def calc_momentum_distribution(self, mu, beta, with_Sigma, with_dc):
things_to_read = ['n_k', 'n_orbitals', 'proj_mat',
'hopping', 'n_parproj', 'proj_mat_all']
value_read = self.read_input_from_hdf(
subgrp=self.bands_data, things_to_read=things_to_read)
den = numpy.zeros([self.n_k, 2-self.SO, self.n_orbitals[0, 0], self.n_orbitals[0, 0]], numpy.complex_)
spn = self.spin_block_names[self.SO]
ikarray = numpy.array(list(range(self.n_k)))
for ik in mpi.slice_array(ikarray):
g_latt = self.lattice_gf(
ik=ik, mu=mu, iw_or_w="iw", beta=beta, with_Sigma=with_Sigma, with_dc=with_dc)
den0 = g_latt.density()
g_latt.invert()
for isp in range(len(spn)):
den[ik, isp, :, :] = den0[spn[isp]][:, :]
#
# eigenvalue
#
# ev[ik, isp, :] = numpy.linalg.eigvalsh(g_latt[spn[isp]].data[len(g_latt[spn[isp]].mesh)//2, :, :])
#
# Collect density matrix across processes
#
den = mpi.all_reduce(mpi.world, den, lambda x, y: x + y)
return den
def HT(res):
import triqs.utility.mpi as mpi
# First compute the eps_hat array
eps_hat = epsilon_hat(
self.dos.eps) if epsilon_hat else numpy.array(
[x * numpy.identity(N1) for x in self.dos.eps])
assert eps_hat.shape[0] == self.dos.eps.shape[
0], "epsilon_hat function behaves incorrectly"
assert eps_hat.shape[1] == eps_hat.shape[
2], "epsilon_hat function behaves incorrectly (result not a square matrix)"
assert N1 == eps_hat.shape[
1], "Size of Sigma and of epsilon_hat mismatch"
res.zero()
# Perform the sum over eps[i]
tmp, tmp2 = res.copy(), res.copy()
tmp << iOmega_n + mu + eta * 1j
if not (Sigma_fnt):
tmp -= Sigma
if field != None: tmp -= field
# I slice all the arrays on the node. Cf reduce operation below.
for d, e_h, e in zip(*[
mpi.slice_array(A)
for A in [self.rho_for_sum, eps_hat, self.dos.eps]
]):
tmp2.copy_from(tmp)
tmp2 -= e_h
if Sigma_fnt: tmp2 -= Sigma(e)
tmp2.invert()
tmp2 *= d
res += tmp2
# sum the res GF of all nodes and returns the results on all nodes...
# Cf Boost.mpi.python, collective communicator for documentation.
# The point is that res is pickable, hence can be transmitted between nodes without further code...
res << mpi.all_reduce(mpi.world, res, lambda x, y: x + y)
mpi.barrier()
def __call__(self,
Sigma,
mu=0,
eta=0,
field=None,
epsilon_hat=None,
result=None,
selected_blocks=()):
"""
- Computes:
result <- \[ \sum_k (\omega + \mu - field - t(k) - Sigma(k,\omega)) \]
if result is None, it returns a new GF with the results.
otherwise, result must be a GF, in which the calculation is done, and which is then returned.
(this allows chain calculation: SK(mu = mu,Sigma = Sigma, result = G).total_density()
which computes the sumK into G, and returns the density of G.
- Sigma can be a X, or a function k-> X or a function k,eps ->X where:
- k is expected to be a 1d-numpy array of size self.dim of float,
containing the k vector in the basis of the RBZ (i.e. -0.5< k_i <0.5)
- eps is t(k)
- X is anything such that X[BlockName] can be added/subtracted to a GFBloc for BlockName in selected_blocks.
e.g. X can be a BlockGf(with at least the selected_blocks), or a dictionnary Blockname -> array
if the array has the same dimension as the GF blocks (for example to add a static Sigma).
- field: Any k independant object to be added to the GF
- epsilon_hat: a function of eps_k returning a matrix, the dimensions of Sigma
- selected_blocks: The calculation is done with the SAME t(k) for all blocks. If this list is not None
only the blocks in this list are calculated.
e.g. G and Sigma have block indices 'up' and 'down'.
if selected_blocks ==None: 'up' and 'down' are calculated
if selected_blocks == ['up']: only 'up' is calculated. 'down' is 0.
"""
assert selected_blocks == (), "selected_blocks not supported for now"
#S = Sigma.view_selected_blocks(selected_blocks) if selected_blocks else Sigma
#Gres = result if result else Sigma.copy()
#G = Gres.view_selected_blocks(selected_blocks) if selected_blocks else Gres
# check Sigma
# case 1) Sigma is a BlockGf
if isinstance(Sigma, BlockGf):
model = Sigma
Sigma_fnt = False
# case 2) Sigma is a function returning a BlockGf
else:
assert callable(
Sigma), "If Sigma is not a BlockGf it must be a function"
Sigma_Nargs = len(inspect.getargspec(Sigma)[0])
assert Sigma_Nargs <= 2, "Sigma must be a function of k or of k and epsilon"
if Sigma_Nargs == 1:
model = Sigma(self.bz_points[0])
elif Sigma_Nargs == 2:
model = Sigma(self.bz_points[0], self.hopping[0])
Sigma_fnt = True
G = result if result else model.copy()
assert isinstance(G, BlockGf), "G must be a BlockGf"
# check input
assert self.orthogonal_basis, "Local_G: must be orthogonal. non ortho cases not checked."
assert len(list(set([g.target_shape[0] for i, g in G]))) == 1
assert self.bz_weights.shape[0] == self.n_kpts(), "Internal Error"
no = list(set([g.target_shape[0] for i, g in G]))[0]
# Initialize
G.zero()
tmp, tmp2 = G.copy(), G.copy()
mupat = mu * numpy.identity(no, numpy.complex_)
tmp << iOmega_n
if field != None: tmp -= field
if not Sigma_fnt: tmp -= Sigma # substract Sigma once for all
# Loop on k points...
for w, k, eps_k in zip(*[
mpi.slice_array(A)
for A in [self.bz_weights, self.bz_points, self.hopping]
]):
eps_hat = epsilon_hat(eps_k) if epsilon_hat else eps_k
tmp2 << tmp
tmp2 -= tmp2.n_blocks * [eps_hat - mupat]
if Sigma_fnt:
if Sigma_Nargs == 1: tmp2 -= Sigma(k)
elif Sigma_Nargs == 2: tmp2 -= Sigma(k, eps_k)
tmp2.invert()
tmp2 *= w
G += tmp2
G << mpi.all_reduce(mpi.world, G, lambda x, y: x + y)
mpi.barrier()
return G
def get_G_w_from_A_w(A_w,
w_points,
np_interp_A=None,
np_omega=2000,
w_min=-10,
w_max=10,
broadening_factor=1.0):
r""" Use Kramers-Kronig to determine the retarded Green function :math:`G(\omega)`
This calculates :math:`G(\omega)` from the spectral function :math:`A(\omega)`.
A numerical broadening of :math:`bf * i\Delta\omega`
is used, with the adjustable broadening factor bf (default is 1).
This function normalizes :math:`A(\omega)`.
Use mpi to save time.
Parameters
----------
A_w : array
Real-frequency spectral function.
w_points : array
Real-frequency grid points.
np_interp_A : int
Number of grid points A_w should be interpolated on before
G_w is calculated. The interpolation is performed on a linear
grid with np_interp_A points from min(w_points) to max(w_points).
np_omega : int
Number of equidistant grid points of the output Green function.
w_min : float
Start point of output Green function.
w_max : float
End point of output Green function.
broadening_factor : float
Factor multiplying the broadening :math:`i\Delta\omega`
Returns
-------
G_w : GfReFreq
TRIQS retarded Green function.
"""
shape_A = np.shape(A_w)
if len(shape_A) == 1:
indices = [0]
matrix_valued = False
elif (len(shape_A) == 3) and (shape_A[0] == shape_A[1]):
indices = list(range(0, shape_A[0]))
matrix_valued = True
else:
raise Exception('A_w has wrong shape, must be n x n x n_w')
if w_min > w_max:
raise Exception('w_min must be smaller than w_max')
if np_interp_A:
w_points_interp = np.linspace(np.min(w_points),
np.max(w_points), np_interp_A)
if matrix_valued:
A_temp = np.zeros((shape_A[0], shape_A[1], np_interp_A), dtype=complex)
for i in range(shape_A[0]):
for j in range(shape_A[1]):
A_temp[i, j, :] = np.interp(w_points_interp,
w_points, A_w[i, j, :])
A_w = A_temp
else:
A_w = np.interp(w_points_interp, w_points, A_w)
w_points = w_points_interp
G_w = GfReFreq(indices=indices, window=(w_min, w_max), n_points=np_omega)
G_w.zero()
iw_points = np.array(list(range(len(w_points))))
for iw in mpi.slice_array(iw_points):
domega = (w_points[min(len(w_points) - 1, iw + 1)] -
w_points[max(0, iw - 1)]) * 0.5
if matrix_valued:
for i in range(shape_A[0]):
for j in range(shape_A[1]):
G_w[i, j] << G_w[i, j] + A_w[i, j, iw] * \
inverse(Omega - w_points[iw] + 1j * domega * broadening_factor) * domega
else:
G_w << G_w + A_w[iw] * \
inverse(Omega - w_points[iw] + 1j * domega * broadening_factor) * domega
G_w << mpi.all_reduce(mpi.world, G_w, lambda x, y: x + y)
mpi.barrier()
return G_w
def mpi_all_reduce_g(g):
g << mpi.all_reduce(mpi.world, g, lambda x, y: x + y)
return g
for isp in range(SK.n_spin_blocks[SK.SO])]
block_ind_list = [block for block, inner in gf_struct]
glist = lambda: [
GfImFreq(indices=inner, mesh=mesh) for block, inner in gf_struct
]
G_latt_orb = BlockGf(name_list=block_ind_list,
block_list=glist(),
make_copies=False)
G_latt_orb.zero()
for ik in mpi.slice_array(ikarray):
G_latt_KS = SK.lattice_gf(ik=ik, beta=beta)
G_latt_KS *= SK.bz_weights[ik]
for bname, gf in G_latt_orb:
add_g_ik = gf.copy()
add_g_ik.zero()
add_g_ik << SK.downfold(
ik, 0, bname, G_latt_KS[bname], gf, shells='csc', ir=None)
gf << gf + add_g_ik
G_latt_orb << mpi.all_reduce(mpi.world, G_latt_orb, lambda x, y: x + y)
mpi.barrier()
if mpi.is_master_node():
ar['DMFT_results']['Iterations']['G_latt_orb_it' +
str(iteration_offset - 1)] = G_latt_orb
if mpi.is_master_node():
del ar
def extract_G_loc(self,
mu=None,
iw_or_w='iw',
with_Sigma=True,
with_dc=True,
broadening=None):
r"""
"""
# +++ADDED
# print_time function is inserted in several places for benchmark
import time
start = [time.time(), time.time()]
def print_time(txt):
# now = time.time()
# print("time {:>8.5f}sec {:>8.5f}sec @ {}".format(now-start[0], now-start[1], txt))
# start[0] = now
pass
# print("\n=====================")
# print("Start extract_G_loc")
print_time("start")
if mu is None:
mu = self.chemical_potential
if iw_or_w == "iw":
G_loc = [
self.Sigma_imp_iw[icrsh].copy()
for icrsh in range(self.n_corr_shells)
] # this list will be returned
beta = G_loc[0].mesh.beta
G_loc_inequiv = [
BlockGf(name_block_generator=[
(block, GfImFreq(indices=inner, mesh=G_loc[0].mesh))
for block, inner in self.gf_struct_solver[ish].items()
],
make_copies=False)
for ish in range(self.n_inequiv_shells)
]
elif iw_or_w == "w":
G_loc = [
self.Sigma_imp_w[icrsh].copy()
for icrsh in range(self.n_corr_shells)
] # this list will be returned
mesh = G_loc[0].mesh
G_loc_inequiv = [
BlockGf(name_block_generator=[
(block, GfReFreq(indices=inner, mesh=mesh))
for block, inner in self.gf_struct_solver[ish].items()
],
make_copies=False)
for ish in range(self.n_inequiv_shells)
]
for icrsh in range(self.n_corr_shells):
G_loc[icrsh].zero() # initialize to zero
print_time("k-sum start")
ikarray = numpy.array(list(range(self.n_k)))
for ik in mpi.slice_array(ikarray):
print_time("in k-loop: k-sum")
if iw_or_w == 'iw':
G_latt = self.lattice_gf(ik=ik,
mu=mu,
iw_or_w=iw_or_w,
with_Sigma=with_Sigma,
with_dc=with_dc,
beta=beta)
elif iw_or_w == 'w':
mesh_parameters = (G_loc[0].mesh.omega_min,
G_loc[0].mesh.omega_max, len(G_loc[0].mesh))
G_latt = self.lattice_gf(ik=ik,
mu=mu,
iw_or_w=iw_or_w,
with_Sigma=with_Sigma,
with_dc=with_dc,
broadening=broadening,
mesh=mesh_parameters)
print_time("in k-loop: lattice_gf")
G_latt *= self.bz_weights[ik]
print_time("in k-loop: *bz_weights")
for icrsh in range(self.n_corr_shells):
# init temporary storage
# tmp = G_loc[icrsh].copy()
# for bname, gf in tmp:
# tmp[bname] << self.downfold(
# ik, icrsh, bname, G_latt[bname], gf)
# G_loc[icrsh] += tmp
# +++MODIFIED
# Sum up directly into G_loc (no temporary storage is introduced)
for bname, gf in G_loc[icrsh]:
self.downfold(ik,
icrsh,
bname,
G_latt[bname],
gf,
overwrite_gf_inp=True,
fac=+1)
print_time("in k-loop: downfold")
print_time("k-sum end")
# Collect data from mpi
for icrsh in range(self.n_corr_shells):
G_loc[icrsh] << mpi.all_reduce(mpi.world, G_loc[icrsh],
lambda x, y: x + y)
mpi.barrier()
print_time("mpi.all_reduce")
# G_loc[:] is now the sum over k projected to the local orbitals.
# here comes the symmetrisation, if needed:
if self.symm_op != 0:
G_loc = self.symmcorr.symmetrize(G_loc)
# G_loc is rotated to the local coordinate system:
if self.use_rotations:
for icrsh in range(self.n_corr_shells):
for bname, gf in G_loc[icrsh]:
G_loc[icrsh][bname] << self.rotloc(
icrsh, gf, direction='toLocal')
# transform to CTQMC blocks:
for ish in range(self.n_inequiv_shells):
for block, inner in self.gf_struct_solver[ish].items():
for ind1 in inner:
for ind2 in inner:
block_sumk, ind1_sumk = self.solver_to_sumk[ish][(
block, ind1)]
block_sumk, ind2_sumk = self.solver_to_sumk[ish][(
block, ind2)]
G_loc_inequiv[ish][block][ind1, ind2] << G_loc[
self.inequiv_to_corr[ish]][block_sumk][ind1_sumk,
ind2_sumk]
print_time("symm, rotations, solver_to_sumk")
# print("End extract_G_loc")
# print("=====================\n")
# return only the inequivalent shells:
return G_loc_inequiv