def test_restrict_irreps_dihedral_even_dihedral(self):
N = 12
dg = DihedralGroup(N)
for rot in range(1, N):
if N % rot == 0:
for axis in range(int(N // rot)):
sg_id = (axis, rot)
for name, irrep in dg.irreps.items():
self.check_restriction(dg, sg_id, irrep)
def test_regular_dihedral(self):
g = DihedralGroup(10)
rr = g.regular_representation
N = 4
size = rr.size * N
p = np.eye(size, size)
p = p[:, np.random.permutation(size)]
repr = directsum([rr]*N, change_of_basis=p)
self.check_disentangle(repr)
def test_mix_dihedral(self):
g = DihedralGroup(10)
rr = directsum(list(g.representations.values()))
N = 3
size = rr.size * N
bcob = ortho_group.rvs(dim=size//5)
bsize = bcob.shape[0]
p = np.eye(size, size)
for i in range(size//bsize):
p[i*bsize:(i+1)*bsize, i*bsize:(i+1)*bsize] = bcob
p = p[:, np.random.permutation(size)]
repr = directsum([rr]*N, change_of_basis=p)
self.check_disentangle(repr)
def test_restrict_rr_dihedral_odd_cyclic_odd(self):
dg = DihedralGroup(9)
repr = dg.regular_representation
sg_id = (None, 3)
self.check_restriction(dg, sg_id, repr)
def test_restrict_irreps_dihedral_odd_flips(self):
dg = DihedralGroup(11)
for axis in range(11):
sg_id = (axis, 1)
for name, irrep in dg.irreps.items():
self.check_restriction(dg, sg_id, irrep)
def test_restrict_rr_dihedral_even_dihedral_odd(self):
dg = DihedralGroup(12)
repr = dg.regular_representation
sg_id = (1, 3)
self.check_restriction(dg, sg_id, repr)
def test_restrict_rr_dihedral_even_cyclic_even(self):
dg = DihedralGroup(8)
repr = dg.regular_representation
sg_id = (None, 4)
self.check_restriction(dg, sg_id, repr)
def test_restrict_dihedral(self):
dg = DihedralGroup(8)
sg_id = (0, 4)
for name, irrep in dg.irreps.items():
self.check_restriction(dg, sg_id, irrep)
def test_restrict_rr_dihedral_odd_flips(self):
dg = DihedralGroup(11)
repr = dg.regular_representation
sg_id = (1, 1)
self.check_restriction(dg, sg_id, repr)
def test_restrict_irreps_dihedral_even_flips(self):
dg = DihedralGroup(12)
sg_id = (1, 1)
for name, irrep in dg.irreps.items():
self.check_restriction(dg, sg_id, irrep)
def test_dihedral_odd(self):
g = DihedralGroup(15)
self.check_group(g)
def test_restrict_rr_dihedral_even_dihedral_even(self):
dg = DihedralGroup(12)
repr = dg.regular_representation
sg_id = (1, 6)
self.check_disentangle(dg.restrict_representation(sg_id, repr))
def test_restrict_rr_dihedral_odd_cyclic_odd(self):
dg = DihedralGroup(9)
repr = dg.regular_representation
sg_id = (0, 3)
self.check_disentangle(dg.restrict_representation(sg_id, repr))
def test_restrict_irreps_dihedral_odd_cyclic(self):
dg = DihedralGroup(13)
sg_id = (0, 13)
for name, irrep in dg.irreps.items():
self.check_disentangle(dg.restrict_representation(sg_id, irrep))
def test_restrict_irreps_dihedral_even_dihedral_odd(self):
dg = DihedralGroup(12)
sg_id = (1, 3)
for name, irrep in dg.irreps.items():
self.check_disentangle(dg.restrict_representation(sg_id, irrep))
def test_dihedral_even(self):
g = DihedralGroup(16)
self.check_group(g)
def test_regular_dihedral(self):
g = DihedralGroup(10)
rr = g.regular_representation
self.check_representation(rr)
self.check_character(rr)
def test_dihedral_rr_small(self):
dg = DihedralGroup(2)
self.dihedral_rr_eval(dg, dg.representations['regular'])
def test_restrict_irreps_dihedral_even_cyclic_even(self):
dg = DihedralGroup(12)
sg_id = (None, 4)
for name, irrep in dg.irreps.items():
self.check_restriction(dg, sg_id, irrep)
def test_mix_dihedral(self):
g = DihedralGroup(10)
rr = directsum(list(g.representations.values()))
self.check_representation(rr)
self.check_character(rr)
def test_restrict_irreps_dihedral_odd_cyclic(self):
dg = DihedralGroup(13)
sg_id = (None, 13)
for name, irrep in dg.irreps.items():
self.check_restriction(dg, sg_id, irrep)
def test_dihedral_rr_large(self):
dg = DihedralGroup(16)
self.dihedral_rr_eval(dg, dg.representations['regular'])