# Source code for gyroid.symmetry

# -*- coding: utf-8 -*-
"""
gyroid.symmetry
===============

"""

import numpy as np
from numpy.linalg import inv

from .common import EPS,BRAVAIS,CARTESIAN

__all__ = ["Symmetry"]

[docs]class Symmetry(object): ''' A :class:`Symmetry` object represents a point group symmetry element in a group. The basis type of a symmetry element should be either `BRAVAIS` or `CARTESIAN`. A symmetry element contains a point group matrix **R** and a translational vector **t**. ''' def __init__(self,dim,basis_type,shape,R=None,t=None): ''' :param dim: space dimension, can be 1, 2 or 3 :type dim: integer :param basis_type: should be either `BRAVAIS` or `CARTESIAN` :type basis_type: string :param shape: the shape of a unit cell :type shape: :class:`Shape` :param R: the point group symmetry matrix :type R: `numpy.array` :param t: the translational symmetry vector. For __eq__ working correctly, it must lie in the first unit cell. :type t: 1D `numpy.array` ''' self.dim = dim self.type = basis_type self.shape = shape if R is not None and np.size(R) == dim*dim: self.R = R else: raise ValueError('Dimensian and R not match') if t is not None and np.size(t) == dim: self.t = self.shape.shift(t,basis_type) else: raise ValueError('Dimensian and t not match')
[docs] def inverse(self): ''' Inverse the symmetry element (both **R** and **t**) :return: the inverse symmetry element of the current object :rtype: :class:`Symmetry` ''' iR = inv(self.R) it = -1.0 * np.dot(iR,self.t) it = self.shape.shift(it,self.type) return Symmetry(self.dim,self.type,self.shape,iR,it)
def __mul__(self,rhs): if self.dim != rhs.dim or self.type != rhs.type: raise ValueError('Incompatible symmetries for multiplication.') R = np.dot(self.R,rhs.R) t = np.dot(self.R,rhs.t) + self.t t = self.shape.shift(t,self.type) return Symmetry(self.dim,self.type,self.shape,R,t) def __eq__(self,rhs): if self.dim != rhs.dim: return False if self.type != rhs.type: return False if np.any(np.abs(self.R - rhs.R) > EPS): return False if np.any(np.abs(self.t - rhs.t) > EPS): return False return True