pymatgen.analysis.elasticity.tensors module

class SquareTensor[source]

Bases: pymatgen.analysis.elasticity.tensors.Tensor

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

Create a SquareTensor object. Note that the constructor uses __new__ rather than __init__ according to the standard method of subclassing numpy ndarrays. Error is thrown when the class is initialized with non-square matrix.

Parameters:
  • input_array (3x3 array-like) – the 3x3 array-like representing the content of the tensor
  • vscale (6x1 array-like) – 6x1 array-like scaling the voigt-notation vector with the tensor entries
det

shorthand for the determinant of the SquareTensor

get_scaled(scale_factor)[source]

Scales the tensor by a certain multiplicative scale factor

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

shorthand for matrix inverse on SquareTensor

is_rotation(tol=0.001, include_improper=True)[source]

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

Parameters:
  • 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
polar_decomposition(side='right')[source]

calculates matrices for polar decomposition

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

trans

shorthand for transpose on SquareTensor

class Tensor[source]

Bases: numpy.ndarray

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

Create a Tensor object. Note that the constructor uses __new__ rather than __init__ according to the standard method of subclassing numpy ndarrays.

Parameters:
  • input_array – (array-like with shape 3^N): array-like representing a tensor quantity in standard (i. e. non-voigt) notation
  • vscale – (N x M array-like): a matrix corresponding to the coefficients of the voigt-notation tensor
convert_to_ieee(structure, initial_fit=True)[source]

Given a structure associated with a tensor, attempts a calculation of the tensor in IEEE format according to the 1987 IEEE standards.

Parameters:
  • structure (Structure) – a structure associated with the tensor to be converted to the IEEE standard
  • initial_fit (bool) – flag to indicate whether initial tensor is fit to the symmetry of the structure. Defaults to true. Note that if false, inconsistent results may be obtained due to symmetrically equivalent, but distinct transformations being used in different versions of spglib.
fit_to_structure(structure, symprec=0.1)[source]

Returns a tensor that is invariant with respect to symmetry operations corresponding to a structure

Parameters:
  • structure (Structure) – structure from which to generate symmetry operations
  • symprec (float) – symmetry tolerance for the Spacegroup Analyzer used to generate the symmetry operations
classmethod from_voigt(voigt_input)[source]

Constructor based on the voigt notation vector or matrix.

Parameters:voigt_input (array-like) – voigt input for a given tensor
static get_voigt_dict(rank)[source]

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

Parameters:rank (int) – Tensor rank to generate the voigt map
is_fit_to_structure(structure, tol=0.01)[source]

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

Parameters:
  • structure (Structure) – structure to be fit to
  • tol (float) – tolerance for symmetry testing
is_symmetric(tol=1e-05)[source]

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

Parameters:tol (float) – tolerance to test for symmetry
is_voigt_symmetric(tol=1e-06)[source]

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

rotate(matrix, tol=0.001)[source]

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

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

transform(symm_op)[source]

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

Parameters:symm_op (SymmOp) – a symmetry operation to apply to the tensor
voigt

Returns the tensor in Voigt notation

voigt_symmetrized

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

zeroed(tol=0.001)[source]

returns the matrix with all entries below a certain threshold (i.e. tol) set to zero

class TensorCollection(tensor_list, base_class=<class 'pymatgen.analysis.elasticity.tensors.Tensor'>)[source]

Bases: collections.abc.Sequence

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

convert_to_ieee(structure)[source]
fit_to_structure(structure, symprec=0.1)[source]
classmethod from_voigt(voigt_input_list, base_class=<class 'pymatgen.analysis.elasticity.tensors.Tensor'>)[source]
is_symmetric(tol=1e-05)[source]
is_voigt_symmetric(tol=1e-06)[source]
rotate(matrix, tol=0.001)[source]
symmetrized
transform(symm_op)[source]
voigt
zeroed(tol=0.001)[source]
symmetry_reduce(tensors, structure, tol=1e-08, **kwargs)[source]

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 of tensors) – 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