metrics

src/beignet/center_of_mass.py

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+import torch
+
+
+def compute_center_of_mass(traj):
+    """Compute the center of mass for each frame.
+
+    Parameters
+    ----------
+    traj : Trajectory
+        Trajectory to compute center of mass for
+
+    Returns
+    -------
+    com : torch.Tensor, shape=(n_frames, 3)
+         Coordinates of the center of mass for each frame
+    """
+
+    com = torch.empty((traj.n_frames, 3))
+
+    masses = torch.tensor([a.element.mass for a in traj.top.atoms])
+    masses /= masses.sum()
+
+    xyz = traj.xyz
+
+    for i, x in enumerate(xyz):
+        com[i, :] = torch.tensordot(masses, x.double().t(), dims=0)
+
+    return com

src/beignet/gyration_tensor.py

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+import torch
+
+
+def _compute_center_of_geometry(traj):
+    """Compute the center of geometry for each frame.
+
+    Parameters
+    ----------
+    traj : Trajectory
+        Trajectory to compute center of geometry for.
+
+    Returns
+    -------
+    centers : torch.Tensor, shape=(n_frames, 3)
+         Coordinates of the center of geometry for each frame.
+
+    """
+
+    centers = torch.zeros((traj.n_frames, 3))
+
+    for i, x in enumerate(traj.xyz):
+        centers[i, :] = torch.mean(x.double().t(), dim=1)
+
+    return centers
+
+
+def gyration_tensor(traj):
+    """Compute the gyration tensor of a trajectory.
+
+        For every frame,
+
+        .. math::
+
+            S_{xy} = \sum_{i_atoms} r^{i}_x r^{i}_y
+
+        Parameters
+        ----------
+        traj : Trajectory
+            Trajectory to compute gyration tensor of.
+
+        Returns
+        -------
+        S_xy:  torch.Tensor, shape=(traj.n_frames, 3, 3), dtype=float64
+            Gyration tensors for each frame.
+
+        References
+        ----------
+        .. [1] https://isg.nist.gov/deepzoomweb/measurement3Ddata_help#shape-metrics-formulas
+
+        """
+    center_of_geom = torch.unsqueeze(_compute_center_of_geometry(traj), dim=1)
+
+    xyz = traj.xyz - center_of_geom
+
+    return torch.einsum('...ji,...jk->...ik', xyz, xyz) / traj.n_atoms

src/beignet/rmsd.py

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+import torch
+from scipy.spatial.transform import Rotation as R
+
+
+# TODO (isaacsoh) parallelize and speed up, eliminate 3-D requirement
+def _rmsd(traj1, traj2):
+    """
+
+    Parameters
+    ----------
+    traj1 : Trajectory
+        For each conformation in this trajectory, compute the RMSD to
+        a particular 'reference' conformation in another trajectory.
+    traj2 : Trajectory
+        The reference conformation to measure distances
+        to.
+
+    Returns
+    -------
+    rmsd_result : torch.Tensor
+        The rmsd calculation of two trajectories.
+    """
+
+    assert traj1.shape == traj2.shape, "Input tensors must have the same shape"
+    assert traj1.dim() == 3, "Input tensors must be 3-D (num_frames, num_atoms, 3)"
+
+    num_frames = traj1.shape[0]  # Number of frames
+
+    # Center the trajectories
+    traj1 = traj1 - traj1.mean(dim=1, keepdim=True)
+    traj2 = traj2 - traj2.mean(dim=1, keepdim=True)
+
+    # Initialization of the resulting RMSD tensor
+    rmsd_result = torch.zeros(num_frames).double()
+
+    for i in range(num_frames):
+        # For each configuration compute the rotation matrix minimizing RMSD using SVD
+        u, s, v = torch.svd(torch.mm(traj1[i].t(), traj2[i]))
+
+        # Determinat of u * v
+        d = (u * v).det().item() < 0.0
+
+        if d:
+            s[-1] = s[-1] * (-1)
+            u[:, -1] = u[:, -1] * (-1)
+
+        # Optimal rotation matrix
+        rot_matrix = torch.mm(v, u.t())
+
+        test = (R.from_matrix(rot_matrix)).as_matrix()
+
+        assert torch.allclose(torch.from_numpy(test), rot_matrix, rtol=1e-03, atol=1e-04)
+
+        # Calculate RMSD and append to resulting tensor
+        traj2[i] = torch.mm(traj2[i], rot_matrix)
+
+        rmsd_result[i] = torch.sqrt(
+            torch.sum((traj1[i] - traj2[i]) ** 2) / traj1.shape[1])
+
+    return rmsd_result