def get_snmw2sf(self, optimize="greedy"):
"""
This computes a matrix elements of W_c: <\Psi\Psi | W_c |\Psi\Psi>.
sf[spin,n,m,w] = X^n V_mu X^m W_mu_nu X^n V_nu X^m,
where n runs from s...f, m runs from 0...norbs, w runs from 0...nff_ia, spin=0...1 or 2.
"""
wpq2si0 = self.si_c(ww = 1j*self.ww_ia).real
v_pab = self.pb.get_ac_vertex_array()
#self.snmw2sf_ncalls += 1
snmw2sf = []
for s in range(self.nspin):
nmw2sf = zeros((len(self.nn[s]), self.norbs, self.nff_ia), dtype=self.dtype)
#nmw2sf = zeros((len(self.nn), self.norbs, self.nff_ia), dtype=self.dtype)
# n runs from s...f or states will be corrected:
# self.nn = [range(self.start_st[s], self.finish_st[s])
xna = self.mo_coeff[0,s,self.nn[s],:,0]
#xna = self.mo_coeff[0,s,self.nn,:,0]
# m runs from 0...norbs
xmb = self.mo_coeff[0,s,:,:,0]
# This calculates nmp2xvx= X^n V_mu X^m for each side
nmp2xvx = einsum('na,pab,mb->nmp', xna, v_pab, xmb, optimize=optimize)
for iw,si0 in enumerate(wpq2si0):
# This calculates nmp2xvx(outer loop)*real.W_mu_nu*nmp2xvx
nmw2sf[:,:,iw] = einsum('nmp,pq,nmq->nm', nmp2xvx, si0, nmp2xvx, optimize=optimize)
snmw2sf.append(nmw2sf)
if self.write_w:
from pyscf.nao.m_restart import write_rst_h5py
print(write_rst_h5py(data = snmw2sf, filename= 'SCREENED_COULOMB.hdf5'))
return snmw2sf
def get_snmw2sf_iter(self, optimize="greedy"):
"""
This computes a matrix elements of W_c: <\Psi(r)\Psi(r) | W_c(r,r',\omega) |\Psi(r')\Psi(r')>.
sf[spin,n,m,w] = X^n V_mu X^m W_mu_nu X^n V_nu X^m,
where n runs from s...f, m runs from 0...norbs, w runs from 0...nff_ia, spin=0...1 or 2.
1- XVX is calculated using dominant product in COO format: gw_xvx('dp_coo')
2- I_nm = W XVX = (1-v\chi_0)^{-1}v\chi_0v
3- S_nm = XVX W XVX = XVX * I_nm
"""
from scipy.sparse.linalg import LinearOperator, lgmres
ww = 1j * self.ww_ia
xvx = self.gw_xvx('blas')
snm2i = []
#convert k_c as full matrix into Operator
k_c_opt = LinearOperator((self.nprod, self.nprod),
matvec=self.gw_vext2veffmatvec,
dtype=self.dtypeComplex)
for s in range(self.nspin):
sf_aux = np.zeros((len(self.nn[s]), self.norbs, self.nprod),
dtype=self.dtypeComplex)
inm = np.zeros((len(self.nn[s]), self.norbs, len(ww)),
dtype=self.dtypeComplex)
# w is complex plane
for iw, w in enumerate(ww):
self.comega_current = w
#print('k_c_opt',k_c_opt.shape)
for n in range(len(self.nn[s])):
for m in range(self.norbs):
# v XVX
a = np.dot(self.kernel_sq, xvx[s][n, m, :])
# \chi_{0}v XVX by using matrix vector
b = self.gw_chi0_mv(a, self.comega_current)
# v\chi_{0}v XVX, this should be equals to bxvx in last approach
a = np.dot(self.kernel_sq, b)
sf_aux[n,
m, :], exitCode = lgmres(k_c_opt,
a,
atol=self.gw_iter_tol,
maxiter=self.maxiter)
if exitCode != 0:
print(
"LGMRES has not achieved convergence: exitCode = {}"
.format(exitCode))
# I= XVX I_aux
inm[:, :, iw] = np.einsum('nmp,nmp->nm',
xvx[s],
sf_aux,
optimize=optimize)
snm2i.append(np.real(inm))
if (self.write_w == True):
from pyscf.nao.m_restart import write_rst_h5py
print(write_rst_h5py(data=snm2i, filename='SCREENED_COULOMB.hdf5'))
return snm2i