def gen_atom_map(self, basis, vectol):
images = self._images
DG = self._distortion_group.matrices
numIm = len(images)
numAtoms = len(images[0].frac_coords)
num_unstar = self._distortion_group.num_unstar
a_map = np.zeros((len(DG), numIm, numAtoms, numAtoms))
for i in range(len(DG)):
for j in range(1, numIm - 1):
atoms1 = images[j].frac_coords
num1 = images[j].species
for k in range(0, numAtoms):
t_coord = np.dot(DG[i].rotation_matrix, atoms1[k])
t_coord = (t_coord + DG[i].translation_vector) % 1.0
if i < num_unstar:
atoms2 = images[j].frac_coords
num2 = images[j].species
else:
atoms2 = images[numIm - 1 - j].frac_coords
num2 = images[numIm - 1 - j].species
for l in range(0, numAtoms):
if closewrapped(
t_coord, atoms2[l], vectol
) and num1[k] == num2[l] and basis[k] == 1:
a_map[i, j, k, l] = 1
return a_map
def obtain_tmat(self, images, vectol, symprec, angle_tolerance):
# -- Generate lattice with DG in input basis
numIm = len(images)
DG = self.matrices
cp_pos = images[0].frac_coords
cp_labels = images[0].species
newimage = images[int(numIm / 2)].copy()
for i in [int(numIm / 2), numIm - 1]:
cp_pos = np.append(cp_pos, images[i].frac_coords, axis=0)
cp_labels = np.append(cp_labels, images[i].species)
newimage.remove_sites(range(len(newimage.species)))
new_pos = [cp_pos[0]]
new_labels = [cp_labels[0]]
for j in range(len(cp_pos[:, 0])):
atom = cp_pos[j]
for i in range(len(DG)):
t_coord = np.dot(atom, np.transpose(DG[i].rotation_matrix))
t_coord = (t_coord + DG[i].translation_vector) % 1.0
if not any([closewrapped(t_coord, m, vectol)
for m in new_pos]):
new_pos = np.append(new_pos, [t_coord], axis=0)
new_labels = np.append(new_labels, cp_labels[j])
for k in range(len(new_labels)):
newimage.append(new_labels[k], new_pos[k])
dataset2 = SpacegroupAnalyzer(
newimage, symprec=symprec,
angle_tolerance=angle_tolerance).get_symmetry_dataset()
return dataset2["transformation_matrix"], dataset2["origin_shift"]
def from_images(
cls,
images: List,
symprec: float,
angle_tolerance: float,
gentol: float,
vectol: List[float],
vectol2: List[float],
):
dataset = cls.get_img_sym_data(images, symprec, angle_tolerance,
gentol)
# -- Finds H, the symmetry operations common for each image
# H[0] is the list of rotations, H[1] is the list of translations
numIm = len(images)
H = [[], []] # type: List[List]
rotH = dataset[0]["rotations"]
tranH = dataset[0]["translations"]
for i in range(0, len(rotH)):
add = True
for data in dataset:
found = False
for j in range(0, len(data["rotations"])):
if np.allclose(
data["rotations"][j], rotH[i],
atol=gentol, rtol=0.0) and closewrapped(
data["translations"][j], tranH[i], vectol2):
found = True
break
if not found:
add = False
break
if add:
H[0].append(rotH[i])
H[1].append(tranH[i])
# -- Finds A*, the starred symmetry operations that map all images to their opposite image
# Astar[0] is the list of rotations, Astar[1] is the list of translations
Astar = [[], []] # type: List[List]
rotA = dataset[int(numIm / 2)]["rotations"]
tranA = dataset[int(numIm / 2)]["translations"]
for i in range(0, len(rotA)):
add = True
for j in range(0, int(numIm / 2)):
positions = images[j].frac_coords
positions = np.dot(positions, np.transpose(rotA[i]))
positions = positions + findtranslation(
images[int(numIm / 2)], rotA[i], tranA[i], gentol, vectol2,
symprec, angle_tolerance)
newimage = images[j].copy()
new_species = newimage.species
for k in range(len(new_species)):
newimage.replace(k, new_species[k], positions[k])
if not atomsequal(newimage, images[numIm - 1 - j], vectol):
add = False
break
if add:
Astar[0].append(rotA[i])
Astar[1].append(tranA[i])
# -- Finds the general distortion group with a direct product of H and A*
# DG[0] is the list of rotations, DG[1] is the list of translations
# The first len(H[0]) operations are unstarred operations; the rest are starred.
DG = []
for i in range(0, len(H[0])):
DG.append(SymmOp.from_rotation_and_translation(H[0][i], H[1][i]))
for i in range(0, len(H[0])):
for j in range(0, len(Astar[0])):
add = True
testrot = np.dot(H[0][i], Astar[0][j])
testtran = standardize(
np.dot(Astar[1][j], np.transpose(H[0][i])) + H[1][i],
gentol)
for k in range(len(H[0]), len(DG)):
if np.allclose(testrot, DG[k].rotation_matrix,
atol=gentol) and closewrapped(
testtran, DG[k].translation_vector,
vectol):
add = False
break
if add:
DG.append(
SymmOp.from_rotation_and_translation(
testrot, testtran))
return cls(matrices=DG, num_unstar=len(H[0]), img_sym_dataset=dataset)
def gen_perturb(path, irrep, io):
images = path.images
DG = path.distortion_group.matrices
num_unstar = path.distortion_group.num_unstar
numIm = len(images)
irrep_tools = IrrepTools()
# -- Generate starting basis
atoms1 = images[0].frac_coords
numAtoms = len(atoms1)
basis = np.zeros(numAtoms)
atoms2 = images[numIm - 1].frac_coords
m_vec = np.dot(np.linalg.inv(images[0].lattice.matrix),
[io.min_move, io.min_move, io.min_move])
for i in range(0, numAtoms):
if not closewrapped(atoms1[i, :], atoms2[i, :], m_vec):
basis[i] = 1
# -- Generate matrix showing atom mapping for each operations
a_map = path.gen_atom_map(basis=basis, vectol=io.vectol)
# -- Generate and apply modes for an irrep of arbitrary dimension
pt = np.zeros((numIm, numAtoms, 3))
pt_mode_init = irrep_tools.projection_diag(images=images,
symmop_list=DG,
irrep=irrep,
num_unstar=num_unstar,
a_map=a_map,
basis=basis)
if not np.any(pt_mode_init):
raise RuntimeError(
f"Uniform random initial perturbation does not contain any non-zero contributions from irrep {irrep.stokes_number}.\
Try a different irrep.")
pt_mode_init = pt_mode_init / np.linalg.norm(
np.ndarray.flatten(pt_mode_init))
pt += io.m_co[0] * pt_mode_init
if io.irr_dim > 1:
for i in range(1, io.irr_dim):
pt_mode = irrep_tools.projection_odiag(
images=images,
symmop_list=DG,
num_unstar=num_unstar,
irrep=irrep,
vec=pt_mode_init,
index=i,
a_map=a_map,
basis=basis,
)
pt += io.m_co[i] * (pt_mode /
np.linalg.norm(np.ndarray.flatten(pt_mode)))
p_vec = [
io.p_mag / np.linalg.norm(images[0].lattice.matrix[m, :])
for m in range(0, 3)
]
# print pt[3]/np.amax(abs(pt[3]))
# print(np.amax(p_vec*(pt[:,:,:]/np.amax(abs(pt)))))
images_alt = []
for i in range(numIm):
image_copy = images[i].copy()
alt_species = image_copy.species
perturbed_coords = image_copy.frac_coords + p_vec * (pt[i, :, :] /
np.amax(abs(pt)))
for j in range(numAtoms):
image_copy.replace(j, alt_species[j], perturbed_coords[j])
images_alt.append(image_copy)
return images_alt, basis
def gen_perturb(path, irrep, io):
images = path.images
DG = path.distortion_group.matrices
num_unstar = path.distortion_group.num_unstar
numIm = len(images)
irrep_tools = IrrepTools()
io.print("\n\n\n\n" + ("=" * 27 + "\n") * 2 +
"\nGenerating perturbations...\n\n" + ("=" * 27 + "\n") * 2 +
"\n")
io.print("***THE FOLLOWING DATA IS FOR THE PERTURBED IMAGES***\n\n")
# -- Generate starting basis
atoms1 = images[0].frac_coords
numAtoms = len(atoms1)
basis = np.zeros(numAtoms)
atoms2 = images[numIm - 1].frac_coords
m_vec = np.dot(np.linalg.inv(images[0].lattice.matrix),
[io.min_move, io.min_move, io.min_move])
for i in range(0, numAtoms):
if not closewrapped(atoms1[i, :], atoms2[i, :], m_vec):
basis[i] = 1
io.print("------- Atoms included in basis:")
symbols = images[0].species
for i in range(0, numAtoms):
if basis[i] == 0:
io.print(str(symbols[i]) + " No")
else:
io.print(str(symbols[i]) + " Yes")
# -- Generate matrix showing atom mapping for each operations
a_map = path.gen_atom_map(basis=basis, vectol=io.vectol)
# -- Generate and apply modes for an irrep of arbitrary dimension
pt = np.zeros((numIm, numAtoms, 3))
pt_mode_init = irrep_tools.projection_diag(images=images,
symmop_list=DG,
irrep=irrep,
num_unstar=num_unstar,
a_map=a_map,
basis=basis)
pt_mode_init = pt_mode_init / \
np.linalg.norm(np.ndarray.flatten(pt_mode_init))
pt += io.m_co[0] * pt_mode_init
if io.irr_dim > 1:
for i in range(1, io.irr_dim):
pt_mode = irrep_tools.projection_odiag(images=images,
symmop_list=DG,
num_unstar=num_unstar,
irrep=irrep,
vec=pt_mode_init,
index=i,
a_map=a_map,
basis=basis)
pt += io.m_co[i] * \
(pt_mode/np.linalg.norm(np.ndarray.flatten(pt_mode)))
p_vec = [
io.p_mag / np.linalg.norm(images[0].lattice.matrix[m, :])
for m in range(0, 3)
]
# print pt[3]/np.amax(abs(pt[3]))
# print(np.amax(p_vec*(pt[:,:,:]/np.amax(abs(pt)))))
images_alt = []
for i in range(numIm):
image_copy = images[i].copy()
alt_species = image_copy.species
perturbed_coords = image_copy.frac_coords + p_vec * (pt[i, :, :] /
np.amax(abs(pt)))
for j in range(numAtoms):
image_copy.replace(j, alt_species[j], perturbed_coords[j])
images_alt.append(image_copy)
return images_alt