pymatgen.core.operations module

This module provides classes that operate on points or vectors in 3D space.

class MagSymmOp(affine_transformation_matrix: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], time_reversal: int, tol: float = 0.01)[source]

Bases: SymmOp

Thin wrapper around SymmOp to extend it to support magnetic symmetry by including a time reversal operator. Magnetic symmetry is similar to conventional crystal symmetry, except symmetry is reduced by the addition of a time reversal operator which acts on an atom’s magnetic moment.

Initializes the MagSymmOp from a 4x4 affine transformation matrix and time reversal operator. In general, this constructor should not be used unless you are transferring rotations. Use the static constructors instead to generate a SymmOp from proper rotations and translation.

Parameters:

  • affine_transformation_matrix (4x4 array) – Representing an affine transformation.

  • time_reversal (int) – 1 or -1

  • tol (float) – Tolerance for determining if matrices are equal.

as_dict() → dict[source]
Returns:

MSONABle dict

as_xyzt_string() → str[source]

Returns a string of the form ‘x, y, z, +1’, ‘-x, -y, z, -1’, ‘-y+1/2, x+1/2, z+1/2, +1’, etc. Only works for integer rotation matrices

classmethod from_dict(d: dict) → MagSymmOp[source]
Parameters:

d – dict

Returns:

MagneticSymmOp from dict representation.

static from_rotation_and_translation_and_time_reversal(rotation_matrix: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]] = ((1, 0, 0), (0, 1, 0), (0, 0, 1)), translation_vec: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]] = (0, 0, 0), time_reversal: int = 1, tol: float = 0.1) → MagSymmOp[source]

Creates a symmetry operation from a rotation matrix, translation vector and time reversal operator.

Parameters:

  • rotation_matrix (3x3 array) – Rotation matrix.

  • translation_vec (3x1 array) – Translation vector.

  • time_reversal (int) – Time reversal operator, +1 or -1.

  • tol (float) – Tolerance to determine if rotation matrix is valid.

Returns:

MagSymmOp object

classmethod from_symmop(symmop, time_reversal) → MagSymmOp[source]

Initialize a MagSymmOp from a SymmOp and time reversal operator.

Parameters:

  • symmop (SymmOp) – SymmOp

  • time_reversal (int) – Time reversal operator, +1 or -1.

Returns:

MagSymmOp object

static from_xyzt_string(xyzt_string: str) → MagSymmOp[source]
Parameters:

xyz_string – string of the form ‘x, y, z, +1’, ‘-x, -y, z, -1’, ‘-2y+1/2, 3x+1/2, z-y+1/2, +1’, etc.

Returns:

MagSymmOp object

operate_magmom(magmom)[source]

Apply time reversal operator on the magnetic moment. Note that magnetic moments transform as axial vectors, not polar vectors.

See ‘Symmetry and magnetic structures’, Rodríguez-Carvajal and Bourée for a good discussion. DOI: 10.1051/epjconf/20122200010

Parameters:

  • magmom – Magnetic moment as electronic_structure.core.Magmom

  • array-like (class or as list or np) –

Returns:

Magnetic moment after operator applied as Magmom class

class SymmOp(affine_transformation_matrix: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], tol: float = 0.01)[source]

Bases: MSONable

A symmetry operation in Cartesian space. Consists of a rotation plus a translation. Implementation is as an affine transformation matrix of rank 4 for efficiency. Read: http://en.wikipedia.org/wiki/Affine_transformation.

affine_matrix[source]

A 4x4 numpy.array representing the symmetry operation.

Initializes the SymmOp from a 4x4 affine transformation matrix. In general, this constructor should not be used unless you are transferring rotations. Use the static constructors instead to generate a SymmOp from proper rotations and translation.

Parameters:

  • affine_transformation_matrix (4x4 array) – Representing an affine transformation.

  • tol (float) – Tolerance for determining if matrices are equal.

apply_rotation_only(vector: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]])[source]

Vectors should only be operated by the rotation matrix and not the translation vector.

Parameters:

vector (3x1 array) – A vector.

Checks if two points are symmetrically related.

Parameters:

  • point_a (3x1 array) – First point.

  • point_b (3x1 array) – Second point.

  • tol (float) – Absolute tolerance for checking distance.

Returns:

True if self.operate(point_a) == point_b or vice versa.

Checks if two vectors, or rather two vectors that connect two points each are symmetrically related. r_a and r_b give the change of unit cells. Two vectors are also considered symmetrically equivalent if starting and end point are exchanged.

Parameters:

  • from_a (3x1 array) – Starting point of the first vector.

  • to_a (3x1 array) – Ending point of the first vector.

  • from_b (3x1 array) – Starting point of the second vector.

  • to_b (3x1 array) – Ending point of the second vector.

  • r_a (3x1 array) – Change of unit cell of the first vector.

  • r_b (3x1 array) – Change of unit cell of the second vector.

  • tol (float) – Absolute tolerance for checking distance.

Returns:

(are_related, is_reversed)

as_dict() → dict[source]
Returns:

MSONAble dict.

as_xyz_string() → str[source]

Returns a string of the form ‘x, y, z’, ‘-x, -y, z’, ‘-y+1/2, x+1/2, z+1/2’, etc. Only works for integer rotation matrices

static from_axis_angle_and_translation(axis: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], angle: float, angle_in_radians: bool = False, translation_vec: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]] = (0, 0, 0)) → SymmOp[source]

Generates a SymmOp for a rotation about a given axis plus translation.

Parameters:

  • axis – The axis of rotation in Cartesian space. For example, [1, 0, 0]indicates rotation about x-axis.

  • angle (float) – Angle of rotation.

  • angle_in_radians (bool) – Set to True if angles are given in radians. Or else, units of degrees are assumed.

  • translation_vec – A translation vector. Defaults to zero.

Returns:

SymmOp for a rotation about given axis and translation.

classmethod from_dict(d) → SymmOp[source]
Parameters:

d – dict

Returns:

SymmOp from dict representation.

static from_origin_axis_angle(origin: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], axis: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], angle: float, angle_in_radians: bool = False) → SymmOp[source]

Generates a SymmOp for a rotation about a given axis through an origin.

Parameters:

  • origin (3x1 array) – The origin which the axis passes through.

  • axis (3x1 array) – The axis of rotation in Cartesian space. For example, [1, 0, 0]indicates rotation about x-axis.

  • angle (float) – Angle of rotation.

  • angle_in_radians (bool) – Set to True if angles are given in radians. Or else, units of degrees are assumed.

Returns:

SymmOp.

static from_rotation_and_translation(rotation_matrix: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]] = ((1, 0, 0), (0, 1, 0), (0, 0, 1)), translation_vec: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]] = (0, 0, 0), tol=0.1)[source]

Creates a symmetry operation from a rotation matrix and a translation vector.

Parameters:

  • rotation_matrix (3x3 array) – Rotation matrix.

  • translation_vec (3x1 array) – Translation vector.

  • tol (float) – Tolerance to determine if rotation matrix is valid.

Returns:

SymmOp object

static from_xyz_string(xyz_string: str) → SymmOp[source]
Parameters:

xyz_string – string of the form ‘x, y, z’, ‘-x, -y, z’, ‘-2y+1/2, 3x+1/2, z-y+1/2’, etc.

Returns:

SymmOp

property inverse: SymmOp[source]

Returns inverse of transformation.

static inversion(origin: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]] = (0, 0, 0)) → SymmOp[source]

Inversion symmetry operation about axis.

Parameters:

origin (3x1 array) – Origin of the inversion operation. Defaults to [0, 0, 0].

Returns:

SymmOp representing an inversion operation about the origin.

operate(point)[source]

Apply the operation on a point.

Parameters:

point – Cartesian coordinate.

Returns:

Coordinates of point after operation.

operate_multi(points)[source]

Apply the operation on a list of points.

Parameters:

points – List of Cartesian coordinates

Returns:

Numpy array of coordinates after operation

static reflection(normal: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], origin: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]] = (0, 0, 0)) → SymmOp[source]

Returns reflection symmetry operation.

Parameters:

  • normal (3x1 array) – Vector of the normal to the plane of reflection.

  • origin (3x1 array) – A point in which the mirror plane passes through.

Returns:

SymmOp for the reflection about the plane

property rotation_matrix: ndarray[source]

A 3x3 numpy.array representing the rotation matrix.

static rotoreflection(axis: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], angle: float, origin: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]] = (0, 0, 0)) → SymmOp[source]

Returns a roto-reflection symmetry operation

Parameters:

  • axis (3x1 array) – Axis of rotation / mirror normal

  • angle (float) – Angle in degrees

  • origin (3x1 array) – Point left invariant by roto-reflection. Defaults to (0, 0, 0).

Returns:

Roto-reflection operation

transform_tensor(tensor: ndarray)[source]

Applies rotation portion to a tensor. Note that tensor has to be in full form, not the Voigt form.

Parameters:

tensor (numpy array) – a rank n tensor

Returns:

Transformed tensor.

property translation_vector: ndarray[source]

A rank 1 numpy.array of dim 3 representing the translation vector.