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path_gqt2.py
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path_gqt2.py
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#!/usr/bin/env python
# @Copyright 2024 Kristjan Haule
Parallel = True
if Parallel :
from mpi4py import MPI
comm = MPI.COMM_WORLD
msize = comm.Get_size()
mrank = comm.Get_rank()
master=0
else:
msize = 1
mrank = 0
master = 0
import sys, os, re
from datetime import date
from numpy import *
from numpy import linalg
from timeit import default_timer as timer
from scipy import optimize
import itertools
from functools import reduce
from numba import jit
#from numba.typed import List
from scipy import special
import subprocess, shutil
import pickle
import glob
#from numpy import unravel_index
from fractions import Fraction
from math import gcd
from cmn import Ry2H,H2eV,Ry2eV,H2Ry,Br2Ang
#from inout import InOut
from kqmesh import KQmesh
import mcommon as mcmn
from kohnsham import KohnShamSystem
from planewaves import PlaneWaves
#from matel2band import MatrixElements2Band
#from productbasis import ProductBasis
from kweights import Kweights
import gwienfile as w2k
import radials as rd # radial wave functions
import lapwcoeff as lapwc # computes lapw coefficients alm,blm,clm
import gaunt as gn
import for_vxcnn as fvxcn # matrix elements for Vxcn
import sphbes
from pylab import linalg as la
la_matmul = matmul #la.matmul
from pylab import *
import path_gqt3 as pg3
def PrintM(A, file=sys.stdout):
ni,nj = shape(A)
for i in range(ni):
for j in range(nj):
print('%6.3f '% A[i,j], end='',file=file)
print(file=file)
def Read_klist(fname):
fg = open(fname, 'r')
name_kpoints={}
kpoints=[]
dx = 10
for il,line in enumerate(fg):
if line[:3]=='END': break
name = line[:10].split()
#FORMAT(A10,4I10,3F5.2,A3) KNAME(kindex), ISX, ISY, ISZ, IDV, WEIGHT(kindex), E1, E2, IPGR(kindex)
#FORMAT(A10,4I5,3F5.2,A3) KNAME(kindex), ISX, ISY, ISZ, IDV, WEIGHT(kindex), E1, E2, IPGR(kindex)
if il==0:
if len(line[20:30].split()) > 1: dx=5
#print('dx=', dx)
kk = [int(line[10+dx*i:10+dx*(i+1)]) for i in range(4)]
ww = [line[10+dx*4+5*i:10+dx*4+5*(i+1)] for i in range(3)] # weight, e1, e2
kpoints.append(kk)
if name:
legnd=line.split()[0]
name_kpoints[il]=legnd
return (array(kpoints),name_kpoints)
def Find_EF(case):
scf = open(case+'.scf','r').readlines()
for line in scf[::-1]:
if line[:4]==':FER':
EF = float(line.split()[-1])
return EF
return 0
class Orbitals:
""" Class which can read dmft.indmfl file and set up rotation matrices and local axes for all atoms.
For orbitals which are not in indmfl file, it sets up cubic harmonics in local axis, which is given
in wien2k structure file.
"""
def __init__(self, strc, in1): #, in1_nlomax):
s2 = sqrt(2.)
T2Cs = [[1]]
# pz px py
T2Cp = [ [0,1,0], [1/s2, 0, -1/s2], [-1j/s2, 0, -1j/s2]]
# z2 x2-y2 xz yz xy
T2Cd = [[0,0,1,0,0],[1/s2,0,0,0,1/s2],[0,1/s2,0,-1/s2,0],[0,1j/s2,0,1j/s2,0],[1j/s2,0,0,0,-1j/s2]]
# fz3 fxz2 fyz2 fz(x2-y2) fxyz fx(x2-3y2) fy(3x2-y2)
T2Cf = [[0,0,0,1,0,0,0],[0,0,1/s2,0,-1/s2,0,0],[0,0,1j/s2,0,1j/s2,0,0],[0,1/s2,0,0,0,1/s2,0],[0,1j/s2,0,0,0,-1j/s2,0],[1/s2,0,0,0,0,0,-1/s2],[1j/s2,0,0,0,0,0,1j/s2]]
self.S2C_T = [ array(T2Cs).T, array(T2Cp).T, array(T2Cd).T, array(T2Cf).T]
self.S2C_N = [['s'],['pz','px','py'],['z2','x2-y2','xz','yz','xy'],['fz3','fxz2','fyz2','fz(x2-y2)','fxyz','fx(x2-3y2)','fy(3x2-y2)']]
self.aname = []
for iat in range(len(strc.mult)):
nam = strc.aname[iat].split()[0] # If space appears in struct file, such name is not working in wannier90, so remove anything after space.
if strc.mult[iat]==1:
self.aname.append( nam )
else:
self.aname += [ nam+str(ieq+1) for ieq in range(strc.mult[iat])]
if in1.nlomax > 0:
# If we have local orbitals, we will increase np_lo to 2
self.np_lo = 2
else:
self.np_lo = 1
def ReadIndmflFile(self, case):
def divmodulo(x,n):
"We want to take modulo and divide in fortran way, so that it is compatible with fortran code"
return ( sign(x)* int(abs(x)/n) , sign(x)*mod(abs(x),n))
fi = open(case+'.indmfl','r')
lines = fi.readlines()
fi.close()
lines = [line.split('#')[0].strip() for line in lines] # strip comments
lines = [line for line in lines if line] # strip blank lines & create generator expression
itr=0
dat = lines[itr].split(); itr+=1
#print('dat=', dat)
hybr_emin, hybr_emax, Qrenorm, projector = float(dat[0]), float(dat[1]), int(dat[2]), int(dat[3])
dat = lines[itr].split(); itr+=1
#print('dat=', dat)
matsubara, broadc, broadnc, om_npts, om_emin, om_emax = int(dat[0]), float(dat[1]), float(dat[2]), int(dat[3]), float(dat[4]), float(dat[5])
if projector>=5:
hybr_emin = int(hybr_emin)
hybr_emax = int(hybr_emax)
self.atoms={}
self.icix={}
self.rotloc={}
self.Lsa=[]
self.icixa=[]
natom = int(lines[itr]); itr+=1
for i in range(natom):
dat=lines[itr].split()
itr+=1
iatom, nL, locrot_shift = [int(x) for x in dat[:3]]
Rmt2=0
if len(dat)>3:
Rmt2 = float(dat[3])
(shift,locrot) = divmodulo(locrot_shift,3)
if locrot<0:
if locrot==-2:
locrot=3*nL
else:
locrot=3
Ls, qsplits, icx = zeros(nL,dtype=int), zeros(nL,dtype=int), zeros(nL,dtype=int)
for il in range(nL):
(Ls[il], qsplits[il], icx[il]) = map(int, lines[itr].split()[:3])
itr+=1
self.Lsa.append( Ls )
self.icixa.append( icx )
new_xyz=[]
for loro in range(abs(locrot)):
new_xyz.append( [float(x) for x in lines[itr].split()] )
itr += 1
if new_xyz:
self.rotloc[iatom-1] = new_xyz
shift_vec = None
if shift:
shift_vec = [float(x) for x in lines[itr].split()]
itr += 1
#print( 'new_xyz=', new_xyz)
#print( 'shift_vec=', shift_vec)
#self.locrot[iatom-1] = (locrot, shift)
self.atoms[iatom-1] = (nL, locrot_shift, shift_vec, Rmt2)
for ix, L, qsplit in zip(icx, Ls, qsplits):
if ix in self.icix:
self.icix[ix] += [(iatom-1, L, qsplit)]
else:
self.icix[ix] = [(iatom-1, L, qsplit)]
self.legends={}
self.legend={}
self.siginds={}
self.cftrans={}
# read the big block of siginds and cftrans
ncp, maxdim, maxsize = [int(e) for e in lines[itr].split()]
itr+=1
for i in range(ncp):
icp, dim, size = [int(e) for e in lines[itr].split()]
itr+=1
self.legends[icp] = lines[itr].split("'")[1::2]
#print('legends=', self.legends[icp])
(iatom,l,qsplit) = self.icix[icp][0]
self.legend[(iatom,l)] = self.legends[icp]
#print('legend[('+str(iatom)+','+str(l)+')]=',self.legend[(iatom,l)])
itr+=1
sigi=[]
for row in range(dim):
sigi.append([int(e) for e in lines[itr].split()])
itr+=1
self.siginds[icp] = array(sigi,dtype=int)
raw_cftrans=[]
for row in range(dim):
raw_cftrans.append([float(e) for e in lines[itr].split()])
itr+=1
raw_cftrans=array(raw_cftrans)
self.cftrans[icp] = raw_cftrans[:,0::2] + raw_cftrans[:,1::2]*1j
#print('atoms=', self.atoms)
#print('icix=', self.icix)
#print('rotloc=', self.rotloc)
#print('Lsa=', self.Lsa)
#print('icixa=', self.icixa)
#print('legends=', self.legends)
#print('sigind=', self.siginds)
#print('cftrans=', self.cftrans)
def FromIndmfl(self):
ndf = len(self.aname)
#ndf = sum(strc.mult)
np_lo = self.np_lo
ip_lo=0
orbts=[]
CFx={}
Sigind={}
for icx in self.icix:
cixs = self.icix[icx]
sigind = self.siginds[icx]
cFx = self.cftrans[icx]
#print('Sigind=', sigind)
ii=0
for x in cixs:
idf,l = x[0:2]
orb = [idf + ndf*ip_lo + ndf*np_lo*(l**2 + mr) for mr in range(2*l+1) if sigind[ii+mr,ii+mr]]
orbts += orb
#print('idf=', idf, 'l=', l, 'ip_lo=', ip_lo, 'ndf=', ndf, 'ind=', orb)
CFx[(idf,l)]=cFx
#print('l=', l, 'ii=', ii, 'sigind=', sigind)
Sigind[(idf,l)]= [sigind[ii+mr,ii+mr] for mr in range(2*l+1)]
ii+=2*l+1
return (orbts, CFx)
def Convert_iorb2text(self, orbs):
lmaxp1 = 4
ndf = len(self.aname)
#print('nn=', lmaxp1**2*self.np_lo*ndf, 'lmaxp1=', lmaxp1, 'np_lo=', self.np_lo, 'ndf=', ndf)
names = zeros( (lmaxp1**2,self.np_lo,ndf), dtype=(unicode_, 20))
for l in range(lmaxp1):
for m in range(-l,l+1):
lm = l**2 + l + m
for idf in range(ndf):
mr_name = str(l+m+1)
#print('(idf,l)=', (idf,l), 'keys=', self.legend.keys())
if (idf,l) in self.legend:
mr_name = self.legend[(idf,l)][l+m]
#print('mr_name=',mr_name)
nm1 = self.aname[idf]+':l='+str(l)+',mr='+mr_name
names[lm,0,idf] = nm1
if self.np_lo>1 :
nm2 = self.aname[idf]+':l='+str(l)+',mr='+mr_name #+',r=2'
names[lm,1,idf] = nm2
names = reshape(names, lmaxp1**2*self.np_lo*ndf)
#for i in range(len(names)):
# print('names['+str(i)+']=', names[i])
#print('orbs=', orbs)
#print('nl_lo=', self.np_lo, 'N=', lmaxp1**2*self.np_lo*ndf)
orb_names = [names[i] for i in orbs]
return orb_names
def FindRelevantOrbitals(self,nbs,nbe,k_ind,rotloc,strc,latgen,ks,kqm,pw,in1,radf,fout,debug=False):
lmaxp1 = min(4,in1.nt)
lomaxp1 = shape(in1.nlo)[0]
ndf = sum(strc.mult)
if in1.nlomax > 0:
# If we have local orbitals, we will increase np_lo to 2
self.np_lo = 2
else:
self.np_lo = 1
alfr = zeros((nbe-nbs,lmaxp1**2,self.np_lo,ndf), dtype=complex)
asmr = zeros((lmaxp1**2*self.np_lo*ndf), dtype=float)
self.largest_ilo = -ones((ndf,lomaxp1),dtype=int)
nextra=0
orbs=[]
for iik,ik in enumerate(k_ind):
kil = ks.klist[ik]
Aeigk = array(ks.all_As[ik][nbs:nbe,:], dtype=complex) # eigenvector from vector file
#alm,blm,clm = lapwc.gap2_set_lapwcoef(kil, ks.indgkir[ik], 1, True, ks.nv[ik], pw.gindex, radf.abcelo[0], strc.rmt, strc.vpos, strc.mult, radf.umt[0], rotloc, latgen.trotij, latgen.Vol, kqm.k2cartes, in1.nLO_at, in1.nlo, in1.lapw, in1.nlomax)
timat_ik, tau_ik = identity(3), array([0,0,0])
alm,blm,clm = lapwc.dmft1_set_lapwcoef(False,1,True,kil,kil,timat_ik,tau_ik,ks.indgkir[ik],ks.nv[ik],pw.gindex,radf.abcelo[0],strc.rmt,strc.vpos,strc.mult,radf.umt[0],
rotloc,latgen.rotij,latgen.tauij,latgen.Vol,kqm.k2cartes,in1.nLO_at,in1.nlo,in1.lapw,in1.nlomax)
(ngi,nLOmax,ntnt,ndf) = shape(clm)
(ngk,ntnt,ndf) = shape(alm)
(nbmax,ngi2) = shape(Aeigk)
# And now change alm,blm,clm to band basis, which we call alfa,beta,gama
alfa = reshape( la_matmul(Aeigk, reshape(alm, (ngk,ntnt*ndf)) ), (nbmax,ntnt,ndf) )
if self.np_lo > 1:
beta = reshape( la_matmul(Aeigk, reshape(blm, (ngi,ntnt*ndf)) ), (nbmax,ntnt,ndf) )
gama = reshape( la_matmul(Aeigk, reshape(clm, (ngi,ntnt*ndf*nLOmax)) ), (nbmax,nLOmax,ntnt,ndf) )
idf2iat = concatenate([[iat]*strc.mult[iat] for iat in range(strc.nat)])
for idf in range(ndf):
iat = idf2iat[idf]
for l in range(lomaxp1):
r = zeros(in1.nLO_at[l,iat])
for ilo in range(in1.lapw[l,iat],in1.nLO_at[l,iat]):
s2 = radf.umtlo[0,iat,l,ilo,2] # <u_l|u_lo>
s3 = radf.umtlo[0,iat,l,ilo,3] # <udot_l|u_lo>
alfa[:,l**2:(l+1)**2,idf] += s2 * gama[:,ilo,l**2:(l+1)**2,idf] #
cg = sqrt(1-s2**2)
cb = s3/cg
gama[:,ilo,l**2:(l+1)**2,idf] = cg*gama[:,ilo,l**2:(l+1)**2,idf] + cb*beta[:,l**2:(l+1)**2,idf]
if iik==0: r[ilo] = sum(abs(gama[:,ilo,l**2:(l+1)**2,idf])**2)
if iik==0 and in1.nLO_at[l,iat]:
print('idf=', idf, 'l=', l, 'ilo=', ilo, 'r=', r, file=fout)
self.largest_ilo[idf,l] = argmax(r)
print('largest_ilo[idf='+str(idf)+',l='+str(l)+']='+str(self.largest_ilo[idf,l]), file=fout)
for idf in range(ndf):
for l in range(lmaxp1):
alfr[:,l**2:(l+1)**2,0,idf] = alfa[:,l**2:(l+1)**2,idf] @ self.S2C_T[l].T
if self.largest_ilo[idf,l]>=0 :
ilo = self.largest_ilo[idf,l]
alfr[:,l**2:(l+1)**2,1,idf] = gama[:,ilo,l**2:(l+1)**2,idf] @ self.S2C_T[l].T
alfr = reshape(alfr,(nbmax,lmaxp1**2*self.np_lo*ndf))
asm = sum(abs(alfr)**2, axis=0)
asmr += asm
alfr = reshape(alfr,(nbmax,lmaxp1**2,self.np_lo,ndf))
ind = sorted( range(len(asm)), key=lambda x: -asmr[x] )
#print('nbmax=', nbmax, 'ind=', ind)
orbs = ind[:nbmax]
#print('orbs=', orbs)
#print('nn=', lmaxp1**2*self.np_lo*ndf, 'lmaxp1=', lmaxp1, 'np_lo=', self.np_lo, 'ndf=', ndf)
#print('orbitals to be used in projection to wanniers=', orbs, file=fout)
orb_names = self.Convert_iorb2text(orbs)
#for i in range(len(orb_names)):
# print(i,orb_names[i], file=fout)
#print('w=', asmr[orbs])
#for ii,i in enumerate(orbs):
# print(ii,i,asmr[i])
return (orbs, orb_names, asmr[orbs])
def Compute_and_Save_Projection_amn(nbs,nbe,rotloc,k_ind, case, orbits, orbs, CFx, strc, latgen, ks, kqm, pw, in1, radf, fout, debug=False):
fo_amn = open(case+'.amn', 'w')
print('# code path_gqt2py', date.today().strftime("%B %d, %Y"), file=fo_amn)
print(nbe-nbs, len(k_ind), len(orbs), orbits.Convert_iorb2text(orbs), file=fo_amn)
tfo_amn = open(case+'.amn2', 'w')
print('# code path_gqt2py', date.today().strftime("%B %d, %Y"), file=tfo_amn)
lmaxp1 = min(4,in1.nt)
lomaxp1 = shape(in1.nlo)[0]
ndf = sum(strc.mult)
icartes2f = linalg.inv(kqm.k2icartes)
print('icartes2f=', icartes2f, file=fout)
#if in1.nlomax > 0:
# # If we have local orbitals, we will increase np_lo to 2
# self.np_lo = 2
#else:
# self.np_lo = 1
self_np_lo = orbits.np_lo
largest_ilo = -ones((ndf,lomaxp1),dtype=int)
alfr = zeros((nbe-nbs,lmaxp1**2,self_np_lo,ndf), dtype=complex)
asmr = zeros((lmaxp1**2*self_np_lo*ndf), dtype=float)
print('The singular values of projection to bands <chi|psi>: ', file=fout)
DMFT1 = True
for iik,ik in enumerate(k_ind):#range(len(kqm.klist)):
kil = ks.klist[ik]
Aeigk = array(ks.all_As[ik][nbs:nbe,:], dtype=complex) # eigenvector from vector file
if DMFT1:
timat_ik, tau_ik = identity(3), array([0,0,0])
alm,blm,clm = lapwc.dmft1_set_lapwcoef(False,1,True,kil,kil,timat_ik,tau_ik,ks.indgkir[ik],ks.nv[ik],pw.gindex,radf.abcelo[0],strc.rmt,strc.vpos,strc.mult,radf.umt[0],
rotloc,latgen.rotij,latgen.tauij,latgen.Vol,kqm.k2cartes,in1.nLO_at,in1.nlo,in1.lapw,in1.nlomax)
else:
alm,blm,clm = lapwc.gap2_set_lapwcoef(kil, ks.indgkir[ik], 1, True, ks.nv[ik], pw.gindex, radf.abcelo[0], strc.rmt, strc.vpos, strc.mult, radf.umt[0], rotloc, latgen.trotij, latgen.Vol, kqm.k2cartes, in1.nLO_at, in1.nlo, in1.lapw, in1.nlomax)
(ngi,nLOmax,ntnt,ndf) = shape(clm)
(ngk,ntnt,ndf) = shape(alm)
(nbmax,ngi2) = shape(Aeigk)
# And now change alm,blm,clm to band basis, which we call alfa,beta,gama
alfa = reshape( la_matmul(Aeigk, reshape(alm, (ngk,ntnt*ndf)) ), (nbmax,ntnt,ndf) )
# We will use two functions, the head and the orthogonalized local orbital, i.e.,
# |1> == |u_l> and |2>= (|u_lo>-|u_l><u_l|u_lo>)/sqrt(1-<u_l|u_lo>^2)
# Note that <1|2>=0 and <2|2>=1
if self_np_lo > 1:
beta = reshape( la_matmul(Aeigk, reshape(blm, (ngk,ntnt*ndf)) ), (nbmax,ntnt,ndf) )
gama = reshape( la_matmul(Aeigk, reshape(clm, (ngk,ntnt*ndf*nLOmax)) ), (nbmax,nLOmax,ntnt,ndf) )
idf2iat = concatenate([[iat]*strc.mult[iat] for iat in range(strc.nat)])
for idf in range(ndf):
iat = idf2iat[idf]
for l in range(lomaxp1):
r = zeros(in1.nLO_at[l,iat])
for ilo in range(in1.lapw[l,iat],in1.nLO_at[l,iat]):
s2 = radf.umtlo[0,iat,l,ilo,2] # <u_l|u_lo>
s3 = radf.umtlo[0,iat,l,ilo,3] # <udot_l|u_lo>
alfa[:,l**2:(l+1)**2,idf] += s2 * gama[:,ilo,l**2:(l+1)**2,idf] #
cg = sqrt(1-s2**2)
cb = s3/cg
gama[:,ilo,l**2:(l+1)**2,idf] = cg*gama[:,ilo,l**2:(l+1)**2,idf] + cb*beta[:,l**2:(l+1)**2,idf]
if iik==0: r[ilo] = sum(abs(gama[:,ilo,l**2:(l+1)**2,idf])**2)
if iik==0 and in1.nLO_at[l,iat]:
largest_ilo[idf,l] = argmax(r)
for idf in range(ndf):
for l in range(lmaxp1):
S2C_T = orbits.S2C_T[l].T
if (idf,l) in CFx:
S2C_T = CFx[(idf,l)].T
alfr[:,l**2:(l+1)**2,0,idf] = alfa[:,l**2:(l+1)**2,idf] @ S2C_T
if largest_ilo[idf,l]>=0 :
ilo = largest_ilo[idf,l]
alfr[:,l**2:(l+1)**2,1,idf] = gama[:,ilo,l**2:(l+1)**2,idf] @ S2C_T
alfr = reshape(alfr,(nbmax,lmaxp1**2*self_np_lo*ndf))
if iik==0:
asm = sum(abs(alfr)**2, axis=0) # sum over all bands, and just retaining orbital indices asm[iorb]
ind = sorted( range(len(asm)), key=lambda x: -asm[x] )
torbs = ind[:nbe-nbs]
print(nbe-nbs, len(k_ind), len(torbs), orbits.Convert_iorb2text(torbs), file=tfo_amn)
psi_chi = conj(alfr[:,orbs]) # psi_chi[nbnd,norbs] using fancy indexing, just for orbs in the indmfl list
tpsi_chi = conj(alfr[:,torbs]) # psi_chi[nbnd,norbs] using fancy indexing, just for orbs in the indmfl list
#asm = sum(abs(alfr)**2, axis=0) # sum over all bands, and just retaining orbital indices asm[iorb]
#asmr += asm
alfr = reshape(alfr,(nbmax,lmaxp1**2,self_np_lo,ndf))
for n in range(len(orbs)):
for m in range(nbmax):
print('%4d%4d %5d %25.12f%25.12f' % (m+1, n+1, iik+1, psi_chi[m,n].real, psi_chi[m,n].imag), file=fo_amn)
for n in range(len(torbs)):
for m in range(nbmax):
print('%4d%4d %5d %25.12f%25.12f' % (m+1, n+1, iik+1, tpsi_chi[m,n].real, tpsi_chi[m,n].imag), file=tfo_amn)
u, s, vh = linalg.svd(psi_chi, full_matrices=True) # uv[nbnd,norb]
print('SVD: ik=%3d'%ik, 'k=(%5.3f,%5.3f,%5.3f)' % tuple(icartes2f@kil), 's=', list(s), file=fout)
fo_amn.close()
tfo_amn.close()
def Compute_and_Save_BandOverlap_Mmn(pairs, pair_umklap, s_distances, s_idistance,nbs,nbe,s_Irredk, case, strc, latgen, ks, kqm, pw, in1, radf, fout, DMFT1=False, debug=False):
def FindInArray(ang, angles):
for ii,a in enumerate(angles):
if linalg.norm(ang-a) < 1e-6:
return ii
return -1
nspin,isp=1,0 # need to do further work for magnetic type calculation
maxlp1 = min(in1.nt,7)
# We are creating a product-like basis, which is serving the plane wave expansion e^{-i*b*r} = 4*pi*i^l * j_l(|b|*r) Y_{lm}^*(-b) Y_{lm}(r), here l is big_l, and |b| is distance
big_l = array([repeat( range(maxlp1), len(s_distances)) for iat in range(strc.nat)]) # index for l [0,0,0,1,1,1,....] each l is repeated as many times as there are distances.
big_d = array([concatenate([ list(range(len(s_distances))) for i in range(maxlp1)]) for iat in range(strc.nat)]) # index for distances
print('big_l for using GW projection <u_big_l|psi^*_{k-q}psi_k>', file=fout)
for iat in range(strc.nat):
for irm in range(len(big_l[iat])):
print(irm, 'iat=', iat, 'l=', big_l[iat,irm], 'id=', big_d[iat,irm], file=fout)
j_l_br = [[ [] for irm in range(len(big_l[iat]))] for iat in range(strc.nat)]
for iat in range(strc.nat):
rp, dh, npt = strc.radial_mesh(iat) # logarithmic radial mesh
for irm,L in enumerate(big_l[iat,:]):
ab = s_distances[big_d[iat,irm]] # this is |b|
ur = special.spherical_jn(L,ab*rp) # j_l(|b|r)
j_l_br[iat][irm] = ur # saving j_l(|b|r)
lomaxp1 = shape(in1.nlo)[0]
num_radial=[]
for iat in range(strc.nat):
tnum_radial = 2*in1.nt
for l in range(lomaxp1):
tnum_radial += len(in1.nLO_at_ind[iat][l])
num_radial.append(tnum_radial)
# Computing all necessary radial integrals <j_lb(br)|u_l2 u_l1>
s3r = zeros( (len(big_l[0]),amax(num_radial),amax(num_radial),strc.nat), order='F' )
for iat in range(strc.nat):
rp, dh, npt = strc.radial_mesh(iat) # logarithmic radial mesh
rwf_all = []
lrw_all = []
# ul functions
for l in range(in1.nt):
rwf_all.append( (radf.ul[isp,iat,l,:npt],radf.us[isp,iat,l,:npt]) )
lrw_all.append((l,1))
# energy derivative ul_dot functions
for l in range(in1.nt):
rwf_all.append( (radf.udot[isp,iat,l,:npt],radf.usdot[isp,iat,l,:npt]) )
lrw_all.append((l,2))
# LO local orbitals
for l in range(lomaxp1):
for ilo in in1.nLO_at_ind[iat][l]:
rwf_all.append( (radf.ulo[isp,iat,l,ilo,:npt],radf.uslo[isp,iat,l,ilo,:npt]) )
lrw_all.append((l,3))
# now performing the integration
for ir2 in range(len(lrw_all)):
l2, it2 = lrw_all[ir2]
a2, b2 = rwf_all[ir2]
for ir1 in range(ir2+1):
l1, it1 = lrw_all[ir1]
a1, b1 = rwf_all[ir1]
a3 = a1[:] * a2[:] #/ rp[:]
b3 = b1[:] * b2[:] #/ rp[:]
for irm in range(len(big_l[iat])): # over all product functions
L = big_l[iat,irm] # L of the product function
if L < abs(l1-l2) or L > (l1+l2): continue # triangular inequality violated
## s3r == < u-product-basis_{irm}| u_{a1,l1} u_{a2,l2} >
rint = rd.rint13g(strc.rel, j_l_br[iat][irm], j_l_br[iat][irm], a3, b3, dh, npt, strc.r0[iat])
#print('ir2=', ir2, 'ir1=', ir1, 'irm=', irm, 'int=', rint)
s3r[irm,ir1,ir2,iat] = rint
s3r[irm,ir2,ir1,iat] = rint
if True:
orb_info = [' core',' u_l ','u_dot',' lo ']
print((' '*5)+'Integrals <j_L(br)| u_(l1)*u_(l2)> for atom %10s' % (strc.aname[iat],), file=fout)
print((' '*13)+'N L l1 u_ l2 u_ <v | u*u>', file=fout)
for irm in range(len(big_l[iat])): # over all product functions
L = big_l[iat,irm] # L of the product function
for ir2 in range(len(lrw_all)):
l2, it2 = lrw_all[ir2]
for ir1 in range(ir2+1):
l1, it1 = lrw_all[ir1]
if abs(s3r[irm,ir1,ir2,iat])>1e-10:
print(('%4d%4d'+(' '*2)+('%4d'*3)+' %s%4d %s%19.11e') % (ir1,ir2,irm,L,l1,orb_info[it1],l2,orb_info[it2],s3r[irm,ir1,ir2,iat]), file=fout)
nmix = array([ maxlp1*len(s_distances) for iat in range(strc.nat)], dtype=int)
loctmatsize = sum([sum([(2*L+1)*strc.mult[iat] for L in big_l[iat]]) for iat in range(strc.nat)])
ncore = zeros(strc.nat, dtype=int) # we do not care about core here, so just set to zero
cgcoef = gn.cmp_all_gaunt(in1.nt) # gaunt coefficients
cfac = [] # precompute 4*pi*(-i)^l, but we repeat the entry (2*lb+1) times, because of degeneracy with respect to m
for lb in range(maxlp1):
cfac += [4*pi*(-1j)**lb] * (2*lb+1)
cfac = array(cfac)
(nnkp, nntot) = len(pairs),len(pairs[0])
G_umklap = zeros(3,dtype=int)
# It turns out there are only a few possible angles Y_lm(b), for which Y_lm needs to be evaluates
# We first find all possible angles of vector b.
b_angles = []
b_pair = zeros((nnkp,nntot), dtype=int)
for iik,ik in enumerate(pairs):
for i in range(len(pairs[ik])):
jk = pairs[ik][i]
k1 = array(ks.klist[ik])
k2 = array(ks.klist[jk])
if s_Irredk:
G_umklap = dot(kqm.k2icartes, pair_umklap[iik,i,:]) # umklap G
b = k2-k1+G_umklap # |k2-k1| is distance between the two k-points
ab = linalg.norm(b)
b_ang = zeros(3)
if ab!=0:
b_ang = b/ab
ic = FindInArray( b_ang, b_angles)
if ic<0:
b_pair[iik,i] = len(b_angles)
b_angles.append(b_ang)
else:
b_pair[iik,i] = ic
print('Found the following angles for b=k2-k1 vector:', file=fout)
for i in range(len(b_angles)):
print(i, b_angles[i], file=fout)
idf = -1
imm = -1
ndf = sum(strc.mult)
Ylmb = zeros((ndf,len(b_angles), maxlp1**2), dtype=complex)
for iat in range(strc.nat):
for ieq in range(strc.mult[iat]):
idf += 1
Ttot = strc.rotloc[iat,:,:] @ latgen.trotij[idf,:,:].T @ kqm.k2cartes[:,:] # All transformations that we need to evaluate Y_lm(b)
for i,b in enumerate(b_angles):
Ylmb[idf,i,:] = sphbes.ylm( dot(Ttot, -b), maxlp1-1)*cfac # 4*pi(-i)^l * Y_lm(-b), which is e^{-i*b*r}/Y^*_{lm}(r)
mpwipw = zeros((1,len(pw.ipwint)),dtype=complex) # will contain Integrate[e^{iG*r},{r in interstitials}]
mpwipw[0,:] = pw.ipwint # mpwipw[0,ipw] = <0|G_{ipw}>_{int}=Integrate[e^{i*(G_{ipw}r)},{r in interstitial}]
#print('writing: ', case+'.mmn', file=fout)
#fo_mmn = open(case+'.mmn', 'w')
#print('# code PyGW:wannier.py', date.today().strftime("%B %d, %Y"), file=fo_mmn)
#print(s_nbe-s_nbs, len(kqm.klist), nntot, file=fo_mmn)
V_rmt = 0
for iat in range(strc.nat):
for ieq in range(strc.mult[iat]):
V_rmt += 4*pi*strc.rmt[iat]**3/3
print('V_rmt/V=', V_rmt/latgen.Vol, 'V_I/V=', 1-V_rmt/latgen.Vol, 'V_rmt=', V_rmt, 'V=', latgen.Vol, file=fout)
ikstart,ikend,sendcounts,displacements = mcmn.mpiSplitArray(mrank, msize, nnkp )
key_pairs = list(pairs.keys())
#print('key_pairs=', key_pairs)
print('processor rank=', mrank, 'with size=', msize, 'will do ikstart=', ikstart, 'ikend=', ikend, 'displacements=',displacements, file=fout)
fout.flush()
M_all=zeros((ikend-ikstart,nntot,nbe-nbs,nbe-nbs),dtype=complex)
#R=zeros((ikend-ikstart,3,nbe-nbs))
idf = -1
for iik in range(ikstart,ikend):
#ibs,ibe = nbs_nbe[iik]
ik = key_pairs[iik]
kil = array(ks.klist[ik]) # kqm.klist[ik,:]/kqm.LCM # k1==kil in semi-cartesian form
if s_Irredk:
# First create alpha, beta, gamma for k
irk = kqm.kii_ind[ik] # the index to the correspodning irreducible k-point
Aeigk = array(ks.all_As[irk][nbs:nbe,:], dtype=complex) # eigenvector from vector file
if not DMFT1:
if kqm.k_ind[irk] != ik: # not irreducible
Aeigk *= exp( 2*pi*1j * ks.phase_arg[ik][:]) # adding phase: e^{i*tau[isym]*(k_irr+G_irr)}, where tau[isym] is the part of the group operation from irreducible to reducible k-point
alm,blm,clm = lapwc.gap2_set_lapwcoef(kil, ks.indgk[ik], 1, True, ks.nv[irk], pw.gindex, radf.abcelo[isp], strc.rmt, strc.vpos, strc.mult, radf.umt[isp], strc.rotloc, latgen.trotij, latgen.Vol, kqm.k2cartes, in1.nLO_at, in1.nlo, in1.lapw, in1.nlomax)
else:
isym = kqm.iksym[ik]
timat_ik, tau_ik = strc.timat[isym,:,:].T, strc.tau[isym,:]
kirr = array(kqm.kirlist[irk,:])/float(kqm.LCM)
alm,blm,clm = lapwc.dmft1_set_lapwcoef(False, 1, True, kil, kirr, timat_ik, tau_ik, ks.indgkir[irk], ks.nv[irk], pw.gindex, radf.abcelo[0], strc.rmt, strc.vpos, strc.mult, radf.umt[0], strc.rotloc, latgen.rotij, latgen.tauij, latgen.Vol, kqm.k2cartes, in1.nLO_at, in1.nlo, in1.lapw, in1.nlomax)
else:
Aeigk = array(ks.all_As[ik][nbs:nbe,:], dtype=complex) # eigenvector from vector file
alm,blm,clm = lapwc.gap2_set_lapwcoef(kil, ks.indgkir[ik], 1, True, ks.nv[ik], pw.gindex, radf.abcelo[isp], strc.rmt, strc.vpos, strc.mult, radf.umt[isp], strc.rotloc, latgen.trotij, latgen.Vol, kqm.k2cartes, in1.nLO_at, in1.nlo, in1.lapw, in1.nlomax)
(ngi,nLOmax,ntnt,ndf) = shape(clm)
(ngi,ntnt,ndf) = shape(alm)
(nbmax,ngi2) = shape(Aeigk)
# And now change alm,blm,clm to band basis, which we call alfa,beta,gama
alfa = reshape( la_matmul(Aeigk, reshape(alm, (ngi,ntnt*ndf)) ), (nbmax,ntnt,ndf) )
beta = reshape( la_matmul(Aeigk, reshape(blm, (ngi,ntnt*ndf)) ), (nbmax,ntnt,ndf) )
if in1.nlomax > 0:
gama = reshape( la_matmul(Aeigk, reshape(clm, (ngi,ntnt*ndf*nLOmax)) ), (nbmax,nLOmax,ntnt,ndf) )
else:
gama = zeros((1,1,1,1),dtype=complex,order='F') # can not have zero size.
if DMFT1 and s_Irredk and kqm.k_ind[irk] != ik: # not irreducible
# For interstitials we need to transform now, because we did not transform the eigenvectors before.
Aeigk *= exp( 2*pi*1j * ks.phase_arg[ik][:]) # phase for reducible: e^{i*tau[isym]*(k_irr+G_irr)}, where tau[isym] is the part of the group operation from irreducible to reducible k-point
if debug:
print('alfa,beta,gama=', file=fout)
for ie in range(shape(alfa)[0]):
for lm in range(shape(alfa)[1]):
print('ie=%3d lm=%3d alfa=%14.10f%14.10f beta=%14.10f%14.10f' % (ie+1,lm+1,alfa[ie,lm,0].real, alfa[ie,lm,0].imag, beta[ie,lm,0].real, beta[ie,lm,0].imag), file=fout)
#M_c = zeros((nntot,ibe-ibs,ibe-ibs),dtype=complex)
for idk,jk in enumerate(pairs[ik]):
#jk = pair[ik,idk]
# M_{m,n} = < psi_{m,k} | e^{-i b r} |psi_{n,k+b}>
# M_{m,n}^* = < psi_{n,k+b}| e^{i b r} |psi_{m,k}>
# M_{m,n}^* = < psi_{n,k-q}| e^{-i q r}|psi_{m,k}> where q=-b. The last form is equivalent to our definition of M matrix element in GW.
# k2 = k1 + b - G_umklap => b = k2-k1+G_umklapp
#kjl = kqm.klist[jk,:]/kqm.LCM # k2==kjl=k+b in semi-cartesian form
kjl = array(ks.klist[jk])
if s_Irredk:
G_umklap = array(dot(kqm.k2icartes,pair_umklap[iik,idk,:]), dtype=int)
bl = kjl-kil + G_umklap
#aq = linalg.norm(b)
t0 = timer()
if s_Irredk:
jrk = kqm.kii_ind[jk]
# And next create alpha, beta, gamma for k+q
Aeigq = array( conj( ks.all_As[jrk][nbs:nbe,:] ), dtype=complex) # eigenvector from vector file
if not DMFT1:
if kqm.k_ind[jrk] != jk: # the k-q-point is reducible, eigenvector needs additional phase
Aeigq *= exp( -2*pi*1j * ks.phase_arg[jk][:] ) # adding phase e^{-i*tau[isym]*(k_irr+G_irr)}
alm,blm,clm = lapwc.gap2_set_lapwcoef(kjl, ks.indgk[jk], 2, True, ks.nv[jrk], pw.gindex, radf.abcelo[isp], strc.rmt, strc.vpos, strc.mult, radf.umt[isp], strc.rotloc, latgen.trotij, latgen.Vol, kqm.k2cartes, in1.nLO_at, in1.nlo, in1.lapw, in1.nlomax)
else:
kjrr = array(kqm.kirlist[jrk,:])/float(kqm.LCM)
isym = kqm.iksym[jk]
timat_ik, tau_ik = strc.timat[isym].T, strc.tau[isym,:]
alm,blm,clm = lapwc.dmft1_set_lapwcoef(False, 2, True, kjl, kjrr, timat_ik, tau_ik, ks.indgkir[jrk], ks.nv[jrk], pw.gindex, radf.abcelo[0], strc.rmt, strc.vpos, strc.mult, radf.umt[0], strc.rotloc, latgen.rotij, latgen.tauij, latgen.Vol, kqm.k2cartes, in1.nLO_at, in1.nlo, in1.lapw, in1.nlomax)
else:
Aeigq = array( conj( ks.all_As[jk][nbs:nbe,:] ), dtype=complex) # eigenvector from vector file
alm,blm,clm = lapwc.gap2_set_lapwcoef(kjl, ks.indgkir[jk], 2, True, ks.nv[jk], pw.gindex, radf.abcelo[isp], strc.rmt, strc.vpos, strc.mult, radf.umt[isp], strc.rotloc, latgen.trotij, latgen.Vol, kqm.k2cartes, in1.nLO_at, in1.nlo, in1.lapw, in1.nlomax)
(ngj,nLOmax,ntnt,ndf) = shape(clm)
(ngj,ntnt,ndf) = shape(alm)
(nbmax,ngj2) = shape(Aeigq)
# And now change alm,blm,clm to band basis, which we call alfa,beta,gama
alfp = reshape( la_matmul(Aeigq, reshape(alm, (ngj,ntnt*ndf)) ), (nbmax,ntnt,ndf) )
betp = reshape( la_matmul(Aeigq, reshape(blm, (ngj,ntnt*ndf)) ), (nbmax,ntnt,ndf) )
if in1.nlomax > 0:
gamp = reshape( la_matmul(Aeigq, reshape(clm, (ngj,ntnt*ndf*nLOmax)) ), (nbmax,nLOmax,ntnt,ndf) )
else:
gamp = zeros((1,1,1,1),dtype=complex,order='F') # can not have zero size
if debug:
print('alfp,betp,gamp=', file=fout)
for ie in range(shape(alfp)[0]):
for lm in range(shape(alfp)[1]):
print('ie=%3d lm=%3d alfp=%14.10f%14.10f betp=%14.10f%14.10f' % (ie+1,lm+1,alfp[ie,lm,0].real, alfp[ie,lm,0].imag, betp[ie,lm,0].real, betp[ie,lm,0].imag), file=fout)
t1 = timer()
#t_times[0] += t1-t0
### The muffin-tin part : mmat[ie1,ie2,im] = < u^{product}_{im,lb} | psi^*_{ie2,k-q} psi_{ie1,k} > e^{-iq.r_atom} where ie1=[nst,nend] and ie2=[mst,mend]
# mmat_mt[ie1,ie2,im] = <j_l(|b|r)|psi^*_{ie2,k+b} psi_{ie1,k} > e^{i*b.r_atom}
big_L = big_l.T
mmat_mt = fvxcn.calc_minm_mt(-bl,0,nbmax,0,nbmax, alfa,beta,gama,alfp,betp,gamp, s3r, strc.vpos,strc.mult, nmix,big_L, in1.nLO_at,ncore,cgcoef,in1.lmax,loctmatsize)
idf = -1
imm=0
psi_psi = zeros((nbmax,nbmax), dtype=complex)
for iat in range(strc.nat):
for ieq in range(strc.mult[iat]):
idf += 1
for irm in range(nmix[iat]):
lb = big_l[iat,irm] #
dimm = 2*lb+1 # lme-lms
if big_d[iat,irm]==s_idistance[iik,idk]:
lms, lme = lb**2, (lb+1)**2
# Now adding 4*pi(-i)^l * Y_lm(-b) so that we have : psi_psi = 4*pi(-i)^l * Y_lm(-b) <j_l(|b|r)Y_lm(r)|psi^*_{ie2,k+b} psi_{ie1,k} > e^{i*b.r_atom}
# Note that 4*pi*(-i)^l Y_lm(-b) Y_lm(r)^* = 4*pi*i^l*Y_lm(b) * Y^*_lm(r) = e^{i*b*r}
# which is psi_psi = < e^{-i*b*(r+r_atom)} | psi^*_{ie2,k+b} psi_{ie1,k} >
psi_psi += dot(mmat_mt[:,:,imm:imm+dimm], Ylmb[idf,idk,lms:lme])
imm += dimm
if DMFT1 and s_Irredk and kqm.k_ind[jrk] != jk: # the k-q-point is reducible, eigenvector needs additional phase
Aeigq *= exp( -2*pi*1j * ks.phase_arg[jk][:] )
## The interstitial part : mmat[ie1,ie2,im]*sqrt(Vol) = < 1 |psi^*_{ie2} psi_{ie1} > = < e^{i*(G_{im}=0)*r}|psi_{ie2,k+q}^* |psi_{ie1,k}>_{Interstitials}
## mmat[ie1,ie2] = Aeigq[ie2,nvj]^* mpwipw(nvj,nvi) Aeigk.T(nvi,ie1)
i_g0 = pw.convert_ig0_2_array() # Instead of dictionary pw.ig0, which converts integer-G_vector into index in fixed basis, we will use fortran compatible integer array
indggq = array(range(len(pw.gindex)),dtype=int)
if s_Irredk:
nvi, nvj = ks.nv[irk], ks.nv[jrk]
mmat_it = fvxcn.calc_minm_is(0,nbmax,0,nbmax,Aeigk,Aeigq,G_umklap,mpwipw,nvi,nvj,ks.indgk[ik],ks.indgk[jk],indggq,pw.gindex,i_g0,latgen.Vol)
else:
nvi, nvj = ks.nv[ik], ks.nv[jk]
mmat_it = fvxcn.calc_minm_is(0,nbmax,0,nbmax,Aeigk,Aeigq,G_umklap,mpwipw,nvi,nvj,ks.indgkir[ik],ks.indgkir[jk],indggq,pw.gindex,i_g0,latgen.Vol)
## Combine MT and interstitial part together
psi_psi1 = mmat_it[:,:,0]*sqrt(latgen.Vol)
psi_psi3 = psi_psi + psi_psi1
# M_{m,n} = < psi_{m,k} | e^{-i b r} |psi_{n,k+b}>
M_m_n = psi_psi3.conj() # M_{ie1,ie2}=<psi_{ie2,k+q}|psi_{ie1,k}>^*
#print(ik+1,jk+1, '%4d'*3 % tuple(pair_umklap[ik,idk,:]), file=fo_mmn)
#for n in range(len(M_m_n)):
# for m in range(len(M_m_n)):
# print('%18.14f %18.14f' % (M_m_n[m,n].real, M_m_n[m,n].imag), file=fo_mmn)
M_all[iik-ikstart,idk,:,:] = M_m_n
#M_c[idk,:,:] = M_m_n
dst=s_distances[s_idistance[iik,idk]]
if s_Irredk:
print('ik=', ik, 'jk=', jk, 'dst=%.5f'%(dst,), 'irk=', irk, 'jrk=', jrk, 'iik=', kqm.k_ind[irk],'!=', ik, 'jjk=', kqm.k_ind[jrk],'!=', jk, 'b=', bl, 'G_umklap=', G_umklap, '<psi|psi>=', file=fout)
else:
print('ik=', ik, 'jk=', jk, 'dst=%.5f'%(dst,), 'b=', bl, 'G_umklap=', G_umklap, '<psi|psi>=', file=fout)
pg3.PrintMC(M_m_n,file=fout)
if debug:
print(file=fout)
pg3.PrintMC(psi_psi,file=fout)
print(file=fout)
pg3.PrintMC(psi_psi1,file=fout)
#dR=zeros((3,nbe-nbs))
#ds=nbs-ibs
## bands are arranged in [ibs,nbs,nbe,ibe]
#for imu in range(3): # over x,y,z in lattice coordinates
# for i in range(nbs-ibs):
# dR[imu,0] += 0.5*(1.0-sum(abs(M_c[ 2*imu,:,i])**2)) # 1-\sum_m |<psi_{m,k}|psi_{i,k+e_{imu}}>|^2
# dR[imu,0] += 0.5*(1.0-sum(abs(M_c[2*imu+1,:,i])**2)) # 1-\sum_m |<psi_{m,k}|psi_{i,k-e_{imu}}>|^2
# for i in range(nbs-ibs,nbe-ibs):
# dR[imu,i-ds] += 0.5*(1.0-sum(abs(M_c[ 2*imu,:,i])**2)) # 1-\sum_m |<psi_{m,k}|psi_{i,k+e_{imu}}>|^2
# dR[imu,i-ds] += 0.5*(1.0-sum(abs(M_c[2*imu+1,:,i])**2)) # 1-\sum_m |<psi_{m,k}|psi_{i,k-e_{imu}}>|^2
# for i in range(nbe-ibs,ibe-ibs):
# dR[imu,-1] += 0.5*(1.0-sum(abs(M_c[ 2*imu,:,i])**2)) # 1-\sum_m |<psi_{m,k}|psi_{i,k+e_{imu}}>|^2
# dR[imu,-1] += 0.5*(1.0-sum(abs(M_c[2*imu+1,:,i])**2)) # 1-\sum_m |<psi_{m,k}|psi_{i,k-e_{imu}}>|^2
#dR[:,0] /= (nbs-ibs+1)
#dR[:,-1] /= (ibe-nbe+1)
#for imu in range(3):
# # average over (|k+e_{imu}-k|^2 , |k-e_{imu}-k|^2)
# dst=0.5*(s_distances[s_idistance[iik,2*imu]]+s_distances[s_idistance[iik,2*imu+1]])
# dR[imu,:] /= dst**2
#print('bands=', [ibs,nbs,nbe,ibe],file=fout)
#for i in range(0,nbe-nbs): # over all the relevant bands, index i
# print('R[ik='+str(ik)+',i='+str(nbs+i)+']=', dR[:,i].tolist(),file=fout)
#R[iik,:,:]=dR
#M_all=zeros((ikend-ikstart,nntot,nbe-nbs,nbe-nbs),dtype=complex)
if Parallel and msize>1:
if mrank==master:
M_gather=zeros((nnkp,nntot,nbe-nbs,nbe-nbs),dtype=complex)
else:
M_gather=None
dsize = nntot*(nbe-nbs)**2*2
comm.Barrier()
comm.Gatherv(M_all,[M_gather,sendcounts*dsize,displacements*dsize,MPI.DOUBLE], root=master)
if mrank==master:
M_all = M_gather
if mrank==master:
save('M_all.npy', M_all)
# M_{m,n} = < psi_{m,k} | e^{-i b r} |psi_{n,k+b}>
# M_all[k,idir,m,n] ~ <u_m(k)|u_n(k+e_{idir}*small)>
#return M_all
def Save_Eigenvalues(case, ks_Ebnd_isp, nbs, nbe):
fo_eig = open(case+'.eig', 'w')
for ik in range(len(ks_Ebnd_isp)):
for i,ib in enumerate(range(nbs,nbe)):
print(i+1,ik+1, ks_Ebnd_isp[ik,ib]*H2eV, file=fo_eig)
#print(i+1,ik+1, ks_Ebnd_isp[irk,ib], file=fo_eig)
fo_eig.close()
def Shift_to_1BZ(k,ndiv):
" This gives k_{1BZ}-k"
g = zeros(3,dtype=int)
for i in range(3):
if k[i]>0:
g[i]=-int(floor(k[i]/ndiv[i]))
elif k[i]<0:
g[i]=int(ceil(-k[i]/ndiv[i]))
return g
def Find_nbs_nbe(Ebnd, nbs, nbe, pairs, fout):
nbs_nbe=[]
for iik,ik in enumerate(pairs):
nbs_nbe.append( pg3.Find_nbs_nbei(ik, Ebnd, pairs[ik], nbs, nbe, fout) )
return nbs_nbe
def Compute_mmn(nbs,nbe):
nspin = 1
kmr=1 # if we want to increase the G-mesh as compared to case.in1 RKmax
pwm=2 # plane wave mesh parameter
(case,fout) = pg3.Initialize('a')
npair = loadtxt(case+'.nnkp')
npair = array(npair,dtype=int)
ii=0
pairs={0:[]}
for pair in npair:
if pair[0]!=ii:
pairs[pair[0]]=[pair[1]]
ii = pair[0]
else:
pairs[pair[0]].append(pair[1])
#print(pairs)
strc = w2k.Struct(case, fout)
latgen = w2k.Latgen(strc, fout)
#latgen.Symoper(strc, fout) #latgen.Symoper(strc, fout) I think symope is called in Latgen initialization
#kqm = KQmesh(nkdivs, k0shift, strc, latgen, fout)
ks = KohnShamSystem(case, strc, nspin, fout)
in1 = w2k.In1File(case, strc, fout)#, io.lomax)
ks.Set_nv(in1.nlo_tot)
fklist = open(case+'.klist', 'r')
line = fklist.readline()
mt = re.search('div:\s*\(\s*(\d+)\s*(\d+)\s*(\d+)\)', line)
nkdivs = [int(mt.group(1)),int(mt.group(2)),int(mt.group(3))]
k0shift=[0,0,0]
if mrank==master: print('kdivs=', nkdivs, file=fout)
kqm = KQmesh(nkdivs, k0shift, strc, latgen, fout)
pw = PlaneWaves(ks.hsrws, kmr, pwm, case, strc, in1, latgen, kqm, False, fout)
nsp, nkp, band_max = shape(ks.Ebnd)
print('nsp=', nsp, 'nkp=', nkp, 'band_max=', band_max, file=fout)
print('len(klist)=', len(ks.klist), file=fout)
ks.PRINT = False
ks.VectorFileRead(case, strc, latgen, kqm, pw, fout, in1, HaveFullBZ=False)
(Elapw, Elo) = w2k.get_linearization_energies(case, in1, strc, nspin, fout)
in1.Add_Linearization_Energy(Elapw, Elo)
Vr = w2k.Read_Radial_Potential(case, strc.nat, nspin, strc.nrpt, fout)
radf = w2k.RadialFunctions(in1,strc,ks.Elapw,ks.Elo,Vr,nspin,fout)
del Vr
radf.get_ABC(in1, strc, fout)
EF=Find_EF(case)
print('EF=', EF, file=fout)
ks.Ebnd -= EF*Ry2H
Irredk = False
if mrank==master:
for ib in range(shape(ks.Ebnd[0])[1]):
Emin = min(ks.Ebnd[0][:,ib])*H2eV
Emax = max(ks.Ebnd[0][:,ib])*H2eV
print('band i=%3d has range %12.6f : %12.6f eV' %(ib,Emin,Emax), file=fout)
if (nbe<=nbs):
print('band i=%3d has range %12.6f : %12.6f eV' %(ib,Emin,Emax))
if (nbe<=nbs):
band_range = input('For which bands do you want to compute Quantum geometric tensor? istart : iend ')
mm = re.search('(\d+)\s*:(\d+)', band_range)
nbs,nbe = int(mm.group(1)),int(mm.group(2))+1
print(str(nbs)+'<= i_band <'+str(nbe))
Save_Eigenvalues(case, ks.Ebnd[0], nbs, nbe)
if Parallel:
comm.Barrier()
(nbs,nbe) = comm.bcast((nbs,nbe), root=master)
nbs_nbe = Find_nbs_nbe(ks.Ebnd[0], nbs, nbe, pairs, fout)
nntot = max([len(p) for p in pairs.values()])
idistance = zeros((len(pairs),nntot),dtype=int)
distances=[]
if mrank==master:
print('pairs of k-points at which we are going to compute M(k,b)_{m,n}= <psi_{m,k}|e^{-i*b*r}|psi_{n,k+b}>',file=fout)
for iik,ik in enumerate(pairs):
for il in range(len(pairs[ik])):
#print('%4d %4d' % (ik, pair[ik,il]), ' %2d %2d %2d'%tuple(pair_umklap[ik,il,:]))
jk = pairs[ik][il]
k1 = array(ks.klist[ik])
k2 = array(ks.klist[jk])
aq = linalg.norm(kqm.k2cartes @ (k1-k2))
ip = where( abs(array(distances)-aq)<1e-7 )[0]
if len(ip):
idistance[iik,il] = ip[0]
else:
idistance[iik,il] = len(distances)
distances.append(aq)
if mrank==master:
print('%4d %4d' % (ik, jk),' %.7f'%(aq,),' k['+str(ik)+']=',ks.klist[ik],'k['+str(jk)+']=', ks.klist[jk], file=fout)
print('distances=', distances, file=fout)
# M_{m,n} = < psi_{m,k} | e^{-i b r} |psi_{n,k+b}>
tnbs = min([nb[0] for nb in nbs_nbe])
tnbe = max([nb[1] for nb in nbs_nbe])
if mrank==master:
print('Final nbs=', tnbs, 'nbe=', tnbe, file=fout)
print(str(tnbs)+'<= i_band <'+str(tnbe))
Compute_and_Save_BandOverlap_Mmn(pairs,None,distances,idistance,tnbs,tnbe,Irredk,case,strc,latgen,ks,kqm, pw, in1, radf, fout, DMFT1=False, debug=False)
if mrank==master:
save('klist.npy', ks.klist)
save('Ebnd.npy', ks.Ebnd[0])
with open('pairs.pkl', 'wb') as f:
pickle.dump(pairs, f)
pickle.dump([nbs,nbe,tnbs,tnbe,latgen.Vol], f)
pickle.dump(distances, f)
pickle.dump(idistance, f)
return
def Compute_amn():
#klist = load('klist.npy')
#Ebnd = load('Ebnd.npy')
with open('pairs.pkl', 'rb') as f:
pairs = pickle.load(f)
[nbs,nbe,tnbs,tnbe,latgen_Vol] = pickle.load(f)
distances = pickle.load(f)
idistance = pickle.load(f)
nbs0,nbe0=nbs,nbe
(case,fout) = pg3.Initialize('a')
#print('shape(klist)=', shape(klist))
print('At reading: nbs,nbe,tnbs,tnbe=', nbs,nbe,tnbs,tnbe, file=fout)
print('At reading: nbs,nbe,tnbs,tnbe=', nbs,nbe,tnbs,tnbe)
nspin = 1
kmr=1 # if we want to increase the G-mesh as compared to case.in1 RKmax
pwm=2 # plane wave mesh parameter
strc = w2k.Struct(case, fout)
latgen = w2k.Latgen(strc, fout)
in1 = w2k.In1File(case, strc, fout)
orbits = Orbitals(strc, in1)
orbits.ReadIndmflFile(case)
orbts, CFx = orbits.FromIndmfl()
#print(orbits.Convert_iorb2text(orbts))
rotloc = copy(strc.rotloc)
for iat in range(len(strc.mult)):
idf0 = sum(strc.mult[:iat])
rotloci = rotloc[iat]
rotlocn = None
for ieq in range(strc.mult[iat]):
idf = idf0+ieq
if idf in orbits.rotloc:
#print('str.rotloc=', rotloci, 'indmfl.rotloc=', orbits.rotloc[idf])
if rotlocn is None:
rotlocn = orbits.rotloc[idf]
else:
if not allclose(orbits.rotloc[idf],rotlocn):
print('WARNING equivalent atoms between ', idf0, 'and', idf0+strc.mult[iat]-1, 'have different rotloc:', file=fout)
print(rotlocn, 'and', orbits.rotloc[idf], file=fout)