mdsuite.utils.linalg module

MDSuite: A Zincwarecode package.

License

This program and the accompanying materials are made available under the terms of the Eclipse Public License v2.0 which accompanies this distribution, and is available at https://www.eclipse.org/legal/epl-v20.html

SPDX-License-Identifier: EPL-2.0

Copyright Contributors to the Zincwarecode Project.

Contact Information

email: zincwarecode@gmail.com github: https://github.com/zincware web: https://zincwarecode.com/

Citation

If you use this module please cite us with:

Summary

mdsuite.utils.linalg.angle_between(v1, v2, acos=True)

Returns the angle in radians between vectors ‘v1’ and ‘v2’.

mdsuite.utils.linalg.apply_minimum_image(r_ij, box_array)

Parameters:

• r_ij (tf.Tensor) – an r_ij matrix of size (batches, atoms, 3)

• box_array (tf.Tensor) – a box array (3,)

mdsuite.utils.linalg.apply_system_cutoff(tensor: Tensor, cutoff: float) → Tensor

Enforce a cutoff on a tensor.

Parameters:

• tensor (tf.Tensor) –

• cutoff (flaot) –

mdsuite.utils.linalg.cartesian_to_spherical_coordinates(point_cartesian, name='cartesian_to_spherical_coordinates')

References

https://www.tensorflow.org/graphics/api_docs/python/tfg/math/math_helpers/cartesian_to_spherical_coordinates

Function to transform Cartesian coordinates to spherical coordinates. This function assumes a right handed coordinate system with z pointing up. When x and y are both 0, the function outputs 0 for phi. Note that the function is not smooth when x = y = 0. .. note:: In the following, A1 to An are optional batch dimensions.

Parameters:

• point_cartesian – A tensor of shape [A1, …, An, 3]. In the last dimension, the data follows the x, y, z order.

• eps – A small float, to be added to the denominator. If left as None, its value is automatically selected using point_cartesian.dtype.

• name – A name for this op. Defaults to “cartesian_to_spherical_coordinates”.

Returns:

• A tensor of shape [A1, …, An, 3]. The last dimensions contains

• (r,`theta`,`phi`), where r is the sphere radius, theta is the polar

• angle and phi is the azimuthal angle. Returns NaN gradient if x = y = 0.

mdsuite.utils.linalg.get2dHistogram(x, y, value_range, nbins=100, dtype=tf.int32)

Bins x, y coordinates of points onto simple square 2d histogram.

Given the tensor x and y: x: x coordinates of points y: y coordinates of points this operation returns a rank 2 Tensor representing the indices of a histogram into which each element of values would be binned. The bins are equal width and determined by the arguments value_range and nbins.

Parameters:

• x (value_range[0] lims for) –

• y (value_range[1] lims for) –

• x –

• y –

• nbins (Scalar int32 Tensor. Number of histogram bins.) –

• dtype (dtype for returned histogram.) –

References

https://gist.github.com/isentropic/a86effab2c007e86912a50f995cac52b

mdsuite.utils.linalg.get_angles(r_ij_mat, indices, acos=True)

Compute the cosine angle for the given triples.

Using :math theta = acos(r_ij * r_ik / (|r_ij| * |r_ik|))

Parameters:

• acos (bool) – Apply tf.math.acos to the output if true. default true.

• r_ij_mat (tf.Tensor) – r_ij matrix. Shape is (n_timesteps, n_atoms, n_atoms, 3)

• indices (tf.Tensor) – Indices of the triples. Shape is (triples, 4) where a single element is composed of (timestep, idx, jdx, kdx)

Returns:

tf.Tensor

Return type:

Tensor with the shape (triples)

mdsuite.utils.linalg.get_partial_triu_indices(n_atoms: int, m_atoms: int, idx: int) → Tensor

Calculate the indices of a slice of the triu values.

Parameters:

• n_atoms (total number of atoms in the system) –

• m_atoms (size of the slice (horizontal)) –

• idx (start index of slize) –

Return type:

tf.Tensor

mdsuite.utils.linalg.spherical_to_cartesian_coordinates(point_spherical, name='spherical_to_cartesian_coordinates')

References

https://www.tensorflow.org/graphics/api_docs/python/tfg/math/math_helpers/spherical_to_cartesian_coordinates

Function to transform Cartesian coordinates to spherical coordinates. .. note:: In the following, A1 to An are optional batch dimensions.

Parameters:

• point_spherical – A tensor of shape [A1, …, An, 3]. The last dimension contains r, theta, and phi that respectively correspond to the radius, polar angle and azimuthal angle; r must be non-negative.

• name – A name for this op. Defaults to “spherical_to_cartesian_coordinates”.

Raises:

• tf.errors.InvalidArgumentError – If r, theta or phi contains out of range:

• data. –

Returns:

• A tensor of shape [A1, …, An, 3], where the last dimension contains the

• cartesian coordinates in x,y,z order.

mdsuite.utils.linalg.unit_vector(vector)

Returns the unit vector of the vector.