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Merge remote-tracking branch 'gernot/analyze_block_structure_from_gf' into analyze_block_structure_from_gf

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Manuel 2018-05-02 11:40:38 -04:00
parent 5675e5a227 f8731f1bfe
commit 07397ca42e
10 changed files with 875 additions and 49 deletions
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107
python/block_structure.py
View File

@ -2,12 +2,13 @@ import copy
import numpy as np
from pytriqs.gf import GfImFreq, BlockGf
from ast import literal_eval
import pytriqs.utility.mpi as mpi
from warnings import warn
class BlockStructure(object):
""" Contains information about the Green function structure.
This class contains information about the structure of the solver
This class contains information about the structure of the solver
and sumk Green functions and the mapping between them.
Parameters
@ -33,19 +34,21 @@ class BlockStructure(object):
solver_to_sumk_block : list of dict
solver_to_sumk_block[ish][from_block] = to_block
maps from the solver block to the sumk block
maps from the solver block to the sumk block
for *inequivalent* correlated shell ish
"""
def __init__(self,gf_struct_sumk=None,
gf_struct_solver=None,
solver_to_sumk=None,
sumk_to_solver=None,
solver_to_sumk_block=None):
solver_to_sumk_block=None,
deg_shells=None):
self.gf_struct_sumk = gf_struct_sumk
self.gf_struct_solver = gf_struct_solver
self.solver_to_sumk = solver_to_sumk
self.sumk_to_solver = sumk_to_solver
self.solver_to_sumk_block = solver_to_sumk_block
self.deg_shells = deg_shells
@classmethod
def full_structure(cls,gf_struct,corr_to_inequiv):
@ -99,20 +102,21 @@ class BlockStructure(object):
gf_struct_sumk = gs_sumk_all,
solver_to_sumk = copy.deepcopy(solver_to_sumk),
sumk_to_solver = solver_to_sumk,
solver_to_sumk_block = s2sblock)
solver_to_sumk_block = s2sblock,
deg_shells = [[] for ish in range(len(gf_struct))])
def pick_gf_struct_solver(self,new_gf_struct):
""" Pick selected orbitals within blocks.
""" Pick selected orbitals within blocks.
This throws away parts of the Green's function that (for some
reason - be sure that you know what you're doing) shouldn't be
reason - be sure that you know what you're doing) shouldn't be
included in the calculation.
To drop an entire block, just don't include it.
To drop a certain index within a block, just don't include it.
If it was before:
If it was before:
[{'up':[0,1],'down':[0,1],'left':[0,1]}]
to choose the 0th index of the up block and the 1st index of
@ -130,11 +134,11 @@ class BlockStructure(object):
Parameters
----------
new_gf_struct : list of dict
formatted the same as gf_struct_solver:
formatted the same as gf_struct_solver:
new_gf_struct[ish][block]=list of indices in that block.
"""
for ish in range(len(self.gf_struct_solver)):
gf_struct = new_gf_struct[ish]
@ -154,24 +158,24 @@ class BlockStructure(object):
new_ind = gf_struct[blk].index(ind)
self.sumk_to_solver[ish][k]=(blk,new_ind)
else:
self.sumk_to_solver[ish][k]=(None,None)
self.sumk_to_solver[ish][k]=(None,None)
# reindexing gf_struct so that it starts with 0
for k in gf_struct:
gf_struct[k]=range(len(gf_struct[k]))
self.gf_struct_solver[ish]=gf_struct
def pick_gf_struct_sumk(self,new_gf_struct):
""" Pick selected orbitals within blocks.
""" Pick selected orbitals within blocks.
This throws away parts of the Green's function that (for some
reason - be sure that you know what you're doing) shouldn't be
reason - be sure that you know what you're doing) shouldn't be
included in the calculation.
To drop an entire block, just don't include it.
To drop a certain index within a block, just don't include it.
If it was before:
If it was before:
[{'up':[0,1],'down':[0,1],'left':[0,1]}]
to choose the 0th index of the up block and the 1st index of
@ -188,11 +192,11 @@ class BlockStructure(object):
Parameters
----------
new_gf_struct : list of dict
formatted the same as gf_struct_solver:
formatted the same as gf_struct_solver:
new_gf_struct[ish][block]=list of indices in that block.
However, the indices are not according to the solver Gf
However, the indices are not according to the solver Gf
but the sumk Gf.
"""
@ -218,7 +222,7 @@ class BlockStructure(object):
Parameters
----------
mapping : list of dict
the dict consists of elements
the dict consists of elements
(from_block,from_index) : (to_block,to_index)
that maps from one structure to the other
"""
@ -254,7 +258,7 @@ class BlockStructure(object):
def create_gf(self,ish=0,gf_function=GfImFreq,**kwargs):
""" Create a zero BlockGf having the gf_struct_solver structure.
When using GfImFreq as gf_function, typically you have to
When using GfImFreq as gf_function, typically you have to
supply beta as keyword argument.
Parameters
@ -284,7 +288,7 @@ class BlockStructure(object):
.. warning::
Elements that are zero in the new structure due to
the new block structure will be just ignored, thus
the new block structure will be just ignored, thus
approximated to zero.
Parameters
@ -292,15 +296,24 @@ class BlockStructure(object):
G : BlockGf
the Gf that should be converted
G_struct : GfStructure
the structure ofthat G
the structure of that G
ish : int
shell index
show_warnings : bool
whether to show warnings when elements of the Green's
show_warnings : bool or float
whether to show warnings when elements of the Green's
function get thrown away
if float, set the threshold for the magnitude of an element
about to be thrown away to trigger a warning
(default: 1.e-10)
**kwargs :
options passed to the constructor for the new Gf
"""
warning_threshold = 1.e-10
if isinstance(show_warnings, float):
warning_threshold = show_warnings
show_warnings = True
G_new = self.create_gf(ish=ish,**kwargs)
for block in G_struct.gf_struct_solver[ish].keys():
for i1 in G_struct.gf_struct_solver[ish][block]:
@ -311,22 +324,24 @@ class BlockStructure(object):
i2_sol = self.sumk_to_solver[ish][i2_sumk]
if i1_sol[0] is None or i2_sol[0] is None:
if show_warnings:
warn(('Element {},{} of block {} of G is not present '+
'in the new structure').format(i1,i2,block))
if mpi.is_master_node():
warn(('Element {},{} of block {} of G is not present '+
'in the new structure').format(i1,i2,block))
continue
if i1_sol[0]!=i2_sol[0]:
if show_warnings:
warn(('Element {},{} of block {} of G is approximated '+
'to zero to match the new structure.').format(
i1,i2,block))
if show_warnings and np.max(np.abs(G[block][i1,i2].data)) > warning_threshold:
if mpi.is_master_node():
warn(('Element {},{} of block {} of G is approximated '+
'to zero to match the new structure. Max abs value: {}').format(
i1,i2,block,np.max(np.abs(G[block][i1,i2].data))))
continue
G_new[i1_sol[0]][i1_sol[1],i2_sol[1]] = \
G[block][i1,i2]
return G_new
def approximate_as_diagonal(self):
""" Create a structure for a GF with zero off-diagonal elements.
""" Create a structure for a GF with zero off-diagonal elements.
.. warning::
In general, this will throw away non-zero elements of the
@ -351,7 +366,8 @@ class BlockStructure(object):
def __eq__(self,other):
def compare(one,two):
if type(one)!=type(two):
return False
if not (isinstance(one, (bool, np.bool_)) and isinstance(two, (bool, np.bool_))):
return False
if one is None and two is None:
return True
if isinstance(one,list) or isinstance(one,tuple):
@ -361,10 +377,10 @@ class BlockStructure(object):
if not compare(x,y):
return False
return True
elif isinstance(one,int):
return one==two
elif isinstance(one,str):
elif isinstance(one,(int,bool, str, np.bool_)):
return one==two
elif isinstance(one,np.ndarray):
return np.all(one==two)
elif isinstance(one,dict):
if set(one.keys()) != set(two.keys()):
return False
@ -375,8 +391,9 @@ class BlockStructure(object):
warn('Cannot compare {}'.format(type(one)))
return False
for prop in [ "gf_struct_sumk", "gf_struct_solver",
"solver_to_sumk", "sumk_to_solver", "solver_to_sumk_block"]:
for prop in [ "gf_struct_sumk", "gf_struct_solver",
"solver_to_sumk", "sumk_to_solver", "solver_to_sumk_block",
"deg_shells"]:
if not compare(getattr(self,prop),getattr(other,prop)):
return False
return True
@ -388,8 +405,8 @@ class BlockStructure(object):
""" Reduce to dict for HDF5 export."""
ret = {}
for element in [ "gf_struct_sumk", "gf_struct_solver",
"solver_to_sumk_block"]:
for element in [ "gf_struct_sumk", "gf_struct_solver",
"solver_to_sumk_block","deg_shells"]:
ret[element] = getattr(self,element)
def construct_mapping(mapping):
@ -436,6 +453,18 @@ class BlockStructure(object):
keys = sorted(element[ish].keys(),key=keyfun)
for k in keys:
s+=' '+str(k)+str(element[ish][k])+'\n'
s += "deg_shells\n"
for ish in range(len(self.deg_shells)):
s+=' shell '+str(ish)+'\n'
for l in range(len(self.deg_shells[ish])):
s+=' equivalent group '+str(l)+'\n'
if isinstance(self.deg_shells[ish][l],dict):
for key, val in self.deg_shells[ish][l].iteritems():
s+=' '+key+('*' if val[1] else '')+':\n'
s+=' '+str(val[0]).replace('\n','\n ')+'\n'
else:
for key in self.deg_shells[ish][l]:
s+=' '+key+'\n'
return s
from pytriqs.archive.hdf_archive_schemes import register_class

463
python/sumk_dft.py
View File

@ -25,12 +25,15 @@ import numpy
import pytriqs.utility.dichotomy as dichotomy
from pytriqs.gf import *
import pytriqs.utility.mpi as mpi
from pytriqs.utility.comparison_tests import assert_arrays_are_close
from pytriqs.archive import *
from symmetry import *
from block_structure import BlockStructure
from sets import Set
from itertools import product
from warnings import warn
from scipy import compress
from scipy.optimize import minimize
class SumkDFT(object):
@ -848,6 +851,414 @@ class SumkDFT(object):
elif (ind1 < 0) and (ind2 < 0):
self.deg_shells[ish].append([block1, block2])
def _get_hermitian_quantity_from_gf(self, G):
""" Convert G to a Hermitian quantity
For G(tau) and G(iw), G(tau) is returned.
For G(t) and G(w), the spectral function is returned.
Parameters
----------
G : list of BlockGf of GfImFreq, GfImTime, GfReFreq or GfReTime
the input Green's function
Returns
-------
gf : list of BlockGf of GfImTime or GfReFreq
the output G(tau) or A(w)
"""
# make a GfImTime from the supplied GfImFreq
if all(isinstance(g_sh._first(), GfImFreq) for g_sh in G):
gf = [BlockGf(name_block_generator = [(name, GfImTime(beta=block.mesh.beta,
indices=block.indices,n_points=len(block.mesh)+1)) for name, block in g_sh])
for g_sh in G]
for ish in range(len(gf)):
for name, g in gf[ish]:
g.set_from_inverse_fourier(G[ish][name])
# keep a GfImTime from the supplied GfImTime
elif all(isinstance(g_sh._first(), GfImTime) for g_sh in G):
gf = G
# make a spectral function from the supplied GfReFreq
elif all(isinstance(g_sh._first(), GfReFreq) for g_sh in G):
gf = [g_sh.copy() for g_sh in G]
for ish in range(len(gf)):
for name, g in gf[ish]:
g << 1.0j*(g-g.conjugate().transpose())/2.0/numpy.pi
elif all(isinstance(g_sh._first(), GfReTime) for g_sh in G):
def get_delta_from_mesh(mesh):
w0 = None
for w in mesh:
if w0 is None:
w0 = w
else:
return w-w0
gf = [BlockGf(
name_block_generator = [(name,
GfReFreq(
window=(-numpy.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh)), numpy.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh))),
n_points=len(block.mesh),
indices=block.indices)) for name, block in g_sh])
for g_sh in G]
for ish in range(len(gf)):
for name, g in gf[ish]:
g.set_from_fourier(G[ish][name])
g << 1.0j*(g-g.conjugate().transpose())/2.0/numpy.pi
else:
raise Exception("G must be a list of BlockGf of either GfImFreq, GfImTime, GfReFreq or GfReTime")
return gf
def analyse_block_structure_from_gf(self, G, threshold=1.e-5, include_shells=None, analyse_deg_shells = True):
r"""
Determines the block structure of local Green's functions by analysing
the structure of the corresponding non-interacting Green's function.
The resulting block structures for correlated shells are
stored in the :class:`SumkDFT.block_structure <dft.block_structure.BlockStructure>`
attribute.
This is a safer alternative to analyse_block_structure, because
the full non-interacting Green's function is taken into account
and not just the density matrix and Hloc.
Parameters
----------
G : list of BlockGf of GfImFreq, GfImTime, GfReFreq or GfReTime
the non-interacting Green's function for each inequivalent correlated shell
threshold : real, optional
If the difference between matrix elements is below threshold,
they are considered to be equal.
include_shells : list of integers, optional
List of correlated shells to be analysed.
If include_shells is not provided all correlated shells will be analysed.
analyse_deg_shells : bool
Whether to call the analyse_deg_shells function
after having finished the block structure analysis
Returns
-------
G : list of BlockGf of GfImFreq or GfImTime
the Green's function transformed into the new block structure
"""
gf = self._get_hermitian_quantity_from_gf(G)
# initialize the variables
self.gf_struct_solver = [{} for ish in range(self.n_inequiv_shells)]
self.sumk_to_solver = [{} for ish in range(self.n_inequiv_shells)]
self.solver_to_sumk = [{} for ish in range(self.n_inequiv_shells)]
self.solver_to_sumk_block = [{}
for ish in range(self.n_inequiv_shells)]
# the maximum value of each matrix element of each block and shell
max_gf = [{name:numpy.max(numpy.abs(g.data),0) for name, g in gf[ish]} for ish in range(self.n_inequiv_shells)]
if include_shells is None:
# include all shells
include_shells = range(self.n_inequiv_shells)
for ish in include_shells:
for sp in self.spin_block_names[self.corr_shells[self.inequiv_to_corr[ish]]['SO']]:
n_orb = self.corr_shells[self.inequiv_to_corr[ish]]['dim']
# gives an index list of entries larger that threshold
maxgf_bool = (abs(max_gf[ish][sp]) > threshold)
# Determine off-diagonal entries in upper triangular part of the
# Green's function
offdiag = Set([])
for i in range(n_orb):
for j in range(i + 1, n_orb):
if maxgf_bool[i, j]:
offdiag.add((i, j))
# Determine the number of non-hybridising blocks in the gf
blocs = [[i] for i in range(n_orb)]
while len(offdiag) != 0:
pair = offdiag.pop()
for b1, b2 in product(blocs, blocs):
if (pair[0] in b1) and (pair[1] in b2):
if blocs.index(b1) != blocs.index(b2): # In separate blocks?
# Merge two blocks
b1.extend(blocs.pop(blocs.index(b2)))
break # Move on to next pair in offdiag
# Set the gf_struct for the solver accordingly
num_blocs = len(blocs)
for i in range(num_blocs):
blocs[i].sort()
self.gf_struct_solver[ish].update(
[('%s_%s' % (sp, i), range(len(blocs[i])))])
# Construct sumk_to_solver taking (sumk_block, sumk_index) --> (solver_block, solver_inner)
# and solver_to_sumk taking (solver_block, solver_inner) -->
# (sumk_block, sumk_index)
for i in range(num_blocs):
for j in range(len(blocs[i])):
block_sumk = sp
inner_sumk = blocs[i][j]
block_solv = '%s_%s' % (sp, i)
inner_solv = j
self.sumk_to_solver[ish][(block_sumk, inner_sumk)] = (
block_solv, inner_solv)
self.solver_to_sumk[ish][(block_solv, inner_solv)] = (
block_sumk, inner_sumk)
self.solver_to_sumk_block[ish][block_solv] = block_sumk
# transform G to the new structure
full_structure = BlockStructure.full_structure(
[{sp:range(self.corr_shells[self.inequiv_to_corr[ish]]['dim'])
for sp in self.spin_block_names[self.corr_shells[self.inequiv_to_corr[ish]]['SO']]}
for ish in range(self.n_inequiv_shells)],None)
G_transformed = [
self.block_structure.convert_gf(G[ish],
full_structure, ish, mesh=G[ish].mesh.copy(), show_warnings=threshold,
gf_function=type(G[ish]._first()))
for ish in range(self.n_inequiv_shells)]
if analyse_deg_shells:
self.analyse_deg_shells(G_transformed, threshold, include_shells)
return G_transformed
def analyse_deg_shells(self, G, threshold=1.e-5, include_shells=None):
r"""
Determines the degenerate shells of local Green's functions by analysing
the structure of the corresponding non-interacting Green's function.
The results are stored in the
:class:`SumkDFT.block_structure <dft.block_structure.BlockStructure>`
attribute.
Due to the implementation and numerics, the maximum difference between
two matrix elements that are detected as equal can be a bit higher
(e.g. a factor of two) than the actual threshold.
Parameters
----------
G : list of BlockGf of GfImFreq or GfImTime
the non-interacting Green's function for each inequivalent correlated shell
threshold : real, optional
If the difference between matrix elements is below threshold,
they are considered to be equal.
include_shells : list of integers, optional
List of correlated shells to be analysed.
If include_shells is not provided all correlated shells will be analysed.
"""
# initialize
self.deg_shells = [[] for ish in range(self.n_inequiv_shells)]
# helper function
def null(A, eps=1e-15):
""" Calculate the null-space of matrix A """
u, s, vh = numpy.linalg.svd(A)
null_mask = (s <= eps)
null_space = compress(null_mask, vh, axis=0)
return null_space.conjugate().transpose()
gf = self._get_hermitian_quantity_from_gf(G)
if include_shells is None:
# include all shells
include_shells = range(self.n_inequiv_shells)
# We consider two blocks equal, if their Green's functions obey
# maybe_conjugate1( v1^dagger G1 v1 ) = maybe_conjugate2( v2^dagger G2 v2 )
# where maybe_conjugate is a function that conjugates the Green's
# function if the flag 'conjugate' is set and the v are unitary
# matrices
#
# for each pair of blocks, we check whether there is a transformation
# maybe_conjugate( T G1 T^dagger ) = G2
# where our goal is to find T
# we just try whether there is such a T with and without conjugation
for ish in include_shells:
for block1 in self.gf_struct_solver[ish].iterkeys():
for block2 in self.gf_struct_solver[ish].iterkeys():
if block1==block2: continue
# check if the blocks are already present in the deg_shells
ind1 = -1
ind2 = -2
for n, ind in enumerate(self.deg_shells[ish]):
if block1 in ind:
ind1 = n
v1 = ind[block1]
if block2 in ind:
ind2 = n
v2 = ind[block2]
# if both are already present, go to the next pair of blocks
if ind1 >= 0 and ind2 >= 0:
continue
gf1 = gf[ish][block1]
gf2 = gf[ish][block2]
# the two blocks have to have the same shape
if gf1.target_shape != gf2.target_shape:
continue
# Instead of directly comparing the two blocks, we
# compare its eigenvalues. As G(tau) is Hermitian,
# they are real and the eigenvector matrix is unitary.
# Thus, if the eigenvalues are equal we can transform
# one block to make it equal to the other (at least
# for tau=0).
e1 = numpy.linalg.eigvalsh(gf1.data[0])
e2 = numpy.linalg.eigvalsh(gf2.data[0])
if numpy.any(abs(e1-e2) > threshold): continue
for conjugate in [False,True]:
if conjugate:
gf2 = gf2.conjugate()
# we want T gf1 T^dagger = gf2
# while for a given tau, T could be calculated
# by diagonalizing gf1 and gf2, this does not
# work for all taus simultaneously because of
# numerical imprecisions
# rather, we rewrite the equation to
# T gf1 = gf2 T
# which is the Sylvester equation.
# For that equation, one can use the Kronecker
# product to get a linear problem, which consists
# of finding the null space of M vec T = 0.
M = numpy.kron(numpy.eye(*gf1.target_shape),gf2.data[0])-numpy.kron(gf1.data[0].transpose(),numpy.eye(*gf1.target_shape))
N = null(M, threshold)
# now we get the intersection of the null spaces
# of all values of tau
for i in range(1,len(gf1.data)):
M = numpy.kron(numpy.eye(*gf1.target_shape),gf2.data[i])-numpy.kron(gf1.data[i].transpose(),numpy.eye(*gf1.target_shape))
# transform M into current null space
M = numpy.dot(M, N)
N = numpy.dot(N, null(M, threshold))
if numpy.size(N) == 0:
break
# no intersection of the null spaces -> no symmetry
if numpy.size(N) == 0: continue
# reshape N: it then has the indices matrix, matrix, number of basis vectors of the null space
N = N.reshape(gf1.target_shape[0], gf1.target_shape[1], -1).transpose([1, 0, 2])
"""
any matrix in the null space can now be constructed as
M = 0
for i in range(N.shape[-1]):
M += y[i]*N[:,:,i]
with coefficients (complex numbers) y[i].
We want to get a set of coefficients y so that M is unitary.
Unitary means M M^dagger = 1.
Thus,
sum y[i] N[:,:,i] y[j].conjugate() N[:,:,j].conjugate().transpose() = eye.
The object N[:,:,i] N[:,:,j] is a four-index object which we call Z.
"""
Z = numpy.einsum('aci,bcj->abij', N, N.conjugate())
"""
function chi2
This function takes a real parameter vector y and reinterprets it as complex.
Then, it calculates the chi2 of
sum y[i] N[:,:,i] y[j].conjugate() N[:,:,j].conjugate().transpose() - eye.
"""
def chi2(y):
# reinterpret y as complex number
y = y.view(numpy.complex_)
ret = 0.0
for a in range(Z.shape[0]):
for b in range(Z.shape[1]):
ret += numpy.abs(numpy.dot(y, numpy.dot(Z[a, b], y.conjugate()))
- (1.0 if a == b else 0.0))**2
return ret
# use the minimization routine from scipy
res = minimize(chi2, numpy.ones(2 * N.shape[-1]))
# if the minimization fails, there is probably no symmetry
if not res.success: continue
# check if the minimization returned zero within the tolerance
if res.fun > threshold: continue
# reinterpret the solution as a complex number
y = res.x.view(numpy.complex_)
# reconstruct the T matrix
T = numpy.zeros(N.shape[:-1], dtype=numpy.complex_)
for i in range(len(y)):
T += N[:, :, i] * y[i]
# transform gf1 using T
G_transformed = gf1.copy()
G_transformed.from_L_G_R(T, gf1, T.conjugate().transpose())
# it does not make sense to check the tails for an
# absolute error because it will usually not hold;
# we could just check the relative error
# (here, we ignore it, reasoning that if the data
# is the same, the tails have to coincide as well)
try:
assert_arrays_are_close(G_transformed.data, gf2.data, threshold)
except (RuntimeError, AssertionError):
# the symmetry does not hold
continue
# Now that we have found a valid T, we have to
# rewrite it to match the convention that
# C1(v1^dagger G1 v1) = C2(v2^dagger G2 v2),
# where C conjugates if the flag is True
# For each group of degenerate shells, the list
# SK.deg_shells[ish] contains a dict. The keys
# of the dict are the block names, the values
# are tuples. The first entry of the tuple is
# the transformation matrix v, the second entry
# is the conjugation flag
# the second block is already present
# set v1 and C1 so that they are compatible with
# C(T gf1 T^dagger) = gf2
# and with
# C1(v1^dagger G1 v1) = C2(v2^dagger G2 v2)
if (ind1 < 0) and (ind2 >= 0):
if conjugate:
self.deg_shells[ish][ind2][block1] = numpy.dot(T.conjugate().transpose(), v2[0].conjugate()), not v2[1]
else:
self.deg_shells[ish][ind2][block1] = numpy.dot(T.conjugate().transpose(), v2[0]), v2[1]
# the first block is already present
# set v2 and C2 so that they are compatible with
# C(T gf1 T^dagger) = gf2
# and with
# C1(v1^dagger G1 v1) = C2(v2^dagger G2 v2)
elif (ind1 >= 0) and (ind2 < 0):
if conjugate:
self.deg_shells[ish][ind1][block2] = numpy.dot(T.conjugate(), v1[0].conjugate()), not v1[1]
else:
self.deg_shells[ish][ind1][block2] = numpy.dot(T, v1[0]), v1[1]
# the blocks are not already present
# we arbitrarily choose v1=eye and C1=False and
# set v2 and C2 so that they are compatible with
# C(T gf1 T^dagger) = gf2
# and with
# C1(v1^dagger G1 v1) = C2(v2^dagger G2 v2)
elif (ind1 < 0) and (ind2 < 0):
d = dict()
d[block1] = numpy.eye(*gf1.target_shape), False
if conjugate:
d[block2] = T.conjugate(), True
else:
d[block2] = T, False
self.deg_shells[ish].append(d)
# a block was found, break out of the loop
break
def density_matrix(self, method='using_gf', beta=40.0):
"""Calculate density matrices in one of two ways.
@ -1212,20 +1623,52 @@ class SumkDFT(object):
Parameters
----------
gf_to_symm : gf_struct_solver like
Input GF.
Input and output GF (i.e., it gets overwritten)
orb : int
Index of an inequivalent shell.
"""
# when reading block_structures written with older versions from
# an h5 file, self.deg_shells might be None
if self.deg_shells is None: return
for degsh in self.deg_shells[orb]:
ss = gf_to_symm[degsh[0]].copy()
ss.zero()
# ss will hold the averaged orbitals in the basis where the
# blocks are all equal
# i.e. maybe_conjugate(v^dagger gf v)
ss = None
n_deg = len(degsh)
for bl in degsh:
ss += gf_to_symm[bl] / (1.0 * n_deg)
for bl in degsh:
gf_to_symm[bl] << ss
for key in degsh:
if ss is None:
ss = gf_to_symm[key].copy()
ss.zero()
helper = ss.copy()
# get the transformation matrix
if isinstance(degsh, dict):
v, C = degsh[key]
else:
# for backward compatibility, allow degsh to be a list
v = numpy.eye(*ss.target_shape)
C = False
# the helper is in the basis where the blocks are all equal
helper.from_L_G_R(v.conjugate().transpose(), gf_to_symm[key], v)
if C:
helper << helper.transpose()
# average over all shells
ss += helper / (1.0 * n_deg)
# now put back the averaged gf to all shells
for key in degsh:
if isinstance(degsh, dict):
v, C = degsh[key]
else:
# for backward compatibility, allow degsh to be a list
v = numpy.eye(*ss.target_shape)
C = False
if C:
gf_to_symm[key].from_L_G_R(v, ss.transpose(), v.conjugate().transpose())
else:
gf_to_symm[key].from_L_G_R(v, ss, v.conjugate().transpose())
def total_density(self, mu=None, iw_or_w="iw", with_Sigma=True, with_dc=True, broadening=None):
r"""
@ -1610,3 +2053,9 @@ class SumkDFT(object):
def __set_solver_to_sumk_block(self,value):
self.block_structure.solver_to_sumk_block = value
solver_to_sumk_block = property(__get_solver_to_sumk_block,__set_solver_to_sumk_block)
def __get_deg_shells(self):
return self.block_structure.deg_shells
def __set_deg_shells(self,value):
self.block_structure.deg_shells = value
deg_shells = property(__get_deg_shells,__set_deg_shells)

4
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@ -2,10 +2,10 @@
FILE(GLOB all_h5_files RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} *.h5)
file(COPY ${CMAKE_CURRENT_SOURCE_DIR}/${all_h5_files} DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
# Copy other files
FILE(COPY SrVO3.pmat SrVO3.struct SrVO3.outputs SrVO3.oubwin SrVO3.ctqmcout SrVO3.symqmc SrVO3.sympar SrVO3.parproj hk_convert_hamiltonian.hk LaVO3-Pnma_hr.dat LaVO3-Pnma.inp DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
FILE(COPY SrVO3.pmat SrVO3.struct SrVO3.outputs SrVO3.oubwin SrVO3.ctqmcout SrVO3.symqmc SrVO3.sympar SrVO3.parproj SrIrO3_rot.h5 hk_convert_hamiltonian.hk LaVO3-Pnma_hr.dat LaVO3-Pnma.inp DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
# List all tests
set(all_tests wien2k_convert hk_convert w90_convert sumkdft_basic srvo3_Gloc srvo3_transp sigma_from_file blockstructure)
set(all_tests wien2k_convert hk_convert w90_convert sumkdft_basic srvo3_Gloc srvo3_transp sigma_from_file blockstructure analyze_block_structure_from_gf analyze_block_structure_from_gf2)
foreach(t ${all_tests})
add_test(NAME ${t} COMMAND python ${CMAKE_CURRENT_SOURCE_DIR}/${t}.py)

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@ -0,0 +1,232 @@
from pytriqs.gf import *
from sumk_dft import SumkDFT
from scipy.linalg import expm
import numpy as np
from pytriqs.utility.comparison_tests import assert_gfs_are_close, assert_arrays_are_close, assert_block_gfs_are_close
from pytriqs.archive import *
import itertools
# The full test checks all different possible combinations of conjugated
# blocks. This takes a few minutes. For a quick test, just checking one
# random value suffices.
# (this parameter affects the second test)
full_test = False
#######################################################################
# First test #
# where we check the analyse_block_structure_from_gf function #
# for the SrIrO3_rot.h5 file #
#######################################################################
beta = 40
SK = SumkDFT(hdf_file = 'SrIrO3_rot.h5')
Sigma = SK.block_structure.create_gf(beta=beta)
SK.put_Sigma([Sigma])
G = SK.extract_G_loc()
# the original block structure
block_structure1 = SK.block_structure.copy()
G_new = SK.analyse_block_structure_from_gf(G)
# the new block structure
block_structure2 = SK.block_structure.copy()
with HDFArchive('analyze_block_structure_from_gf.out.h5','w') as ar:
ar['bs1'] = block_structure1
ar['bs2'] = block_structure2
# check whether the block structure is the same as in the reference
with HDFArchive('analyze_block_structure_from_gf.out.h5','r') as ar,\
HDFArchive('analyze_block_structure_from_gf.ref.h5','r') as ar2:
assert ar['bs1'] == ar2['bs1'], 'bs1 not equal'
a1 = ar['bs2']
a2 = ar2['bs2']
assert a1==block_structure2, "writing/reading block structure incorrect"
# we set the deg_shells to None because the transformation matrices
# have a phase freedom and will, therefore, not be equal in general
a1.deg_shells = None
a2.deg_shells = None
assert a1==a2, 'bs2 not equal'
# check if deg shells are correct
assert len(SK.deg_shells[0])==1, "wrong number of equivalent groups"
# check if the Green's functions that are found to be equal in the
# routine are indeed equal
for d in SK.deg_shells[0]:
assert len(d)==2, "wrong number of shells in equivalent group"
# the convention is that for every degenerate shell, the transformation
# matrix v and the conjugate bool is saved
# then,
# maybe_conjugate1( v1^dagger G1 v1 ) = maybe_conjugate2( v2^dagger G2 v2 )
# therefore, to test, we calculate
# maybe_conjugate( v^dagger G v )
# for all degenerate shells and check that they are all equal
normalized_gfs = []
for key in d:
normalized_gf = G_new[0][key].copy()
normalized_gf.from_L_G_R(d[key][0].conjugate().transpose(), G_new[0][key], d[key][0])
if d[key][1]:
normalized_gf << normalized_gf.transpose()
normalized_gfs.append(normalized_gf)
for i in range(len(normalized_gfs)):
for j in range(i+1,len(normalized_gfs)):
assert_arrays_are_close(normalized_gfs[i].data, normalized_gfs[j].data, 1.e-5)
# the tails have to be compared using a relative error
for o in range(normalized_gfs[i].tail.order_min,normalized_gfs[i].tail.order_max+1):
if np.abs(normalized_gfs[i].tail[o][0,0]) < 1.e-10:
continue
assert np.max(np.abs((normalized_gfs[i].tail[o]-normalized_gfs[j].tail[o])/(normalized_gfs[i].tail[o][0,0]))) < 1.e-5, \
"tails are different"
#######################################################################
# Second test #
# where a Green's function is constructed from a random model #
# and the analyse_block_structure_from_gf function is tested for that #
# model #
#######################################################################
# helper function to get random Hermitian matrix
def get_random_hermitian(dim):
herm = np.random.rand(dim,dim)+1.0j*np.random.rand(dim,dim)
herm = herm + herm.conjugate().transpose()
return herm
# helper function to get random unitary matrix
def get_random_transformation(dim):
herm = get_random_hermitian(dim)
T = expm(1.0j*herm)
return T
# we will conjugate the Green's function blocks according to the entries
# of conjugate_values
# for each of the 5 blocks that will be constructed, there is an entry
# True or False that says whether it will be conjugated
if full_test:
# in the full test we check all combinations
conjugate_values = list(itertools.product([False, True], repeat=5))
else:
# in the quick test we check a random combination
conjugate_values = [np.random.rand(5)>0.5]
for conjugate in conjugate_values:
# construct a random block-diagonal Hloc
Hloc = np.zeros((10,10), dtype=np.complex_)
# the Hloc of the first three 2x2 blocks is equal
Hloc0 = get_random_hermitian(2)
Hloc[:2,:2] = Hloc0
Hloc[2:4,2:4] = Hloc0
Hloc[4:6,4:6] = Hloc0
# the Hloc of the last two 2x2 blocks is equal
Hloc1 = get_random_hermitian(2)
Hloc[6:8,6:8] = Hloc1
Hloc[8:,8:] = Hloc1
# construct the hybridization delta
# this is equal for all 2x2 blocks
V = get_random_hermitian(2) # the hopping elements from impurity to bath
b1 = np.random.rand() # the bath energy of the first bath level
b2 = np.random.rand() # the bath energy of the second bath level
delta = G[0]['ud'][:2,:2].copy()
delta[0,0] << (V[0,0]*V[0,0].conjugate()*inverse(Omega-b1)+V[0,1]*V[0,1].conjugate()*inverse(Omega-b2))/2.0
delta[0,1] << (V[0,0]*V[1,0].conjugate()*inverse(Omega-b1)+V[0,1]*V[1,1].conjugate()*inverse(Omega-b2))/2.0
delta[1,0] << (V[1,0]*V[0,0].conjugate()*inverse(Omega-b1)+V[1,1]*V[0,1].conjugate()*inverse(Omega-b2))/2.0
delta[1,1] << (V[1,0]*V[1,0].conjugate()*inverse(Omega-b1)+V[1,1]*V[1,1].conjugate()*inverse(Omega-b2))/2.0
# construct G
G[0].zero()
for i in range(0,10,2):
G[0]['ud'][i:i+2,i:i+2] << inverse(Omega-delta)
G[0]['ud'] << inverse(inverse(G[0]['ud']) - Hloc)
# for testing symm_deg_gf below, we need this
# we construct it so that for every group of degenerate blocks of G[0], the
# mean of the blocks of G_noisy is equal to G[0]
G_noisy = G[0].copy()
noise1 = np.random.randn(*delta.target_shape)
G_noisy['ud'][:2,:2].data[:,:,:] += noise1
G_noisy['ud'][2:4,2:4].data[:,:,:] -= noise1/2.0
G_noisy['ud'][4:6,4:6].data[:,:,:] -= noise1/2.0
noise2 = np.random.randn(*delta.target_shape)
G_noisy['ud'][6:8,6:8].data[:,:,:] += noise2
G_noisy['ud'][8:,8:].data[:,:,:] -= noise2
# for testing backward-compatibility in symm_deg_gf, we need the
# un-transformed Green's functions
G_pre_transform = G[0].copy()
G_noisy_pre_transform = G_noisy.copy()
# transform each block using a random transformation matrix
for i in range(0,10,2):
T = get_random_transformation(2)
G[0]['ud'][i:i+2,i:i+2].from_L_G_R(T, G[0]['ud'][i:i+2,i:i+2], T.conjugate().transpose())
G_noisy['ud'][i:i+2,i:i+2].from_L_G_R(T, G_noisy['ud'][i:i+2,i:i+2], T.conjugate().transpose())
# if that block shall be conjugated, go ahead and do it
if conjugate[i//2]:
G[0]['ud'][i:i+2,i:i+2] << G[0]['ud'][i:i+2,i:i+2].transpose()
G_noisy['ud'][i:i+2,i:i+2] << G_noisy['ud'][i:i+2,i:i+2].transpose()
# analyse the block structure
G_new = SK.analyse_block_structure_from_gf(G, 1.e-7)
# transform G_noisy etc. to the new block structure
G_noisy = SK.block_structure.convert_gf(G_noisy, block_structure1, beta = G_noisy.mesh.beta)
G_pre_transform = SK.block_structure.convert_gf(G_pre_transform, block_structure1, beta = G_noisy.mesh.beta)
G_noisy_pre_transform = SK.block_structure.convert_gf(G_noisy_pre_transform, block_structure1, beta = G_noisy.mesh.beta)
assert len(SK.deg_shells[0]) == 2, "wrong number of equivalent groups found"
assert sorted([len(d) for d in SK.deg_shells[0]]) == [2,3], "wrong number of members in the equivalent groups found"
for d in SK.deg_shells[0]:
if len(d)==2:
assert 'ud_3' in d, "shell ud_3 missing"
assert 'ud_4' in d, "shell ud_4 missing"
if len(d)==3:
assert 'ud_0' in d, "shell ud_0 missing"
assert 'ud_1' in d, "shell ud_1 missing"
assert 'ud_2' in d, "shell ud_2 missing"
# the convention is that for every degenerate shell, the transformation
# matrix v and the conjugate bool is saved
# then,
# maybe_conjugate1( v1^dagger G1 v1 ) = maybe_conjugate2( v2^dagger G2 v2 )
# therefore, to test, we calculate
# maybe_conjugate( v^dagger G v )
# for all degenerate shells and check that they are all equal
normalized_gfs = []
for key in d:
normalized_gf = G_new[0][key].copy()
normalized_gf.from_L_G_R(d[key][0].conjugate().transpose(), G_new[0][key], d[key][0])
if d[key][1]:
normalized_gf << normalized_gf.transpose()
normalized_gfs.append(normalized_gf)
for i in range(len(normalized_gfs)):
for j in range(i+1,len(normalized_gfs)):
# here, we use a threshold that is 1 order of magnitude less strict
# because of numerics
assert_gfs_are_close(normalized_gfs[i], normalized_gfs[j], 1.e-6)
# now we check symm_deg_gf
# symmetrizing the GF has is has to leave it unchanged
G_new_symm = G_new[0].copy()
SK.symm_deg_gf(G_new_symm, 0)
assert_block_gfs_are_close(G_new[0], G_new_symm, 1.e-6)
# symmetrizing the noisy GF, which was carefully constructed,
# has to give the same result as G_new[0]
SK.symm_deg_gf(G_noisy, 0)
assert_block_gfs_are_close(G_new[0], G_noisy, 1.e-6)
# check backward compatibility of symm_deg_gf
# first, construct the old format of the deg shells
for ish in range(len(SK.deg_shells)):
for gr in range(len(SK.deg_shells[ish])):
SK.deg_shells[ish][gr] = SK.deg_shells[ish][gr].keys()
# symmetrizing the GF as is has to leave it unchanged
G_new_symm << G_pre_transform
SK.symm_deg_gf(G_new_symm, 0)
assert_block_gfs_are_close(G_new_symm, G_pre_transform, 1.e-6)
# symmetrizing the noisy GF pre transform, which was carefully constructed,
# has to give the same result as G_pre_transform
SK.symm_deg_gf(G_noisy_pre_transform, 0)
assert_block_gfs_are_close(G_noisy_pre_transform, G_pre_transform, 1.e-6)

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@ -0,0 +1,115 @@
from pytriqs.gf import *
from sumk_dft import SumkDFT
import numpy as np
from pytriqs.utility.comparison_tests import assert_block_gfs_are_close
# here we test the SK.analyze_block_structure_from_gf function
# with GfReFreq, GfReTime
# helper function to get random Hermitian matrix
def get_random_hermitian(dim):
herm = np.random.rand(dim,dim)+1.0j*np.random.rand(dim,dim)
herm = herm + herm.conjugate().transpose()
return herm
# helper function to get random unitary matrix
def get_random_transformation(dim):
herm = get_random_hermitian(dim)
T = expm(1.0j*herm)
return T
# construct a random block-diagonal Hloc
Hloc = np.zeros((10,10), dtype=np.complex_)
# the Hloc of the first three 2x2 blocks is equal
Hloc0 = get_random_hermitian(2)
Hloc[:2,:2] = Hloc0
Hloc[2:4,2:4] = Hloc0
Hloc[4:6,4:6] = Hloc0
# the Hloc of the last two 2x2 blocks is equal
Hloc1 = get_random_hermitian(2)
Hloc[6:8,6:8] = Hloc1
Hloc[8:,8:] = Hloc1
# construct the hybridization delta
# this is equal for all 2x2 blocks
V = get_random_hermitian(2) # the hopping elements from impurity to bath
b1 = np.random.rand() # the bath energy of the first bath level
b2 = np.random.rand() # the bath energy of the second bath level
delta = GfReFreq(window=(-5,5), indices=range(2), n_points=1001)
delta[0,0] << (V[0,0]*V[0,0].conjugate()*inverse(Omega-b1)+V[0,1]*V[0,1].conjugate()*inverse(Omega-b2+0.02j))/2.0
delta[0,1] << (V[0,0]*V[1,0].conjugate()*inverse(Omega-b1)+V[0,1]*V[1,1].conjugate()*inverse(Omega-b2+0.02j))/2.0
delta[1,0] << (V[1,0]*V[0,0].conjugate()*inverse(Omega-b1)+V[1,1]*V[0,1].conjugate()*inverse(Omega-b2+0.02j))/2.0
delta[1,1] << (V[1,0]*V[1,0].conjugate()*inverse(Omega-b1)+V[1,1]*V[1,1].conjugate()*inverse(Omega-b2+0.02j))/2.0
# construct G
G = BlockGf(name_block_generator=(('ud',GfReFreq(window=(-5,5), indices=range(10), n_points=1001)),))
for i in range(0,10,2):
G['ud'][i:i+2,i:i+2] << inverse(Omega-delta+0.02j)
G['ud'] << inverse(inverse(G['ud']) - Hloc)
SK = SumkDFT(hdf_file = 'SrIrO3_rot.h5', use_dft_blocks=False)
G_new = SK.analyse_block_structure_from_gf([G])
G_new_symm = G_new[0].copy()
SK.symm_deg_gf(G_new_symm, 0)
assert_block_gfs_are_close(G_new[0], G_new_symm)
assert SK.gf_struct_sumk == [[('ud', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])], [('ud', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])]],\
"wrong gf_struct_sumk"
for i in range(5):
assert 'ud_{}'.format(i) in SK.gf_struct_solver[0], "missing block"
assert SK.gf_struct_solver[0]['ud_{}'.format(i)] == range(2), "wrong block size"
for i in range(10):
assert SK.sumk_to_solver[0]['ud',i] == ('ud_{}'.format(i/2), i%2), "wrong mapping"
assert len(SK.deg_shells[0]) == 2, "wrong number of equivalent groups found"
assert sorted([len(d) for d in SK.deg_shells[0]]) == [2,3], "wrong number of members in the equivalent groups found"
for d in SK.deg_shells[0]:
if len(d)==2:
assert 'ud_3' in d, "shell ud_3 missing"
assert 'ud_4' in d, "shell ud_4 missing"
if len(d)==3:
assert 'ud_0' in d, "shell ud_0 missing"
assert 'ud_1' in d, "shell ud_1 missing"
assert 'ud_2' in d, "shell ud_2 missing"
def get_delta_from_mesh(mesh):
w0 = None
for w in mesh:
if w0 is None:
w0 = w
else:
return w-w0
Gt = BlockGf(name_block_generator = [(name,
GfReTime(window=(-np.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh)), np.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh))),
n_points=len(block.mesh),
indices=block.indices)) for name, block in G])
Gt['ud'].set_from_inverse_fourier(G['ud'])
G_new = SK.analyse_block_structure_from_gf([Gt])
G_new_symm = G_new[0].copy()
SK.symm_deg_gf(G_new_symm, 0)
assert_block_gfs_are_close(G_new[0], G_new_symm)
assert SK.gf_struct_sumk == [[('ud', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])], [('ud', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])]],\
"wrong gf_struct_sumk"
for i in range(5):
assert 'ud_{}'.format(i) in SK.gf_struct_solver[0], "missing block"
assert SK.gf_struct_solver[0]['ud_{}'.format(i)] == range(2), "wrong block size"
for i in range(10):
assert SK.sumk_to_solver[0]['ud',i] == ('ud_{}'.format(i/2), i%2), "wrong mapping"
assert len(SK.deg_shells[0]) == 2, "wrong number of equivalent groups found"
assert sorted([len(d) for d in SK.deg_shells[0]]) == [2,3], "wrong number of members in the equivalent groups found"
for d in SK.deg_shells[0]:
if len(d)==2:
assert 'ud_3' in d, "shell ud_3 missing"
assert 'ud_4' in d, "shell ud_4 missing"
if len(d)==3:
assert 'ud_0' in d, "shell ud_0 missing"
assert 'ud_1' in d, "shell ud_1 missing"
assert 'ud_2' in d, "shell ud_2 missing"

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@ -21,7 +21,8 @@ sk_pick1 = BlockStructure(gf_struct_sumk = SK.gf_struct_sumk,
gf_struct_solver = SK.gf_struct_solver,
solver_to_sumk = SK.solver_to_sumk,
sumk_to_solver = SK.sumk_to_solver,
solver_to_sumk_block = SK.solver_to_sumk_block)
solver_to_sumk_block = SK.solver_to_sumk_block,
deg_shells = SK.deg_shells)
assert sk_pick1 == pick1, 'constructing block structure from SumkDFT properties failed'
# check pick_gf_struct_sumk

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