def HT(Res) :
# First compute the eps_hat array
eps_hat = Epsilon_Hat(self.dos.eps) if Epsilon_Hat else numpy.array( [ x* numpy.identity (Sigma.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 Sigma.N1 == eps_hat.shape[1], "Size of Sigma and of epsilon_hat mismatch"
Res.zero()
Sigma_fnt = callable(Sigma)
if Sigma_fnt : assert len(inspect.getargspec(Sigma)[0]) ==1, "Sigma function is not of the correct type. See Documentation"
# Perform the sum over eps[i]
tmp,tmp2 = Res.copy(),Res.copy()
tmp <<= GF_Initializers.A_Omega_Plus_B(1,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 itertools.izip (*[MPI.slice_array(A) for A in [self.rho_for_sum,eps_hat,self.dos.eps]]):
tmp2.copyFrom(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 simplepointdensmat(self):
ntoi = self.names_to_ind[self.SO]
bln = self.blocnames[self.SO]
MMat = [numpy.zeros( [self.N_Orbitals[0][ntoi[bl]],self.N_Orbitals[0][ntoi[bl]]], numpy.complex_) for bl in bln]
densmat = [ {} for icrsh in xrange(self.N_corr_shells)]
for icrsh in xrange(self.N_corr_shells):
for bl in self.blocnames[self.corr_shells[icrsh][4]]:
densmat[icrsh][bl] = numpy.zeros([self.corr_shells[icrsh][3],self.corr_shells[icrsh][3]], numpy.complex_)
ikarray=numpy.array(range(self.Nk))
for ik in MPI.slice_array(ikarray):
unchangedsize = all( [ self.N_Orbitals[ik][ntoi[bln[ib]]]==len(MMat[ib])
for ib in range(self.NspinblocsGF[self.SO]) ] )
if (not unchangedsize):
MMat = [numpy.zeros( [self.N_Orbitals[ik][ntoi[bl]],self.N_Orbitals[ik][ntoi[bl]]], numpy.complex_) for bl in bln]
for ibl,bl in enumerate(bln):
ind = ntoi[bl]
for inu in range(self.N_Orbitals[ik][ind]):
if ( (self.Hopping[ik][ind][inu,inu]-self.hfield*(1-2*ibl)) < 0.0):
MMat[ibl][inu,inu] = 1.0
else:
MMat[ibl][inu,inu] = 0.0
for icrsh in range(self.N_corr_shells):
for ibn,bn in enumerate(self.blocnames[self.corr_shells[icrsh][4]]):
isp = self.names_to_ind[self.corr_shells[icrsh][4]][bn]
#print ik, bn, isp
densmat[icrsh][bn] += self.BZ_weights[ik] * numpy.dot( numpy.dot(self.Proj_Mat[ik][isp][icrsh],MMat[ibn]) ,
self.Proj_Mat[ik][isp][icrsh].transpose().conjugate() )
# get data from nodes:
for icrsh in range(self.N_corr_shells):
for sig in densmat[icrsh]:
densmat[icrsh][sig] = MPI.all_reduce(MPI.world,densmat[icrsh][sig],lambda x,y : x+y)
MPI.barrier()
if (self.symm_op!=0): densmat = self.Symm_corr.symmetrise(densmat)
# Rotate to local coordinate system:
if (self.use_rotations):
for icrsh in xrange(self.N_corr_shells):
for bn in densmat[icrsh]:
if (self.rotmat_timeinv[icrsh]==1): densmat[icrsh][bn] = densmat[icrsh][bn].conjugate()
densmat[icrsh][bn] = numpy.dot( numpy.dot(self.rotmat[icrsh].conjugate().transpose(),densmat[icrsh][bn]) ,
self.rotmat[icrsh])
return densmat
def extract_Gloc(self, mu=None, withSigma = True):
"""
extracts the local downfolded Green function at the chemical potential of the class.
At the end, the local G is rotated from the gloabl coordinate system to the local system.
if withSigma = False: Sigma is not included => non-interacting local GF
"""
if (mu is None): mu = self.Chemical_Potential
Gloc = [ self.Sigmaimp[icrsh].copy() for icrsh in xrange(self.N_corr_shells) ] # this list will be returned
for icrsh in xrange(self.N_corr_shells): Gloc[icrsh].zero() # initialize to zero
ikarray=numpy.array(range(self.Nk))
for ik in MPI.slice_array(ikarray):
S = self.latticeGF_Matsubara(ik=ik,mu=mu,withSigma = withSigma)
S *= self.BZ_weights[ik]
for icrsh in xrange(self.N_corr_shells):
tmp = Gloc[icrsh].copy() # init temporary storage
for sig,gf in tmp: tmp[sig] <<= self.downfold(ik,icrsh,sig,S[sig],gf)
Gloc[icrsh] += tmp
#collect data from MPI:
for icrsh in xrange(self.N_corr_shells):
Gloc[icrsh] <<= MPI.all_reduce(MPI.world,Gloc[icrsh],lambda x,y : x+y)
MPI.barrier()
# Gloc[:] is now the sum over k projected to the local orbitals.
# here comes the symmetrisation, if needed:
if (self.symm_op!=0): Gloc = self.Symm_corr.symmetrise(Gloc)
# Gloc is rotated to the local coordinate system:
if (self.use_rotations):
for icrsh in xrange(self.N_corr_shells):
for sig,gf in Gloc[icrsh]: Gloc[icrsh][sig] <<= self.rotloc(icrsh,gf,direction='toLocal')
# transform to CTQMC blocks:
Glocret = [ GF( Name_Block_Generator = [ (a,GFBloc_ImFreq(Indices = al, Mesh = Gloc[0].mesh)) for a,al in self.GFStruct_Solver[i] ],
Copy = False) for i in xrange(self.N_inequiv_corr_shells) ]
for ish in xrange(self.N_inequiv_corr_shells):
for ibl in range(len(self.GFStruct_Solver[ish])):
for i in range(len(self.GFStruct_Solver[ish][ibl][1])):
for j in range(len(self.GFStruct_Solver[ish][ibl][1])):
bl = self.GFStruct_Solver[ish][ibl][0]
ind1 = self.GFStruct_Solver[ish][ibl][1][i]
ind2 = self.GFStruct_Solver[ish][ibl][1][j]
Glocret[ish][bl][ind1,ind2] <<= Gloc[self.invshellmap[ish]][self.mapinv[ish][bl]][ind1,ind2]
# return only the inequivalent shells:
return Glocret
def density_gf(self, Beta=40):
"""Calculates the density without setting up Gloc. It is useful for Hubbard I, and very fast."""
densmat = [{} for icrsh in xrange(self.N_corr_shells)]
for icrsh in xrange(self.N_corr_shells):
for bl in self.blocnames[self.corr_shells[icrsh][4]]:
densmat[icrsh][bl] = numpy.zeros(
[self.corr_shells[icrsh][3], self.corr_shells[icrsh][3]], numpy.complex_
)
ikarray = numpy.array(range(self.Nk))
for ik in MPI.slice_array(ikarray):
Gupf = self.latticeGF_Matsubara(ik=ik, mu=self.Chemical_Potential)
Gupf *= self.BZ_weights[ik]
dm = Gupf.density()
MMat = [dm[bl] for bl in self.blocnames[self.SO]]
for icrsh in range(self.N_corr_shells):
for ibn, bn in enumerate(self.blocnames[self.corr_shells[icrsh][4]]):
isp = self.names_to_ind[self.corr_shells[icrsh][4]][bn]
# print ik, bn, isp
densmat[icrsh][bn] += numpy.dot(
numpy.dot(self.Proj_Mat[ik][isp][icrsh], MMat[ibn]),
self.Proj_Mat[ik][isp][icrsh].transpose().conjugate(),
)
# get data from nodes:
for icrsh in range(self.N_corr_shells):
for sig in densmat[icrsh]:
densmat[icrsh][sig] = MPI.all_reduce(MPI.world, densmat[icrsh][sig], lambda x, y: x + y)
MPI.barrier()
if self.symm_op != 0:
densmat = self.Symm_corr.symmetrise(densmat)
# Rotate to local coordinate system:
if self.use_rotations:
for icrsh in xrange(self.N_corr_shells):
for bn in densmat[icrsh]:
if self.rotmat_timeinv[icrsh] == 1:
densmat[icrsh][bn] = densmat[icrsh][bn].conjugate()
densmat[icrsh][bn] = numpy.dot(
numpy.dot(self.rotmat[icrsh].conjugate().transpose(), densmat[icrsh][bn]), self.rotmat[icrsh]
)
return densmat
def HT(Res):
# First compute the eps_hat array
eps_hat = Epsilon_Hat(
self.dos.eps) if Epsilon_Hat else numpy.array(
[x * numpy.identity(Sigma.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 Sigma.N1 == eps_hat.shape[
1], "Size of Sigma and of epsilon_hat mismatch"
Res.zero()
Sigma_fnt = callable(Sigma)
if Sigma_fnt:
assert len(
inspect.getargspec(Sigma)[0]
) == 1, "Sigma function is not of the correct type. See Documentation"
# Perform the sum over eps[i]
tmp, tmp2 = Res.copy(), Res.copy()
tmp <<= GF_Initializers.A_Omega_Plus_B(1, 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 itertools.izip(*[
MPI.slice_array(A)
for A in [self.rho_for_sum, eps_hat, self.dos.eps]
]):
tmp2.copyFrom(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 total_density(self, mu):
"""
Calculates the total charge for the energy window for a given mu. Since in general N_Orbitals depends on k,
the calculation is done in the following order:
G_aa'(k,iw) -> n(k) = Tr G_aa'(k,iw) -> sum_k n_k
mu: chemical potential
The calculation is done in the global coordinate system, if distinction is made between local/global!
"""
dens = 0.0
ikarray = numpy.array(range(self.Nk))
for ik in MPI.slice_array(ikarray):
S = self.latticeGF_Matsubara(ik=ik, mu=mu)
dens += self.BZ_weights[ik] * S.total_density()
# collect data from MPI:
dens = MPI.all_reduce(MPI.world, dens, lambda x, y: x + y)
MPI.barrier()
return dens
def __call__(self,
Sigma,
mu=0,
eta=0,
Field=None,
Epsilon_Hat=None,
Res=None,
SelectedBlocks=()):
"""
- Computes :
Res <- \[ \sum_k (\omega + \mu - Field - t(k) - Sigma(k,\omega)) \]
if Res is None, it returns a new GF with the results.
otherwise, Res must be a GF, in which the calculation is done, and which is then returned.
(this allows chain calculation : SK(mu = mu,Sigma = Sigma, Res = 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 SelectedBlocks.
e.g. X can be a GF (with at least the SelectedBlocks), 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
- SelectedBlocks : 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 SelectedBlocks ==None : 'up' and 'down' are calculated
if SelectedBlocks == ['up'] : only 'up' is calculated. 'down' is 0.
"""
S = Sigma.View_SelectedBlocks(
SelectedBlocks) if SelectedBlocks else Sigma
Gres = Res if Res else Sigma.copy()
G = Gres.View_SelectedBlocks(
SelectedBlocks) if SelectedBlocks else Gres
# check input
assert self.Orthogonal_Basis, "Local_G : must be orthogonal. non ortho cases not checked."
assert isinstance(G, GF), "G must be a GF"
assert len(list(set([g.N1 for i, g in G]))) == 1
assert self.BZ_weights.shape[0] == self.N_kpts(), "Internal Error"
no = list(set([g.N1 for i, g in G]))[0]
Sigma_Nargs = len(
inspect.getargspec(Sigma)[0]) if callable(Sigma) else 0
assert Sigma_Nargs <= 2, "Sigma function is not of the correct type. See Documentation"
# 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 Sigma_Nargs == 0: tmp -= Sigma # substract Sigma once for all
# Loop on k points...
for w, k, eps_k in izip(*[
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.NBlocks * [eps_hat - mupat]
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 Gres
def __call__ (self, Sigma, mu=0, eta = 0, Field = None, Epsilon_Hat=None, Res = None, SelectedBlocks = ()):
"""
- Computes :
Res <- \[ \sum_k (\omega + \mu - Field - t(k) - Sigma(k,\omega)) \]
if Res is None, it returns a new GF with the results.
otherwise, Res must be a GF, in which the calculation is done, and which is then returned.
(this allows chain calculation : SK(mu = mu,Sigma = Sigma, Res = 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 SelectedBlocks.
e.g. X can be a GF (with at least the SelectedBlocks), 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
- SelectedBlocks : 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 SelectedBlocks ==None : 'up' and 'down' are calculated
if SelectedBlocks == ['up'] : only 'up' is calculated. 'down' is 0.
"""
S = Sigma.View_SelectedBlocks(SelectedBlocks) if SelectedBlocks else Sigma
Gres = Res if Res else Sigma.copy()
G = Gres.View_SelectedBlocks(SelectedBlocks) if SelectedBlocks else Gres
# check input
assert self.Orthogonal_Basis, "Local_G : must be orthogonal. non ortho cases not checked."
assert isinstance(G,GF), "G must be a GF"
assert len(list(set([g.N1 for i,g in G]))) == 1
assert self.BZ_weights.shape[0] == self.N_kpts(), "Internal Error"
no = list(set([g.N1 for i,g in G]))[0]
Sigma_Nargs = len(inspect.getargspec(Sigma)[0]) if callable (Sigma) else 0
assert Sigma_Nargs <=2 , "Sigma function is not of the correct type. See Documentation"
# 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 Sigma_Nargs==0: tmp -= Sigma # substract Sigma once for all
# Loop on k points...
for w, k, eps_k in izip(*[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.NBlocks * [eps_hat - mupat]
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 Gres
def partial_charges(self):
"""Calculates the orbitally-resolved density matrix for all the orbitals considered in the input.
The theta-projectors are used, hence case.parproj data is necessary"""
#thingstoread = ['Dens_Mat_below','N_parproj','Proj_Mat_pc','rotmat_all']
#retval = self.read_input_from_HDF(SubGrp=self.ParProjdata,thingstoread=thingstoread)
retval = self.read_ParProj_input_from_HDF()
if not retval: return retval
if self.symm_op:
self.Symm_par = Symmetry(self.HDFfile, subgroup=self.Symmpardata)
# Density matrix in the window
bln = self.blocnames[self.SO]
ntoi = self.names_to_ind[self.SO]
self.Dens_Mat_window = [[
numpy.zeros([self.shells[ish][3], self.shells[ish][3]],
numpy.complex_) for ish in range(self.N_shells)
] for isp in range(len(bln))] # init the density matrix
mu = self.Chemical_Potential
GFStruct_proj = [[(al, range(self.shells[i][3])) for al in bln]
for i in xrange(self.N_shells)]
if hasattr(self, "Sigmaimp"):
Gproj = [
GF(Name_Block_Generator=[
(a, GFBloc_ImFreq(Indices=al, Mesh=self.Sigmaimp[0].mesh))
for a, al in GFStruct_proj[ish]
],
Copy=False) for ish in xrange(self.N_shells)
]
else:
Gproj = [
GF(Name_Block_Generator=[(a, GFBloc_ImFreq(Indices=al,
Beta=40))
for a, al in GFStruct_proj[ish]],
Copy=False) for ish in xrange(self.N_shells)
]
for ish in xrange(self.N_shells):
Gproj[ish].zero()
ikarray = numpy.array(range(self.Nk))
#print MPI.rank, MPI.slice_array(ikarray)
#print "K-Sum starts on node",MPI.rank," at ",datetime.now()
for ik in MPI.slice_array(ikarray):
#print MPI.rank, ik, datetime.now()
S = self.latticeGF_Matsubara(ik=ik, mu=mu)
S *= self.BZ_weights[ik]
for ish in xrange(self.N_shells):
tmp = Gproj[ish].copy()
for ir in xrange(self.N_parproj[ish]):
for sig, gf in tmp:
tmp[sig] <<= self.downfold_pc(ik, ir, ish, sig, S[sig],
gf)
Gproj[ish] += tmp
#print "K-Sum done on node",MPI.rank," at ",datetime.now()
#collect data from MPI:
for ish in xrange(self.N_shells):
Gproj[ish] <<= MPI.all_reduce(MPI.world, Gproj[ish],
lambda x, y: x + y)
MPI.barrier()
#print "Data collected on node",MPI.rank," at ",datetime.now()
# Symmetrisation:
if (self.symm_op != 0): Gproj = self.Symm_par.symmetrise(Gproj)
#print "Symmetrisation done on node",MPI.rank," at ",datetime.now()
for ish in xrange(self.N_shells):
# Rotation to local:
if (self.use_rotations):
for sig, gf in Gproj[ish]:
Gproj[ish][sig] <<= self.rotloc_all(ish,
gf,
direction='toLocal')
isp = 0
for sig, gf in Gproj[ish]: #dmg.append(Gproj[ish].density()[sig])
self.Dens_Mat_window[isp][ish] = Gproj[ish].density()[sig]
isp += 1
# add Density matrices to get the total:
Dens_Mat = [[
self.Dens_Mat_below[ntoi[bln[isp]]][ish] +
self.Dens_Mat_window[isp][ish] for ish in range(self.N_shells)
] for isp in range(len(bln))]
return Dens_Mat
def DOSpartial(self, broadening=0.01):
"""calculates the orbitally-resolved DOS"""
assert hasattr(self, "Sigmaimp"), "Set Sigma First!!"
#thingstoread = ['Dens_Mat_below','N_parproj','Proj_Mat_pc','rotmat_all']
#retval = self.read_input_from_HDF(SubGrp=self.ParProjdata, thingstoread=thingstoread)
retval = self.read_ParProj_input_from_HDF()
if not retval: return retval
if self.symm_op:
self.Symm_par = Symmetry(self.HDFfile, subgroup=self.Symmpardata)
mu = self.Chemical_Potential
GFStruct_proj = [[(al, range(self.shells[i][3]))
for al in self.blocnames[self.SO]]
for i in xrange(self.N_shells)]
Gproj = [
GF(Name_Block_Generator=[
(a, GFBloc_ReFreq(Indices=al, Mesh=self.Sigmaimp[0].mesh))
for a, al in GFStruct_proj[ish]
],
Copy=False) for ish in xrange(self.N_shells)
]
for ish in range(self.N_shells):
Gproj[ish].zero()
Msh = [x for x in self.Sigmaimp[0].mesh]
N_om = len(Msh)
DOS = {}
for bn in self.blocnames[self.SO]:
DOS[bn] = numpy.zeros([N_om], numpy.float_)
DOSproj = [{} for ish in range(self.N_shells)]
DOSproj_orb = [{} for ish in range(self.N_shells)]
for ish in range(self.N_shells):
for bn in self.blocnames[self.SO]:
dl = self.shells[ish][3]
DOSproj[ish][bn] = numpy.zeros([N_om], numpy.float_)
DOSproj_orb[ish][bn] = numpy.zeros([dl, dl, N_om],
numpy.float_)
ikarray = numpy.array(range(self.Nk))
for ik in MPI.slice_array(ikarray):
S = self.latticeGF_realfreq(ik=ik, mu=mu, broadening=broadening)
S *= self.BZ_weights[ik]
# non-projected DOS
for iom in range(N_om):
for sig, gf in S:
DOS[sig][iom] += gf._data.array[:, :, iom].imag.trace() / (
-3.1415926535)
#projected DOS:
for ish in xrange(self.N_shells):
tmp = Gproj[ish].copy()
for ir in xrange(self.N_parproj[ish]):
for sig, gf in tmp:
tmp[sig] <<= self.downfold_pc(ik, ir, ish, sig, S[sig],
gf)
Gproj[ish] += tmp
# collect data from MPI:
for sig in DOS:
DOS[sig] = MPI.all_reduce(MPI.world, DOS[sig], lambda x, y: x + y)
for ish in xrange(self.N_shells):
Gproj[ish] <<= MPI.all_reduce(MPI.world, Gproj[ish],
lambda x, y: x + y)
MPI.barrier()
if (self.symm_op != 0): Gproj = self.Symm_par.symmetrise(Gproj)
# rotation to local coord. system:
if (self.use_rotations):
for ish in xrange(self.N_shells):
for sig, gf in Gproj[ish]:
Gproj[ish][sig] <<= self.rotloc_all(ish,
gf,
direction='toLocal')
for ish in range(self.N_shells):
for sig, gf in Gproj[ish]:
for iom in range(N_om):
DOSproj[ish][sig][
iom] += gf._data.array[:, :, iom].imag.trace() / (
-3.1415926535)
DOSproj_orb[ish][
sig][:, :, :] += gf._data.array[:, :, :].imag / (
-3.1415926535)
if (MPI.IS_MASTER_NODE()):
# output to files
for bn in self.blocnames[self.SO]:
f = open('./DOScorr%s.dat' % bn, 'w')
for i in range(N_om):
f.write("%s %s\n" % (Msh[i], DOS[bn][i]))
f.close()
# partial
for ish in range(self.N_shells):
f = open('DOScorr%s_proj%s.dat' % (bn, ish), 'w')
for i in range(N_om):
f.write("%s %s\n" % (Msh[i], DOSproj[ish][bn][i]))
f.close()
for i in range(self.shells[ish][3]):
for j in range(i, self.shells[ish][3]):
Fname = './DOScorr' + bn + '_proj' + str(
ish) + '_' + str(i) + '_' + str(j) + '.dat'
f = open(Fname, 'w')
for iom in range(N_om):
f.write("%s %s\n" %
(Msh[iom], DOSproj_orb[ish][bn][i, j,
iom]))
f.close()
def partial_charges(self):
"""Calculates the orbitally-resolved density matrix for all the orbitals considered in the input.
The theta-projectors are used, hence case.parproj data is necessary"""
#thingstoread = ['Dens_Mat_below','N_parproj','Proj_Mat_pc','rotmat_all']
#retval = self.read_input_from_HDF(SubGrp=self.ParProjdata,thingstoread=thingstoread)
retval = self.read_ParProj_input_from_HDF()
if not retval: return retval
if self.symm_op: self.Symm_par = Symmetry(self.HDFfile,subgroup=self.Symmpardata)
# Density matrix in the window
bln = self.blocnames[self.SO]
ntoi = self.names_to_ind[self.SO]
self.Dens_Mat_window = [ [numpy.zeros([self.shells[ish][3],self.shells[ish][3]],numpy.complex_) for ish in range(self.N_shells)]
for isp in range(len(bln)) ] # init the density matrix
mu = self.Chemical_Potential
GFStruct_proj = [ [ (al, range(self.shells[i][3])) for al in bln ] for i in xrange(self.N_shells) ]
if hasattr(self,"Sigmaimp"):
Gproj = [GF(Name_Block_Generator = [ (a,GFBloc_ImFreq(Indices = al, Mesh = self.Sigmaimp[0].mesh)) for a,al in GFStruct_proj[ish] ], Copy = False)
for ish in xrange(self.N_shells)]
else:
Gproj = [GF(Name_Block_Generator = [ (a,GFBloc_ImFreq(Indices = al, Beta = 40)) for a,al in GFStruct_proj[ish] ], Copy = False)
for ish in xrange(self.N_shells)]
for ish in xrange(self.N_shells): Gproj[ish].zero()
ikarray=numpy.array(range(self.Nk))
#print MPI.rank, MPI.slice_array(ikarray)
#print "K-Sum starts on node",MPI.rank," at ",datetime.now()
for ik in MPI.slice_array(ikarray):
#print MPI.rank, ik, datetime.now()
S = self.latticeGF_Matsubara(ik=ik,mu=mu)
S *= self.BZ_weights[ik]
for ish in xrange(self.N_shells):
tmp = Gproj[ish].copy()
for ir in xrange(self.N_parproj[ish]):
for sig,gf in tmp: tmp[sig] <<= self.downfold_pc(ik,ir,ish,sig,S[sig],gf)
Gproj[ish] += tmp
#print "K-Sum done on node",MPI.rank," at ",datetime.now()
#collect data from MPI:
for ish in xrange(self.N_shells):
Gproj[ish] <<= MPI.all_reduce(MPI.world,Gproj[ish],lambda x,y : x+y)
MPI.barrier()
#print "Data collected on node",MPI.rank," at ",datetime.now()
# Symmetrisation:
if (self.symm_op!=0): Gproj = self.Symm_par.symmetrise(Gproj)
#print "Symmetrisation done on node",MPI.rank," at ",datetime.now()
for ish in xrange(self.N_shells):
# Rotation to local:
if (self.use_rotations):
for sig,gf in Gproj[ish]: Gproj[ish][sig] <<= self.rotloc_all(ish,gf,direction='toLocal')
isp = 0
for sig,gf in Gproj[ish]: #dmg.append(Gproj[ish].density()[sig])
self.Dens_Mat_window[isp][ish] = Gproj[ish].density()[sig]
isp+=1
# add Density matrices to get the total:
Dens_Mat = [ [ self.Dens_Mat_below[ntoi[bln[isp]]][ish]+self.Dens_Mat_window[isp][ish] for ish in range(self.N_shells)]
for isp in range(len(bln)) ]
return Dens_Mat
def DOSpartial(self,broadening=0.01):
"""calculates the orbitally-resolved DOS"""
assert hasattr(self,"Sigmaimp"), "Set Sigma First!!"
#thingstoread = ['Dens_Mat_below','N_parproj','Proj_Mat_pc','rotmat_all']
#retval = self.read_input_from_HDF(SubGrp=self.ParProjdata, thingstoread=thingstoread)
retval = self.read_ParProj_input_from_HDF()
if not retval: return retval
if self.symm_op: self.Symm_par = Symmetry(self.HDFfile,subgroup=self.Symmpardata)
mu = self.Chemical_Potential
GFStruct_proj = [ [ (al, range(self.shells[i][3])) for al in self.blocnames[self.SO] ] for i in xrange(self.N_shells) ]
Gproj = [GF(Name_Block_Generator = [ (a,GFBloc_ReFreq(Indices = al, Mesh = self.Sigmaimp[0].mesh)) for a,al in GFStruct_proj[ish] ], Copy = False )
for ish in xrange(self.N_shells)]
for ish in range(self.N_shells): Gproj[ish].zero()
Msh = [x for x in self.Sigmaimp[0].mesh]
N_om = len(Msh)
DOS = {}
for bn in self.blocnames[self.SO]:
DOS[bn] = numpy.zeros([N_om],numpy.float_)
DOSproj = [ {} for ish in range(self.N_shells) ]
DOSproj_orb = [ {} for ish in range(self.N_shells) ]
for ish in range(self.N_shells):
for bn in self.blocnames[self.SO]:
dl = self.shells[ish][3]
DOSproj[ish][bn] = numpy.zeros([N_om],numpy.float_)
DOSproj_orb[ish][bn] = numpy.zeros([dl,dl,N_om],numpy.float_)
ikarray=numpy.array(range(self.Nk))
for ik in MPI.slice_array(ikarray):
S = self.latticeGF_realfreq(ik=ik,mu=mu,broadening=broadening)
S *= self.BZ_weights[ik]
# non-projected DOS
for iom in range(N_om):
for sig,gf in S: DOS[sig][iom] += gf._data.array[:,:,iom].imag.trace()/(-3.1415926535)
#projected DOS:
for ish in xrange(self.N_shells):
tmp = Gproj[ish].copy()
for ir in xrange(self.N_parproj[ish]):
for sig,gf in tmp: tmp[sig] <<= self.downfold_pc(ik,ir,ish,sig,S[sig],gf)
Gproj[ish] += tmp
# collect data from MPI:
for sig in DOS:
DOS[sig] = MPI.all_reduce(MPI.world,DOS[sig],lambda x,y : x+y)
for ish in xrange(self.N_shells):
Gproj[ish] <<= MPI.all_reduce(MPI.world,Gproj[ish],lambda x,y : x+y)
MPI.barrier()
if (self.symm_op!=0): Gproj = self.Symm_par.symmetrise(Gproj)
# rotation to local coord. system:
if (self.use_rotations):
for ish in xrange(self.N_shells):
for sig,gf in Gproj[ish]: Gproj[ish][sig] <<= self.rotloc_all(ish,gf,direction='toLocal')
for ish in range(self.N_shells):
for sig,gf in Gproj[ish]:
for iom in range(N_om): DOSproj[ish][sig][iom] += gf._data.array[:,:,iom].imag.trace()/(-3.1415926535)
DOSproj_orb[ish][sig][:,:,:] += gf._data.array[:,:,:].imag / (-3.1415926535)
if (MPI.IS_MASTER_NODE()):
# output to files
for bn in self.blocnames[self.SO]:
f=open('./DOScorr%s.dat'%bn, 'w')
for i in range(N_om): f.write("%s %s\n"%(Msh[i],DOS[bn][i]))
f.close()
# partial
for ish in range(self.N_shells):
f=open('DOScorr%s_proj%s.dat'%(bn,ish),'w')
for i in range(N_om): f.write("%s %s\n"%(Msh[i],DOSproj[ish][bn][i]))
f.close()
for i in range(self.shells[ish][3]):
for j in range(i,self.shells[ish][3]):
Fname = './DOScorr'+bn+'_proj'+str(ish)+'_'+str(i)+'_'+str(j)+'.dat'
f=open(Fname,'w')
for iom in range(N_om): f.write("%s %s\n"%(Msh[iom],DOSproj_orb[ish][bn][i,j,iom]))
f.close()
def calc_DensityCorrection(self, Filename="densmat.dat"):
""" Calculates the density correction in order to feed it back to the DFT calculations."""
assert type(Filename) == StringType, "Filename has to be a string!"
ntoi = self.names_to_ind[self.SO]
bln = self.blocnames[self.SO]
# Set up deltaN:
deltaN = {}
for ib in bln:
deltaN[ib] = [
numpy.zeros([self.N_Orbitals[ik][ntoi[ib]], self.N_Orbitals[ik][ntoi[ib]]], numpy.complex_)
for ik in range(self.Nk)
]
ikarray = numpy.array(range(self.Nk))
dens = {}
for ib in bln:
dens[ib] = 0.0
for ik in MPI.slice_array(ikarray):
S = self.latticeGF_Matsubara(ik=ik, mu=self.Chemical_Potential)
for sig, g in S:
deltaN[sig][ik] = S[sig].density()
dens[sig] += self.BZ_weights[ik] * S[sig].total_density()
# put MPI Barrier:
for sig in deltaN:
for ik in range(self.Nk):
deltaN[sig][ik] = MPI.all_reduce(MPI.world, deltaN[sig][ik], lambda x, y: x + y)
dens[sig] = MPI.all_reduce(MPI.world, dens[sig], lambda x, y: x + y)
MPI.barrier()
# now save to file:
if MPI.IS_MASTER_NODE():
if self.SP == 0:
f = open(Filename, "w")
else:
f = open(Filename + "up", "w")
f1 = open(Filename + "dn", "w")
# write chemical potential (in Rydberg):
f.write("%.14f\n" % (self.Chemical_Potential / self.EnergyUnit))
if self.SP != 0:
f1.write("%.14f\n" % (self.Chemical_Potential / self.EnergyUnit))
# write beta in ryderg-1
f.write("%.14f\n" % (S.Beta * self.EnergyUnit))
if self.SP != 0:
f1.write("%.14f\n" % (S.Beta * self.EnergyUnit))
if self.SP == 0:
for ik in range(self.Nk):
f.write("%s\n" % self.N_Orbitals[ik][0])
for inu in range(self.N_Orbitals[ik][0]):
for imu in range(self.N_Orbitals[ik][0]):
valre = (deltaN["up"][ik][inu, imu].real + deltaN["down"][ik][inu, imu].real) / 2.0
valim = (deltaN["up"][ik][inu, imu].imag + deltaN["down"][ik][inu, imu].imag) / 2.0
f.write("%.14f %.14f " % (valre, valim))
f.write("\n")
f.write("\n")
f.close()
elif (self.SP == 1) and (self.SO == 0):
for ik in range(self.Nk):
f.write("%s\n" % self.N_Orbitals[ik][0])
for inu in range(self.N_Orbitals[ik][0]):
for imu in range(self.N_Orbitals[ik][0]):
f.write(
"%.14f %.14f " % (deltaN["up"][ik][inu, imu].real, deltaN["up"][ik][inu, imu].imag)
)
f.write("\n")
f.write("\n")
f.close()
for ik in range(self.Nk):
f1.write("%s\n" % self.N_Orbitals[ik][1])
for inu in range(self.N_Orbitals[ik][1]):
for imu in range(self.N_Orbitals[ik][1]):
f1.write(
"%.14f %.14f " % (deltaN["down"][ik][inu, imu].real, deltaN["down"][ik][inu, imu].imag)
)
f1.write("\n")
f1.write("\n")
f1.close()
else:
for ik in range(self.Nk):
f.write("%s\n" % self.N_Orbitals[ik][0])
for inu in range(self.N_Orbitals[ik][0]):
for imu in range(self.N_Orbitals[ik][0]):
f.write(
"%.14f %.14f " % (deltaN["ud"][ik][inu, imu].real, deltaN["ud"][ik][inu, imu].imag)
)
f.write("\n")
f.write("\n")
f.close()
for ik in range(self.Nk):
f1.write("%s\n" % self.N_Orbitals[ik][0])
for inu in range(self.N_Orbitals[ik][0]):
for imu in range(self.N_Orbitals[ik][0]):
f1.write(
"%.14f %.14f " % (deltaN["ud"][ik][inu, imu].real, deltaN["ud"][ik][inu, imu].imag)
)
f1.write("\n")
f1.write("\n")
f1.close()
return deltaN, dens
def __call__ (self, Sigma, mu=0, eta = 0, Field = None, Res = None, SelectedBlocks = () ):
"""
- Computes :
Res <- \[ \sum_k (\omega + \mu - Field - t(k) - Sigma(k,\omega)) \]
if Res is None, it returns a new GF with the results.
otherwise, Res must be a GF, in which the calculation is done, and which is then returned.
(this allows chain calculation : SK(mu = mu,Sigma = Sigma, Res = 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 SelectedBlocks.
e.g. X can be a GF (with at least the SelectedBlocks), 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 Array_with_GF_Indices to be added to the GF
- SelectedBlocks : 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 SelectedBlocks ==None : 'up' and 'down' are calculated
if SelectedBlocks == ['up'] : only 'up' is calculated. 'down' is 0.
"""
if Field : assert isinstance(Field,Array_with_GF_Indices) , " Field must be a Array_with_GF_Indices object. Cf Example"
S = Sigma.View_SelectedBlocks(SelectedBlocks) if SelectedBlocks else Sigma
Gres = Res if Res else Sigma.copy()
G = Gres.View_SelectedBlocks(SelectedBlocks) if SelectedBlocks else Gres
# check input
assert self.Orthogonal_Basis, "Local_G : must be orthogonal. non ortho cases not checked."
assert isinstance(G,GF), "G must be a GF"
assert list(set([ g.N1 for i,g in G])) == [self.Hopping.shape[1]],"G size and hopping size mismatch"
assert self.BZ_weights.shape[0] == self.N_kpts(), "Internal Error"
Sigma_Nargs = len(inspect.getargspec(Sigma)[0]) if callable (Sigma) else 0
assert Sigma_Nargs <=2 , "Sigma function is not of the correct type. See Documentation"
#init
G.zero()
#tmp,tmp2 = GF(G),GF(G)
tmp,tmp2 = G.copy(),G.copy()
mupat = mu * self.Mu_Pattern
tmp <<= GF_Initializers.A_Omega_Plus_B(A=1,B=0)
#tmp.Set_Omega()
##tmp += tmp.Nblocks() * [ mupat ]
if Field : tmp -= Field
if Sigma_Nargs==0: tmp -= Sigma # substract Sigma once for all
# Loop on k points...
for w, k, eps_k in izip(*[MPI.slice_array(A) for A in [self.BZ_weights, self.BZ_Points, self.Hopping]]):
tmp2 <<= tmp
#tmp2.copy_from(tmp)
tmp2 -= tmp2.NBlocks * [eps_k -mupat ]
#tmp2.save("tmp2_w")
#Sigma.save("S_w")
if Sigma_Nargs == 1: tmp2 -= Sigma (k)
elif Sigma_Nargs ==2: tmp2 -= Sigma (k,eps_k)
tmp2.invert()
tmp2 *= w
G += tmp2
#G.save("GG1")
#print mu,mupat,eps_k
#assert 0
#print G['up'][1,1]._data
G <<= MPI.all_reduce(MPI.world,G,lambda x,y : x+y)
MPI.barrier()
return Res