def fromsp(cls, geom, P, S=None):
""" Read and return the object with possible overlap """
# Calculate maximum number of connections per row
nc = 0
# Ensure list of csr format (to get dimensions)
if isspmatrix(P):
P = [P]
# Number of dimensions
dim = len(P)
# Sort all indices for the passed sparse matrices
for i in range(dim):
P[i] = P[i].tocsr()
P[i].sort_indices()
# Figure out the maximum connections per
# row to reduce number of re-allocations to 0
for i in range(P[0].shape[0]):
nc = max(nc, P[0][i, :].getnnz())
# Create the sparse object
v = cls(geom, dim, P[0].dtype, nc, orthogonal=S is None)
for i in range(dim):
for jo, io, vv in ispmatrixd(P[i]):
v[jo, io, i] = vv
if not S is None:
for jo, io, vv in ispmatrixd(S):
v.S[jo, io] = vv
return v
def _Hk_non_collinear(self, k=(0, 0, 0), dtype=None):
""" Return the Hamiltonian in a ``scipy.sparse.csr_matrix`` at `k` for a non-collinear
Hamiltonian.
Parameters
----------
k: ``array_like``, `[0,0,0]`
k-point
dtype : ``numpy.dtype``
default to `numpy.complex128`
"""
if dtype is None:
dtype = np.complex128
if np.dtype(dtype).kind != 'c':
raise ValueError(
"Non-collinear Hamiltonian setup requires a complex matrix")
exp = np.exp
dot = np.dot
k = np.asarray(k, np.float64)
k.shape = (-1, )
no = self.no * 2
s = (no, no)
H = csr_matrix(s, dtype=dtype)
# get back-dimension of the intrinsic sparse matrix
no = self.no
# Get the reciprocal lattice vectors dotted with k
kr = dot(self.rcell, k)
for si in range(self.sc.n_s):
isc = self.sc_off[si, :]
phase = exp(-1j * dot(kr, dot(self.cell, isc)))
# diagonal elements
Hf1 = self.tocsr(0)[:, si * no:(si + 1) * no] * phase
for i, j, h in ispmatrixd(Hf1):
H[i * 2, j * 2] += h
Hf1 = self.tocsr(1)[:, si * no:(si + 1) * no] * phase
for i, j, h in ispmatrixd(Hf1):
H[1 + i * 2, 1 + j * 2] += h
# off-diagonal elements
Hf1 = self.tocsr(2)[:, si * no:(si + 1) * no]
Hf2 = self.tocsr(3)[:, si * no:(si + 1) * no]
# We expect Hf1 and Hf2 to be aligned equivalently!
# TODO CHECK
for i, j, hr in ispmatrixd(Hf1):
# get value for the imaginary part
hi = Hf2[i, j]
H[i * 2, 1 + j * 2] += (hr - 1j * hi) * phase
H[1 + i * 2, j * 2] += (hr + 1j * hi) * phase
del Hf1, Hf2
return H
def sp2HS(cls, geom, H, S=None):
""" Returns a tight-binding model from a preset H, S and Geometry
"""
# Calculate number of connections
nc = 0
has_S = not S is None
# Ensure csr format
H = H.tocsr()
if has_S:
S = S.tocsr()
for i in range(geom.no):
nc = max(nc, H[i, :].getnnz())
if has_S:
nc = max(nc, S[i, :].getnnz())
# Create the Hamiltonian
ham = cls(geom, nnzpr=nc, orthogonal=not has_S, dtype=H.dtype)
# Copy data to the model
if has_S:
for jo, io in ispmatrix(H):
ham.S[jo, io] = S[jo, io]
# If the Hamiltonian for one reason or the other
# is zero in the diagonal, then we *must* account for
# this as it isn't captured in the above loop.
skip_S = np.all(H.row == S.row)
skip_S = skip_S and np.all(H.col == S.col)
skip_S = False
if not skip_S:
# Re-convert back to allow index retrieval
H = H.tocsr()
for jo, io, s in ispmatrixd(S):
ham[jo, io] = (H[jo, io], s)
else:
for jo, io, h in ispmatrixd(H):
ham[jo, io] = h
return ham
def _Sk_non_collinear(self, k=(0, 0, 0), dtype=None):
""" Return the Hamiltonian in a ``scipy.sparse.csr_matrix`` at `k`.
Parameters
----------
k: ``array_like``, `[0,0,0]`
k-point
dtype : ``numpy.dtype``
default to `numpy.complex128`
"""
if dtype is None:
dtype = np.complex128
if not np.allclose(k, 0.):
if np.dtype(dtype).kind != 'c':
raise ValueError(
"Hamiltonian setup at k different from Gamma requires a complex matrix"
)
exp = np.exp
dot = np.dot
k = np.asarray(k, np.float64)
k.shape = (-1, )
# Get the overlap matrix
Sf = self.tocsr(self.S_idx)
no = self.no * 2
s = (no, no)
S = csr_matrix(s, dtype=dtype)
# Get back dimensionality of the intrinsic orbitals
no = self.no
# Get the reciprocal lattice vectors dotted with k
kr = dot(self.rcell, k)
for si in range(self.sc.n_s):
isc = self.sc_off[si, :]
phase = exp(-1j * dot(kr, dot(self.cell, isc)))
# Setup the overlap for this k-point
sf = Sf[:, si * no:(si + 1) * no]
for i, j, s in ispmatrixd(sf):
S[i * 2, j * 2] += s
S[1 + i * 2, 1 + j * 2] += s
del Sf
return S
def write_hamiltonian(self, ham, hermitian=True, **kwargs):
""" Writes the Hamiltonian model to the file
Writes a Hamiltonian model to the intrinsic Hamiltonian file format.
The file can be constructed by the implict force of Hermiticity,
or without.
Utilizing the Hermiticity we reduce the file-size by approximately
50%.
Parameters
----------
ham : `Hamiltonian` model
hermitian : boolean=True
whether the stored data is halved using the Hermitian property
"""
ham.finalize()
# We use the upper-triangular form of the Hamiltonian
# and the overlap matrix for hermitian problems
geom = ham.geometry
# First write the geometry
self.write_geometry(geom, **kwargs)
# We default to the advanced layuot if we have more than one
# orbital on any one atom
advanced = kwargs.get(
'advanced',
np.any(np.array([a.no for a in geom.atom.atom], np.int32) > 1))
fmt = kwargs.get('fmt', 'g')
if advanced:
fmt1_str = ' {{0:d}}[{{1:d}}] {{2:d}}[{{3:d}}] {{4:{0}}}\n'.format(
fmt)
fmt2_str = ' {{0:d}}[{{1:d}}] {{2:d}}[{{3:d}}] {{4:{0}}} {{5:{0}}}\n'.format(
fmt)
else:
fmt1_str = ' {{0:d}} {{1:d}} {{2:{0}}}\n'.format(fmt)
fmt2_str = ' {{0:d}} {{1:d}} {{2:{0}}} {{3:{0}}}\n'.format(fmt)
# We currently force the model to be finalized
# before we can write it
# This should be easily circumvented
H = ham.tocsr(0)
if not ham.orthogonal:
S = ham.tocsr(ham.S_idx)
# If the model is Hermitian we can
# do with writing out half the entries
if hermitian:
herm_acc = kwargs.get('herm_acc', 1e-6)
# We check whether it is Hermitian (not S)
for i, isc in enumerate(geom.sc.sc_off):
oi = i * geom.no
oj = geom.sc_index(-isc) * geom.no
# get the difference between the ^\dagger elements
diff = H[:, oi:oi + geom.no] - \
H[:, oj:oj + geom.no].transpose()
diff.eliminate_zeros()
if np.any(np.abs(diff.data) > herm_acc):
amax = np.amax(np.abs(diff.data))
warn(
SileWarning(
'The model could not be asserted to be Hermitian '
'within the accuracy required ({0}).'.format(
amax)))
hermitian = False
del diff
if hermitian:
# Remove all double stuff
for i, isc in enumerate(geom.sc.sc_off):
if np.any(isc < 0):
# We have ^\dagger element, remove it
o = i * geom.no
# Ensure that we remove all nullified quantities
# (setting elements to zero will add them internally
# :(, hence this actually constructs the full matrix
# Therefore we do it on a row basis, to limit memory
# requirements
for j in range(geom.no):
H[j, o:o + geom.no] = 0.
H.eliminate_zeros()
if not ham.orthogonal:
S[j, o:o + geom.no] = 0.
S.eliminate_zeros()
o = geom.sc_index(np.zeros([3], np.int32))
# Get upper-triangular matrix of the unit-cell H and S
ut = triu(H[:, o:o + geom.no], k=0).tocsr()
for j in range(geom.no):
H[j, o:o + geom.no] = 0.
H[j, o:o + geom.no] = ut[j, :]
H.eliminate_zeros()
if not ham.orthogonal:
ut = triu(S[:, o:o + geom.no], k=0).tocsr()
for j in range(geom.no):
S[j, o:o + geom.no] = 0.
S[j, o:o + geom.no] = ut[j, :]
S.eliminate_zeros()
# Ensure that S and H have the same sparsity pattern
for jo, io in ispmatrix(S):
H[jo, io] = H[jo, io]
del ut
# Start writing of the model
# We loop on all super-cells
for i, isc in enumerate(geom.sc.sc_off):
# Check that we have any contributions in this
# sub-section
Hsub = H[:, i * geom.no:(i + 1) * geom.no]
if not ham.orthogonal:
Ssub = S[:, i * geom.no:(i + 1) * geom.no]
if Hsub.getnnz() == 0:
continue
# We have a contribution, write out the information
self._write('\nbegin matrix {0:d} {1:d} {2:d}\n'.format(*isc))
if advanced:
for jo, io, h in ispmatrixd(Hsub):
o = np.array([jo, io], np.int32)
a = geom.o2a(o)
o = o - geom.a2o(a)
if not ham.orthogonal:
s = Ssub[jo, io]
elif jo == io:
s = 1.
else:
s = 0.
if s == 0.:
self._write(fmt1_str.format(a[0], o[0], a[1], o[1], h))
else:
self._write(
fmt2_str.format(a[0], o[0], a[1], o[1], h, s))
else:
for jo, io, h in ispmatrixd(Hsub):
if not ham.orthogonal:
s = Ssub[jo, io]
elif jo == io:
s = 1.
else:
s = 0.
if s == 0.:
self._write(fmt1_str.format(jo, io, h))
else:
self._write(fmt2_str.format(jo, io, h, s))
self._write('end matrix {0:d} {1:d} {2:d}\n'.format(*isc))
