diffpy.structure.spacegroupmod

Symmetry operations as functions on vectors or arrays.

class SymOp(R, t)

The transformation of coordinates to a symmetry-related position.

The SymOp operation involves rotation and translation in cell coordinates.

Parameters:
  • R (ndarray) – The 3x3 matrix of rotation for this symmetry operation.
  • t (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:ndarray
t

The translation of cell coordinates applied after rotation R.

Type:ndarray
__call__(vec)

Return symmetry-related position for the specified coordinates.

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

Implement the (self == symop) test of equality.

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

is_identity()

Check if this SymOp is an identity operation.

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

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
iter_symops()

Iterate over all symmetry operations in the space group.

Yields:SymOp – Generate all symmetry operations for this space group.
check_group_name(name)

Check if given name matches this space group.

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

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