diffpy.structure.spacegroupmod

Symmetry operations as functions on vectors or arrays.

class diffpy.structure.spacegroupmod.SpaceGroup(number=None, num_sym_equiv=None, num_primitive_sym_equiv=None, short_name=None, point_group_name=None, crystal_system=None, pdb_name=None, symop_list=None)[source]

Definition and basic operations for a specific space group.

Provide standard names and all symmetry operations contained in one space group.

Parameters:

number (int) – The space group number.
num_sym_equiv (int) – The number of symmetry equivalent sites for a general position.
num_primitive_sym_equiv (int) – The number of symmetry equivalent sites in a primitive unit cell.
short_name (str) – The short Hermann-Mauguin symbol of the space group.
point_group_name (str) – The point group of this space group.
crystal_system (str) – The crystal system of this space group.
pdb_name (str) – The full Hermann-Mauguin symbol of the space group.
symop_list (list of SymOp) – The symmetry operations contained in this space group.

number

A unique space group number. This may be incremented by several thousands to facilitate unique values for multiple settings of the same space group. Use number % 1000 to get the standard space group number from International Tables.

Type:: int

num_sym_equiv

The number of symmetry equivalent sites for a general position.

Type:: int

num_primitive_sym_equiv

The number of symmetry equivalent sites in a primitive unit cell.

Type:: int

short_name

The short Hermann-Mauguin symbol of the space group.

Type:: str

point_group_name

The point group to which this space group belongs to.

Type:: str

crystal_system

The crystal system of this space group. The possible values are "TRICLINIC", "MONOCLINIC", "ORTHORHOMBIC", "TETRAGONAL", "TRIGONAL" "HEXAGONAL", "CUBIC".

Type:: str

pdb_name

The full Hermann-Mauguin symbol of the space group.

Type:: str

symop_list

A list of SymOp objects for all symmetry operations in this space group.

Type:: list of SymOp

check_group_name(name)[source]

Check if given name matches this space group.

Parameters:: name (str or int) – The space group identifier, a string name or number.
Returns:: True if the specified name matches one of the recognized names of this space group or if it equals its number. Return False otherwise.
Return type:: bool

iter_equivalent_positions(vec)[source]

Generate symmetry equivalent positions for the specified position.

The initial position must be in fractional coordinates and so are the symmetry equivalent positions yielded by iteration. This generates num_sym_equiv positions regardless of initial coordinates being a special symmetry position or not.

Parameters:: vec (numpy.ndarray) – The initial position in fractional coordinates.
Yields:: numpy.ndarray – The symmetry equivalent positions in fractional coordinates. The positions may be duplicate or outside of the 0 <= x < 1 unit cell bounds.

iter_symops()[source]

Iterate over all symmetry operations in the space group.

Yields:: SymOp – Generate all symmetry operations for this space group.

class diffpy.structure.spacegroupmod.SymOp(R, t)[source]

The transformation of coordinates to a symmetry-related position.

The SymOp operation involves rotation and translation in cell coordinates.

Parameters:

R (numpy.ndarray) – The 3x3 matrix of rotation for this symmetry operation.
t (numpy.ndarray) – The vector of translation in this symmetry operation.

R

The 3x3 matrix of rotation pertaining to unit cell coordinates. This may be identity, simple rotation, improper rotation, mirror or inversion. The determinant of R is either +1 or -1.

Type:: numpy.ndarray

t

The translation of cell coordinates applied after rotation R.

Type:: numpy.ndarray

__call__(vec)[source]

Return symmetry-related position for the specified coordinates.

Parameters:: vec (numpy.ndarray) – The initial position in fractional cell coordinates.
Returns:: The transformed position after this symmetry operation.
Return type:: numpy.ndarray

__eq__(symop)[source]

Implement the self == symop test of equality.

Return True when self and symop difference is within tiny round-off errors.

is_identity()[source]

Check if this SymOp is an identity operation.

Returns:: True if this is an identity operation within a small round-off. Return False otherwise.
Return type:: bool