def __init__(self):
bond = 1.42
sq3h = 3.**.5 * 0.5
self.sc = SuperCell(
np.array([[1.5, sq3h, 0.], [1.5, -sq3h, 0.], [0., 0., 10.]],
np.float64) * bond,
nsc=[3, 3, 1])
n = 60
rf = np.linspace(0, bond * 1.01, n)
rf = (rf, rf)
orb = SphericalOrbital(1, rf, 2.)
C = Atom(6, orb.toAtomicOrbital())
self.g = Geometry(
np.array([[0., 0., 0.], [1., 0., 0.]], np.float64) * bond,
atom=C,
sc=self.sc)
self.D = DensityMatrix(self.g)
self.DS = DensityMatrix(self.g, orthogonal=False)
def func(D, ia, idxs, idxs_xyz):
idx = D.geom.close(ia,
R=(0.1, 1.44),
idx=idxs,
idx_xyz=idxs_xyz)
ia = ia * 3
i0 = idx[0] * 3
i1 = idx[1] * 3
# on-site
p = 1.
D.D[ia, i0] = p
D.D[ia + 1, i0 + 1] = p
D.D[ia + 2, i0 + 2] = p
# nn
p = 0.1
# on-site directions
D.D[ia, ia + 1] = p
D.D[ia, ia + 2] = p
D.D[ia + 1, ia] = p
D.D[ia + 1, ia + 2] = p
D.D[ia + 2, ia] = p
D.D[ia + 2, ia + 1] = p
D.D[ia, i1 + 1] = p
D.D[ia, i1 + 2] = p
D.D[ia + 1, i1] = p
D.D[ia + 1, i1 + 2] = p
D.D[ia + 2, i1] = p
D.D[ia + 2, i1 + 1] = p
self.func = func
def test_transform_nonortho(self, setup):
D = DensityMatrix(setup.g, spin='polarized', orthogonal=False)
a = np.arange(3)
a[-1] = 1.
for ia in setup.g:
D[ia, ia] = a
Dt = D.transform(spin='unpolarized', dtype=np.float32)
assert np.abs(0.5 * D.tocsr(0) + 0.5 * D.tocsr(1) - Dt.tocsr(0)).sum() == 0
assert np.abs(D.tocsr(-1) - Dt.tocsr(-1)).sum() == 0
Dt = D.transform(spin='polarized')
assert np.abs(D.tocsr(0) - Dt.tocsr(0)).sum() == 0
assert np.abs(D.tocsr(1) - Dt.tocsr(1)).sum() == 0
Dt = D.transform(spin='polarized', orthogonal=True)
assert np.abs(D.tocsr(0) - Dt.tocsr(0)).sum() == 0
assert np.abs(D.tocsr(1) - Dt.tocsr(1)).sum() == 0
Dt = D.transform(spin='non-colinear', orthogonal=False)
assert np.abs(D.tocsr(0) - Dt.tocsr(0)).sum() == 0
assert np.abs(D.tocsr(1) - Dt.tocsr(1)).sum() == 0
assert np.abs(Dt.tocsr(2)).sum() == 0
assert np.abs(Dt.tocsr(3)).sum() == 0
assert np.abs(D.tocsr(-1) - Dt.tocsr(-1)).sum() == 0
Dt = D.transform(spin='so', orthogonal=True)
assert np.abs(D.tocsr(0) - Dt.tocsr(0)).sum() == 0
assert np.abs(D.tocsr(1) - Dt.tocsr(1)).sum() == 0
assert np.abs(Dt.tocsr(-1)).sum() == 0
def test_rho2(self, setup):
bond = 1.42
sq3h = 3.**.5 * 0.5
sc = SuperCell(np.array(
[[1.5, sq3h, 0.], [1.5, -sq3h, 0.], [0., 0., 10.]], np.float64) *
bond,
nsc=[3, 3, 1])
n = 60
rf = np.linspace(0, bond * 1.01, n)
rf = (rf, rf)
orb = SphericalOrbital(1, rf, 2.)
C = Atom(6, orb)
g = Geometry(np.array([[0., 0., 0.], [1., 0., 0.]], np.float64) * bond,
atom=C,
sc=sc)
D = DensityMatrix(g)
D.construct([[0.1, bond + 0.01], [1., 0.1]])
grid = Grid(0.2, geometry=D.geom)
D.density(grid)
D = DensityMatrix(g, spin=Spin('P'))
D.construct([[0.1, bond + 0.01], [(1., 0.5), (0.1, 0.1)]])
grid = Grid(0.2, geometry=D.geom)
D.density(grid)
D.density(grid, [1., -1])
D.density(grid, 0)
D.density(grid, 1)
D = DensityMatrix(g, spin=Spin('NC'))
D.construct([[0.1, bond + 0.01],
[(1., 0.5, 0.01, 0.01), (0.1, 0.1, 0.1, 0.1)]])
grid = Grid(0.2, geometry=D.geom)
D.density(grid)
D.density(grid, [[1., 0.], [0., -1]])
D = DensityMatrix(g, spin=Spin('SO'))
D.construct([[0.1, bond + 0.01],
[(1., 0.5, 0.01, 0.01, 0.01, 0.01, 0., 0.),
(0.1, 0.1, 0.1, 0.1, 0., 0., 0., 0.)]])
grid = Grid(0.2, geometry=D.geom)
D.density(grid)
D.density(grid, [[1., 0.], [0., -1]])
D.density(grid, Spin.X)
D.density(grid, Spin.Y)
D.density(grid, Spin.Z)
def test_nc_multiple_fail(sisl_tmp, sisl_system):
f = sisl_tmp('gr.nc', _dir)
H = Hamiltonian(sisl_system.gtb)
DM = DensityMatrix(sisl_system.gtb)
sile = ncSileSiesta(f, 'w')
H.construct([sisl_system.R, sisl_system.t])
H.write(sile)
DM[0, 0] = 1.
DM.write(sile)
def test_nc_multiple_fail(sisl_tmp, sisl_system):
# writing two different sparse matrices to the same
# file will fail
f = sisl_tmp('gr.nc', _dir)
H = Hamiltonian(sisl_system.gtb)
DM = DensityMatrix(sisl_system.gtb)
with ncSileSiesta(f, 'w') as sile:
H.construct([sisl_system.R, sisl_system.t])
H.write(sile)
DM[0, 0] = 1.
with pytest.raises(ValueError):
DM.write(sile)
def test_nc_density_matrix(sisl_tmp, sisl_system):
f = sisl_tmp('grDM.nc', _dir)
dm = DensityMatrix(sisl_system.gtb)
for _, ix in dm.iter_orbitals():
dm[ix, ix] = ix / 2.
dm.write(ncSileSiesta(f, 'w'))
ndm = ncSileSiesta(f).read_density_matrix()
# Assert they are the same
assert np.allclose(dm.cell, ndm.cell)
assert np.allclose(dm.xyz, ndm.xyz)
dm.finalize()
assert np.allclose(dm._csr._D[:, 0], ndm._csr._D[:, 0])
assert sisl_system.g.atoms.equal(ndm.atoms, R=False)
def test_nc_DM_non_colinear(sisl_tmp):
DM1 = DensityMatrix(sisl.geom.graphene(), spin=sisl.Spin('NC'))
DM1.construct(([0.1, 1.44], [[0.1, 0.2, 0.3, 0.4], [0.2, 0.3, 0.4, 0.5]]))
f1 = sisl_tmp('DM1.nc', _dir)
f2 = sisl_tmp('DM2.nc', _dir)
DM1.write(f1)
DM1.finalize()
DM2 = sisl.get_sile(f1).read_density_matrix()
DM2.write(f2)
DM3 = sisl.get_sile(f2).read_density_matrix()
assert DM1._csr.spsame(DM2._csr)
assert np.allclose(DM1._csr._D, DM2._csr._D)
assert DM1._csr.spsame(DM3._csr)
assert np.allclose(DM1._csr._D, DM3._csr._D)
def test_orbital_momentum(self, setup):
bond = 1.42
sq3h = 3.**.5 * 0.5
sc = SuperCell(np.array([[1.5, sq3h, 0.],
[1.5, -sq3h, 0.],
[0., 0., 10.]], np.float64) * bond, nsc=[3, 3, 1])
orb = AtomicOrbital('px', R=bond * 1.001)
C = Atom(6, orb)
g = Geometry(np.array([[0., 0., 0.],
[1., 0., 0.]], np.float64) * bond,
atoms=C, sc=sc)
D = DensityMatrix(g, spin=Spin('SO'))
D.construct([[0.1, bond + 0.01], [(1., 0.5, 0.01, 0.01, 0.01, 0.01, 0., 0.), (0.1, 0.1, 0.1, 0.1, 0., 0., 0., 0.)]])
D.orbital_momentum("atom")
D.orbital_momentum("orbital")
def test_nc_multiple_checks(sisl_tmp, sisl_system, sort):
f = sisl_tmp('gr.nc', _dir)
H = Hamiltonian(sisl_system.gtb)
DM = DensityMatrix(sisl_system.gtb)
sile = ncSileSiesta(f, 'w')
H.construct([sisl_system.R, sisl_system.t])
H.write(sile, sort=sort)
shuffle = np.random.shuffle
for io in range(len(H)):
edges = H.edges(io) # get all edges
shuffle(edges)
DM[io, edges] = 2.
DM.write(sile, sort=sort)
def test_nc_DM_spin_orbit_nc2dm2nc(sisl_tmp):
DM1 = DensityMatrix(sisl.geom.graphene(), orthogonal=False, spin=sisl.Spin('SO'))
DM1.construct(([0.1, 1.44],
[[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.],
[0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.]]))
f1 = sisl_tmp('DM1.nc', _dir)
f2 = sisl_tmp('DM2.DM', _dir)
DM1.finalize()
DM1.write(f1)
DM2 = sisl.get_sile(f1).read_density_matrix()
DM2.write(f2)
DM3 = sisl.get_sile(f2).read_density_matrix()
assert DM1._csr.spsame(DM2._csr)
assert np.allclose(DM1._csr._D, DM2._csr._D)
assert DM1._csr.spsame(DM3._csr)
assert np.allclose(DM1._csr._D, DM3._csr._D)
def test_read_write_density_matrix(self, sisl_tmp, sisl_system, sile):
G = sisl_system.g.rotate(-30, sisl_system.g.cell[2, :])
DM = DensityMatrix(G, orthogonal=True)
DM.construct([[0.1, 1.45], [0.1, -2.7]])
f = sisl_tmp('test_read_write_density_matrix.win', _dir)
# Write
sile(f, mode='w').write_density_matrix(DM)
# Read 1
try:
dm = sile(f, mode='r').read_density_matrix(geometry=DM.geom)
assert DM.spsame(dm)
except UnicodeDecodeError as e:
pass
# Read 2
try:
dm = DensityMatrix.read(sile(f, mode='r'), geometry=DM.geom)
assert DM.spsame(dm)
except UnicodeDecodeError as e:
pass
def test_spin_rotate_so(self, setup):
bond = 1.42
sq3h = 3.**.5 * 0.5
sc = SuperCell(np.array([[1.5, sq3h, 0.],
[1.5, -sq3h, 0.],
[0., 0., 10.]], np.float64) * bond, nsc=[3, 3, 1])
orb = AtomicOrbital('px', R=bond * 1.001)
C = Atom(6, orb)
g = Geometry(np.array([[0., 0., 0.],
[1., 0., 0.]], np.float64) * bond,
atoms=C, sc=sc)
D = DensityMatrix(g, spin=Spin('SO'))
D.construct([[0.1, bond + 0.01], [(1., 0.5, 0.01, 0.01, 0.01, 0.01, 0.2, 0.2), (0.1, 0.2, 0.1, 0.1, 0., 0.1, 0.2, 0.3)]])
D_mull = D.mulliken()
d = D.spin_rotate([45, 60, 90], rad=False)
d_mull = d.mulliken()
assert not np.allclose(D_mull, d_mull)
assert np.allclose(D_mull[:, 0], d_mull[:, 0])
def test_rho_fail_nc(self, setup):
bond = 1.42
sq3h = 3.**.5 * 0.5
sc = SuperCell(np.array([[1.5, sq3h, 0.],
[1.5, -sq3h, 0.],
[0., 0., 10.]], np.float64) * bond, nsc=[3, 3, 1])
n = 60
rf = np.linspace(0, bond * 1.01, n)
rf = (rf, rf)
orb = SphericalOrbital(1, rf, 2.)
C = Atom(6, orb)
g = Geometry(np.array([[0., 0., 0.],
[1., 0., 0.]], np.float64) * bond,
atoms=C, sc=sc)
D = DensityMatrix(g, spin=Spin('NC'))
D.construct([[0.1, bond + 0.01], [(1., 0.5, 0.01, 0.01), (0.1, 0.1, 0.1, 0.1)]])
grid = Grid(0.2, geometry=D.geometry)
with pytest.raises(ValueError):
D.density(grid, [1., 0.])
def test_transform(self, setup):
D = DensityMatrix(setup.g, spin='so')
a = np.arange(8)
for ia in setup.g:
D[ia, ia] = a
Dcsr = [D.tocsr(i) for i in range(D.shape[2])]
Dt = D.transform(spin='unpolarized', dtype=np.float32)
assert np.abs(0.5 * Dcsr[0] + 0.5 * Dcsr[1] - Dt.tocsr(0)).sum() == 0
Dt = D.transform(spin='polarized', orthogonal=False)
assert np.abs(Dcsr[0] - Dt.tocsr(0)).sum() == 0
assert np.abs(Dcsr[1] - Dt.tocsr(1)).sum() == 0
assert np.abs(Dt.tocsr(2)).sum() != 0
Dt = D.transform(spin='non-colinear', orthogonal=False)
assert np.abs(Dcsr[0] - Dt.tocsr(0)).sum() == 0
assert np.abs(Dcsr[1] - Dt.tocsr(1)).sum() == 0
assert np.abs(Dcsr[2] - Dt.tocsr(2)).sum() == 0
assert np.abs(Dcsr[3] - Dt.tocsr(3)).sum() == 0
assert np.abs(Dt.tocsr(-1)).sum() != 0
def test_nc_multiple_checks(sisl_tmp, sisl_system, sort):
f = sisl_tmp('gr.nc', _dir)
H = Hamiltonian(sisl_system.gtb)
DM = DensityMatrix(sisl_system.gtb)
with ncSileSiesta(f, 'w') as sile:
H.construct([sisl_system.R, sisl_system.t])
H.write(sile, sort=sort)
# fix seed
np.random.seed(42)
shuffle = np.random.shuffle
for io in range(len(H)):
edges = H.edges(io) # get all edges
shuffle(edges)
DM[io, edges] = 2.
if not sort:
with pytest.raises(ValueError):
DM.write(sile, sort=sort)
else:
DM.write(sile, sort=sort)
def test_spin_align_pol(self, setup):
bond = 1.42
sq3h = 3.**.5 * 0.5
sc = SuperCell(np.array([[1.5, sq3h, 0.],
[1.5, -sq3h, 0.],
[0., 0., 10.]], np.float64) * bond, nsc=[3, 3, 1])
orb = AtomicOrbital('px', R=bond * 1.001)
C = Atom(6, orb)
g = Geometry(np.array([[0., 0., 0.],
[1., 0., 0.]], np.float64) * bond,
atoms=C, sc=sc)
D = DensityMatrix(g, spin=Spin('p'))
D.construct([[0.1, bond + 0.01], [(1., 0.5), (0.1, 0.2)]])
D_mull = D.mulliken()
v = np.array([1, 2, 3])
d = D.spin_align(v)
d_mull = d.mulliken()
assert D_mull.shape == (len(D), 2)
assert d_mull.shape == (len(D), 4)
assert not np.allclose(-np.diff(D_mull, axis=1), d_mull[:, 3])
assert np.allclose(D_mull.sum(1), d_mull[:, 0])
def test_spin_align_nc(self, setup):
bond = 1.42
sq3h = 3.**.5 * 0.5
sc = SuperCell(np.array(
[[1.5, sq3h, 0.], [1.5, -sq3h, 0.], [0., 0., 10.]], np.float64) *
bond,
nsc=[3, 3, 1])
orb = AtomicOrbital('px', R=bond * 1.001)
C = Atom(6, orb)
g = Geometry(np.array([[0., 0., 0.], [1., 0., 0.]], np.float64) * bond,
atom=C,
sc=sc)
D = DensityMatrix(g, spin=Spin('nc'))
D.construct([[0.1, bond + 0.01],
[(1., 0.5, 0.01, 0.01), (0.1, 0.2, 0.1, 0.1)]])
D_mull = D.mulliken()
v = np.array([1, 2, 3])
d = D.spin_align(v)
d_mull = d.mulliken()
assert not np.allclose(D_mull, d_mull)
assert np.allclose(D_mull[:, 0], d_mull[:, 0])
