def test_sparse_orbital_bz_spin_orbit():
M = SparseOrbitalBZSpin(geom.graphene(), spin=Spin('SO'))
M.construct(([0.1, 1.44], [[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8],
[0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]]))
new = (M + M.transpose(True)) / 2
assert np.abs((M - new)._csr._D).sum() == 0
def test_sparse_orbital_bz_spin_orbit_warns_hermitian():
M = SparseOrbitalBZSpin(geom.graphene(), spin=Spin('SO'))
with pytest.warns(SislWarning, match='Hermitian'):
M.construct(([0.1, 1.44],
[[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8],
[0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]]))
def test_sparse_orbital_transform_fail():
M = SparseOrbitalBZSpin(geom.graphene(),
spin='polarized',
orthogonal=False,
dtype=np.int32)
M.construct(([0.1, 1.44], [(1, 2, 3), (4, 5, 6)]))
M.finalize()
with pytest.raises(ValueError):
M.transform(np.zeros([2, 2]), spin='unpolarized')
def test_sparse_orbital_transform_basis():
M = SparseOrbitalBZSpin(geom.graphene(),
spin='polarized',
orthogonal=False)
M.construct(([0.1, 1.44], [(3., 2., 1.), (0.3, 0.2, 0.)]))
M.finalize()
Mcsr = [M.tocsr(i) for i in range(M.shape[2])]
Mt = M.transform(orthogonal=True).transform(orthogonal=False)
assert M.dim == Mt.dim
assert np.abs(Mcsr[0] - Mt.tocsr(0)).sum() == 0
assert np.abs(Mcsr[1] - Mt.tocsr(1)).sum() == 0
assert np.abs(Mcsr[-1] - Mt.tocsr(-1)).sum() == 0
def test_sparse_orbital_bz_spin_orbit():
M = SparseOrbitalBZSpin(geom.graphene(), spin=Spin('SO'))
M.construct(([0.1, 1.44], [[0.1, 0.2, 0.3, 0.4, 0.0, 0.0, 0.3, -0.4],
[0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]]))
M.finalize()
MT = M.transpose()
MH = M.transpose(True)
assert np.abs((M - MT)._csr._D).sum() != 0
assert np.abs((M - MH)._csr._D).sum() == 0
assert np.abs((MT - MH)._csr._D).sum() != 0
def test_sparse_orbital_bz_non_colinear_trs_kramers_theorem():
M = SparseOrbitalBZSpin(geom.graphene(), spin=Spin('NC'))
M.construct(([0.1, 1.44], [[0.1, 0.2, 0.3, 0.4], [0.2, 0.3, 0.4, 0.5]]))
M.finalize()
M = (M + M.transpose(True)) * 0.5
MTRS = (M + M.trs()) * 0.5
# This will in principle also work for M since the above parameters preserve
# TRS
k = np.array([0.1, 0.1, 0])
eig1 = MTRS.eigh(k=k)
eig2 = MTRS.eigh(k=-k)
assert np.allclose(eig1, eig2)
def test_sparse_orbital_bz_non_colinear():
M = SparseOrbitalBZSpin(geom.graphene(), spin=Spin('NC'))
M.construct(([0.1, 1.44], [[0.1, 0.2, 0.3, 0.4], [0.2, 0.3, 0.4, 0.5]]))
M.finalize()
MT = M.transpose()
MH = M.transpose(True)
assert np.abs((M - MT)._csr._D).sum() != 0
# For a non-collinear with construct we don't take
# into account the imaginary parts... :(
# Transposing and Hermitian transpose are the same for NC
# There are only 1 imaginary part which will change sign regardless
assert np.abs((MT - MH)._csr._D).sum() != 0
assert np.abs((M - MH)._csr._D).sum() == 0
def test_sparse_orbital_bz_non_colinear():
M = SparseOrbitalBZSpin(geom.graphene(), spin=Spin('NC'))
M.construct(([0.1, 1.44], [[0.1, 0.2, 0.3, 0.4], [0.2, 0.3, 0.4, 0.5]]))
MT = M.transpose()
MH = M.transpose(True)
assert np.abs((M - MT)._csr._D).sum() != 0
assert np.abs((M - MH)._csr._D).sum() != 0
assert np.abs((MT - MH)._csr._D).sum() != 0
def test_pickle_non_orthogonal_spin():
import pickle as p
gr = _get()
sp = SparseOrbitalBZSpin(gr, spin=Spin('p'), orthogonal=False)
sp[0, 0, :] = 0.5
sp[1, 1, :] = 0.5
sp.S[0, 0] = 1.
sp.S[1, 1] = 1.
s = p.dumps(sp)
SP = p.loads(s)
assert sp.spsame(SP)
assert np.allclose(sp.eigh(), SP.eigh())
def test_sparse_orbital_bz_non_colinear():
M = SparseOrbitalBZSpin(geom.graphene(), spin=Spin('NC'))
M.construct(([0.1, 1.44], [[0.1, 0.2, 0.3, 0.4], [0.2, 0.3, 0.4, 0.5]]))
MT = M.transpose()
MH = M.transpose(True)
assert np.abs((M - MT)._csr._D).sum() != 0
# For a non-collinear with construct we don't take
# into account the imaginary parts... :(
# This should be fixed
assert np.abs((M - MH)._csr._D).sum() == 0
assert np.abs((MT - MH)._csr._D).sum() != 0
def test_sparse_orbital_transform_matrix():
M = SparseOrbitalBZSpin(geom.graphene(),
spin='polarized',
orthogonal=False,
dtype=np.int32)
M.construct(([0.1, 1.44], [(1, 2, 3), (4, 5, 6)]))
M.finalize()
Mcsr = [M.tocsr(i) for i in range(M.shape[2])]
Mt = M.transform(spin='unpolarized',
matrix=np.ones((1, 3)),
orthogonal=True)
assert Mt.dim == 1
assert np.abs(Mcsr[0] + Mcsr[1] + Mcsr[2] - Mt.tocsr(0)).sum() == 0
Mt = M.transform(spin='polarized', matrix=np.ones((2, 3)), orthogonal=True)
assert Mt.dim == 2
assert np.abs(Mcsr[0] + Mcsr[1] + Mcsr[2] - Mt.tocsr(1)).sum() == 0
Mt = M.transform(matrix=np.ones((3, 3)), dtype=np.float64)
assert Mt.dim == 3
assert np.abs(Mcsr[0] + Mcsr[1] + Mcsr[2] - Mt.tocsr(2)).sum() == 0
Mt = M.transform(spin='non-colinear',
matrix=np.ones((4, 3)),
orthogonal=True,
dtype=np.float64)
assert Mt.dim == 4
assert np.abs(Mcsr[0] + Mcsr[1] + Mcsr[2] - Mt.tocsr(3)).sum() == 0
Mt = M.transform(spin='non-colinear',
matrix=np.ones((5, 3)),
dtype=np.float64)
assert Mt.dim == 5
assert np.abs(Mcsr[0] + Mcsr[1] + Mcsr[2] - Mt.tocsr(4)).sum() == 0
Mt = M.transform(spin='so',
matrix=np.ones((8, 3)),
orthogonal=True,
dtype=np.float64)
assert Mt.dim == 8
assert np.abs(Mcsr[0] + Mcsr[1] + Mcsr[2] - Mt.tocsr(7)).sum() == 0
Mt = M.transform(spin='so', matrix=np.ones((9, 3)), dtype=np.float64)
assert Mt.dim == 9
assert np.abs(Mcsr[0] + Mcsr[1] + Mcsr[2] - Mt.tocsr(8)).sum() == 0
def test_sparse_orbital_transform_combinations():
M = SparseOrbitalBZSpin(geom.graphene(),
spin='polarized',
orthogonal=False,
dtype=np.int32)
M.construct(([0.1, 1.44], [(3, 2, 1), (2, 1, 0)]))
M.finalize()
Mcsr = [M.tocsr(i) for i in range(M.shape[2])]
Mt = M.transform(spin='non-colinear', dtype=np.float64,
orthogonal=True).transform(spin='polarized',
orthogonal=False)
assert M.dim == Mt.dim
assert np.abs(Mcsr[0] - Mt.tocsr(0)).sum() == 0
assert np.abs(Mcsr[1] - Mt.tocsr(1)).sum() == 0
assert np.abs(Mcsr[-1] - Mt.tocsr(-1)).sum() == 0
Mt = M.transform(dtype=np.float128,
orthogonal=True).transform(spin='so',
dtype=np.float64,
orthogonal=False)
assert np.abs(Mcsr[0] - Mt.tocsr(0)).sum() == 0
assert np.abs(Mcsr[1] - Mt.tocsr(1)).sum() == 0
assert np.abs(Mt.tocsr(2)).sum() == 0
assert np.abs(Mcsr[-1] - Mt.tocsr(-1)).sum() == 0
Mt = M.transform(spin='polarized',
orthogonal=True).transform(spin='so',
dtype=np.float64,
orthogonal=False)
assert np.abs(Mcsr[0] - Mt.tocsr(0)).sum() == 0
assert np.abs(Mcsr[1] - Mt.tocsr(1)).sum() == 0
assert np.abs(Mt.tocsr(2)).sum() == 0
assert np.abs(Mcsr[-1] - Mt.tocsr(-1)).sum() == 0
Mt = M.transform(spin='unpolarized', dtype=np.float32,
orthogonal=True).transform(dtype=np.complex128,
orthogonal=False)
assert np.abs(0.5 * Mcsr[0] + 0.5 * Mcsr[1] - Mt.tocsr(0)).sum() == 0
def test_sparse_orbital_transform_nonortho_so():
M = SparseOrbitalBZSpin(geom.graphene(), spin='so', orthogonal=False)
a = np.arange(M.spin.size + 1) + 0.3
M.construct(([0.1, 1.44], [a, a + 0.1]))
M.finalize()
Mcsr = [M.tocsr(i) for i in range(M.shape[2])]
Mt = M.transform(spin='unpolarized')
assert np.abs(0.5 * Mcsr[0] + 0.5 * Mcsr[1] - Mt.tocsr(0)).sum() == 0
assert np.abs(Mcsr[-1] - Mt.tocsr(-1)).sum() == 0
Mt = M.transform(spin='polarized')
assert np.abs(Mcsr[0] - Mt.tocsr(0)).sum() == 0
assert np.abs(Mcsr[1] - Mt.tocsr(1)).sum() == 0
assert np.abs(Mcsr[-1] - Mt.tocsr(-1)).sum() == 0
Mt = M.transform(spin='non-colinear')
assert np.abs(Mcsr[0] - Mt.tocsr(0)).sum() == 0
assert np.abs(Mcsr[1] - Mt.tocsr(1)).sum() == 0
assert np.abs(Mcsr[2] - Mt.tocsr(2)).sum() == 0
assert np.abs(Mcsr[3] - Mt.tocsr(3)).sum() == 0
assert np.abs(Mcsr[-1] - Mt.tocsr(-1)).sum() == 0
Mt = M.transform(spin='so')
assert np.abs(Mcsr[0] - Mt.tocsr(0)).sum() == 0
assert np.abs(Mcsr[1] - Mt.tocsr(1)).sum() == 0
assert np.abs(Mcsr[2] - Mt.tocsr(2)).sum() == 0
assert np.abs(Mcsr[3] - Mt.tocsr(3)).sum() == 0
assert np.abs(Mcsr[-1] - Mt.tocsr(-1)).sum() == 0
