dft_tools/python/sumk_dft_tools.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
from pytriqs.gf.local import *
import pytriqs.utility.mpi as mpi
from symmetry import *
from sumk_dft import SumkDFT

class SumkDFTTools(SumkDFT):
    """Extends the SumkDFT class with some tools for analysing the data."""


    def __init__(self, hdf_file, 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', 
                 transp_data = 'dft_transp_input', misc_data = 'dft_misc_input'):

        SumkDFT.__init__(self, hdf_file=hdf_file, h_field=h_field, use_dft_blocks=use_dft_blocks,
                          dft_data=dft_data, symmcorr_data=symmcorr_data, parproj_data=parproj_data, 
                          symmpar_data=symmpar_data, bands_data=bands_data, transp_data=transp_data, 
                          misc_data=misc_data)


    def dos_wannier_basis(self, mu=None, broadening=None, mesh=None, with_Sigma=True, with_dc=True, save_to_file=True):

        if (mesh is None) and (not with_Sigma):
            raise ValueError, "lattice_gf: Give the mesh=(om_min,om_max,n_points) for the lattice GfReFreq."
        if mesh is None: 
            om_mesh = [x.real for x in self.Sigma_imp_w[0].mesh]
            om_min = om_mesh[0]
            om_max = om_mesh[-1]
            n_om = len(om_mesh)
            mesh = (om_min,om_max,n_om)
        else: 
            om_min,om_max,n_om = mesh
            delta_om = (om_max-om_min)/(n_om-1)
            om_mesh = [om_min + delta_om * i for i in range(n_om)]

        G_loc = []
        for icrsh in range(self.n_corr_shells):
            spn = self.spin_block_names[self.corr_shells[icrsh]['SO']]
            glist = [ GfReFreq(indices = inner, window = (om_min,om_max), n_points = n_om) for block,inner in self.gf_struct_sumk[icrsh]]
            G_loc.append(BlockGf(name_list = spn, block_list = glist, make_copies=False))
        for icrsh in range(self.n_corr_shells): G_loc[icrsh].zero()

        DOS = { sp: numpy.zeros([n_om],numpy.float_) for sp in self.spin_block_names[self.SO] }
        DOSproj     = [ {} for ish in range(self.n_inequiv_shells) ]
        DOSproj_orb = [ {} 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]]['SO']]:
                dim = self.corr_shells[self.inequiv_to_corr[ish]]['dim']
                DOSproj[ish][sp] = numpy.zeros([n_om],numpy.float_)
                DOSproj_orb[ish][sp] = numpy.zeros([n_om,dim,dim],numpy.float_)

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

            G_latt_w = self.lattice_gf(ik=ik,mu=mu,iw_or_w="w",broadening=broadening,mesh=mesh,with_Sigma=with_Sigma,with_dc=with_dc)
            G_latt_w *= self.bz_weights[ik]

            # Non-projected DOS
            for iom in range(n_om):
                for bname,gf in G_latt_w:
                    DOS[bname][iom] -= gf.data[iom,:,:].imag.trace()/numpy.pi

            # Projected DOS:
            for icrsh in range(self.n_corr_shells):
                tmp = G_loc[icrsh].copy()
                for bname,gf in tmp: tmp[bname] << self.downfold(ik,icrsh,bname,G_latt_w[bname],gf) # downfolding G
                G_loc[icrsh] += tmp

        # Collect data from mpi:
        for bname in DOS:
            DOS[bname] = mpi.all_reduce(mpi.world, DOS[bname], lambda x,y : x+y)
        for icrsh in range(self.n_corr_shells):
            G_loc[icrsh] << mpi.all_reduce(mpi.world, G_loc[icrsh], lambda x,y : x+y)
        mpi.barrier()

        # Symmetrize and rotate to local coord. system if needed:
        if self.symm_op != 0: G_loc = self.symmcorr.symmetrize(G_loc)
        if self.use_rotations:
            for icrsh in range(self.n_corr_shells):
                for bname,gf in G_loc[icrsh]: G_loc[icrsh][bname] << self.rotloc(icrsh,gf,direction='toLocal')

        # G_loc can now also be used to look at orbitally-resolved quantities
        for ish in range(self.n_inequiv_shells):
            for bname,gf in G_loc[self.inequiv_to_corr[ish]]: # loop over spins
                for iom in range(n_om): DOSproj[ish][bname][iom] -= gf.data[iom,:,:].imag.trace()/numpy.pi
                DOSproj_orb[ish][bname][:,:,:] -= gf.data[:,:,:].imag/numpy.pi

        # Write to files
        if save_to_file and mpi.is_master_node():
            for sp in self.spin_block_names[self.SO]:
                f = open('DOS_wann_%s.dat'%sp, 'w')
                for iom in range(n_om): f.write("%s    %s\n"%(om_mesh[iom],DOS[sp][iom]))
                f.close()

                # Partial
                for ish in range(self.n_inequiv_shells):
                    f = open('DOS_wann_%s_proj%s.dat'%(sp,ish),'w')
                    for iom in range(n_om): f.write("%s    %s\n"%(om_mesh[iom],DOSproj[ish][sp][iom]))
                    f.close()

                    # Orbitally-resolved
                    for i in range(self.corr_shells[self.inequiv_to_corr[ish]]['dim']):
                        for j in range(i,self.corr_shells[self.inequiv_to_corr[ish]]['dim']):
                            f = open('DOS_wann_'+sp+'_proj'+str(ish)+'_'+str(i)+'_'+str(j)+'.dat','w')
                            for iom in range(n_om): f.write("%s    %s\n"%(om_mesh[iom],DOSproj_orb[ish][sp][iom,i,j]))
                            f.close()

        return DOS, DOSproj, DOSproj_orb


    def dos_parproj_basis(self, mu=None, broadening=None, mesh=None, with_Sigma=True, with_dc=True, save_to_file=True):
        """Calculates the orbitally-resolved DOS"""

        things_to_read = ['n_parproj','proj_mat_all','rot_mat_all','rot_mat_all_time_inv']
        value_read = self.read_input_from_hdf(subgrp=self.parproj_data,things_to_read = things_to_read)
        if not value_read: return value_read
        if self.symm_op: self.symmpar = Symmetry(self.hdf_file,subgroup=self.symmpar_data)

        if (mesh is None) and (not with_Sigma):
            raise ValueError, "lattice_gf: Give the mesh=(om_min,om_max,n_points) for the lattice GfReFreq."
        if mesh is None: 
            om_mesh = [x.real for x in self.Sigma_imp_w[0].mesh]
            om_min = om_mesh[0]
            om_max = om_mesh[-1]
            n_om = len(om_mesh)
            mesh = (om_min,om_max,n_om)
        else: 
            om_min,om_max,n_om = mesh
            delta_om = (om_max-om_min)/(n_om-1)
            om_mesh = [om_min + delta_om * i for i in range(n_om)]

        G_loc = []
        spn = self.spin_block_names[self.SO]
        gf_struct_parproj = [ [ (sp, range(self.shells[ish]['dim'])) for sp in spn ] 
                              for ish in range(self.n_shells) ]
        for ish in range(self.n_shells): 
            glist = [ GfReFreq(indices = inner, window = (om_min,om_max), n_points = n_om) for block,inner in gf_struct_parproj[ish] ]
            G_loc.append(BlockGf(name_list = spn, block_list = glist, make_copies=False))
        for ish in range(self.n_shells): G_loc[ish].zero()

        DOS = { sp: numpy.zeros([n_om],numpy.float_) for sp in self.spin_block_names[self.SO] }
        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 sp in self.spin_block_names[self.SO]:
                dim = self.shells[ish]['dim']
                DOSproj[ish][sp] = numpy.zeros([n_om],numpy.float_)
                DOSproj_orb[ish][sp] = numpy.zeros([n_om,dim,dim],numpy.float_)

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

            G_latt_w = self.lattice_gf(ik=ik,mu=mu,iw_or_w="w",broadening=broadening,mesh=mesh,with_Sigma=with_Sigma,with_dc=with_dc)
            G_latt_w *= self.bz_weights[ik]

            # Non-projected DOS
            for iom in range(n_om):
                for bname,gf in G_latt_w:
                    DOS[bname][iom] -= gf.data[iom,:,:].imag.trace()/numpy.pi

            # Projected DOS:
            for ish in range(self.n_shells):
                tmp = G_loc[ish].copy()
                for ir in range(self.n_parproj[ish]):
                    for bname,gf in tmp: tmp[bname] << self.downfold(ik,ish,bname,G_latt_w[bname],gf,shells='all',ir=ir)
                    G_loc[ish] += tmp

        # Collect data from mpi:
        for bname in DOS:
            DOS[bname] = mpi.all_reduce(mpi.world, DOS[bname], lambda x,y : x+y)
        for ish in range(self.n_shells):
            G_loc[ish] << mpi.all_reduce(mpi.world, G_loc[ish], lambda x,y : x+y)
        mpi.barrier()

        # Symmetrize and rotate to local coord. system if needed:
        if self.symm_op != 0: G_loc = self.symmpar.symmetrize(G_loc)
        if self.use_rotations:
            for ish in range(self.n_shells):
                for bname,gf in G_loc[ish]: G_loc[ish][bname] << self.rotloc(ish,gf,direction='toLocal',shells='all')

        # G_loc can now also be used to look at orbitally-resolved quantities
        for ish in range(self.n_shells):
            for bname,gf in G_loc[ish]:
                for iom in range(n_om): DOSproj[ish][bname][iom] -= gf.data[iom,:,:].imag.trace()/numpy.pi
                DOSproj_orb[ish][bname][:,:,:] -= gf.data[:,:,:].imag/numpy.pi

        # Write to files
        if save_to_file and mpi.is_master_node():
            for sp in self.spin_block_names[self.SO]:
                f = open('DOS_parproj_%s.dat'%sp, 'w')
                for iom in range(n_om): f.write("%s    %s\n"%(om_mesh[iom],DOS[sp][iom]))
                f.close()

                # Partial
                for ish in range(self.n_shells):
                    f = open('DOS_parproj_%s_proj%s.dat'%(sp,ish),'w')
                    for iom in range(n_om): f.write("%s    %s\n"%(om_mesh[iom],DOSproj[ish][sp][iom]))
                    f.close()

                    # Orbitally-resolved
                    for i in range(self.shells[ish]['dim']):
                        for j in range(i,self.shells[ish]['dim']):
                            f = open('DOS_parproj_'+sp+'_proj'+str(ish)+'_'+str(i)+'_'+str(j)+'.dat','w')
                            for iom in range(n_om): f.write("%s    %s\n"%(om_mesh[iom],DOSproj_orb[ish][sp][iom,i,j]))
                            f.close()

        return DOS, DOSproj, DOSproj_orb


    def spaghettis(self,broadening=None,plot_shift=0.0,plot_range=None,ishell=None,mu=None,save_to_file='Akw_'):
        """ Calculates the correlated band structure with a real-frequency self energy."""

        assert hasattr(self,"Sigma_imp_w"), "spaghettis: Set Sigma_imp_w first."
        things_to_read = ['n_k','n_orbitals','proj_mat','hopping','n_parproj','proj_mat_all']
        value_read = self.read_input_from_hdf(subgrp=self.bands_data,things_to_read=things_to_read)
        if not value_read: return value_read
        things_to_read = ['rot_mat_all','rot_mat_all_time_inv']
        value_read = self.read_input_from_hdf(subgrp=self.parproj_data,things_to_read = things_to_read)
        if not value_read: return value_read

        if mu is None: mu = self.chemical_potential
        spn = self.spin_block_names[self.SO]
        mesh = [x.real for x in self.Sigma_imp_w[0].mesh]
        n_om = len(mesh)

        if plot_range is None:
            om_minplot = mesh[0] - 0.001
            om_maxplot = mesh[n_om-1] + 0.001
        else:
            om_minplot = plot_range[0]
            om_maxplot = plot_range[1]

        if ishell is None:
            Akw = { sp: numpy.zeros([self.n_k,n_om],numpy.float_) for sp in spn }
        else:
            Akw = { sp: numpy.zeros([self.shells[ishell]['dim'],self.n_k,n_om],numpy.float_) for sp in spn }

        if not ishell is None:
            gf_struct_parproj =  [ (sp, range(self.shells[ishell]['dim'])) for sp in spn ]
            G_loc = BlockGf(name_block_generator = [ (block,GfReFreq(indices = inner, mesh = self.Sigma_imp_w[0].mesh))
                                                     for block,inner in gf_struct_parproj ], make_copies = False)
            G_loc.zero()

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

            G_latt_w = self.lattice_gf(ik=ik,mu=mu,iw_or_w="w",broadening=broadening)

            if ishell is None:
                # Non-projected A(k,w)
                for iom in range(n_om):
                    if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
                        for bname,gf in G_latt_w: Akw[bname][ik,iom] += gf.data[iom,:,:].imag.trace()/(-1.0*numpy.pi)
                        Akw[bname][ik,iom] += ik*plot_shift                       # shift Akw for plotting stacked k-resolved eps(k) curves

            else: # ishell not None
                # Projected A(k,w):
                G_loc.zero()
                tmp = G_loc.copy()
                for ir in range(self.n_parproj[ishell]):
                    for bname,gf in tmp: tmp[bname] << self.downfold(ik,ishell,bname,G_latt_w[bname],gf,shells='all',ir=ir)
                    G_loc += tmp

                # Rotate to local frame
                if self.use_rotations:
                    for bname,gf in G_loc: G_loc[bname] << self.rotloc(ishell,gf,direction='toLocal',shells='all')

                for iom in range(n_om):
                    if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
                        for ish in range(self.shells[ishell]['dim']):
                            for sp in spn:
                                Akw[sp][ish,ik,iom] = G_loc[sp].data[iom,ish,ish].imag/(-1.0*numpy.pi)

        if save_to_file and mpi.is_master_node():
            if ishell is None:
                for sp in spn: # loop over GF blocs:
                    f = open(save_to_file+sp+'.dat','w')   # Open file for storage:
                    for ik in range(self.n_k):
                        for iom in range(n_om):
                            if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
                                if plot_shift > 0.0001:
                                    f.write('%s      %s\n'%(mesh[iom],Akw[sp][ik,iom]))
                                else:
                                    f.write('%s     %s      %s\n'%(ik,mesh[iom],Akw[sp][ik,iom]))
                        f.write('\n')
                    f.close()

            else: # ishell is not None
                for sp in spn:
                    for ish in range(self.shells[ishell]['dim']):
                        f = open(save_to_file+sp+'_proj'+str(ish)+'.dat','w')   # Open file for storage:
                        for ik in range(self.n_k):
                            for iom in range(n_om):
                                if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
                                    if plot_shift > 0.0001:
                                        f.write('%s      %s\n'%(mesh[iom],Akw[sp][ish,ik,iom]))
                                    else:
                                        f.write('%s     %s      %s\n'%(ik,mesh[iom],Akw[sp][ish,ik,iom]))
                            f.write('\n')
                        f.close()

        return Akw

    def partial_charges(self,beta=40,mu=None,with_Sigma=True,with_dc=True):
        """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"""

        things_to_read = ['dens_mat_below','n_parproj','proj_mat_all','rot_mat_all','rot_mat_all_time_inv']
        value_read = self.read_input_from_hdf(subgrp=self.parproj_data,things_to_read = things_to_read)
        if not value_read: return value_read
        if self.symm_op: self.symmpar = Symmetry(self.hdf_file,subgroup=self.symmpar_data)

        spn = self.spin_block_names[self.SO]
        ntoi = self.spin_names_to_ind[self.SO]
        # Density matrix in the window
        self.dens_mat_window = [ [ numpy.zeros([self.shells[ish]['dim'],self.shells[ish]['dim']],numpy.complex_) 
                                   for ish in range(self.n_shells) ]
                                 for isp in range(len(spn)) ]
        # Set up G_loc
        gf_struct_parproj = [ [ (sp, range(self.shells[ish]['dim'])) for sp in spn ]  
                              for ish in range(self.n_shells) ]
        if with_Sigma:
            G_loc = [ BlockGf(name_block_generator = [ (block,GfImFreq(indices = inner, mesh = self.Sigma_imp_iw[0].mesh)) 
                                                      for block,inner in gf_struct_parproj[ish] ], make_copies = False)
                     for ish in range(self.n_shells)]
            beta = self.Sigma_imp_iw[0].mesh.beta
        else:
            G_loc = [ BlockGf(name_block_generator = [ (block,GfImFreq(indices = inner, beta = beta)) 
                                                      for block,inner in gf_struct_parproj[ish] ], make_copies = False)
                     for ish in range(self.n_shells)]
        for ish in range(self.n_shells): G_loc[ish].zero()

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

            G_latt_iw = self.lattice_gf(ik=ik,mu=mu,iw_or_w="iw",beta=beta,with_Sigma=with_Sigma,with_dc=with_dc)
            G_latt_iw *= self.bz_weights[ik]
            for ish in range(self.n_shells):
                tmp = G_loc[ish].copy()
                for ir in range(self.n_parproj[ish]):
                    for bname,gf in tmp: tmp[bname] << self.downfold(ik,ish,bname,G_latt_iw[bname],gf,shells='all',ir=ir)
                    G_loc[ish] += tmp

        # Collect data from mpi:
        for ish in range(self.n_shells):
            G_loc[ish] << mpi.all_reduce(mpi.world, G_loc[ish], lambda x,y : x+y)
        mpi.barrier()

        # Symmetrize and rotate to local coord. system if needed:
        if self.symm_op != 0: G_loc = self.symmpar.symmetrize(G_loc)
        if self.use_rotations:
            for ish in range(self.n_shells):
                for bname,gf in G_loc[ish]: G_loc[ish][bname] << self.rotloc(ish,gf,direction='toLocal',shells='all')

        for ish in range(self.n_shells):
            isp = 0
            for bname,gf in G_loc[ish]:
                self.dens_mat_window[isp][ish] = G_loc[ish].density()[bname]
                isp += 1

        # Add density matrices to get the total:
        dens_mat = [ [ self.dens_mat_below[ntoi[spn[isp]]][ish] + self.dens_mat_window[isp][ish] 
                       for ish in range(self.n_shells) ]
                     for isp in range(len(spn)) ]

        return dens_mat


    def print_hamiltonian(self):
        """ Print Hamiltonian for checks."""
        if self.SP == 1 and self.SO == 0:
            f1 = open('hamup.dat','w')
            f2 = open('hamdn.dat','w')
            for ik in range(self.n_k):
                for i in range(self.n_orbitals[ik,0]):
                    f1.write('%s    %s\n'%(ik,self.hopping[ik,0,i,i].real))
                for i in range(self.n_orbitals[ik,1]):
                    f2.write('%s    %s\n'%(ik,self.hopping[ik,1,i,i].real))
                f1.write('\n')
                f2.write('\n')
            f1.close()
            f2.close()
        else:
            f = open('ham.dat','w')
            for ik in range(self.n_k):
                for i in range(self.n_orbitals[ik,0]):
                    f.write('%s    %s\n'%(ik,self.hopping[ik,0,i,i].real))
                f.write('\n')
            f.close()


# ----------------- transport -----------------------

    def read_transport_input_from_hdf(self):
        """
        Reads the data for transport calculations from the HDF file
        """
        thingstoread = ['band_window_optics','velocities_k']
        self.read_input_from_hdf(subgrp=self.transp_data,things_to_read = thingstoread)
        thingstoread = ['band_window','lattice_angles','lattice_constants','lattice_type','n_symmetries','rot_symmetries']
        self.read_input_from_hdf(subgrp=self.misc_data,things_to_read = thingstoread)
    
    
    def cellvolume(self, lattice_type, lattice_constants, latticeangle):
        """
        Calculate cell volume: volumecc conventional cell, volumepc, primitive cell.
        """
        a = lattice_constants[0]
        b = lattice_constants[1]
        c = lattice_constants[2]
        c_al = numpy.cos(latticeangle[0])
        c_be = numpy.cos(latticeangle[1])
        c_ga = numpy.cos(latticeangle[2])
        volumecc = a * b * c * numpy.sqrt(1 + 2 * c_al * c_be * c_ga - c_al ** 2 - c_be * 82 - c_ga ** 2)
      
        det = {"P":1, "F":4, "B":2, "R":3, "H":1, "CXY":2, "CYZ":2, "CXZ":2}
        volumepc = volumecc / det[lattice_type]
      
        return volumecc, volumepc


    def transport_distribution(self, directions=['xx'], energy_window=None, Om_mesh=[0.0], beta=40.0, with_Sigma=False, n_om=None, broadening=0.0):
        """
        calculate Tr A(k,w) v(k) A(k, w+Om) v(k).
        energy_window: regime for omega integral
        Om_mesh: mesh for optic conductivitity. Om_mesh is repinned to the self-energy mesh!
        directions: list of directions: xx,yy,zz,xy,yz,zx. 
        with_Sigma: Use Sigma_w = 0 if False (In this case it is necessary to specifiy the energywindow (energy_window),
        the number of omega points (n_om) in the window and the broadening (broadening)).
        """
       
        # Check if wien converter was called and read transport subgroup form hdf file
        if mpi.is_master_node():
            ar = HDFArchive(self.hdf_file, 'a')
            if not (self.transp_data in ar): raise IOError, "transport_distribution: No %s subgroup in hdf file found! Call convert_transp_input first." %self.transp_data
        self.read_transport_input_from_hdf()
        
        if mpi.is_master_node():
            # k-dependent-projections.
            assert self.k_dep_projection == 1, "transport_distribution: k dependent projection is not implemented!"
            # positive Om_mesh
            assert all(Om >= 0.0 for Om in Om_mesh), "transport_distribution: Om_mesh should not contain negative values!"

        # Check if energy_window is sufficiently large and correct

        if (energy_window[0] >= energy_window[1] or energy_window[0] >= 0 or energy_window[1] <= 0):
            assert 0, "transport_distribution: energy_window wrong!"

        if (abs(self.fermi_dis(energy_window[0]*beta)*self.fermi_dis(-energy_window[0]*beta)) > 1e-5
            or abs(self.fermi_dis(energy_window[1]*beta)*self.fermi_dis(-energy_window[1]*beta)) > 1e-5):
                mpi.report("\n####################################################################")
                mpi.report("transport_distribution: WARNING - energy window might be too narrow!")
                mpi.report("####################################################################\n")

        n_inequiv_spin_blocks = self.SP + 1 - self.SO  # up and down are equivalent if SP = 0
        self.directions = directions
        dir_to_int = {'x':0, 'y':1, 'z':2}
            
        # calculate A(k,w)
        #######################################
        
        # Define mesh for Greens function and in the specified energy window
        if (with_Sigma == True):
            self.omega = numpy.array([round(x.real,12) for x in self.Sigma_imp_w[0].mesh])
            mesh = None
            mu = self.chemical_potential
            n_om = len(self.omega)
            mpi.report("Using omega mesh provided by Sigma!")

            if energy_window is not None:
                # Find according window in Sigma mesh
                ioffset = numpy.sum(self.omega < energy_window[0]-max(Om_mesh))
                self.omega = self.omega[numpy.logical_and(self.omega >= energy_window[0]-max(Om_mesh), self.omega <= energy_window[1]+max(Om_mesh))]
                n_om = len(self.omega)
                
                # Truncate Sigma to given omega window
		        # In the future there should be an option in gf to manipulate the mesh (e.g. truncate) directly.
		        # For now we stick with this: 
                for icrsh in range(self.n_corr_shells):
                    Sigma_save = self.Sigma_imp_w[icrsh].copy()
                    spn = self.spin_block_names[self.corr_shells[icrsh]['SO']]
                    glist = lambda : [ GfReFreq(indices = inner, window=(self.omega[0], self.omega[-1]),n_points=n_om) for block, inner in self.gf_struct_sumk[icrsh]]
                    self.Sigma_imp_w[icrsh] = BlockGf(name_list = spn, block_list = glist(),make_copies=False)
                    for i,g in self.Sigma_imp_w[icrsh]:
                        for iL in g.indices:
                            for iR in g.indices:
                                for iom in xrange(n_om):
                                    g.data[iom,iL,iR] = Sigma_save[i].data[ioffset+iom,iL,iR]             
        else:
            assert n_om is not None, "transport_distribution: Number of omega points (n_om) needed to calculate transport distribution!"
            assert energy_window is not None, "transport_distribution: Energy window needed to calculate transport distribution!"
            assert broadening != 0.0 and broadening is not None, "transport_distribution: Broadening necessary to calculate transport distribution!"
            self.omega = numpy.linspace(energy_window[0]-max(Om_mesh),energy_window[1]+max(Om_mesh),n_om)
            mesh = [energy_window[0]-max(Om_mesh), energy_window[1]+max(Om_mesh), n_om]
            mu = 0.0

        # Define mesh for optic conductivity
        d_omega = round(numpy.abs(self.omega[0] - self.omega[1]), 12)
        iOm_mesh = numpy.array([round((Om / d_omega),0) for Om in Om_mesh])
        self.Om_mesh = iOm_mesh * d_omega

        if mpi.is_master_node():
            print "Chemical potential: ", mu
            print "Using n_om = %s points in the energy_window [%s,%s]"%(n_om, self.omega[0], self.omega[-1]),
            print "where the omega vector is:"
            print self.omega
            print "Calculation requested for Omega mesh:   ", numpy.array(Om_mesh)
            print "Omega mesh automatically repinned to:  ", self.Om_mesh
        
        self.Gamma_w = {direction: numpy.zeros((len(self.Om_mesh), n_om), dtype=numpy.float_) for direction in self.directions}
        
        # Sum over all k-points
        ikarray = numpy.array(range(self.n_k))
        for ik in mpi.slice_array(ikarray):
            # Calculate G_w  for ik and initialize A_kw
            G_w = self.lattice_gf(ik, mu, iw_or_w="w", beta=beta, broadening=broadening, mesh=mesh, with_Sigma=with_Sigma)
            A_kw = [numpy.zeros((self.n_orbitals[ik][isp], self.n_orbitals[ik][isp], n_om), dtype=numpy.complex_) 
				for isp in range(n_inequiv_spin_blocks)]
            
            for isp in range(n_inequiv_spin_blocks):
                # Obtain A_kw from G_w (swapaxes is used to have omega in the 3rd dimension)
                A_kw[isp].real = -copy.deepcopy(G_w[self.spin_block_names[self.SO][isp]].data.swapaxes(0,1).swapaxes(1,2)).imag / numpy.pi 
                b_min = max(self.band_window[isp][ik, 0], self.band_window_optics[isp][ik, 0])
                b_max = min(self.band_window[isp][ik, 1], self.band_window_optics[isp][ik, 1])
                A_i = slice(b_min - self.band_window[isp][ik, 0], b_max - self.band_window[isp][ik, 0] + 1)
                v_i = slice(b_min - self.band_window_optics[isp][ik, 0], b_max - self.band_window_optics[isp][ik, 0] + 1)
                
                # loop over all symmetries
                for R in self.rot_symmetries:
                    # get transformed velocity under symmetry R
                    vel_R = copy.deepcopy(self.velocities_k[isp][ik])
                    for nu1 in range(self.band_window_optics[isp][ik, 1] - self.band_window_optics[isp][ik, 0] + 1):
                        for nu2 in range(self.band_window_optics[isp][ik, 1] - self.band_window_optics[isp][ik, 0] + 1):
                            vel_R[nu1][nu2][:] = numpy.dot(R, vel_R[nu1][nu2][:])
                    
                    # calculate Gamma_w for each direction from the velocities vel_R and the spectral function A_kw
                    for direction in self.directions:
                        for iw in xrange(n_om):
                            for iq in range(len(self.Om_mesh)):
                                if(iw + iOm_mesh[iq] >= n_om or self.omega[iw] < -self.Om_mesh[iq] + energy_window[0] or self.omega[iw] > self.Om_mesh[iq] + energy_window[1]): continue
                                self.Gamma_w[direction][iq, iw] += (numpy.dot(numpy.dot(numpy.dot(vel_R[v_i, v_i, dir_to_int[direction[0]]], 
                                                                    A_kw[isp][A_i, A_i, iw]), vel_R[v_i, v_i, dir_to_int[direction[1]]]), 
                                                                    A_kw[isp][A_i, A_i, iw + iOm_mesh[iq]]).trace().real * self.bz_weights[ik])
        
	for direction in self.directions: 
            self.Gamma_w[direction] = (mpi.all_reduce(mpi.world, self.Gamma_w[direction], lambda x, y : x + y) 
					/ self.cellvolume(self.lattice_type, self.lattice_constants, self.lattice_angles)[1] / self.n_symmetries)

        
    def transport_coefficient(self, direction, iq=0, n=0, beta=40):
        """
        calculates the transport coefficients A_n in a given direction and for a given Omega. (see documentation)
        A_1 is set to nan if requested for Omega != 0.0
        iq: index of Omega point in Om_mesh
        direction: 'xx','yy','zz','xy','xz','yz'
        """
        if not (mpi.is_master_node()): return
        
        assert hasattr(self,'Gamma_w'), "transport_coefficient: Run transport_distribution first or load data from h5!"
        A = 0.0
        omegaT = self.omega * beta
        d_omega = self.omega[1] - self.omega[0]
        if (self.Om_mesh[iq] == 0.0):
            for iw in xrange(self.Gamma_w[direction].shape[1]):
                A += self.Gamma_w[direction][iq, iw] * self.fermi_dis(omegaT[iw]) * self.fermi_dis(-omegaT[iw]) * numpy.float(omegaT[iw])**n * d_omega
        elif (n == 0.0):
            for iw in xrange(self.Gamma_w[direction].shape[1]):
                A += (self.Gamma_w[direction][iq, iw] * (self.fermi_dis(omegaT[iw]) - self.fermi_dis(omegaT[iw] + self.Om_mesh[iq] * beta)) 
                     / (self.Om_mesh[iq] * beta) * d_omega)
        else:
                A = numpy.nan
        return A *  numpy.pi * (2.0-self.SP)

    
    def conductivity_and_seebeck(self, beta=40):
        """
        Calculates the Seebeck coefficient and the conductivity for a given Gamma_w
        """    
        if not (mpi.is_master_node()): return
    
        assert hasattr(self,'Gamma_w'), "conductivity_and_seebeck: Run transport_distribution first or load data from h5!"
        n_q = self.Gamma_w[self.directions[0]].shape[0]
        
        A0 = {direction: numpy.full((n_q,),numpy.nan) for direction in self.directions}              
        A1 = {direction: numpy.full((n_q,),numpy.nan) for direction in self.directions}
        self.seebeck = {direction: numpy.nan for direction in self.directions}
        self.optic_cond = {direction: numpy.full((n_q,),numpy.nan) for direction in self.directions}
        
        for direction in self.directions:
            for iq in xrange(n_q):
                A0[direction][iq] = self.transport_coefficient(direction, iq=iq, n=0, beta=beta)
                A1[direction][iq] = self.transport_coefficient(direction, iq=iq, n=1, beta=beta)
                print "A_0 in direction %s for Omega = %.2f    %e a.u." % (direction, self.Om_mesh[iq], A0[direction][iq])
                print "A_1 in direction %s for Omega = %.2f    %e a.u." % (direction, self.Om_mesh[iq], A1[direction][iq])
                if ~numpy.isnan(A1[direction][iq]):
                    # Seebeck is overwritten if there is more than one Omega = 0 in Om_mesh
                    self.seebeck[direction] = - A1[direction][iq] / A0[direction][iq] * 86.17
            self.optic_cond[direction] = beta * A0[direction] * 10700.0 / numpy.pi
            for iq in xrange(n_q):
               print "Conductivity in direction %s for Omega = %.2f       %f  x 10^4 Ohm^-1 cm^-1" % (direction, self.Om_mesh[iq], self.optic_cond[direction][iq])
               if not (numpy.isnan(A1[direction][iq])):
                    print "Seebeck in direction      %s for Omega = 0.00      %f  x 10^(-6) V/K" % (direction, self.seebeck[direction])
          

    def fermi_dis(self, x):
        """
        fermi distribution at x = omega * beta
        """
        return 1.0/(numpy.exp(x)+1)