diffpy.structure.spacegroupmod¶
Symmetry operations as functions on vectors or arrays.

class
SymOp
(R, t)¶ The transformation of coordinates to a symmetryrelated 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 symmetryrelated 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 roundoff errors.

is_identity
()¶ Check if this SymOp is an identity operation.
Returns: bool – True
if this is an identity operation within a small roundoff. ReturnFalse
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 HermannMauguin 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 HermannMauguin 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

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