09667316 0.64242921 0.07604475 -0.67404400 +O 2.09773698 3.94934306 5.95298281 -0.64242921 0.07604475 0.67404400 +O 6.11428897 0.06720893 2.08012117 -0.64242921 -0.07604475 -0.67404400 +O 4.08376092 1.93643082 1.91881502 -0.07604475 0.67404400 0.64242921 +O -0.06720893 6.09667316 5.93536701 0.07604475 -0.67404400 0.64242921 +O 3.94934306 5.95298281 2.09773698 0.07604475 0.67404400 -0.64242921 +O 0.06720893 2.08012117 6.11428897 -0.07604475 -0.67404400 -0.64242921 +O 1.93667830 5.96551886 4.11780851 0.16790409 0.11332189 -0.45537065 +O 6.09642569 1.94896687 -0.10125652 -0.16790409 0.11332189 0.45537065 +O 5.95323029 6.08413711 3.91529547 0.16790409 -0.11332189 0.45537065 +O 2.07987369 2.06758512 0.10125652 -0.16790409 -0.11332189 -0.45537065 +O 5.96551886 4.11780851 1.93667830 0.11332189 -0.45537065 0.16790409 +O 1.94896687 -0.10125652 6.09642569 0.11332189 0.45537065 -0.16790409 +O 6.08413711 3.91529547 5.95323029 -0.11332189 0.45537065 0.16790409 +O 2.06758512 0.10125652 2.07987369 -0.11332189 -0.45537065 -0.16790409 +O 4.11780851 1.93667830 5.96551886 -0.45537065 0.16790409 0.11332189 +O -0.10125652 6.09642569 1.94896687 0.45537065 -0.16790409 0.11332189 +O 3.91529547 5.95323029 6.08413711 0.45537065 0.16790409 -0.11332189 +O 0.10125652 2.07987369 2.06758512 -0.45537065 -0.16790409 -0.11332189 +40 +Lattice="7.7868701381371945 0.0 0.0 0.0 8.051008560092948 0.0 0.0 0.06860232591698869 8.050720445897836" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.417001594877 pbc="T T T" +Ba 3.86373984 0.11644563 7.98570008 0.18736194 -0.17547188 0.29955692 +Ba 3.90385001 0.08799397 4.06634018 0.12190963 0.03337626 -0.57636214 +Ba 3.89351995 4.14520483 7.99121318 0.01419892 -0.02378605 0.11774136 +Ba 3.86507996 4.07087993 3.96862976 0.09482331 0.27278556 0.17599278 +Ba 0.02727974 8.04659496 0.01988144 0.07346696 0.26775905 -0.26939968 +Ba 0.06540971 0.03536485 4.02548014 -0.27079038 0.42419731 -0.28862793 +Ba 7.76711641 4.09411984 0.01830537 0.34676803 -0.34550870 -0.16967147 +Ba 7.65754502 4.08498974 4.06587998 1.03627053 0.13391719 -0.54910870 +Ti 2.00460980 2.03949965 2.06013018 -0.33876315 -0.18343767 0.58208927 +Ti 1.95011027 2.16460039 6.13807047 0.22755754 0.25360976 -0.71042331 +Ti 1.93455989 6.00892990 1.89837976 0.69919659 0.00564460 0.46151379 +Ti 1.97281990 6.15153007 5.90883046 0.30638294 -0.02318544 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0.00000000 0.00000000 0.00000000 +Ti 1.93285651 6.04791104 1.93285651 -0.00228597 0.00228597 -0.00228597 +Ti 6.04791104 1.93285651 1.93285651 0.00228597 -0.00228597 -0.00228597 +Ti 1.93285651 1.93285651 6.04791104 -0.00228597 -0.00228597 0.00228597 +Ti 6.04791104 6.04791104 6.04791104 0.00228597 0.00228597 0.00228597 +Ti 2.05752727 5.92324028 5.92324028 0.00228597 -0.00228597 -0.00228597 +Ti 5.92324028 2.05752727 5.92324028 -0.00228597 0.00228597 -0.00228597 +Ti 5.92324028 5.92324028 2.05752727 -0.00228597 -0.00228597 0.00228597 +Ti 2.05752727 2.05752727 2.05752727 0.00228597 0.00228597 0.00228597 +O 1.99501392 1.99450394 3.96014305 0.00639433 0.00939378 0.00635911 +O 1.99501392 5.98626360 4.02062450 0.00639433 -0.00939378 -0.00635911 +O 5.98575363 1.99450394 4.02062450 -0.00639433 0.00939378 -0.00635911 +O 5.98575363 5.98626360 3.96014305 -0.00639433 -0.00939378 0.00635911 +O 3.96014305 1.99501392 1.99450394 0.00635911 0.00639433 0.00939378 +O 4.02062450 1.99501392 5.98626360 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1.99421000 5.95668004 0.27425058 0.05090939 0.03881183 +Ti 5.94351989 5.98276034 2.04245037 0.34507187 -0.72208687 0.11357205 +Ti 5.92428986 5.97512968 6.01173969 0.08048710 -0.08100518 -0.10359669 +40 +Lattice="7.942700125744312 0.0 0.0 -0.02177094104466516 7.942668354943809 0.0 -0.02177094104466516 0.021715342143784948 7.942636584143306" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.09427648703 pbc="T T T" +Ba 4.01403254 0.06931038 7.91338997 -0.38896446 -0.03504311 0.35812279 +Ba 3.99422027 7.92718009 3.97784004 0.03527991 0.41120193 0.27388831 +Ba 3.89302233 4.06971723 0.17964005 0.85984760 -0.29767384 -0.95238495 +Ba 4.00879036 4.07416990 3.97397036 -0.08788648 -0.26975577 0.12074029 +Ba 7.91168626 0.02229675 0.05901029 0.62257412 0.47182468 -0.68582017 +Ba 0.14410361 7.90850998 4.05903986 -0.99738979 0.76940699 0.22117761 +Ba 0.07144062 3.99833698 0.06477034 -0.46060156 -0.19603813 -0.53082713 +Ba 0.03636724 4.00266019 3.87717982 -0.01700888 0.02175076 1.13471010 +O 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2.09672033 1.95507975 -0.25890289 -0.07888582 0.06967998 +Ti 5.91883977 2.05397987 5.88962016 0.62488425 -0.32480592 0.58246902 +Ti 6.05316036 6.11447006 2.01637992 -1.15269985 -0.32577188 0.24101521 +Ti 5.94662016 5.93862980 6.02959993 0.07489778 0.22966302 -0.44099176 +40 +Lattice="7.917729840813734 0.0 0.0 0.0 7.917729840813734 0.0 0.0 0.0 7.917729840813734" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29613.933019241165 pbc="T T T" +Ba 3.96461003 3.89688018 0.00480606 -0.03277205 0.42058568 -0.15778912 +Ba 4.00079959 0.03458623 3.98563001 -0.06351987 -0.18379839 0.19490967 +Ba 0.03409058 3.95384983 3.90637987 0.42335939 0.19034957 0.59257963 +Ba 7.91109082 0.03389580 4.02419015 0.44012452 -0.51109726 -0.56521024 +Ba 7.89650637 4.01530962 0.04157679 0.64333629 -0.15899728 -0.54987052 +Ba 3.95386012 0.09662243 0.11448087 0.53969641 -1.07079248 -1.13812144 +Ba 3.91779961 3.92592004 3.89180967 0.17130335 0.01840113 0.78950299 +Ba 7.83113600 0.02822433 7.86522817 0.45177034 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0.00000000 0.00000000 0.00000000 +Ba 3.98683562 3.98683562 3.98683562 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 3.98683562 0.00000000 0.00000000 0.00000000 +Ba 3.98683562 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 3.98683562 3.98683562 0.00000000 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 3.98683562 3.98683562 0.00000000 0.00000000 0.00000000 +Ba 3.98683562 0.00000000 3.98683562 0.00000000 0.00000000 0.00000000 +Ba 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 2.02610632 5.94756493 1.96072930 0.11701836 -0.11701836 -0.11701836 +Ti 1.96072930 2.02610632 5.94756493 -0.11701836 0.11701836 -0.11701836 +Ti 5.94756493 1.96072930 2.02610632 -0.11701836 -0.11701836 0.11701836 +Ti 6.01294194 6.01294194 6.01294194 0.11701836 0.11701836 0.11701836 +Ti 5.94756493 2.02610632 6.01294194 -0.11701836 0.11701836 0.11701836 +Ti 6.01294194 5.94756493 2.02610632 0.11701836 -0.11701836 0.11701836 +Ti 2.02610632 6.01294194 5.94756493 0.11701836 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7.944350100279959" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.839528126588 pbc="T T T" +Ba 3.96490994 4.00327003 7.89887664 0.22038108 0.02266093 0.64693764 +Ba 3.93250017 0.01828233 3.99932010 0.36041184 -0.07372535 -0.04570522 +Ba 0.01703586 3.95833043 3.99806013 -0.21582920 0.11659644 -0.05220574 +Ba 0.04087924 0.00164369 3.97474028 -0.29340452 0.19413552 0.29084936 +Ba 0.03612693 3.95462995 0.09398961 -0.33842145 0.31493828 -0.59017462 +Ba 3.98460001 7.91896234 0.01861679 -0.09527146 0.15561448 -0.15739599 +Ba 3.98254004 3.96591967 3.96577985 0.14058072 0.25395609 -0.23106838 +Ba 0.02329363 0.04691933 7.92627829 -0.07664613 -0.29283168 -0.14196398 +Ti 5.91976982 1.88364036 2.04427989 -0.04972385 0.57536609 0.13772808 +Ti 1.96285983 5.98973968 1.95581002 0.80967587 -0.50298208 -0.26529105 +Ti 2.02404007 2.06827977 5.91154980 -0.27548856 -0.66116432 0.08357628 +Ti 5.95150988 5.98559988 6.01316042 0.20368022 0.26401990 0.35156570 +Ti 1.99864039 5.99696030 5.90584973 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8.028683677989143 0.0 0.0 0.06841203031087872 8.028388597722195" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.114335756196 pbc="T T T" +Ba 3.88067048 0.07737238 8.01866027 0.01537237 0.19849816 0.00276342 +Ba 3.88863997 0.08978594 4.00117039 -0.05798172 -0.09413169 0.04873166 +Ba 3.88713041 4.12448443 8.01955716 -0.10369002 -0.08248947 -0.04906153 +Ba 3.88506019 4.09842030 3.99473997 -0.05963288 -0.10944929 0.10834834 +Ba 0.00397970 0.10280441 7.99241521 -0.02019267 0.01970442 0.23598382 +Ba 7.74918986 0.08797818 4.00117039 0.13306616 -0.10423329 -0.02685517 +Ba 0.00495347 4.05768991 0.00768451 -0.01958178 -0.04523213 -0.13506185 +Ba 0.00036730 4.08656972 3.98955044 0.02488571 -0.02388658 0.12027749 +Ti 1.94473038 2.11259999 2.03663002 0.11945320 0.09733297 0.01211324 +Ti 1.94119020 2.13064027 6.06241011 -0.00297862 0.23412440 0.16062478 +Ti 1.94531977 6.13556051 2.05420982 -0.12052689 -0.05114516 -0.00354709 +Ti 1.94794986 6.15680007 6.07141006 0.13618054 0.01980572 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3.99702615 0.04622651 0.04127998 0.01856079 -0.07505436 0.07666567 +Ba 3.99301314 0.03439034 3.99116988 -0.03256456 -0.05534377 -0.08963868 +Ba 4.00616320 4.00329688 0.04478978 -0.07172581 -0.17481419 -0.07373307 +Ba 4.01486044 4.00578995 4.02545007 -0.24122758 0.04692829 -0.26262045 +Ba 0.04232999 0.05628678 0.05368038 0.05759477 -0.14689946 -0.12535696 +Ba 0.00780572 0.04782966 4.00958979 0.29114401 -0.08007778 -0.03169039 +Ba 0.03753403 3.99027677 0.00313021 -0.01376646 -0.00735053 0.05107239 +Ba 0.01377928 4.04097038 3.97441016 0.14638422 -0.21448477 0.24546142 +O 1.95940007 4.00766967 2.04987036 0.15142641 0.19886789 0.03214985 +O 1.99423974 4.02512991 5.97388013 -0.08526447 -0.02803068 0.12965045 +O 2.02406314 0.05908971 2.04436990 -0.11834274 -0.19117669 -0.11736649 +O 1.98198278 0.06181973 6.06101020 0.03876349 -0.04113739 -0.22552303 +O 5.97034972 3.96103028 2.04490006 -0.03581521 -0.05565358 0.07558683 +O 5.96801989 3.96337041 5.97276038 -0.26894356 -0.01032426 0.17513815 +O 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pbc="T T T" +Ba 1.96633027 1.92657996 8.19737190 -0.23366108 0.18529838 0.25407976 +Ba 1.92324021 1.93775988 4.09885008 0.07753290 0.06496252 0.03389562 +Ba 1.96458028 5.85880983 8.17605236 -0.18412724 -0.01400094 0.29944070 +Ba 1.99299982 5.85067032 4.08116965 -0.50574730 0.02843537 0.24275276 +Ba 5.84163978 2.03339963 8.18039489 0.15132433 -0.47195504 0.25633976 +Ba 5.88750997 1.93257010 4.11525027 -0.19593015 0.11809154 -0.04555918 +Ba 5.83860016 5.91603033 0.02341499 0.08669451 -0.46101962 -0.11411481 +Ba 5.90029997 5.83463982 4.11763960 -0.17994688 0.10064223 0.09161586 +Ti 7.78418692 7.77386988 2.11618997 0.00014192 0.25676939 0.25503364 +Ti 7.81588681 7.80169306 6.23535994 -0.36756902 0.02794583 -0.16103796 +Ti 0.01401242 3.88310982 2.16941027 -0.16881092 -0.10319791 -0.51166007 +Ti 0.00040018 3.88789005 6.24385977 -0.44136045 0.10685633 0.28042071 +Ti 3.86505031 7.78865060 2.17656029 0.34292191 0.34050173 -1.00294209 +Ti 3.89456017 0.03683027 6.21218020 0.47655140 -0.10637271 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energy=-29610.013273818095 pbc="T T T" +Ba 2.00987991 1.97202963 1.94769989 -0.13059276 0.95777295 -0.03410286 +Ba 6.17628985 6.06129010 2.03216997 -1.18440207 -0.55874854 -0.29055934 +Ba 5.99380033 1.94080033 5.99262999 -1.06447322 1.07711739 -1.39032121 +Ba 2.00924031 5.89511967 6.07214975 -0.39814021 0.52681750 0.48557494 +Ba 5.86617982 1.97496989 1.89886028 0.31890061 0.19177319 0.44990911 +Ba 2.06769959 6.03066998 2.20903995 -0.85419426 -0.56063753 -1.36067047 +Ba 1.97181030 2.08827016 5.90724973 0.44769257 -0.34749076 0.96840678 +Ba 6.08754026 5.93699969 5.96546965 -0.64249580 0.82525675 0.15183084 +Ti 4.02664977 4.05733953 4.06933029 0.78526710 -0.54783061 -0.58563148 +Ti 7.97991484 3.81669972 0.08992793 2.19724831 2.64471924 -0.47122819 +Ti 3.80025975 7.93271227 0.06887465 0.59417783 2.25800193 -1.51128878 +Ti 7.89622205 0.05772041 3.92376006 -0.01525307 -0.24679659 0.06210037 +Ti 3.81620021 0.07574618 3.96653985 2.11974523 -0.09383524 1.15534166 +Ti 0.05565031 3.95958987 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0.42762613 -0.22524586 +Ti 1.94851977 6.13695034 6.01175031 -0.01684253 -0.72226324 0.26048258 +Ti 5.96019003 2.04801984 2.09943006 -0.01883436 -0.13692281 -0.17836411 +Ti 5.95877994 2.07248041 6.05965040 -0.99269985 -0.53970978 -0.17320854 +Ti 6.07866991 5.97039014 2.10065992 -0.09404581 0.48833862 -1.06445291 +Ti 5.91559047 6.03550028 6.03006001 0.14718537 0.56455589 0.30335443 +40 +Lattice="7.827029925656354 0.0 0.0 0.0 7.827029925656354 0.0 0.0 0.0 8.21049177577411" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29614.836579092866 pbc="T T T" +Ba 1.89181035 1.94946034 0.02265456 0.58151309 0.07902800 0.13417353 +Ba 1.90491984 1.96710012 4.07364034 0.47637528 -0.09735431 0.31398209 +Ba 1.96438962 5.87756958 8.16743294 0.08142838 -0.26634058 0.50279208 +Ba 1.98101971 5.83394015 4.10768009 -0.05202807 0.30316032 0.04467395 +Ba 5.86383002 1.94727034 0.00035456 -0.09832258 0.04725251 0.11980364 +Ba 5.89428969 1.97517996 4.12954960 -0.22143369 -0.10534658 0.05682267 +Ba 5.89042000 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energy=-29615.21669505014 stress="4.590788075997259e-06 -0.0 -0.0 -0.0 4.590788075997259e-06 -0.0 -0.0 -0.0 4.590788075997259e-06" pbc="T T T" +Ba 1.98884289 5.96630151 5.96630151 -0.00050908 0.00050908 0.00050908 +Ba 5.96630151 1.98884289 5.96630151 0.00050908 -0.00050908 0.00050908 +Ba 1.98884289 1.98884289 1.98884289 -0.00050908 -0.00050908 -0.00050908 +Ba 5.96630151 5.96630151 1.98884289 0.00050908 0.00050908 -0.00050908 +Ba 5.96630151 1.98884289 1.98884289 0.00050908 -0.00050908 -0.00050908 +Ba 1.98884289 5.96630151 1.98884289 -0.00050908 0.00050908 -0.00050908 +Ba 1.98884289 1.98884289 5.96630151 -0.00050908 -0.00050908 0.00050908 +Ba 5.96630151 5.96630151 5.96630151 0.00050908 0.00050908 0.00050908 +Ti 3.97757220 3.97757220 3.97757220 0.00000000 0.00000000 0.00000000 +Ti 0.00000000 3.97757220 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 3.97757220 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +Ti 0.00000000 0.00000000 3.97757220 0.00000000 0.00000000 0.00000000 +Ti 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1.98878802 1.98878802 0.00000026 0.00000026 0.00000026 +Ba 5.96636406 5.96636406 5.96636406 -0.00000026 -0.00000026 -0.00000026 +Ti -0.00000000 3.97757604 -0.00000000 0.00000000 0.00000000 0.00000000 +Ti 3.97757604 -0.00000000 -0.00000000 0.00000000 0.00000000 0.00000000 +Ti 3.97757604 3.97757604 3.97757604 0.00000000 0.00000000 0.00000000 +Ti -0.00000000 -0.00000000 3.97757604 0.00000000 0.00000000 0.00000000 +Ti -0.00000000 3.97757604 3.97757604 0.00000000 0.00000000 0.00000000 +Ti 3.97757604 -0.00000000 3.97757604 0.00000000 0.00000000 0.00000000 +Ti 3.97757604 3.97757604 -0.00000000 0.00000000 0.00000000 0.00000000 +Ti 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 +O 0.00005367 0.00005367 1.98879147 -0.00067594 -0.00067594 -0.00011313 +O 0.00005367 3.97752237 1.98878455 -0.00067594 0.00067594 0.00011339 +O 3.97752237 0.00005367 1.98878455 0.00067594 -0.00067594 0.00011339 +O 3.97752237 3.97752237 1.98879152 0.00067594 0.00067594 -0.00011596 +O 1.98878455 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5.96636753 3.97762971 0.00067594 -0.00011339 -0.00067594 +O -0.00005367 5.96636061 -0.00005367 0.00067594 0.00011313 0.00067594 +O 5.96636056 3.97762971 3.97762971 0.00011596 -0.00067594 -0.00067594 +O 5.96636753 -0.00005367 3.97762971 -0.00011339 0.00067594 -0.00067594 +O 5.96636753 3.97762971 -0.00005367 -0.00011339 -0.00067594 0.00067594 +O 5.96636061 -0.00005367 -0.00005367 0.00011313 0.00067594 0.00067594 +40 +Lattice="7.923900047063135 0.0 0.0 -0.021719410029000054 7.923868351462947 0.0 -0.021719410029000054 0.021663942728670612 7.923836655862758" Properties=species:S:1:pos:R:3:forces:R:3 energy=-29615.11478338346 pbc="T T T" +Ba 3.97839212 0.06701876 0.05399029 0.28144632 -0.19047246 -0.14546813 +Ba 3.98892139 0.04251014 3.97251021 0.06590072 0.06073923 0.24295125 +Ba 3.99525101 4.02704803 0.02806011 0.03542594 -0.10670181 0.03682154 +Ba 3.99615988 3.99520029 3.99296972 -0.00086261 0.11468843 0.08664695 +Ba 0.07365107 0.01389852 0.03646024 -0.25377945 0.11354969 -0.00405951 +Ba 0.02034461 0.04093011 3.99073993 0.12076060 0.05975887 0.11888858 +Ba 0.02753159 3.97445869 0.03543964 0.01445371 0.24647649 -0.03045472 +Ba 0.01677173 3.99788966 4.00170027 0.01374383 0.09660303 0.07262826 +O 2.04037970 3.98694993 2.04845019 -0.00519517 -0.00436033 -0.07893415 +O 2.01897011 4.01781986 5.97287975 0.02165409 -0.14325878 0.11341985 +O 2.05906108 0.01253006 2.02797008 0.01318025 -0.03071800 0.00269195 +O 2.05261103 0.05328030 5.98287972 -0.09499995 -0.11033761 0.09204806 +O 6.03424006 3.97793015 2.04045973 -0.09963796 -0.21000848 -0.02932395 +O 5.98208970 3.98249987 6.01930034 0.05350080 -0.09734557 -0.14691386 +O 6.03430107 0.01848963 2.04242010 -0.11103026 -0.00393533 -0.08851588 +O 6.01111099 0.02022021 6.01956024 -0.11053841 0.09120166 -0.11546439 +O 2.07143980 2.01600023 4.02768987 -0.22188363 0.01741845 -0.14500225 +O 2.06424094 2.01631878 0.07239037 -0.04750679 0.02995155 -0.11324270 +O 2.00627999 5.98901995 4.01178026 0.05872014 -0.03282810 -0.06507539 +O 2.02746136 5.96803825 0.03838971 0.12814970 -0.00926368 0.23791755 +O 6.01429006 2.00039966 4.03281029 -0.01619409 0.05445005 0.05171414 +O 6.02953089 2.00756841 0.07578022 -0.08921728 -0.09079491 -0.09859049 +O 6.02103013 5.97040988 4.00270977 -0.13562261 0.00798328 0.19551363 +O 5.97930128 5.96105809 0.04872961 0.07863282 0.01701042 0.05921379 +O 0.08995845 2.00313024 2.03809999 0.07440875 0.01192221 0.02555754 +O 0.07129450 2.00410012 6.01198024 0.11093153 0.09335059 -0.07861482 +O 0.06021213 5.98853025 2.02269989 0.40067300 -0.14683416 -0.05822366 +O 0.03748876 5.97508022 5.97756991 0.28627125 0.05031032 0.08017728 +O 4.05168027 2.01055018 2.02863014 0.05120686 0.03380075 0.03002406 +O 4.02378972 2.01861988 5.97408973 0.17536749 0.00433565 0.24420544 +O 4.05491005 5.96189010 2.05314035 -0.43664017 0.02827519 -0.14040666 +O 4.01770021 5.97210004 5.94907002 -0.00098628 0.08015080 0.12100177 +Ti 1.98365012 2.06134000 2.02469988 0.15263174 -0.10825064 -0.04711135 +Ti 1.97710022 2.02300972 5.97977989 -0.08320064 0.04002025 -0.18690892 +Ti 1.97576980 6.00264985 1.99869998 -0.31416927 0.13501068 0.04428854 +Ti 1.93278978 5.98863009 5.94618968 0.14288854 -0.08439132 -0.04079364 +Ti 5.96785996 2.07637005 2.00287033 -0.31685401 0.00608786 -0.07621701 +Ti 5.93108990 2.04048984 5.97432983 -0.02508471 0.04863164 -0.11829697 +Ti 5.93916039 6.04712987 2.01476965 0.17069734 -0.16399344 -0.15809353 +Ti 5.90802026 6.01309989 5.96703984 -0.08724216 0.09176781 0.11000182 diff --git a/examples/sample_selection/sample_selection_librascal.py b/examples/sample_selection/sample_selection_librascal.py new file mode 100644 index 00000000..33b75c79 --- /dev/null +++ b/examples/sample_selection/sample_selection_librascal.py @@ -0,0 +1,190 @@ +""" +Sample Selection with FPS and CUR (librascal) +============================================= + +.. start-body + +In this tutorial we generate descriptors using librascal, then select a subset +of structures using both the farthest-point sampling (FPS) and CUR algorithms +implemented in scikit-matter. + +First, import all the necessary packages +""" +# %% + +import ase.io +import numpy as np +from sklearn.decomposition import PCA + +import chemiscope +from rascal.representations import SphericalInvariants +from rascal.utils import FPSFilter +from skmatter import sample_selection, feature_selection + + +# %% +# Load molecular data +# ------------------- +# +# Load 100 example BTO structures from file, reading them using +# `ASE `_. + +# Load a subset of structures of the example dataset +n_frames = 250 +frames = ase.io.read("./dataset/input-fps.xyz", f":{n_frames}", format="extxyz") + +# librascal requires the atomic positions to be wrapped in the cell +for frame in frames: + frame.wrap(eps=1.0e-12) + + +# %% +# Compute SOAP descriptor using librascal +# --------------------------------------- +# +# First, define the librascal hyperparameters used to compute SOAP. + +# librascal hyperparameters +soap_hypers = { + "soap_type": "PowerSpectrum", + "interaction_cutoff": 6.0, + "max_radial": 8, + "max_angular": 6, + "gaussian_sigma_constant": 0.3, + "gaussian_sigma_type": "Constant", + "cutoff_function_type": "RadialScaling", + "cutoff_smooth_width": 0.5, + "cutoff_function_parameters": { + "rate": 1, + "scale": 3.5, + "exponent": 4, + }, + "radial_basis": "GTO", + "normalize": True, + "optimization": { + "Spline": { + "accuracy": 1.0e-05, + }, + }, + "compute_gradients": False, +} + +# Generate a SOAP spherical expansion +soap = SphericalInvariants(**soap_hypers) + +# Perform a data trasnformation and get the descriptor with samples as atomic environments +atom_dscrptr = soap.transform(frames).get_features(soap) + +# Calculate the stucture features as the mean over the atomic features for each +# structure +struct_dscrptr = np.zeros((len(frames), atom_dscrptr.shape[1])) +atom_idx_start = 0 +for i, frame in enumerate(frames): + atom_idx_stop = atom_idx_start + len(frame.numbers) + struct_dscrptr[i] = atom_dscrptr[atom_idx_start:atom_idx_stop].mean(axis=0) + atom_idx_start = atom_idx_stop + +print("atom feature descriptor shape:", atom_dscrptr.shape) +print("structure feature descriptor shape:", struct_dscrptr.shape) + + +# %% +# Perform structure (i.e. sample) selection +# ----------------------------------------- +# +# Using FPS and CUR algorithms implemented in scikit-matter, select a subset of +# the structures. skmatter assumes that our descriptor is represented as a 2D +# matrix, with the samples along axis 0 and features along axis 1. +# +# For more info on the functions: `skmatter +# `_ + +# Define the number of structures to select using FPS/CUR +n_structures = 25 + +# FPS sample selection +struct_fps = sample_selection.FPS(n_to_select=n_structures, initialize="random").fit( + struct_dscrptr +) +struct_fps_idxs = struct_fps.selected_idx_ + +# CUR sample selection +struct_cur = sample_selection.CUR(n_to_select=n_structures).fit(struct_dscrptr) +struct_cur_idxs = struct_cur.selected_idx_ + +print("Structure indices obtained with FPS ", struct_fps_idxs) +print("Structure indices obtained with CUR ", struct_cur_idxs) + +# Slice structure descriptor along axis 0 to contain only the selected structures +struct_dscrptr_fps = struct_dscrptr[struct_fps_idxs, :] +struct_dscrptr_cur = struct_dscrptr[struct_cur_idxs, :] +assert struct_dscrptr_fps.shape == struct_dscrptr_cur.shape + +print("Structure descriptor shape before selection ", struct_dscrptr.shape) +print("Structure descriptor shape after selection ", struct_dscrptr_fps.shape) + + +# %% +# Visualize selected structures with chemiscope +# --------------------------------------------- +# +# 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. +# +# Note: chemiscope widgets are not currently integrated into our sphinx gallery: +# coming soon. + +# Generate a structure PCA +struct_dscrptr_pca = PCA(n_components=2).fit_transform(struct_dscrptr) +assert struct_dscrptr_pca.shape == (n_frames, 2) + +# 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 + selection_levels.append(level) + + +properties = { + "PC1": struct_dscrptr_pca[:, 0], + "PC2": struct_dscrptr_pca[:, 1], + "Selection: (1) CUR, (2) FPS, (3) both": np.array(selection_levels), +} + + +# Display with chemiscope. This currently does not work - as raised in issue #8 +# https://github.com/lab-cosmo/software-cookbook/issues/8 +# chemiscope.show(frames, properties=properties) + + +# %% +# 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. + +# 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_dscrptr +) +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_dscrptr[:, feat_fps_idxs] + +print("atomic descriptor shape before selection ", atom_dscrptr.shape) +print("atomic descriptor shape after selection ", atom_dscrptr_fps.shape) + +# %% diff --git a/ipynb_to_gallery.py b/ipynb_to_gallery.py new file mode 100755 index 00000000..80bff5b5 --- /dev/null +++ b/ipynb_to_gallery.py @@ -0,0 +1,47 @@ +#!/usr/bin/env python +""" +Code is from +https://gist.github.com/chsasank/7218ca16f8d022e02a9c0deb94a310fe + +Convert jupyter notebook to sphinx gallery notebook styled examples. + +Usage: python ipynb_to_gallery.py + +Dependencies: +pypandoc: install using `pip install pypandoc` +""" +import pypandoc as pdoc +import json + +def convert_ipynb_to_gallery(file_name): + python_file = "" + + nb_dict = json.load(open(file_name)) + cells = nb_dict['cells'] + + for i, cell in enumerate(cells): + if i == 0: + assert cell['cell_type'] == 'markdown', \ + 'First cell has to be markdown' + + md_source = ''.join(cell['source']) + rst_source = pdoc.convert_text(md_source, 'rst', 'md') + python_file = '"""\n' + rst_source + '\n"""' + else: + if cell['cell_type'] == 'markdown': + md_source = ''.join(cell['source']) + rst_source = pdoc.convert_text(md_source, 'rst', 'md') + commented_source = '\n'.join(['# ' + x for x in + rst_source.split('\n')]) + python_file = python_file + "\n\n\n # %% \n" + \ + commented_source + elif cell['cell_type'] == 'code': + source = ''.join(cell['source']) + python_file = python_file + '\n' * 2 + source + + python_file = python_file.replace("\n%", "\n# %") + open(file_name.replace('.ipynb', '.py'), 'w').write(python_file) + +if __name__ == '__main__': + import sys + convert_ipynb_to_gallery(sys.argv[-1]) diff --git a/latest/.doctrees/environment.pickle b/latest/.doctrees/environment.pickle new file mode 100644 index 0000000000000000000000000000000000000000..de8eccd4346bf487f755326dc6053ca5b6c46ca8 GIT binary patch literal 260715 zcmeFa37lNlStn}kQfZfMS&o-nm%LQVUDcbqC3V!EwB?qpNZm4O*_M%&>f2SfyXvaC zs$929-EE-|2m#65fFYHHkOT+=12Zfyfxu%JhAn|WfB<2e47?eZFz-Ev-SF@!; ze#y$0tL~nsE7@FnD)8w2)xNK*Ua!X74Q8=eopB@SLaJP{taP?ib?=dFRLa?0B3U%c znOt_h>TXTWmP^m!SM~jI3 zWgh>pW_Gz7(S=iWH_g*nsBU>FS9P}~WY12uTs@DroKlJgk=Yi@L^9hmJ2E>nyYRo= z?gqS(Wm1LwLUyt0?vw*nzc-%{FTB}pD_pforEJ=AFj;q#W0fmBTWh6k<(+IH?^G{i zE_W-St&|g2v(|E|kjAv`7f+LmW-e!yRuj2`nNB+8)tpte++AgBshBg%mcsx-Gj1g5 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algorithms +implemented in scikit-matter. + +First, import all the necessary packages +""" + +# %% + +import ase.io +import numpy as np +from rascal.representations import SphericalInvariants +from sklearn.decomposition import PCA +from skmatter import feature_selection, sample_selection + + +# %% +# Load molecular data +# ------------------- +# +# Load 100 example BTO structures from file, reading them using +# `ASE `_. + +# Load a subset of structures of the example dataset +n_frames = 250 +frames = ase.io.read("./dataset/input-fps.xyz", f":{n_frames}", format="extxyz") + +# librascal requires the atomic positions to be wrapped in the cell +for frame in frames: + frame.wrap(eps=1.0e-12) + + +# %% +# Compute SOAP descriptor using librascal +# --------------------------------------- +# +# First, define the librascal hyperparameters used to compute SOAP. + +# librascal hyperparameters +soap_hypers = { + "soap_type": "PowerSpectrum", + "interaction_cutoff": 6.0, + "max_radial": 8, + "max_angular": 6, + "gaussian_sigma_constant": 0.3, + "gaussian_sigma_type": "Constant", + "cutoff_function_type": "RadialScaling", + "cutoff_smooth_width": 0.5, + "cutoff_function_parameters": { + "rate": 1, + "scale": 3.5, + "exponent": 4, + }, + "radial_basis": "GTO", + "normalize": True, + "optimization": { + "Spline": { + "accuracy": 1.0e-05, + }, + }, + "compute_gradients": False, +} + +# Generate a SOAP spherical expansion +soap = SphericalInvariants(**soap_hypers) + +# Perform a data trasnformation and get the descriptor with samples as atomic +# environments +atom_dscrptr = soap.transform(frames).get_features(soap) + +# Calculate the stucture features as the mean over the atomic features for each +# structure +struct_dscrptr = np.zeros((len(frames), atom_dscrptr.shape[1])) +atom_idx_start = 0 +for i, frame in enumerate(frames): + atom_idx_stop = atom_idx_start + len(frame.numbers) + struct_dscrptr[i] = atom_dscrptr[atom_idx_start:atom_idx_stop].mean(axis=0) + atom_idx_start = atom_idx_stop + +print("atom feature descriptor shape:", atom_dscrptr.shape) +print("structure feature descriptor shape:", struct_dscrptr.shape) + + +# %% +# Perform structure (i.e. sample) selection +# ----------------------------------------- +# +# Using FPS and CUR algorithms implemented in scikit-matter, select a subset of +# the structures. skmatter assumes that our descriptor is represented as a 2D +# matrix, with the samples along axis 0 and features along axis 1. +# +# For more info on the functions: `skmatter +# `_ + +# Define the number of structures to select using FPS/CUR +n_structures = 25 + +# FPS sample selection +struct_fps = sample_selection.FPS(n_to_select=n_structures, initialize="random").fit( + struct_dscrptr +) +struct_fps_idxs = struct_fps.selected_idx_ + +# CUR sample selection +struct_cur = sample_selection.CUR(n_to_select=n_structures).fit(struct_dscrptr) +struct_cur_idxs = struct_cur.selected_idx_ + +print("Structure indices obtained with FPS ", struct_fps_idxs) +print("Structure indices obtained with CUR ", struct_cur_idxs) + +# Slice structure descriptor along axis 0 to contain only the selected structures +struct_dscrptr_fps = struct_dscrptr[struct_fps_idxs, :] +struct_dscrptr_cur = struct_dscrptr[struct_cur_idxs, :] +assert struct_dscrptr_fps.shape == struct_dscrptr_cur.shape + +print("Structure descriptor shape before selection ", struct_dscrptr.shape) +print("Structure descriptor shape after selection ", struct_dscrptr_fps.shape) + + +# %% +# Visualize selected structures with chemiscope +# --------------------------------------------- +# +# 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. +# +# Note: chemiscope widgets are not currently integrated into our sphinx gallery: +# coming soon. + +# Generate a structure PCA +struct_dscrptr_pca = PCA(n_components=2).fit_transform(struct_dscrptr) +assert struct_dscrptr_pca.shape == (n_frames, 2) + +# 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 + selection_levels.append(level) + + +properties = { + "PC1": struct_dscrptr_pca[:, 0], + "PC2": struct_dscrptr_pca[:, 1], + "Selection: (1) CUR, (2) FPS, (3) both": np.array(selection_levels), +} + + +# Display with chemiscope. This currently does not work - as raised in issue #8 +# https://github.com/lab-cosmo/software-cookbook/issues/8 +# chemiscope.show(frames, properties=properties) + + +# %% +# 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. + +# 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_dscrptr +) +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_dscrptr[:, feat_fps_idxs] + +print("atomic descriptor shape before selection ", atom_dscrptr.shape) +print("atomic descriptor shape after selection ", atom_dscrptr_fps.shape) + +# %% diff --git a/latest/_downloads/5ee7c668c022f1e7e8282ea24c67c0fb/lode_tutorial.py b/latest/_downloads/5ee7c668c022f1e7e8282ea24c67c0fb/lode_tutorial.py new file mode 100644 index 00000000..1c654d6e --- /dev/null +++ b/latest/_downloads/5ee7c668c022f1e7e8282ea24c67c0fb/lode_tutorial.py @@ -0,0 +1,391 @@ +""" +LODE Tutorial +============= + +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 +# structures of the charge-charge structures. + +frames = ase.io.read("dataset/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/latest/_downloads/76541ec3f2a2c0e75aa5ac99c3cab20e/gaas_map.ipynb b/latest/_downloads/76541ec3f2a2c0e75aa5ac99c3cab20e/gaas_map.ipynb new file mode 100644 index 00000000..21cc5a7e --- /dev/null +++ b/latest/_downloads/76541ec3f2a2c0e75aa5ac99c3cab20e/gaas_map.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# PCA/PCovR Visualization for the rattled GaAs training dataset\n\nThis example uses ``rascaline`` and ``metatensor`` to compute\nstructural properties for the structures in a training for a ML model.\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" + ] + }, + { + "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" + ] + }, + { + "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)\")\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.\")\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.)\")" + ] + }, + { + "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\n# shows chemiscope if run in a jupyter environment\nif chemiscope.jupyter._is_running_in_notebook():\n from IPython.display import display\n\n display(cs)\nelse:\n cs.save(\"gaas_map.chemiscope.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": "3.11.7" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/latest/_downloads/bd58737fee6cee3544e6e7429ec023f1/lode_tutorial.ipynb b/latest/_downloads/bd58737fee6cee3544e6e7429ec023f1/lode_tutorial.ipynb new file mode 100644 index 00000000..cc5d7a26 --- /dev/null +++ b/latest/_downloads/bd58737fee6cee3544e6e7429ec023f1/lode_tutorial.ipynb @@ -0,0 +1,446 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# LODE Tutorial\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\nstructures of the charge-charge structures.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "frames = ase.io.read(\"dataset/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": "3.11.7" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/latest/_downloads/bf627fc2e9873db239d4716ae77bb54b/roy_gch.py b/latest/_downloads/bf627fc2e9873db239d4716ae77bb54b/roy_gch.py new file mode 100644 index 00000000..5b59ae97 --- /dev/null +++ b/latest/_downloads/bf627fc2e9873db239d4716ae77bb54b/roy_gch.py @@ -0,0 +1,292 @@ +""" +Generalized Convex Hull construction for the polymorphs of ROY +============================================================== + +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. +""" + +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 + +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") + +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``. +# This runs only in a notebook, and +# requires having the ``chemiscope`` package installed. +# + +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}}], + }, +) + + +if chemiscope.jupyter._is_running_in_notebook(): + from IPython.display import display + + display(cs) +else: + 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") + + +# %% +# 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) + + +# %% +# 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 ``chemiscope``. This runs only in a notebook, and +# requires having the ``chemiscope`` package installed. + +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}) + +# shows chemiscope if not run in terminal + +cs = chemiscope.show( + 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, + } + ], + }, +) + +if chemiscope.jupyter._is_running_in_notebook(): + from IPython.display import display + + display(cs) +else: + cs.save("roy_gch.json.gz") diff --git a/latest/_downloads/c234d1126d228edfa069b509e3d5c272/roy_gch.ipynb b/latest/_downloads/c234d1126d228edfa069b509e3d5c272/roy_gch.ipynb new file mode 100644 index 00000000..2303324b --- /dev/null +++ b/latest/_downloads/c234d1126d228edfa069b509e3d5c272/roy_gch.ipynb @@ -0,0 +1,248 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Generalized Convex Hull construction for the polymorphs of ROY\n\nThis notebook analyzes the structures of 264 polymorphs of ROY, from\n[Beran et Al, Chemical Science\n(2022)](https://doi.org/10.1039/D1SC06074K)_, comparing the\nconventional 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" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import 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\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\")\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``.\nThis runs only in a notebook, and\nrequires having the ``chemiscope`` package installed.\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)\n\n\nif chemiscope.jupyter._is_running_in_notebook():\n from IPython.display import display\n\n display(cs)\nelse:\n 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\")" + ] + }, + { + "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)" + ] + }, + { + "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 ``chemiscope``. This runs only in a notebook, and\nrequires having the ``chemiscope`` package installed.\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# shows chemiscope if not run in terminal\n\ncs = chemiscope.show(\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)\n\nif chemiscope.jupyter._is_running_in_notebook():\n from IPython.display import display\n\n display(cs)\nelse:\n cs.save(\"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": "3.11.7" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/latest/_downloads/cb2b037563d576b77358c4e2fe6b4432/gaas_map.py b/latest/_downloads/cb2b037563d576b77358c4e2fe6b4432/gaas_map.py new file mode 100644 index 00000000..00d181b7 --- /dev/null +++ b/latest/_downloads/cb2b037563d576b77358c4e2fe6b4432/gaas_map.py @@ -0,0 +1,252 @@ +""" +PCA/PCovR Visualization for the rattled GaAs training dataset +============================================================= + +This example uses ``rascaline`` and ``metatensor`` to compute +structural properties for the structures in a training for a ML model. +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``. + +""" + +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 + + +###################################################################### +# 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)") +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.") + +# 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.)") + + +###################################################################### +# 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", + ], + }, +) + +# shows chemiscope if run in a jupyter environment +if chemiscope.jupyter._is_running_in_notebook(): + from IPython.display import display + + display(cs) +else: + cs.save("gaas_map.chemiscope.json.gz") diff --git a/latest/_downloads/e1ca15af773f318752c2e2473a52e689/sample_selection_librascal.ipynb b/latest/_downloads/e1ca15af773f318752c2e2473a52e689/sample_selection_librascal.ipynb new file mode 100644 index 00000000..577c6d6f --- /dev/null +++ b/latest/_downloads/e1ca15af773f318752c2e2473a52e689/sample_selection_librascal.ipynb @@ -0,0 +1,133 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Sample Selection with FPS and CUR (librascal)\n\n.. start-body\n\nIn this tutorial we generate descriptors using librascal, then select a subset\nof structures using both the farthest-point sampling (FPS) and CUR algorithms\nimplemented in scikit-matter.\n\nFirst, import all the necessary packages\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import ase.io\nimport numpy as np\nfrom rascal.representations import SphericalInvariants\nfrom sklearn.decomposition import PCA\nfrom skmatter import feature_selection, sample_selection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Load molecular data\n\nLoad 100 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 structures of the example dataset\nn_frames = 250\nframes = ase.io.read(\"./dataset/input-fps.xyz\", f\":{n_frames}\", format=\"extxyz\")\n\n# librascal requires the atomic positions to be wrapped in the cell\nfor frame in frames:\n frame.wrap(eps=1.0e-12)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute SOAP descriptor using librascal\n\nFirst, define the librascal hyperparameters used to compute SOAP.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# librascal hyperparameters\nsoap_hypers = {\n \"soap_type\": \"PowerSpectrum\",\n \"interaction_cutoff\": 6.0,\n \"max_radial\": 8,\n \"max_angular\": 6,\n \"gaussian_sigma_constant\": 0.3,\n \"gaussian_sigma_type\": \"Constant\",\n \"cutoff_function_type\": \"RadialScaling\",\n \"cutoff_smooth_width\": 0.5,\n \"cutoff_function_parameters\": {\n \"rate\": 1,\n \"scale\": 3.5,\n \"exponent\": 4,\n },\n \"radial_basis\": \"GTO\",\n \"normalize\": True,\n \"optimization\": {\n \"Spline\": {\n \"accuracy\": 1.0e-05,\n },\n },\n \"compute_gradients\": False,\n}\n\n# Generate a SOAP spherical expansion\nsoap = SphericalInvariants(**soap_hypers)\n\n# Perform a data trasnformation and get the descriptor with samples as atomic\n# environments\natom_dscrptr = soap.transform(frames).get_features(soap)\n\n# Calculate the stucture features as the mean over the atomic features for each\n# structure\nstruct_dscrptr = np.zeros((len(frames), atom_dscrptr.shape[1]))\natom_idx_start = 0\nfor i, frame in enumerate(frames):\n atom_idx_stop = atom_idx_start + len(frame.numbers)\n struct_dscrptr[i] = atom_dscrptr[atom_idx_start:atom_idx_stop].mean(axis=0)\n atom_idx_start = atom_idx_stop\n\nprint(\"atom feature descriptor shape:\", atom_dscrptr.shape)\nprint(\"structure feature descriptor shape:\", struct_dscrptr.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Perform structure (i.e. sample) selection\n\nUsing FPS and CUR algorithms implemented in scikit-matter, select a subset of\nthe structures. skmatter assumes that our descriptor is represented as a 2D\nmatrix, with the samples along axis 0 and features along axis 1.\n\nFor more info on the functions: [skmatter](https://scikit-cosmo.readthedocs.io/en/latest/selection.html)\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Define the number of structures to select using FPS/CUR\nn_structures = 25\n\n# FPS sample selection\nstruct_fps = sample_selection.FPS(n_to_select=n_structures, initialize=\"random\").fit(\n struct_dscrptr\n)\nstruct_fps_idxs = struct_fps.selected_idx_\n\n# CUR sample selection\nstruct_cur = sample_selection.CUR(n_to_select=n_structures).fit(struct_dscrptr)\nstruct_cur_idxs = struct_cur.selected_idx_\n\nprint(\"Structure indices obtained with FPS \", struct_fps_idxs)\nprint(\"Structure indices obtained with CUR \", struct_cur_idxs)\n\n# Slice structure descriptor along axis 0 to contain only the selected structures\nstruct_dscrptr_fps = struct_dscrptr[struct_fps_idxs, :]\nstruct_dscrptr_cur = struct_dscrptr[struct_cur_idxs, :]\nassert struct_dscrptr_fps.shape == struct_dscrptr_cur.shape\n\nprint(\"Structure descriptor shape before selection \", struct_dscrptr.shape)\nprint(\"Structure descriptor shape after selection \", struct_dscrptr_fps.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Visualize selected structures with chemiscope\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\nNote: chemiscope widgets are not currently integrated into our sphinx gallery:\ncoming soon.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Generate a structure PCA\nstruct_dscrptr_pca = PCA(n_components=2).fit_transform(struct_dscrptr)\nassert struct_dscrptr_pca.shape == (n_frames, 2)\n\n# 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 selection_levels.append(level)\n\n\nproperties = {\n \"PC1\": struct_dscrptr_pca[:, 0],\n \"PC2\": struct_dscrptr_pca[:, 1],\n \"Selection: (1) CUR, (2) FPS, (3) both\": np.array(selection_levels),\n}\n\n\n# Display with chemiscope. This currently does not work - as raised in issue #8\n# https://github.com/lab-cosmo/software-cookbook/issues/8\n# chemiscope.show(frames, properties=properties)" + ] + }, + { + "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": [ + "# 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_dscrptr\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_dscrptr[:, feat_fps_idxs]\n\nprint(\"atomic descriptor shape before selection \", atom_dscrptr.shape)\nprint(\"atomic descriptor shape after selection \", atom_dscrptr_fps.shape)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + 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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 for the rattled GaAs training dataset +============================================================= + +This example uses ``rascaline`` and ``metatensor`` to compute +structural properties for the structures in a training for a ML model. +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``. + +.. GENERATED FROM PYTHON SOURCE LINES 13-30 + +.. 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 + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 31-37 + +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 37-51 + +.. 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 52-65 + +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 65-88 + +.. 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 89-92 + +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 92-100 + +.. 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)") + 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 101-108 + +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 108-135 + +.. 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 136-139 + +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 139-144 + +.. code-block:: Python + + + sf_energy = StandardFlexibleScaler().fit_transform(cohesive_peratom.reshape(-1, 1)) + sf_feats = StandardFlexibleScaler().fit_transform(features) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 145-157 + +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 157-181 + +.. 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.") + + # 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.)") + + + + + +.. 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 182-189 + +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 189-253 + +.. 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", + ], + }, + ) + + # shows chemiscope if run in a jupyter environment + if chemiscope.jupyter._is_running_in_notebook(): + from IPython.display import display + + display(cs) + else: + cs.save("gaas_map.chemiscope.json.gz") + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + /home/runner/work/software-cookbook/software-cookbook/.tox/gaas_map/conda/lib/python3.11/site-packages/chemiscope/jupyter.py:245: UserWarning: chemiscope.show only works inside a jupyter notebook + warnings.warn("chemiscope.show only works inside a jupyter notebook") + + + + + +.. _sphx_glr_download_examples_gaas_map_gaas_map.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + .. 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 ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/latest/_sources/examples/gaas_map/sg_execution_times.rst.txt b/latest/_sources/examples/gaas_map/sg_execution_times.rst.txt new file mode 100644 index 00000000..6ae60406 --- /dev/null +++ b/latest/_sources/examples/gaas_map/sg_execution_times.rst.txt @@ -0,0 +1,37 @@ + +:orphan: + +.. _sphx_glr_examples_gaas_map_sg_execution_times: + + +Computation times +================= +**00:48.747** total execution time for 1 file **from examples/gaas_map**: + +.. container:: + + .. raw:: html + + + + + + + + .. list-table:: + :header-rows: 1 + :class: table table-striped sg-datatable + + * - Example + - Time + - Mem (MB) + * - :ref:`sphx_glr_examples_gaas_map_gaas_map.py` (``gaas_map.py``) + - 00:48.747 + - 0.0 diff --git a/latest/_sources/examples/lode_linear/lode_tutorial.rst.txt b/latest/_sources/examples/lode_linear/lode_tutorial.rst.txt new file mode 100644 index 00000000..93115cbe --- /dev/null +++ b/latest/_sources/examples/lode_linear/lode_tutorial.rst.txt @@ -0,0 +1,724 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/lode_linear/lode_tutorial.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_tutorial.py: + + +LODE Tutorial +============= + +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 13-24 + +.. 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 25-39 + +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 +structures of the charge-charge structures. + +.. GENERATED FROM PYTHON SOURCE LINES 40-44 + +.. code-block:: Python + + + frames = ase.io.read("dataset/charge-charge.xyz", ":") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 45-52 + +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 53-57 + +.. code-block:: Python + + + y = ase_to_tensormap(frames, energy="energy", forces="forces") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 58-69 + +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 70-82 + +.. 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 83-84 + +And next the hyperparaters for the LODE / long-range (LR) part + +.. GENERATED FROM PYTHON SOURCE LINES 85-103 + +.. 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 104-106 + +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 106-111 + +.. code-block:: Python + + + calculator_sr = SphericalExpansion(**SR_HYPERS) + calculator_lr = LodeSphericalExpansion(**LR_HYPERS) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 112-132 + +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 133-138 + +.. 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 139-145 + +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 146-151 + +.. 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 152-161 + +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 162-167 + +.. 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 168-170 + +For linear models only: Sum features up over atoms (``samples``) in the same +structure. + +.. GENERATED FROM PYTHON SOURCE LINES 171-178 + +.. 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 179-185 + +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 186-193 + +.. 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 194-215 + +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 216-220 + +.. code-block:: Python + + + X_sr = metatensor.join([co, ps_sr], axis="properties") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 221-228 + +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 229-233 + +.. code-block:: Python + + + X_lr = metatensor.join([co, ps_sr, ps_lr], axis="properties") + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 234-241 + +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 242-247 + +.. code-block:: Python + + + clf_sr = Ridge() + clf_lr = Ridge() + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 248-254 + +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 255-259 + +.. code-block:: Python + + + r_cut = 6.0 + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 260-262 + +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 263-268 + +.. 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 269-271 + +For doing the split we define two ``Labels`` instances and combine them in a +:py:class:`List`. + +.. GENERATED FROM PYTHON SOURCE LINES 272-278 + +.. 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 279-280 + +That we use as input to the :py:func:`metatensor.split()` function + +.. GENERATED FROM PYTHON SOURCE LINES 281-293 + +.. 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 294-301 + +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 302-307 + +.. 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 308-313 + +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 314-334 + +.. 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 335-341 + +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 342-348 + +.. 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 349-350 + +and select only the indices corresponding to our test set. + +.. GENERATED FROM PYTHON SOURCE LINES 354-355 + +Next we calculate the predicted SR and LR ``TensorMaps``. + +.. GENERATED FROM PYTHON SOURCE LINES 356-361 + +.. code-block:: Python + + + y_sr_pred = clf_sr.predict(X_sr) + y_lr_pred = clf_lr.predict(X_lr) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 362-363 + +And, finally perform the plot. + +.. GENERATED FROM PYTHON SOURCE LINES 364-392 + +.. 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_tutorial_001.png + :alt: lode tutorial + :srcset: /examples/lode_linear/images/sphx_glr_lode_tutorial_001.png + :class: sphx-glr-single-img + + + + + + +.. _sphx_glr_download_examples_lode_linear_lode_tutorial.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: lode_tutorial.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: lode_tutorial.py ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/latest/_sources/examples/lode_linear/sg_execution_times.rst.txt b/latest/_sources/examples/lode_linear/sg_execution_times.rst.txt new file mode 100644 index 00000000..87bee085 --- /dev/null +++ b/latest/_sources/examples/lode_linear/sg_execution_times.rst.txt @@ -0,0 +1,37 @@ + +:orphan: + +.. _sphx_glr_examples_lode_linear_sg_execution_times: + + +Computation times +================= +**00:09.253** total execution time for 1 file **from examples/lode_linear**: + +.. container:: + + .. raw:: html + + + + + + + + .. list-table:: + :header-rows: 1 + :class: table table-striped sg-datatable + + * - Example + - Time + - Mem (MB) + * - :ref:`sphx_glr_examples_lode_linear_lode_tutorial.py` (``lode_tutorial.py``) + - 00:09.253 + - 0.0 diff --git a/latest/_sources/examples/roy_gch/roy_gch.rst.txt b/latest/_sources/examples/roy_gch/roy_gch.rst.txt new file mode 100644 index 00000000..6b250303 --- /dev/null +++ b/latest/_sources/examples/roy_gch/roy_gch.rst.txt @@ -0,0 +1,534 @@ + +.. 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 +============================================================== + +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. + +.. GENERATED FROM PYTHON SOURCE LINES 16-28 + +.. code-block:: Python + + + 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 29-30 + +Loads the structures (that also contain properties in the ``info`` field) + +.. GENERATED FROM PYTHON SOURCE LINES 30-42 + +.. 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 43-48 + +Energy-density hull +------------------- + +The Directional Convex Hull routines can be used to compute a +conventional density-energy hull + +.. GENERATED FROM PYTHON SOURCE LINES 48-52 + +.. 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 53-55 + +We can get the indices of the selection, and compute the distance from +the hull + +.. GENERATED FROM PYTHON SOURCE LINES 55-60 + +.. code-block:: Python + + + sel = dch_builder.selected_idx_ + dch_dist = dch_builder.score_samples(density.reshape(-1, 1), energy) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 61-72 + +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 73-87 + +.. 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") + + 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 88-95 + +Interactive visualization +^^^^^^^^^^^^^^^^^^^^^^^^^ + +You can also visualize the hull with ``chemiscope``. +This runs only in a notebook, and +requires having the ``chemiscope`` package installed. + + +.. GENERATED FROM PYTHON SOURCE LINES 95-124 + +.. 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}}], + }, + ) + + + if chemiscope.jupyter._is_running_in_notebook(): + from IPython.display import display + + display(cs) + else: + cs.save("roy_ch.json.gz") + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + /home/runner/work/software-cookbook/software-cookbook/.tox/roy_gch/conda/lib/python3.11/site-packages/chemiscope/jupyter.py:245: UserWarning: chemiscope.show only works inside a jupyter notebook + warnings.warn("chemiscope.show only works inside a jupyter notebook") + + + + +.. GENERATED FROM PYTHON SOURCE LINES 125-137 + +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 140-148 + +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 148-171 + +.. 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 172-178 + +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 178-190 + +.. 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") + + + + + +.. 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 191-195 + +Builds the Generalized Convex Hull +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Builds a convex hull on the first two PCA features + +.. GENERATED FROM PYTHON SOURCE LINES 195-202 + +.. 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 203-205 + +Generates a 3D Plot + + +.. GENERATED FROM PYTHON SOURCE LINES 205-217 + +.. 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) + + + + + +.. 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 218-221 + +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 221-228 + +.. 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 0.8537845044693283 kJ/mol + Mean hull energy for 'other' structures 5.198871581845225 kJ/mol + + + + +.. GENERATED FROM PYTHON SOURCE LINES 229-231 + +Visualize in ``chemiscope``. This runs only in a notebook, and +requires having the ``chemiscope`` package installed. + +.. GENERATED FROM PYTHON SOURCE LINES 231-293 + +.. 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}) + + # shows chemiscope if not run in terminal + + cs = chemiscope.show( + 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, + } + ], + }, + ) + + if chemiscope.jupyter._is_running_in_notebook(): + from IPython.display import display + + display(cs) + else: + cs.save("roy_gch.json.gz") + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + /home/runner/work/software-cookbook/software-cookbook/.tox/roy_gch/conda/lib/python3.11/site-packages/chemiscope/jupyter.py:245: UserWarning: chemiscope.show only works inside a jupyter notebook + warnings.warn("chemiscope.show only works inside a jupyter notebook") + + + + + +.. _sphx_glr_download_examples_roy_gch_roy_gch.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + .. 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 ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/latest/_sources/examples/roy_gch/sg_execution_times.rst.txt b/latest/_sources/examples/roy_gch/sg_execution_times.rst.txt new file mode 100644 index 00000000..c08ed0de --- /dev/null +++ b/latest/_sources/examples/roy_gch/sg_execution_times.rst.txt @@ -0,0 +1,37 @@ + +:orphan: + +.. _sphx_glr_examples_roy_gch_sg_execution_times: + + +Computation times +================= +**00:18.164** total execution time for 1 file **from examples/roy_gch**: + +.. container:: + + .. raw:: html + + + + + + + + .. list-table:: + :header-rows: 1 + :class: table table-striped sg-datatable + + * - Example + - Time + - Mem (MB) + * - :ref:`sphx_glr_examples_roy_gch_roy_gch.py` (``roy_gch.py``) + - 00:18.164 + - 0.0 diff --git a/latest/_sources/examples/sample_selection/sample_selection_librascal.rst.txt b/latest/_sources/examples/sample_selection/sample_selection_librascal.rst.txt new file mode 100644 index 00000000..137a5441 --- /dev/null +++ b/latest/_sources/examples/sample_selection/sample_selection_librascal.rst.txt @@ -0,0 +1,342 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "examples/sample_selection/sample_selection_librascal.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_librascal.py: + + +Sample Selection with FPS and CUR (librascal) +============================================= + +.. start-body + +In this tutorial we generate descriptors using librascal, then select a subset +of structures using both the farthest-point sampling (FPS) and CUR algorithms +implemented in scikit-matter. + +First, import all the necessary packages + +.. GENERATED FROM PYTHON SOURCE LINES 15-23 + +.. code-block:: Python + + + import ase.io + import numpy as np + from rascal.representations import SphericalInvariants + from sklearn.decomposition import PCA + from skmatter import feature_selection, sample_selection + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 24-29 + +Load molecular data +------------------- + +Load 100 example BTO structures from file, reading them using +`ASE `_. + +.. GENERATED FROM PYTHON SOURCE LINES 29-39 + +.. code-block:: Python + + + # Load a subset of structures of the example dataset + n_frames = 250 + frames = ase.io.read("./dataset/input-fps.xyz", f":{n_frames}", format="extxyz") + + # librascal requires the atomic positions to be wrapped in the cell + for frame in frames: + frame.wrap(eps=1.0e-12) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 40-44 + +Compute SOAP descriptor using librascal +--------------------------------------- + +First, define the librascal hyperparameters used to compute SOAP. + +.. GENERATED FROM PYTHON SOURCE LINES 44-90 + +.. code-block:: Python + + + # librascal hyperparameters + soap_hypers = { + "soap_type": "PowerSpectrum", + "interaction_cutoff": 6.0, + "max_radial": 8, + "max_angular": 6, + "gaussian_sigma_constant": 0.3, + "gaussian_sigma_type": "Constant", + "cutoff_function_type": "RadialScaling", + "cutoff_smooth_width": 0.5, + "cutoff_function_parameters": { + "rate": 1, + "scale": 3.5, + "exponent": 4, + }, + "radial_basis": "GTO", + "normalize": True, + "optimization": { + "Spline": { + "accuracy": 1.0e-05, + }, + }, + "compute_gradients": False, + } + + # Generate a SOAP spherical expansion + soap = SphericalInvariants(**soap_hypers) + + # Perform a data trasnformation and get the descriptor with samples as atomic + # environments + atom_dscrptr = soap.transform(frames).get_features(soap) + + # Calculate the stucture features as the mean over the atomic features for each + # structure + struct_dscrptr = np.zeros((len(frames), atom_dscrptr.shape[1])) + atom_idx_start = 0 + for i, frame in enumerate(frames): + atom_idx_stop = atom_idx_start + len(frame.numbers) + struct_dscrptr[i] = atom_dscrptr[atom_idx_start:atom_idx_stop].mean(axis=0) + atom_idx_start = atom_idx_stop + + print("atom feature descriptor shape:", atom_dscrptr.shape) + print("structure feature descriptor shape:", struct_dscrptr.shape) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + atom feature descriptor shape: (10000, 2688) + structure feature descriptor shape: (250, 2688) + + + + +.. GENERATED FROM PYTHON SOURCE LINES 91-100 + +Perform structure (i.e. sample) selection +----------------------------------------- + +Using FPS and CUR algorithms implemented in scikit-matter, select a subset of +the structures. skmatter assumes that our descriptor is represented as a 2D +matrix, with the samples along axis 0 and features along axis 1. + +For more info on the functions: `skmatter +`_ + +.. GENERATED FROM PYTHON SOURCE LINES 100-126 + +.. code-block:: Python + + + # Define the number of structures to select using FPS/CUR + n_structures = 25 + + # FPS sample selection + struct_fps = sample_selection.FPS(n_to_select=n_structures, initialize="random").fit( + struct_dscrptr + ) + struct_fps_idxs = struct_fps.selected_idx_ + + # CUR sample selection + struct_cur = sample_selection.CUR(n_to_select=n_structures).fit(struct_dscrptr) + struct_cur_idxs = struct_cur.selected_idx_ + + print("Structure indices obtained with FPS ", struct_fps_idxs) + print("Structure indices obtained with CUR ", struct_cur_idxs) + + # Slice structure descriptor along axis 0 to contain only the selected structures + struct_dscrptr_fps = struct_dscrptr[struct_fps_idxs, :] + struct_dscrptr_cur = struct_dscrptr[struct_cur_idxs, :] + assert struct_dscrptr_fps.shape == struct_dscrptr_cur.shape + + print("Structure descriptor shape before selection ", struct_dscrptr.shape) + print("Structure descriptor shape after selection ", struct_dscrptr_fps.shape) + + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Structure indices obtained with FPS [172 220 2 196 97 195 140 219 194 75 238 120 163 58 166 70 114 71 + 222 40 110 39 223 55 130] + Structure indices obtained with CUR [203 140 219 2 110 196 194 97 156 120 55 71 223 166 198 238 70 183 + 19 128 172 229 130 68 39] + Structure descriptor shape before selection (250, 2688) + Structure descriptor shape after selection (25, 2688) + + + + +.. GENERATED FROM PYTHON SOURCE LINES 127-136 + +Visualize selected structures with chemiscope +--------------------------------------------- + +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. + +Note: chemiscope widgets are not currently integrated into our sphinx gallery: +coming soon. + +.. GENERATED FROM PYTHON SOURCE LINES 136-164 + +.. code-block:: Python + + + # Generate a structure PCA + struct_dscrptr_pca = PCA(n_components=2).fit_transform(struct_dscrptr) + assert struct_dscrptr_pca.shape == (n_frames, 2) + + # 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 + selection_levels.append(level) + + + properties = { + "PC1": struct_dscrptr_pca[:, 0], + "PC2": struct_dscrptr_pca[:, 1], + "Selection: (1) CUR, (2) FPS, (3) both": np.array(selection_levels), + } + + + # Display with chemiscope. This currently does not work - as raised in issue #8 + # https://github.com/lab-cosmo/software-cookbook/issues/8 + # chemiscope.show(frames, properties=properties) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 165-171 + +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 171-189 + +.. code-block:: Python + + + # 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_dscrptr + ) + 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_dscrptr[:, feat_fps_idxs] + + print("atomic descriptor shape before selection ", atom_dscrptr.shape) + print("atomic descriptor shape after selection ", atom_dscrptr_fps.shape) + + + + + +.. rst-class:: sphx-glr-script-out + + .. code-block:: none + + Feature indices obtained with FPS [2607 0 1064 560 21 7 195 728 35 2016 1071 567 1089 203 + 189 2240 588 28 632 1232 1344 1085 735 91 756 130 196 2023 + 1098 1036 637 133 462 193 1092 630 1096 707 210 634 812 749 + 202 84 636 315 2247 643 917 1141 2048 209 644 151 1197 483 + 1204 592 2037 1211 651 1820 1176 657 147 1210 1040 1960 924 77 + 1472 322 1078 616 1981 1112 2492 1105 650 518 129 14 252 504 + 641 1931 688 2050 2429 1987 455 1365 140 1148 672 1091 2433 1103 + 805 1106 139 126 1253 2044 1208 1476 2436 1218 194 1029 1470 378 + 469 259 784 1260 595 1042 1596 1008 1351 623 1936 217 931 1099 + 1537 1848 476 2496 1927 910 706 2104 973 2282 1540 679 1154 83 + 2093 980 2268 207 2498 1934 266 655 1983 1372 539 42 1904 70 + 692 1475 1600 1988 1316 585 74 1015 1120 581 798 2442 2041 1043 + 1033 63 1309 1474 629 2113 693 742 131 1985 258 1992 1113 2440 + 49 1145 2254 329 1183 1813 690 959 700 1127 137 490 2156 2072 + 686 511 840 1162] + atomic descriptor shape before selection (10000, 2688) + atomic descriptor shape after selection (10000, 200) + + + + + +.. _sphx_glr_download_examples_sample_selection_sample_selection_librascal.py: + +.. only:: html + + .. container:: sphx-glr-footer sphx-glr-footer-example + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: sample_selection_librascal.ipynb ` + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: sample_selection_librascal.py ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/latest/_sources/examples/sample_selection/sg_execution_times.rst.txt b/latest/_sources/examples/sample_selection/sg_execution_times.rst.txt new file mode 100644 index 00000000..8f6e997b --- /dev/null +++ b/latest/_sources/examples/sample_selection/sg_execution_times.rst.txt @@ -0,0 +1,37 @@ + +:orphan: + +.. _sphx_glr_examples_sample_selection_sg_execution_times: + + +Computation times +================= +**00:03.464** total execution time for 1 file **from examples/sample_selection**: + +.. container:: + + .. raw:: html + + + + + + + + .. list-table:: + :header-rows: 1 + :class: table table-striped sg-datatable + + * - Example + - Time + - Mem (MB) + * - :ref:`sphx_glr_examples_sample_selection_sample_selection_librascal.py` (``sample_selection_librascal.py``) + - 00:03.464 + - 0.0 diff --git a/latest/_sources/index.rst.txt b/latest/_sources/index.rst.txt new file mode 100644 index 00000000..bbf6f3f9 --- /dev/null +++ b/latest/_sources/index.rst.txt @@ -0,0 +1,15 @@ +COSMO Software Cookbook +======================= + +.. include:: ../../README.rst + :start-after: marker-intro-start + :end-before: marker-intro-end + +.. toctree:: + :caption: Table of Contents + :maxdepth: 1 + + examples/roy_gch/roy_gch + examples/lode_linear/lode_tutorial + examples/sample_selection/sample_selection_librascal + examples/gaas_map/gaas_map diff --git a/latest/_sources/sg_execution_times.rst.txt b/latest/_sources/sg_execution_times.rst.txt new file mode 100644 index 00000000..f8768406 --- /dev/null +++ b/latest/_sources/sg_execution_times.rst.txt @@ -0,0 +1,37 @@ + +:orphan: + +.. _sphx_glr_sg_execution_times: + + +Computation times +================= +**00:48.747** total execution time for 1 file **from all galleries**: + +.. container:: + + .. raw:: html + + + + + + + + .. list-table:: + :header-rows: 1 + :class: table table-striped sg-datatable + + * - Example + - Time + - Mem (MB) + * - :ref:`sphx_glr_examples_gaas_map_gaas_map.py` (``../../examples/gaas_map/gaas_map.py``) + - 00:48.747 + - 0.0 diff --git a/latest/_static/basic.css b/latest/_static/basic.css new file mode 100644 index 00000000..30fee9d0 --- /dev/null +++ b/latest/_static/basic.css @@ -0,0 +1,925 @@ +/* + * basic.css + * ~~~~~~~~~ + * + * Sphinx stylesheet -- basic theme. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; +} + +div.section::after { + display: block; + content: ''; + clear: left; +} + +/* -- relbar 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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/latest/_static/documentation_options.js b/latest/_static/documentation_options.js new file mode 100644 index 00000000..7e4c114f --- /dev/null +++ b/latest/_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/latest/_static/file.png b/latest/_static/file.png new file mode 100644 index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3 GIT binary patch literal 286 zcmV+(0pb3MP)s`hMrGg#P~ix$^RISR_I47Y|r1 z_CyJOe}D1){SET-^Amu_i71Lt6eYfZjRyw@I6OQAIXXHDfiX^GbOlHe=Ae4>0m)d(f|Me07*qoM6N<$f}vM^LjV8( literal 0 HcmV?d00001 diff --git a/latest/_static/jupyterlite_badge_logo.svg b/latest/_static/jupyterlite_badge_logo.svg new file mode 100644 index 00000000..5de36d7f --- /dev/null +++ b/latest/_static/jupyterlite_badge_logo.svg @@ -0,0 +1,3 @@ + + +launchlaunchlitelite \ No newline at end of file diff --git a/latest/_static/language_data.js b/latest/_static/language_data.js new file mode 100644 index 00000000..250f5665 --- /dev/null +++ b/latest/_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 2007-2023 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, is 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 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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 globalThis === 'object') return globalThis;\n\ttry {\n\t\treturn this || new Function('return this')();\n\t} catch (e) {\n\t\tif (typeof window === 'object') return window;\n\t}\n})();","__webpack_require__.o = (obj, prop) => (Object.prototype.hasOwnProperty.call(obj, prop))","import Gumshoe from \"./gumshoe-patched.js\";\n\n////////////////////////////////////////////////////////////////////////////////\n// Scroll Handling\n////////////////////////////////////////////////////////////////////////////////\nvar tocScroll = null;\nvar header = null;\nvar lastScrollTop = window.pageYOffset || document.documentElement.scrollTop;\nconst GO_TO_TOP_OFFSET = 64;\n\nfunction scrollHandlerForHeader() {\n if (Math.floor(header.getBoundingClientRect().top) == 0) {\n header.classList.add(\"scrolled\");\n } else {\n header.classList.remove(\"scrolled\");\n }\n}\n\nfunction scrollHandlerForBackToTop(positionY) {\n if (positionY < GO_TO_TOP_OFFSET) {\n 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\ No newline at end of file diff --git a/latest/_static/searchtools.js b/latest/_static/searchtools.js new file mode 100644 index 00000000..7918c3fa --- /dev/null +++ b/latest/_static/searchtools.js @@ -0,0 +1,574 @@ +/* + * searchtools.js + * ~~~~~~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for the full-text search. + * + * :copyright: Copyright 2007-2023 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) + ); + // 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.` + ); +}; +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); +}; + +/** + * 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) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() }); + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent !== undefined) return docContent.textContent; + console.warn( + "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you 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); + }, + + /** + * execute search (requires search index to be loaded) + */ + query: (query) => { + 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; + + // 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]); + + // array of [docname, title, anchor, descr, score, filename] + let results = []; + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + let score = Math.round(100 * queryLower.length / title.length) + results.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score, + 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] of foundEntries) { + let score = Math.round(100 * queryLower.length / entry.length) + results.push([ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // lookup as object + objectTerms.forEach((term) => + results.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + results.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item))); + + // now sort the results by score (in opposite order of appearance, since the + // display function below uses pop() to retrieve items) and then + // alphabetically + results.sort((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; + }); + + // 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; + }, []); + + results = results.reverse(); + + // 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); + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord) && !terms[word]) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord) && !titleTerms[word]) + arr.push({ files: titleTerms[word], 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.get(file).indexOf(word) === -1) + fileMap.get(file).push(word); + else fileMap.set(file, [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) => { + const text = Search.htmlToText(htmlText); + 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/latest/_static/sg_gallery-binder.css b/latest/_static/sg_gallery-binder.css new file mode 100644 index 00000000..420005d2 --- /dev/null +++ b/latest/_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/latest/_static/sg_gallery-dataframe.css b/latest/_static/sg_gallery-dataframe.css new file mode 100644 index 00000000..fac74c43 --- /dev/null +++ b/latest/_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/latest/_static/sg_gallery-rendered-html.css b/latest/_static/sg_gallery-rendered-html.css new file mode 100644 index 00000000..93dc2ffb --- /dev/null +++ b/latest/_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/latest/_static/sg_gallery.css b/latest/_static/sg_gallery.css new file mode 100644 index 00000000..72227837 --- /dev/null +++ b/latest/_static/sg_gallery.css @@ -0,0 +1,342 @@ +/* +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]:hover:after { + background: var(--sg-tooltip-background); + -webkit-border-radius: 4px; + -moz-border-radius: 4px; + border-radius: 4px; + color: var(--sg-tooltip-foreground); + content: attr(tooltip); + padding: 10px; + z-index: 98; + width: 100%; + height: 100%; + position: absolute; + pointer-events: none; + top: 0; + box-sizing: border-box; + overflow: hidden; + backdrop-filter: blur(3px); +} + +.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); +} + +.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/latest/_static/skeleton.css b/latest/_static/skeleton.css new file mode 100644 index 00000000..467c878c --- /dev/null +++ b/latest/_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/latest/_static/sphinx_highlight.js b/latest/_static/sphinx_highlight.js new file mode 100644 index 00000000..8a96c69a --- /dev/null +++ b/latest/_static/sphinx_highlight.js @@ -0,0 +1,154 @@ +/* Highlighting 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( + '

" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!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.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(() => { + /* Do not call 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/latest/_static/styles/furo-extensions.css b/latest/_static/styles/furo-extensions.css new file mode 100644 index 00000000..bc447f22 --- /dev/null +++ b/latest/_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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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\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\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\n display: block\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\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: #646776; // 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: #2962ff;\n --color-brand-content: #2a5adf;\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 --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--hover: var(--color-brand-content);\n --color-link-underline: var(--color-background-border);\n --color-link-underline--hover: var(--color-foreground-border);\n}\n\n@mixin colors-dark {\n --color-problematic: #ee5151;\n\n // Base Colors\n --color-foreground-primary: #ffffffcc; // 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: #2b8cee;\n --color-brand-content: #368ce2;\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 // 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-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 &: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)\n text-decoration-color: var(--color-link-underline--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\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 vertical-align: middle\n\n.theme-toggle\n cursor: pointer\n border: none\n padding: 0\n background: transparent\n\n.theme-toggle svg\n vertical-align: middle\n height: 1rem\n width: 1rem\n color: var(--color-foreground-primary)\n display: none\n\n.theme-toggle-header\n float: left\n padding: 1rem 0.5rem\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: 1rem\n width: 1rem\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 svg\n color: inherit\n height: 1rem\n width: 1rem\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: $full-width - $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\n display: flex\n .toc-content-icon, .theme-toggle-content\n display: none\n .theme-toggle-header\n display: block\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: 1.25rem\n width: 1.25rem\n\n // Add a scroll margin for the content\n :target\n scroll-margin-top: var(--header-height)\n\n // Show back-to-top below the header\n .back-to-top\n top: calc(var(--header-height) + 0.5rem)\n\n // Center the page, and accommodate for the header.\n .page\n flex-direction: column\n justify-content: center\n .content\n margin-left: auto\n margin-right: auto\n\n@media (max-width: $content-width + 2* $content-padding)\n // Content should respect window limits.\n .content\n width: 100%\n overflow-x: auto\n\n@media (max-width: $content-width)\n .content\n padding: 0 $content-padding--small\n // Don't float sidebars to the right.\n article aside.sidebar\n float: none\n width: 100%\n margin: 1rem 0\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: 3.5rem\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\n.versionmodified\n font-style: italic\ndiv.versionadded, div.versionchanged, div.deprecated\n p\n margin-top: 0.125rem\n margin-bottom: 0.125rem\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 > p,\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",".table-wrapper\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: 0.5rem\n\n@media (max-width: $full-width - $sidebar-width)\n :target\n scroll-margin-top: calc(0.5rem + var(--header-height))\n\n // When a heading is selected\n section > span:target\n scroll-margin-top: calc(0.8rem + 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 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

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