def _symmetric(self):
if abs(self._eigenvalues[0] - self._eigenvalues[1]) < self.tolerance:
idx = 2
elif abs(self._eigenvalues[0] - self._eigenvalues[2]) < self.tolerance:
idx = 1
else:
idx = 0
main_axis = self._eigenvectors[idx, :]
self.check_order_rot(main_axis)
self.rot_sym.append((main_axis, self._max_order))
# Obtain all the c2 vectors perpendicular to main axis
for ida, axis in enumerate(self._eigenvectors):
if ida != idx:
p_axis = axis
break
for angle in np.linspace(0, 360, 144, endpoint=False):
axis = np.matmul(np.array(rotation_matrix(main_axis, angle)),
np.array(p_axis))
c2 = rotation_matrix(axis, 360 / 2)
if self.check_op(c2):
self.sym_op.append(c2)
self.rot_sym.append((axis / np.linalg.norm(axis), 2))
self.check_consistency()
if len(self.rot_sym) >= 2:
self._dihedral()
elif len(self.rot_sym) == 1:
self._cyclic()
else:
self._no_rot_axis()
def check_order_rot(self, axis):
order = 0
for i in list(range(2, 9)):
Cn = rotation_matrix(axis, 360 / i)
if self.check_op(Cn):
order = i
self.sym_op.append(Cn)
self._max_order = order
def _improper_rot(self):
for axis, order in self.rot_sym:
if order == 2:
ref_mat = reflection(axis)
for n in range(20, 0, -2):
Cn = rotation_matrix(axis, 360 / n)
Sn = np.dot(Cn, ref_mat)
if self.check_op(Sn):
self.rot_sym.append((axis, 'S' + str(n)))
self.sym_op.append(Sn)
break
def orthogonal_c4(c3, c4):
def calculate_angle(axis1, axis2):
axis1 /= np.linalg.norm(axis1)
axis2 /= np.linalg.norm(axis2)
return np.arccos(
np.dot(axis1, axis2) /
(np.linalg.norm(axis1) * np.linalg.norm(axis2))) * 180 / np.pi
perfect_c3_c4 = 125.26438968275465
c3 /= np.linalg.norm(c3)
c4 /= np.linalg.norm(c4)
angle_c3_c4 = calculate_angle(c3, c4)
diff_angle = perfect_c3_c4 - angle_c3_c4
if abs(diff_angle) <= 1E-8:
new_c4 = c4
else:
new_c4 = np.dot(rotation_matrix(np.cross(c3, c4), diff_angle), c4)
warn('ChangedAxisWarning: Set C4 axis to: {}'.format(new_c4))
rot_mat = rotation_matrix(c3, 120.0)
c4_2 = np.dot(rot_mat, new_c4)
return new_c4, c4_2 / np.linalg.norm(c4_2)
def _asymmetric(self):
for axis in self._eigenvectors:
c2 = rotation_matrix(axis, 180)
if self.check_op(c2):
self.sym_op.append(c2)
self.rot_sym.append((axis, 2))
if len(self.sym_op) == 0:
self._no_rot_axis()
elif len(self.sym_op) == 1:
self._cyclic()
else:
self._dihedral()
def mirror_plane(self, main_axis):
m_type = ''
if self.check_op(reflection(main_axis)):
self.rot_sym.append((main_axis, 'Sh'))
self.sym_op.append(reflection(main_axis))
m_type = 'h'
else:
# Sv planes #
p_axis = np.random.randn(3)
p_axis -= np.dot(p_axis, main_axis) * main_axis
p_axis /= np.linalg.norm(p_axis)
for angle in np.linspace(0, 360, 144, endpoint=False):
axis = np.matmul(np.array(rotation_matrix(main_axis, angle)),
np.array(p_axis))
possible_mirror = reflection(axis)
if self.check_op(possible_mirror):
m_type = 'v'
self.rot_sym.append((axis, 'Sv'))
self.sym_op.append(possible_mirror)
# Sd planes #
c2_axes, gt_axes = [], []
for axis, order in self.rot_sym:
if order == 2:
c2_axes.append(axis)
if order == self._max_order:
gt_axes.append(axis)
for c2_1, c2_2 in itertools.combinations(c2_axes, 2):
c2_vector = c2_1 + c2_2
if all(c2_vector < 1e-8):
continue
else:
c2_vector /= np.linalg.norm(c2_vector)
for gt_vector in gt_axes:
p_axis = np.cross(c2_vector, gt_vector)
possible_mirror = reflection(p_axis)
if self.check_op(reflection(p_axis)):
m_type = 'd'
self.rot_sym.append(
(p_axis / np.linalg.norm(p_axis), 'Sd'))
self.sym_op.append(possible_mirror)
return m_type
def _spherical(self):
# I or Ih
for axis in self._eigenvectors:
c5 = rotation_matrix(axis, 360 / 5)
if self.check_op(c5):
self.sym_op.append(c5)
self.rot_sym.append((axis, 5))
self.schoenflies_symbol = "I"
self._max_order = 5
if self.schoenflies_symbol and self.check_op(inversion()):
self.schoenflies_symbol += 'h'
# O or Oh
if not self.schoenflies_symbol:
for axis in self._eigenvectors:
c4 = rotation_matrix(axis, 360 / 4)
if self.check_op(c4):
self.sym_op.append(c4)
self.rot_sym.append((axis, 4))
self.schoenflies_symbol = "O"
self._max_order = 4
if self.schoenflies_symbol and self.check_op(inversion()):
self.schoenflies_symbol += 'h'
# Obtain all the c2 vectors and matrices
for angle1 in np.linspace(0, 360, 72, endpoint=False):
axis1 = np.matmul(np.array(rotation_matrix([1, 0, 0], angle1)),
np.array([0, 0, 1]))
for angle2 in np.linspace(0, 180, 72, endpoint=False):
axis2 = np.matmul(np.array(rotation_matrix([0, 1, 0], angle2)),
axis1)
c2 = rotation_matrix(axis2, 360 / 2)
if self.check_op(c2):
self.sym_op.append(c2)
self.rot_sym.append((axis2 / np.linalg.norm(axis2), 2))
if self.rot_sym:
self.check_consistency()
# T or Td, Th
m_type = ''
if not self.schoenflies_symbol:
# Obtain all the c3 vectors and matrices
for angle1 in np.linspace(0, 360, 72, endpoint=False):
axis1 = np.matmul(np.array(rotation_matrix([1, 0, 0], angle1)),
np.array([0, 0, 1]))
for angle2 in np.linspace(0, 180, 72, endpoint=False):
axis2 = np.matmul(
np.array(rotation_matrix([0, 1, 0], angle2)), axis1)
c3 = rotation_matrix(axis2, 360 / 3)
if self.check_op(c3):
self.sym_op.append(c3)
self.rot_sym.append((axis2 / np.linalg.norm(axis2), 3))
self.schoenflies_symbol = "T"
self._max_order = 3
self.check_consistency()
for axis, order in self.rot_sym:
if order == 3:
m_type = self.mirror_plane(axis)
break
if m_type == '':
if self.check_op(inversion()):
self.rot_sym.append(([0, 0, 0], 'i'))
self.sym_op.append(inversion())
self.schoenflies_symbol += 'h'
# else:
# self.schoenflies_symbol += 'd'
else:
self.schoenflies_symbol += 'd'
self._improper_rot()