schrodinger.application.matsci.elasticity.tensors module¶

This module provides a base class for tensor-like objects and methods for basic tensor manipulation. It also provides a class, SquareTensor, that provides basic methods for creating and manipulating rank 2 tensors

class schrodinger.application.matsci.elasticity.tensors.Tensor(input_array, vscale=None, check_rank=None)¶

Bases: numpy.ndarray

Base class for doing useful general operations on Nth order tensors, without restrictions on the type (stress, elastic, strain, piezo, etc.)

zeroed(tol=0.001)¶: returns the matrix with all entries below a certain threshold (i.e. tol) set to zero

transform(symm_op)¶

Applies a transformation (via a symmetry operation) to a tensor.

Args:: symm_op (SymmOp): a symmetry operation to apply to the tensor

rotate(matrix, tol=0.001)¶

Applies a rotation directly, and tests input matrix to ensure a valid rotation.

Args:: matrix (3x3 array-like): rotation matrix to be applied to tensor tol (float): tolerance for testing rotation matrix validity

einsum_sequence(other_arrays, einsum_string=None)¶: Calculates the result of an einstein summation expression

property symmetrized¶: Returns a generally symmetrized tensor, calculated by taking the sum of the tensor and its transpose with respect to all possible permutations of indices

property voigt_symmetrized¶: Returns a “voigt”-symmetrized tensor, i. e. a voigt-notation tensor such that it is invariant wrt permutation of indices

is_symmetric(tol=1e-05)¶

Tests whether a tensor is symmetric or not based on the residual with its symmetric part, from self.symmetrized

Args:: tol (float): tolerance to test for symmetry

is_fit_to_structure(structure, tol=0.01)¶

Tests whether a tensor is invariant with respect to the symmetry operations of a particular structure by testing whether the residual of the symmetric portion is below a tolerance

Args:: structure (Structure): structure to be fit to tol (float): tolerance for symmetry testing

property voigt¶: Returns the tensor in Voigt notation

is_voigt_symmetric(tol=1e-06)¶: Tests symmetry of tensor to that necessary for voigt-conversion by grouping indices into pairs and constructing a sequence of possible permutations to be used in a tensor transpose

static get_voigt_dict(rank)¶

Returns a dictionary that maps indices in the tensor to those in a voigt representation based on input rank

Args:: rank (int): Tensor rank to generate the voigt map

classmethod from_voigt(voigt_input)¶

Constructor based on the voigt notation vector or matrix.

Args:: voigt_input (array-like): voigt input for a given tensor

classmethod from_values_indices(values, indices, populate=False, structure=None, voigt_rank=None, vsym=True, verbose=False)¶

Creates a tensor from values and indices, with options for populating the remainder of the tensor.

Parameters

values (list[float]) – numbers to place at indices
indices – array-like collection of indices to place values at
populate (bool) – whether to populate the tensor
structure (Structure) – structure to base population or fit_to_structure on
voigt_rank (int) – full tensor rank to indicate the shape of the resulting tensor. This is necessary if one provides a set of indices more minimal than the shape of the tensor they want, e.g. Tensor.from_values_indices((0, 0), 100)
vsym (bool) – whether to voigt symmetrize during the optimization procedure
verbose (bool) – whether to populate verbosely

class schrodinger.application.matsci.elasticity.tensors.TensorCollection(tensor_list, base_class=<class 'schrodinger.application.matsci.elasticity.tensors.Tensor'>)¶

Bases: collections.abc.Sequence

A sequence of tensors that can be used for fitting data or for having a tensor expansion

__init__(tensor_list, base_class=<class 'schrodinger.application.matsci.elasticity.tensors.Tensor'>)¶

__len__()¶

zeroed(tol=0.001)¶

transform(symm_op)¶

rotate(matrix, tol=0.001)¶

property symmetrized¶

is_symmetric(tol=1e-05)¶

fit_to_structure(structure, symprec=0.1)¶

is_fit_to_structure(structure, tol=0.01)¶

property voigt¶

property ranks¶

is_voigt_symmetric(tol=1e-06)¶

classmethod from_voigt(voigt_input_list, base_class=<class 'schrodinger.application.matsci.elasticity.tensors.Tensor'>)¶

convert_to_ieee(structure, initial_fit=True, refine_rotation=True)¶

class schrodinger.application.matsci.elasticity.tensors.SquareTensor(input_array, vscale=None)¶

Bases: schrodinger.application.matsci.elasticity.tensors.Tensor

Base class for doing useful general operations on second rank tensors (stress, strain etc.).

property trans¶: shorthand for transpose on SquareTensor

property inv¶: shorthand for matrix inverse on SquareTensor

property det¶: shorthand for the determinant of the SquareTensor

is_rotation(tol=0.001, include_improper=True)¶

Test to see if tensor is a valid rotation matrix, performs a test to check whether the inverse is equal to the transpose and if the determinant is equal to one within the specified tolerance

Args:

tol (float): tolerance to both tests of whether the: the determinant is one and the inverse is equal to the transpose
include_improper (bool): whether to include improper: rotations in the determination of validity

refine_rotation()¶

Helper method for refining rotation matrix by ensuring that second and third rows are perpindicular to the first. Gets new y vector from an orthogonal projection of x onto y and the new z vector from a cross product of the new x and y

Args:: tol to test for rotation
Returns:: new rotation matrix

get_scaled(scale_factor)¶

Scales the tensor by a certain multiplicative scale factor

Args:

scale_factor (float): scalar multiplier to be applied to the: SquareTensor object

property principal_invariants¶: Returns a list of principal invariants for the tensor, which are the values of the coefficients of the characteristic polynomial for the matrix

polar_decomposition(side='right')¶: calculates matrices for polar decomposition

schrodinger.application.matsci.elasticity.tensors.get_uvec(vec)¶: Gets a unit vector parallel to input vector

schrodinger.application.matsci.elasticity.tensors.get_spglib_symmops(spg_cell, symprec=0.01, cartesian=False)¶

schrodinger.application.matsci.elasticity.tensors.symmetry_reduce(tensors, struct, tol=1e-08, **kwargs)¶

Function that converts a list of tensors corresponding to a structure and returns a dictionary consisting of unique tensor keys with symmop values corresponding to transformations that will result in derivative tensors from the original list

Parameters

tensors (list[Tensor]) – list of Tensor objects to test for symmetrically-equivalent duplicates
structure (Structure) – structure from which to get symmetry
tol (float) – tolerance for tensor equivalence
kwargs – keyword arguments for the SpacegroupAnalyzer

Returns

dictionary consisting of unique tensors with symmetry operations corresponding to those which will reconstruct the remaining tensors as values

schrodinger.application.matsci.elasticity.tensors.get_tkd_value(tensor_keyed_dict, tensor, allclose_kwargs=None)¶

Helper function to find a value in a tensor-keyed- dictionary using an approximation to the key. This is useful if rounding errors in construction occur or hashing issues arise in tensor-keyed-dictionaries (e. g. from symmetry_reduce). Resolves most hashing issues, and is preferable to redefining eq methods in the base tensor class.

Parameters

tensor_keyed_dict (dict) – dict with Tensor keys
tensor – tensor to find value of in the dict
allclose_kwargs (dict) – dict of keyword-args to pass to allclose.

schrodinger.application.matsci.elasticity.tensors.get_symmetric(array)¶

Return a symmetric matrix from a square matrix.

Parameters: array (numpy.array) – Input array
Return numpy.array: Symmetrized array