dft_tools/python/sumk_dft.py

 
################################################################################
#
# TRIQS: a Toolbox for Research in Interacting Quantum Systems
#
# Copyright (C) 2011 by M. Aichhorn, L. Pourovskii, V. Vildosola
#
# TRIQS is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
#
# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
# details.
#
# You should have received a copy of the GNU General Public License along with
# TRIQS. If not, see <http://www.gnu.org/licenses/>.
#
################################################################################

from types import *
import numpy
import pytriqs.utility.dichotomy as dichotomy
from pytriqs.gf.local import *
import pytriqs.utility.mpi as mpi
from pytriqs.archive import *
from symmetry import *

class SumkDFT:
    """This class provides a general SumK method for combining ab-initio code and pytriqs."""


    def __init__(self, hdf_file, mu = 0.0, h_field = 0.0, use_dft_blocks = False, 
	         dft_data = 'dft_input', symmcorr_data = 'dft_symmcorr_input', parproj_data = 'dft_parproj_input', 
                 symmpar_data = 'dft_symmpar_input', bands_data = 'dft_bands_input', dft_output = 'dft_output'):
        """
        Initialises the class from data previously stored into an HDF5
        """

        if not type(hdf_file) == StringType:
            mpi.report("Give a string for the HDF5 filename to read the input!")
        else:
            self.hdf_file = hdf_file
            self.dft_data = dft_data
            self.symmcorr_data = symmcorr_data
            self.parproj_data = parproj_data
            self.symmpar_data = symmpar_data
            self.bands_data = bands_data
            self.dft_output = dft_output
            self.G_upfold = None
            self.h_field = h_field

            # read input from HDF:
            things_to_read = ['energy_unit','n_k','k_dep_projection','SP','SO','charge_below','density_required',
                              'symm_op','n_shells','shells','n_corr_shells','corr_shells','use_rotations','rot_mat',
                              'rot_mat_time_inv','n_reps','dim_reps','T','n_orbitals','proj_mat','bz_weights','hopping',
                              'n_inequiv_shells', 'corr_to_inequiv', 'inequiv_to_corr']
            self.subgroup_present, self.value_read = self.read_input_from_hdf(subgrp = self.dft_data, things_to_read = things_to_read)

            if self.SO and (abs(self.h_field) > 0.000001):
                self.h_field = 0.0
                mpi.report("For SO, the external magnetic field is not implemented, setting it to 0!")

            self.spin_block_names = [ ['up','down'], ['ud'] ]
            self.n_spin_blocks = [2,1]
            # convert spin_block_names to indices -- if spin polarized, differentiate up and down blocks 
            self.spin_names_to_ind = [{}, {}]
            for iso in range(2): # SO = 0 or 1
                for isp in range(self.n_spin_blocks[iso]):
                    self.spin_names_to_ind[iso][self.spin_block_names[iso][isp]] = isp * self.SP

            # GF structure used for the local things in the k sums
            # Most general form allowing for all hybridisation, i.e. largest blocks possible
            self.gf_struct_sumk = [ [ (sp, range( self.corr_shells[icrsh][3])) for sp in self.spin_block_names[self.corr_shells[icrsh][4]] ]
                                   for icrsh in range(self.n_corr_shells) ]

            #-----
            # If these quantities are not in HDF, set them up
            optional_things = ['gf_struct_solver','sumk_to_solver','solver_to_sumk','solver_to_sumk_block','chemical_potential','dc_imp','dc_energ','deg_shells']
            self.subgroup_present, self.value_read = self.read_input_from_hdf(subgrp = self.dft_output, things_to_read = [], 
                                                                              optional_things = optional_things)
            if (not self.subgroup_present) or (not self.value_read['gf_struct_solver']):
                # No gf_struct was stored in HDF, so first set a standard one:
                self.gf_struct_solver = [ dict([ (sp, range(self.corr_shells[self.inequiv_to_corr[ish]][3]) )
                                                        for sp in self.spin_block_names[self.corr_shells[self.inequiv_to_corr[ish]][4]] ])
                                          for ish in range(self.n_inequiv_shells)
                                        ]
                # Set standard (identity) maps from gf_struct_sumk <-> gf_struct_solver
                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) ]
                for ish in range(self.n_inequiv_shells):
                    for block,inner_list in self.gf_struct_sumk[self.inequiv_to_corr[ish]]:
                        self.solver_to_sumk_block[ish][block] = block
                        for inner in inner_list:
                            self.sumk_to_solver[ish][(block,inner)] = (block,inner)
                            self.solver_to_sumk[ish][(block,inner)] = (block,inner)

            if (not self.subgroup_present) or (not self.value_read['dc_imp']):
                self.__init_dc() # initialise the double counting

            if (not self.subgroup_present) or (not self.value_read['chemical_potential']):
                self.chemical_potential = mu

            if (not self.subgroup_present) or (not self.value_read['deg_shells']):
                self.deg_shells = [ [] for ish in range(self.n_inequiv_shells)]
            #-----

            if self.symm_op:
                self.symmcorr = Symmetry(hdf_file,subgroup=self.symmcorr_data)

            # Analyse the block structure and determine the smallest blocks, if desired
            if use_dft_blocks: dm = self.analyse_block_structure()

################
# HDF5 FUNCTIONS
################

    def read_input_from_hdf(self, subgrp, things_to_read=[], optional_things=[]):
        """
        Reads data from the HDF file
        """

        value_read = True
        # initialise variables on all nodes to ensure mpi broadcast works at the end
        for it in things_to_read: setattr(self,it,0)
        for it in optional_things: setattr(self,it,0)

        if mpi.is_master_node():
            ar = HDFArchive(self.hdf_file,'a')
            if subgrp in ar:
                subgroup_present = True
                # first read the necessary things:
                for it in things_to_read:
                    if it in ar[subgrp]:
                        setattr(self,it,ar[subgrp][it])
                    else:
                        mpi.report("Loading %s failed!"%it)
                        value_read = False

                if value_read and (len(optional_things) > 0):
                    # if successfully read necessary items, read optional things:
                    value_read = {}
                    for it in optional_things:
                        if it in ar[subgrp]:
                            setattr(self,it,ar[subgrp][it])
                            value_read['%s'%it] = True
                        else:
                            value_read['%s'%it] = False
            else:
                if (len(things_to_read) != 0): mpi.report("Loading failed: No %s subgroup in HDF5!"%subgrp)
                subgroup_present = False
                value_read = False

            del ar

        # now do the broadcasting:
        for it in things_to_read: setattr(self,it,mpi.bcast(getattr(self,it)))
        for it in optional_things: setattr(self,it,mpi.bcast(getattr(self,it)))
        subgroup_present = mpi.bcast(subgroup_present)
        value_read = mpi.bcast(value_read)

        return subgroup_present, value_read


    def save(self,things_to_save):
        """Saves given quantities into the 'dft_output' subgroup of the HDF5 archive"""

        if not (mpi.is_master_node()): return # do nothing on nodes
        ar = HDFArchive(self.hdf_file,'a')
        if not self.dft_output in ar: ar.create_group(self.dft_output)
        for it in things_to_save: 
            try:
                ar[self.dft_output][it] = getattr(self,it)
            except:
                mpi.report("%s not found, and so not stored."%it)
        del ar

################
# CORE FUNCTIONS
################

    def downfold(self,ik,icrsh,bname,gf_to_downfold,gf_inp):
        """Downfolding a block of the Greens function"""

        gf_downfolded = gf_inp.copy()
        isp = self.spin_names_to_ind[self.SO][bname]       # get spin index for proj. matrices
        dim = self.corr_shells[icrsh][3]
        n_orb = self.n_orbitals[ik,isp]
        projmat = self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb]

        gf_downfolded.from_L_G_R(projmat,gf_to_downfold,projmat.conjugate().transpose())

        return gf_downfolded


    def upfold(self,ik,icrsh,bname,gf_to_upfold,gf_inp):
        """Upfolding a block of the Greens function"""

        gf_upfolded = gf_inp.copy()
        isp = self.spin_names_to_ind[self.SO][bname]       # get spin index for proj. matrices
        dim = self.corr_shells[icrsh][3]
        n_orb = self.n_orbitals[ik,isp]
        projmat = self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb]

        gf_upfolded.from_L_G_R(projmat.conjugate().transpose(),gf_to_upfold,projmat)

        return gf_upfolded


    def rotloc(self,icrsh,gf_to_rotate,direction):
        """Local <-> Global rotation of a GF block.
           direction: 'toLocal' / 'toGlobal' """

        assert ((direction == 'toLocal') or (direction == 'toGlobal')),"Give direction 'toLocal' or 'toGlobal' in rotloc!"

        gf_rotated = gf_to_rotate.copy()

        if direction == 'toGlobal':

            if (self.rot_mat_time_inv[icrsh] == 1) and self.SO:
                gf_rotated << gf_rotated.transpose()
                gf_rotated.from_L_G_R(self.rot_mat[icrsh].conjugate(),gf_rotated,self.rot_mat[icrsh].transpose())
            else:
                gf_rotated.from_L_G_R(self.rot_mat[icrsh],gf_rotated,self.rot_mat[icrsh].conjugate().transpose())

        elif direction == 'toLocal':

            if (self.rot_mat_time_inv[icrsh] == 1) and self.SO:
                gf_rotated << gf_rotated.transpose()
                gf_rotated.from_L_G_R(self.rot_mat[icrsh].transpose(),gf_rotated,self.rot_mat[icrsh].conjugate())
            else:
                gf_rotated.from_L_G_R(self.rot_mat[icrsh].conjugate().transpose(),gf_rotated,self.rot_mat[icrsh])

        return gf_rotated


    def lattice_gf_matsubara(self,ik,mu,beta=40,with_Sigma=True):
        """Calculates the lattice Green function from the DFT hopping and the self energy at k-point number ik
           and chemical potential mu."""

        ntoi = self.spin_names_to_ind[self.SO]
        spn = self.spin_block_names[self.SO]

        if not hasattr(self,"Sigma_imp"): with_Sigma = False

        if with_Sigma:
            stmp = self.add_dc()
            beta = self.Sigma_imp[0].mesh.beta        # override beta if Sigma is present

        # Do we need to set up G_upfold?
        set_up_G_upfold = False # assume not
        if self.G_upfold is None: # yes if not G_upfold provided
            set_up_G_upfold = True
        else: # yes if inconsistencies present in existing G_upfold
            GFsize = [ gf.N1 for bname,gf in self.G_upfold]
            unchangedsize = all( [ self.n_orbitals[ik,ntoi[spn[isp]]] == GFsize[isp]
                                   for isp in range(self.n_spin_blocks[self.SO]) ] )
            if (not unchangedsize) or (self.G_upfold.mesh.beta != beta): set_up_G_upfold = True

        # Set up G_upfold
        if set_up_G_upfold:
            block_structure = [ range(self.n_orbitals[ik,ntoi[sp]]) for sp in spn ]
            gf_struct = [ (spn[isp], block_structure[isp]) for isp in range(self.n_spin_blocks[self.SO]) ]
            block_ind_list = [block for block,inner in gf_struct]
            if with_Sigma:
                glist = lambda : [ GfImFreq(indices = inner, mesh = self.Sigma_imp[0].mesh) for block,inner in gf_struct]
            else:
                glist = lambda : [ GfImFreq(indices = inner, beta = beta) for block,inner in gf_struct]
            self.G_upfold = BlockGf(name_list = block_ind_list, block_list = glist(), make_copies = False)
            self.G_upfold.zero()

        self.G_upfold << iOmega_n
        idmat = [numpy.identity(self.n_orbitals[ik,ntoi[sp]],numpy.complex_) for sp in spn]
        M = copy.deepcopy(idmat)
        for isp in range(self.n_spin_blocks[self.SO]):
            ind = ntoi[spn[isp]]
            n_orb = self.n_orbitals[ik,ind]
            M[isp] = self.hopping[ik,ind,0:n_orb,0:n_orb] - (idmat[isp]*mu) - (idmat[isp] * self.h_field * (1-2*isp))
        self.G_upfold -= M

        if with_Sigma:
            for icrsh in range(self.n_corr_shells):
                for bname,gf in self.G_upfold: gf -= self.upfold(ik,icrsh,bname,stmp[icrsh][bname],gf)

        self.G_upfold.invert()

	return self.G_upfold


    def put_Sigma(self, Sigma_imp):
        """Puts the impurity self energies for inequivalent atoms into the class, respects the multiplicity of the atoms."""

        assert isinstance(Sigma_imp,list), "Sigma_imp has to be a list of Sigmas for the correlated shells, even if it is of length 1!"
        assert len(Sigma_imp) == self.n_inequiv_shells, "give exactly one Sigma for each inequivalent corr. shell!"

        # init self.Sigma_imp:
        if all(type(gf) == GfImFreq for bname,gf in Sigma_imp[0]):
            # Imaginary frequency Sigma:
            self.Sigma_imp = [ BlockGf( name_block_generator = [ (block,GfImFreq(indices = inner, mesh = Sigma_imp[0].mesh)) for block,inner in self.gf_struct_sumk[icrsh] ],
                                  make_copies = False) for icrsh in range(self.n_corr_shells) ]
        elif all(type(gf) == GfReFreq for bname,gf in Sigma_imp[0]):
            # Real frequency Sigma:
            self.Sigma_imp = [ BlockGf( name_block_generator = [ (block,GfReFreq(indices = inner, mesh = Sigma_imp[0].mesh)) for block,inner in self.gf_struct_sumk[icrsh] ],
                                  make_copies = False) for icrsh in range(self.n_corr_shells) ]
        else:
            raise ValueError, "This type of Sigma is not handled."

        # transform the CTQMC blocks to the full matrix:
        for icrsh in range(self.n_corr_shells):
            ish = self.corr_to_inequiv[icrsh]    # ish is the index of the inequivalent shell corresponding to icrsh
            for block,inner in self.gf_struct_solver[ish].iteritems():
                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)]
                        self.Sigma_imp[icrsh][block_sumk][ind1_sumk,ind2_sumk] << Sigma_imp[ish][block][ind1,ind2]

        # rotation from local to global coordinate system:
        if self.use_rotations:
            for icrsh in range(self.n_corr_shells):
                for bname,gf in self.Sigma_imp[icrsh]: self.Sigma_imp[icrsh][bname] << self.rotloc(icrsh, gf, direction = 'toGlobal')


    def extract_G_loc(self, mu = None, with_Sigma = True):
        """
        Extracts the local downfolded Green function at the chemical potential of the class.
        At the end, the local G is rotated from the global coordinate system to the local system.
        if with_Sigma = False: Sigma is not included => non-interacting local GF
        """

        if mu is None: mu = self.chemical_potential
        Gloc = [ self.Sigma_imp[icrsh].copy() for icrsh in range(self.n_corr_shells) ]   # this list will be returned
        for icrsh in range(self.n_corr_shells): Gloc[icrsh].zero()                       # initialize to zero
        beta = Gloc[0].mesh.beta

        ikarray = numpy.array(range(self.n_k))
        for ik in mpi.slice_array(ikarray):

            S = self.lattice_gf_matsubara(ik = ik, mu = mu, with_Sigma = with_Sigma, beta = beta)
            S *= self.bz_weights[ik]

            for icrsh in range(self.n_corr_shells):
                tmp = Gloc[icrsh].copy()                  # init temporary storage
                for bname,gf in tmp: tmp[bname] << self.downfold(ik,icrsh,bname,S[bname],gf)
                Gloc[icrsh] += tmp

        # collect data from mpi
        for icrsh in range(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.symmcorr.symmetrize(Gloc)

        # Gloc is rotated to the local coordinate system:
        if self.use_rotations:
            for icrsh in range(self.n_corr_shells):
                for bname,gf in Gloc[icrsh]: Gloc[icrsh][bname] << self.rotloc(icrsh,gf,direction = 'toLocal')

        # transform to CTQMC blocks:
        Glocret = [ BlockGf( name_block_generator = [ (block,GfImFreq(indices = inner, mesh = Gloc[0].mesh)) for block,inner in self.gf_struct_solver[ish].iteritems() ],
                        make_copies = False) for ish in range(self.n_inequiv_shells)  ]
        for ish in range(self.n_inequiv_shells):

            for block,inner in self.gf_struct_solver[ish].iteritems():
                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)]
                        Glocret[ish][block][ind1,ind2] << Gloc[self.inequiv_to_corr[ish]][block_sumk][ind1_sumk,ind2_sumk]

        # return only the inequivalent shells:
        return Glocret


    def analyse_block_structure(self, threshold = 0.00001, include_shells = None, dm = None):
        """ Determines the Green's function block structure from simple point integration."""

        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) ]

        if dm is None: dm = self.density_matrix(method = 'using_point_integration')
        dens_mat = [ dm[self.inequiv_to_corr[ish]] for ish in range(self.n_inequiv_shells) ]

        if include_shells is None: 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]][4]]:
                dmbool = (abs(dens_mat[ish][sp]) > threshold)  # gives an index list of entries larger that threshold

                # Determine off-diagonal entries in upper triangular part of density matrix
                offdiag = []
                for i in range(len(dmbool)):
                    for j in range(i+1,len(dmbool)):
                        if dmbool[i,j]: offdiag.append([i,j])

                # Determine the number of non-hybridising blocks in the gf
                num_blocs = len(dmbool)
                blocs = [ [i] for i in range(num_blocs) ]
                for i in range(len(offdiag)):
                    for j in range(len(blocs[offdiag[i][1]])): blocs[offdiag[i][0]].append(blocs[offdiag[i][1]][j])
                    del blocs[offdiag[i][1]]
                    for j in range(i+1,len(offdiag)):
                        if offdiag[j][0] == offdiag[i][1]: offdiag[j][0] = offdiag[i][0]
                        if offdiag[j][1] == offdiag[i][1]: offdiag[j][1] = offdiag[i][0]
                        if offdiag[j][0] > offdiag[i][1]: offdiag[j][0] -= 1
                        if offdiag[j][1] > offdiag[i][1]: offdiag[j][1] -= 1
                        offdiag[j].sort()
                    num_blocs -= 1

                # Set the gf_struct for the solver accordingly
                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

            # now calculate degeneracies of orbitals:
            dm = {}
            for block,inner in self.gf_struct_solver[ish].iteritems():
                # get dm for the blocks:
                dm[block] = numpy.zeros([len(inner),len(inner)],numpy.complex_)
                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)]
                        dm[block][ind1,ind2] = dens_mat[ish][block_sumk][ind1_sumk,ind2_sumk]

            for block1 in self.gf_struct_solver[ish].iterkeys():
                for block2 in self.gf_struct_solver[ish].iterkeys(): 
                    if dm[block1].shape == dm[block2].shape:
                        if ( (abs(dm[block1] - dm[block2]) < threshold).all() ) and (block1 != block2):
                            # check if it was already there:
                            ind1 = -1
                            ind2 = -2
                            for n,ind in enumerate(self.deg_shells[ish]):
                                if block1 in ind: ind1 = n
                                if block2 in ind: ind2 = n
                            if (ind1 < 0) and (ind2 >= 0):
                                self.deg_shells[ish][ind2].append(block1)
                            elif (ind1 >= 0) and (ind2 < 0):
                                self.deg_shells[ish][ind1].append(block2)
                            elif (ind1 < 0) and (ind2 < 0):
                                self.deg_shells[ish].append([block1,block2])

        things_to_save = ['gf_struct_solver','sumk_to_solver','solver_to_sumk','solver_to_sumk_block','deg_shells']
        self.save(things_to_save)

        return dens_mat


    def density_matrix(self, method = 'using_gf', beta = 40.0):
        """Calculate density matrices in one of two ways:
            if 'using_gf': First get upfolded gf (g_loc is not set up), then density matrix.
                              It is useful for Hubbard I, and very quick.
                              No assumption on the hopping structure is made (ie diagonal or not).
            if 'using_point_integration': Only works for diagonal hopping matrix (true in wien2k).
        """
        dens_mat = [ {} for icrsh in range(self.n_corr_shells)]
        for icrsh in range(self.n_corr_shells):
            for sp in self.spin_block_names[self.corr_shells[icrsh][4]]:
                dens_mat[icrsh][sp] = numpy.zeros([self.corr_shells[icrsh][3],self.corr_shells[icrsh][3]], numpy.complex_)

        ikarray = numpy.array(range(self.n_k))
        for ik in mpi.slice_array(ikarray):

            if method == "using_gf":

                G_upfold = self.lattice_gf_matsubara(ik = ik, beta = beta, mu = self.chemical_potential)
                G_upfold *= self.bz_weights[ik]
                dm = G_upfold.density()
                MMat = [dm[sp] for sp in self.spin_block_names[self.SO]]

            elif method == "using_point_integration":

                ntoi = self.spin_names_to_ind[self.SO]
                spn = self.spin_block_names[self.SO]
                unchangedsize = all( [self.n_orbitals[ik,ntoi[sp]] == self.n_orbitals[0,ntoi[sp]] for sp in spn] )
                if unchangedsize:
                    dim = self.n_orbitals[0,ntoi[sp]]
                else:
                    dim = self.n_orbitals[ik,ntoi[sp]]
                MMat = [numpy.zeros( [dim,dim], numpy.complex_) for sp in spn]

                for isp, sp in enumerate(spn):
                    ind = ntoi[sp]
                    for inu in range(self.n_orbitals[ik,ind]):
                        if (self.hopping[ik,ind,inu,inu] - self.h_field*(1-2*isp)) < 0.0: # only works for diagonal hopping matrix (true in wien2k)
                            MMat[isp][inu,inu] = 1.0
                        else:
                            MMat[isp][inu,inu] = 0.0

            for icrsh in range(self.n_corr_shells):
                for isp, sp in enumerate(self.spin_block_names[self.corr_shells[icrsh][4]]):
                    isp = self.spin_names_to_ind[self.corr_shells[icrsh][4]][sp]
                    dim = self.corr_shells[icrsh][3]
                    n_orb = self.n_orbitals[ik,isp]
                    projmat = self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb]
                    if method == "using_gf":
                        dens_mat[icrsh][sp] += numpy.dot( numpy.dot(projmat,MMat[isp]),
                                                          projmat.transpose().conjugate() )
                    elif method == "using_point_integration":
                        dens_mat[icrsh][sp] += self.bz_weights[ik] * numpy.dot( numpy.dot(projmat,MMat[isp]) ,
                                                                                projmat.transpose().conjugate() )

        # get data from nodes:
        for icrsh in range(self.n_corr_shells):
            for bname in dens_mat[icrsh]:
                dens_mat[icrsh][bname] = mpi.all_reduce(mpi.world, dens_mat[icrsh][bname], lambda x,y : x+y)
        mpi.barrier()

        if self.symm_op != 0: dens_mat = self.symmcorr.symmetrize(dens_mat)

        # Rotate to local coordinate system:
        if self.use_rotations:
            for icrsh in range(self.n_corr_shells):
                for bl in dens_mat[icrsh]:
                    if self.rot_mat_time_inv[icrsh] == 1: dens_mat[icrsh][bl] = dens_mat[icrsh][bl].conjugate()
                    dens_mat[icrsh][bl] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),dens_mat[icrsh][bl]),
                                                    self.rot_mat[icrsh] )

        return dens_mat


    # For simple dft input, get crystal field splittings.
    def eff_atomic_levels(self):
        """Calculates the effective atomic levels needed as input for the Hubbard I Solver."""

        # define matrices for inequivalent shells:
        eff_atlevels = [ {} for ish in range(self.n_inequiv_shells) ]
        for ish in range(self.n_inequiv_shells):
            for sp in self.spin_block_names[self.corr_shells[self.inequiv_to_corr[ish]][4]]:
                eff_atlevels[ish][sp] = numpy.identity(self.corr_shells[self.inequiv_to_corr[ish]][3], numpy.complex_)

        # Chemical Potential:
        for ish in range(self.n_inequiv_shells):
            for ii in eff_atlevels[ish]: eff_atlevels[ish][ii] *= -self.chemical_potential

        # double counting term:
        for ish in range(self.n_inequiv_shells):
            for ii in eff_atlevels[ish]:
                eff_atlevels[ish][ii] -= self.dc_imp[self.inequiv_to_corr[ish]][ii]

        # sum over k:
        if not hasattr(self,"Hsumk"):
            # calculate the sum over k. Does not depend on mu, so do it only once:
            self.Hsumk = [ {} for icrsh in range(self.n_corr_shells) ]
            for icrsh in range(self.n_corr_shells):
                for sp in self.spin_block_names[self.corr_shells[icrsh][4]]:
                    dim = self.corr_shells[icrsh][3]  #*(1+self.corr_shells[icrsh][4])
                    self.Hsumk[icrsh][sp] = numpy.zeros([dim,dim],numpy.complex_)

            for icrsh in range(self.n_corr_shells):
                dim = self.corr_shells[icrsh][3]
                for isp, sp in enumerate(self.spin_block_names[self.corr_shells[icrsh][4]]):
                    isp = self.spin_names_to_ind[self.corr_shells[icrsh][4]][sp]
                    for ik in range(self.n_k):
                        n_orb = self.n_orbitals[ik,isp]
                        MMat = numpy.identity(n_orb, numpy.complex_)
                        MMat = self.hopping[ik,isp,0:n_orb,0:n_orb] - (1-2*isp) * self.h_field * MMat
                        projmat = self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb]
                        self.Hsumk[icrsh][sp] += self.bz_weights[ik] * numpy.dot( numpy.dot(projmat,MMat),
                                                                                  projmat.conjugate().transpose() )

            # symmetrisation:
            if self.symm_op != 0: self.Hsumk = self.symmcorr.symmetrize(self.Hsumk)

            # Rotate to local coordinate system:
            if self.use_rotations:
                for icrsh in range(self.n_corr_shells):
                    for bl in self.Hsumk[icrsh]:

                        if self.rot_mat_time_inv[icrsh] == 1: self.Hsumk[icrsh][bl] = self.Hsumk[icrsh][bl].conjugate()
                        self.Hsumk[icrsh][bl] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),self.Hsumk[icrsh][bl]) ,
                                                           self.rot_mat[icrsh] )

        # add to matrix:
        for ish in range(self.n_inequiv_shells):
            for bl in eff_atlevels[ish]:
                eff_atlevels[ish][bl] += self.Hsumk[self.inequiv_to_corr[ish]][bl]


        return eff_atlevels


    def __init_dc(self):

        # construct the density matrix dm_imp and double counting arrays
        self.dc_imp = [ {} for icrsh in range(self.n_corr_shells)]
        for icrsh in range(self.n_corr_shells):
            dim = self.corr_shells[icrsh][3]
            spn = self.spin_block_names[self.corr_shells[icrsh][4]]
            for sp in spn: self.dc_imp[icrsh][sp] = numpy.zeros([dim,dim],numpy.float_)
        self.dc_energ = [0.0 for icrsh in range(self.n_corr_shells)]


    def set_dc(self,dens_mat,U_interact,J_hund,orb=0,use_dc_formula=0,use_val=None):
        """Sets the double counting term for inequiv orbital orb:
           use_dc_formula = 0: fully-localised limit (FLL),
           use_dc_formula = 1: Held's formula,
           use_dc_formula = 2: around mean-field (AMF).
           Be sure that you are using the correct interaction Hamiltonian!"""

        for icrsh in range(self.n_corr_shells):

            iorb = self.corr_to_inequiv[icrsh]    # iorb is the index of the inequivalent shell corresponding to icrsh

            if iorb != orb: continue # ignore this orbital

            Ncr = {}
            dim = self.corr_shells[icrsh][3] #*(1+self.corr_shells[icrsh][4])

            spn = self.spin_block_names[self.corr_shells[icrsh][4]]
            for sp in spn:
                self.dc_imp[icrsh][sp] = numpy.identity(dim,numpy.float_)
                Ncr[sp] = 0.0

            for block,inner in self.gf_struct_solver[iorb].iteritems():
                bl = self.solver_to_sumk_block[iorb][block]
                Ncr[bl] += dens_mat[block].real.trace()

            Ncrtot = 0.0

            spn = self.spin_block_names[self.corr_shells[icrsh][4]]
            for sp in spn: 
                Ncrtot += Ncr[sp]

            # average the densities if there is no SP:
            if self.SP == 0:
                for sp in spn: Ncr[sp] = Ncrtot / len(spn)
            # correction for SO: we have only one block in this case, but in DC we need N/2
            elif self.SP == 1 and self.SO == 1:
                for sp in spn: Ncr[sp] = Ncrtot / 2.0

            if use_val is None:

                if use_dc_formula == 0: # FLL

                    self.dc_energ[icrsh] = U_interact / 2.0 * Ncrtot * (Ncrtot-1.0)
                    for sp in spn:
                        Uav = U_interact*(Ncrtot-0.5) - J_hund*(Ncr[sp] - 0.5)
                        self.dc_imp[icrsh][sp] *= Uav
                        self.dc_energ[icrsh]  -= J_hund / 2.0 * (Ncr[sp]) * (Ncr[sp]-1.0)
                        mpi.report("DC for shell %(icrsh)i and block %(sp)s = %(Uav)f"%locals())

                elif use_dc_formula == 1: # Held's formula, with U_interact the interorbital onsite interaction

                    self.dc_energ[icrsh] = (U_interact + (dim-1)*(U_interact-2.0*J_hund) + (dim-1)*(U_interact-3.0*J_hund))/(2*dim-1) / 2.0 * Ncrtot * (Ncrtot-1.0)
                    for sp in spn:
                        Uav =(U_interact + (dim-1)*(U_interact-2.0*J_hund) + (dim-1)*(U_interact-3.0*J_hund))/(2*dim-1) * (Ncrtot-0.5)
                        self.dc_imp[icrsh][sp] *= Uav
                        mpi.report("DC for shell %(icrsh)i and block %(sp)s = %(Uav)f"%locals())

                elif use_dc_formula == 2: # AMF

                    self.dc_energ[icrsh] = 0.5 * U_interact * Ncrtot * Ncrtot
                    for sp in spn:
                        Uav = U_interact*(Ncrtot - Ncr[sp]/dim) - J_hund * (Ncr[sp] - Ncr[sp]/dim)
                        self.dc_imp[icrsh][sp] *= Uav
                        self.dc_energ[icrsh] -= (U_interact + (dim-1)*J_hund)/dim * 0.5 * Ncr[sp] * Ncr[sp]
                        mpi.report("DC for shell %(icrsh)i and block %(sp)s = %(Uav)f"%locals())

                # output:
                mpi.report("DC energy for shell %s = %s"%(icrsh,self.dc_energ[icrsh]))

            else:

                self.dc_energ[icrsh] = use_val * Ncrtot
                for sp in spn:
                    self.dc_imp[icrsh][sp] *= use_val

                # output:
                mpi.report("DC for shell %(icrsh)i = %(use_val)f"%locals())
                mpi.report("DC energy = %s"%self.dc_energ[icrsh])


    def add_dc(self):
        """Substracts the double counting term from the impurity self energy."""

        # Be careful: Sigma_imp is already in the global coordinate system!!
        sres = [s.copy() for s in self.Sigma_imp]
        for icrsh in range(self.n_corr_shells):
            for bname,gf in sres[icrsh]:
                # Transform dc_imp to global coordinate system
                dccont = numpy.dot(self.rot_mat[icrsh],numpy.dot(self.dc_imp[icrsh][bname],self.rot_mat[icrsh].conjugate().transpose()))
                sres[icrsh][bname] -= dccont

        return sres # list of self energies corrected by DC


    def symm_deg_gf(self,gf_to_symm,orb):
        """Symmetrises a GF for the given degenerate shells self.deg_shells"""

        for degsh in self.deg_shells[orb]:
            #loop over degenerate shells:
            ss = gf_to_symm[degsh[0]].copy()
            ss.zero()
            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


    def total_density(self, mu):
        """
        Calculates the total charge for the energy window for a given chemical potential 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

        The calculation is done in the global coordinate system, if distinction is made between local/global!
        """

        dens = 0.0
        ikarray = numpy.array(range(self.n_k))
        for ik in mpi.slice_array(ikarray):

            S = self.lattice_gf_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 set_mu(self,mu):
        """Sets a new chemical potential"""

        self.chemical_potential = mu


    def find_mu(self, precision = 0.01):
        """
        Searches for mu in order to give the desired charge
        A desired precision can be specified in precision.
        """

        F = lambda mu : self.total_density(mu = mu)
        density = self.density_required - self.charge_below

        self.chemical_potential = dichotomy.dichotomy(function = F,
                                         x_init = self.chemical_potential, y_value = density,
                                         precision_on_y = precision, delta_x = 0.5, max_loops = 100, 
                                         x_name = "Chemical Potential", y_name = "Total Density",
                                         verbosity = 3)[0]

        return self.chemical_potential
 

    def calc_density_correction(self,filename = 'dens_mat.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.spin_names_to_ind[self.SO]
        spn = self.spin_block_names[self.SO]
        dens = {sp: 0.0 for sp in spn}

        # Set up deltaN:
        deltaN = {}
        for sp in spn:
            deltaN[sp] = [numpy.zeros([self.n_orbitals[ik,ntoi[sp]],self.n_orbitals[ik,ntoi[sp]]], numpy.complex_) for ik in range(self.n_k)]

        ikarray = numpy.array(range(self.n_k))
        for ik in mpi.slice_array(ikarray):
            S = self.lattice_gf_matsubara(ik = ik, mu = self.chemical_potential)
            for bname,gf in S:
                deltaN[bname][ik] = S[bname].density()
                dens[bname] += self.bz_weights[ik] * S[bname].total_density()

        #put mpi Barrier:
        for bname in deltaN:
            for ik in range(self.n_k):
                deltaN[bname][ik] = mpi.all_reduce(mpi.world, deltaN[bname][ik], lambda x,y : x+y)
            dens[bname] = mpi.all_reduce(mpi.world, dens[bname], 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.energy_unit))
            if self.SP != 0: f1.write("%.14f\n"%(self.chemical_potential/self.energy_unit))
            # write beta in ryderg-1
            f.write("%.14f\n"%(S.mesh.beta*self.energy_unit))
            if self.SP != 0: f1.write("%.14f\n"%(S.mesh.beta*self.energy_unit))

            if self.SP == 0: # no spin-polarization

                for ik in range(self.n_k):
                    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: # with spin-polarization

                # dict of filename: (spin index, block_name)
                if self.SO == 0: to_write = {f: (0, 'up'), f1: (1, 'down')}
                if self.SO == 1: to_write = {f: (0, 'ud'), f1: (0, 'ud')}
                for fout in to_write.iterkeys():
                    isp, sp = to_write[fout]
                    for ik in range(self.n_k):
                        fout.write("%s\n"%self.n_orbitals[ik,isp])
                        for inu in range(self.n_orbitals[ik,isp]):
                            for imu in range(self.n_orbitals[ik,isp]):
                                fout.write("%.14f  %.14f "%(deltaN[bn][ik][inu,imu].real,deltaN[bn][ik][inu,imu].imag))
                            fout.write("\n")
                        fout.write("\n")
                    fout.close()

        return deltaN, dens

################
# FIXME LEAVE UNDOCUMENTED
################

    # FIXME Merge with find_mu?
    def find_mu_nonint(self, dens_req, orb = None, precision = 0.01):

        def F(mu):
            gnonint = self.extract_G_loc(mu = mu, with_Sigma = False)

            if orb is None:
                dens = 0.0
                for ish in range(self.n_inequiv_shells):
                    dens += gnonint[ish].total_density()
            else:
                dens = gnonint[orb].total_density()

            return dens


        self.chemical_potential = dichotomy.dichotomy(function = F,
                                         x_init = self.chemical_potential, y_value = dens_req,
                                         precision_on_y = precision, delta_x = 0.5, max_loops = 100, 
                                         x_name = "Chemical Potential", y_name = "Total Density",
                                         verbosity = 3)[0]

        return self.chemical_potential


    def find_dc(self,orb,guess,dens_mat,dens_req=None,precision=0.01):
        """Searches for DC in order to fulfill charge neutrality.
           If dens_req is given, then DC is set such that the LOCAL charge of orbital
           orb coincides with dens_req."""

        mu = self.chemical_potential

        def F(dc):
            self.set_dc(dens_mat = dens_mat, U_interact = 0, J_hund = 0, orb = orb, use_val = dc)
            if dens_req is None:
                return self.total_density(mu = mu)
            else:
                return self.extract_G_loc()[orb].total_density()


        if dens_req is None:
            density = self.density_required - self.charge_below
        else:
            density = dens_req

        dcnew = dichotomy.dichotomy(function = F,
                                    x_init = guess, y_value = density,
                                    precision_on_y = precision, delta_x = 0.5,
                                    max_loops = 100, x_name = "Double Counting", y_name= "Total Density",
                                    verbosity = 3)[0]

        return dcnew


    # Check that the density matrix from projectors (DM = P Pdagger) is correct (ie matches DFT)
    def check_projectors(self):

        dens_mat = [numpy.zeros([self.corr_shells[icrsh][3],self.corr_shells[icrsh][3]],numpy.complex_)
                   for icrsh in range(self.n_corr_shells)]

        for ik in range(self.n_k):
            for icrsh in range(self.n_corr_shells):
                dim = self.corr_shells[icrsh][3]
                n_orb = self.n_orbitals[ik,0]
                projmat = self.proj_mat[ik,0,icrsh,0:dim,0:n_orb]
                dens_mat[icrsh][:,:] += numpy.dot(projmat, projmat.transpose().conjugate()) * self.bz_weights[ik]

        if self.symm_op != 0: dens_mat = self.symmcorr.symmetrize(dens_mat)

        # Rotate to local coordinate system:
        if self.use_rotations:
            for icrsh in range(self.n_corr_shells):
                if self.rot_mat_time_inv[icrsh] == 1: dens_mat[icrsh] = dens_mat[icrsh].conjugate()
                dens_mat[icrsh] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),dens_mat[icrsh]) ,
                                            self.rot_mat[icrsh] )

        return dens_mat


    # Determine the number of equivalent shells
    def sorts_of_atoms(self,lst):
        """
        This routine should determine the number of sorts in the double list lst
        """
        sortlst = [ lst[i][1] for i in range(len(lst)) ]
        sorts = len(set(sortlst))
        return sorts


    # Determine the number of atoms
    def number_of_atoms(self,lst):
        """
        This routine should determine the number of atoms in the double list lst
        """
        atomlst = [ lst[i][0] for i in range(len(lst)) ]
        atoms = len(set(atomlst))
        return atoms