def laplace_coo(
self): # Compute matrix of Laplace brakets for the whole molecule
from pyscf.nao.m_overlap_coo import overlap_coo
from pyscf.nao.m_laplace_am import laplace_am
return overlap_coo(self, funct=laplace_am)
for i, dref in enumerate(dipcoo):
dref = dref.toarray()
dprd = np.einsum('p,pab->ab', mom1[:, i], vpab)
xyz2err.append([
abs(dprd - dref).sum() / dref.size,
np.amax(abs(dref - dprd))
])
return xyz2err
#
#
#
if __name__ == '__main__':
from pyscf.nao import prod_basis_c, nao
from pyscf.nao.m_overlap_coo import overlap_coo
from pyscf import gto
import numpy as np
mol = gto.M(atom='O 0 0 0; H 0 0 0.5; H 0 0.5 0',
basis='ccpvdz') # coordinates in Angstrom!
sv = nao(gto=mol)
print(sv.atom2s)
s_ref = overlap_coo(sv).todense()
pb = prod_basis_c()
pb.init_prod_basis_pp_batch(sv)
mom0, mom1 = pb.comp_moments()
pab2v = pb.get_ac_vertex_array()
s_chk = einsum('pab,p->ab', pab2v, mom0)
print(abs(s_chk - s_ref).sum() / s_chk.size, abs(s_chk - s_ref).max())
def overlap_coo(self, **kvargs): # Compute overlap matrix for the molecule
from pyscf.nao.m_overlap_coo import overlap_coo
return overlap_coo(self, **kvargs)
def pb_ae(self, sv, tol_loc=1e-5, tol_biloc=1e-6, ac_rcut_ratio=1.0):
""" It should work with GTOs as well."""
from pyscf.nao import coulomb_am, get_atom2bas_s, conv_yzx2xyz_c, prod_log_c, ls_part_centers, comp_coulomb_den
from pyscf.nao.m_overlap_coo import overlap_coo
from pyscf.nao.m_prod_biloc import prod_biloc_c
from scipy.sparse import csr_matrix
from pyscf import gto
self.sv = sv
self.tol_loc = tol_loc
self.tol_biloc = tol_biloc
self.ac_rcut_ratio = ac_rcut_ratio
self.ac_rcut = ac_rcut_ratio * max(sv.ao_log.sp2rcut)
self.prod_log = prod_log_c().init_prod_log_dp(
sv.ao_log, tol_loc) # local basis (for each specie)
self.hkernel_csr = csr_matrix(
overlap_coo(sv, self.prod_log,
coulomb_am)) # compute local part of Coulomb interaction
self.c2s = zeros(
(sv.natm + 1), dtype=int64
) # global product Center (atom) -> start in case of atom-centered basis
for gc, sp in enumerate(sv.atom2sp):
self.c2s[gc + 1] = self.c2s[gc] + self.prod_log.sp2norbs[sp] #
c2s = self.c2s # What is the meaning of this copy ?? ... This is a pointer to self.c2s
self.bp2info = [
] # going to be some information including indices of atoms, list of contributing centres, conversion coefficients
for ia1, n1 in enumerate(sv.atom2s[1:] - sv.atom2s[0:-1]):
for ia2, n2 in enumerate(sv.atom2s[ia1 + 2:] - sv.atom2s[ia1 + 1:-1]):
ia2 += ia1 + 1
mol2 = gto.Mole(atom=[sv._atom[ia1], sv._atom[ia2]],
basis=sv.basis,
unit='bohr').build()
bs = get_atom2bas_s(mol2._bas)
ss = (bs[0], bs[1], bs[1], bs[2], bs[0], bs[1], bs[1], bs[2])
eri = mol2.intor('cint2e_sph',
shls_slice=ss).reshape(n1, n2, n1, n2)
eri = conv_yzx2xyz_c(mol2).conv_yzx2xyz_4d(eri, 'pyscf2nao',
ss).reshape(
n1 * n2, n1 * n2)
ee, xx = np.linalg.eigh(
eri
) # This the simplest way. TODO: diag in each m-channel separately
mu2d = [domi for domi, eva in enumerate(ee) if eva > tol_biloc
] # The choice of important linear combinations is here
nprod = len(mu2d)
if nprod < 1:
continue # Skip the rest of operations in case there is no large linear combinations.
# add new vertex
vrtx = zeros([nprod, n1, n2])
for p, d in enumerate(mu2d):
vrtx[p, :, :] = xx[:, d].reshape(n1, n2)
#print(ia1,ia2,nprod,abs(einsum('pab,qab->pq', lambdx, lambdx).reshape(nprod,nprod)-np.identity(nprod)).sum())
lc2c = ls_part_centers(
sv, ia1, ia2, ac_rcut_ratio) # list of participating centers
lc2s = zeros(
(len(lc2c) + 1), dtype=int64
) # local product center -> start for the current bilocal pair
for lc, c in enumerate(lc2c):
lc2s[lc + 1] = lc2s[lc] + self.prod_log.sp2norbs[sv.atom2sp[c]]
npbp = lc2s[
-1] # size of the functions which will contribute to the given pair ia1,ia2
hkernel_bp = np.zeros(
(npbp,
npbp)) # this is local kernel for the current bilocal pair
for lc1, c1 in enumerate(lc2c):
for lc2, c2 in enumerate(lc2c):
for i1 in range(lc2s[lc1 + 1] - lc2s[lc1]):
for i2 in range(lc2s[lc2 + 1] - lc2s[lc2]):
hkernel_bp[i1 + lc2s[lc1], i2 + lc2s[
lc2]] = self.hkernel_csr[i1 + c2s[c1], i2 + c2s[
c2]] # element-by-element construction here
inv_hk = np.linalg.inv(hkernel_bp)
llp = np.zeros((npbp, nprod))
for c, s, f in zip(lc2c, lc2s, lc2s[1:]):
n3 = sv.atom2s[c + 1] - sv.atom2s[c]
lcd = self.prod_log.sp2lambda[sv.atom2sp[c]]
mol3 = gto.Mole(
atom=[sv._atom[ia1], sv._atom[ia2], sv._atom[c]],
basis=sv.basis,
unit='bohr',
spin=1).build()
bs = get_atom2bas_s(mol3._bas)
ss = (bs[2], bs[3], bs[2], bs[3], bs[0], bs[1], bs[1], bs[2])
tci_ao = mol3.intor('cint2e_sph',
shls_slice=ss).reshape(n3, n3, n1, n2)
tci_ao = conv_yzx2xyz_c(mol3).conv_yzx2xyz_4d(
tci_ao, 'pyscf2nao', ss)
lp = einsum('lcd,cdp->lp', lcd,
einsum('cdab,pab->cdp', tci_ao, vrtx))
llp[s:f, :] = lp
cc = einsum('ab,bc->ac', inv_hk, llp)
pbiloc = prod_biloc_c(atoms=array([ia1, ia2]),
vrtx=vrtx,
cc2a=lc2c,
cc2s=lc2s,
cc=cc.T)
self.bp2info.append(pbiloc)
#print(ia1, ia2, len(mu2d), lc2c, hkernel_bp.sum(), inv_hk.sum())
self.dpc2s, self.dpc2t, self.dpc2sp = self.init_c2s_domiprod(
) # dominant product's counting
return self
""" Our standard minimal check """
dipcoo = self.sv.dipole_coo(**kw)
mom0,mom1 = self.comp_moments()
vpab = self.get_ac_vertex_array()
xyz2err = []
for i,dref in enumerate(dipcoo):
dref = dref.toarray()
dprd = np.einsum('p,pab->ab', mom1[:,i],vpab)
xyz2err.append([abs(dprd-dref).sum()/dref.size, np.amax(abs(dref-dprd))])
return xyz2err
#
#
#
if __name__=='__main__':
from pyscf.nao import prod_basis_c, nao
from pyscf.nao.m_overlap_coo import overlap_coo
from pyscf import gto
import numpy as np
mol = gto.M(atom='O 0 0 0; H 0 0 0.5; H 0 0.5 0', basis='ccpvdz') # coordinates in Angstrom!
sv = nao(gto=mol)
print(sv.atom2s)
s_ref = overlap_coo(sv).todense()
pb = prod_basis_c()
pb.init_prod_basis_pp_batch(sv)
mom0,mom1=pb.comp_moments()
pab2v = pb.get_ac_vertex_array()
s_chk = einsum('pab,p->ab', pab2v,mom0)
print(abs(s_chk-s_ref).sum()/s_chk.size, abs(s_chk-s_ref).max())
def laplace_coo(self): # Compute matrix of Laplace brakets for the whole molecule from pyscf.nao.m_overlap_coo import overlap_coo from pyscf.nao.m_laplace_am import laplace_am return overlap_coo(self, funct=laplace_am)
def overlap_coo(self, **kw): # Compute overlap matrix for the molecule from pyscf.nao.m_overlap_coo import overlap_coo return overlap_coo(self, **kw)
def pb_ae(self, sv, tol_loc=1e-5, tol_biloc=1e-6, ac_rcut_ratio=1.0):
""" It should work with GTOs as well."""
from pyscf.nao import coulomb_am, get_atom2bas_s, conv_yzx2xyz_c, prod_log_c, ls_part_centers, comp_coulomb_den
from pyscf.nao.m_overlap_coo import overlap_coo
from pyscf.nao.m_prod_biloc import prod_biloc_c
from scipy.sparse import csr_matrix
from pyscf import gto
self.sv = sv
self.tol_loc = tol_loc
self.tol_biloc = tol_biloc
self.ac_rcut_ratio = ac_rcut_ratio
self.ac_rcut = ac_rcut_ratio*max(sv.ao_log.sp2rcut)
self.prod_log = prod_log_c().init_prod_log_dp(sv.ao_log, tol_loc) # local basis (for each specie)
self.hkernel_csr = csr_matrix(overlap_coo(sv, self.prod_log, coulomb_am)) # compute local part of Coulomb interaction
self.c2s = zeros((sv.natm+1), dtype=int64) # global product Center (atom) -> start in case of atom-centered basis
for gc,sp in enumerate(sv.atom2sp): self.c2s[gc+1]=self.c2s[gc]+self.prod_log.sp2norbs[sp] #
c2s = self.c2s # What is the meaning of this copy ?? ... This is a pointer to self.c2s
self.bp2info = [] # going to be some information including indices of atoms, list of contributing centres, conversion coefficients
for ia1,n1 in enumerate(sv.atom2s[1:]-sv.atom2s[0:-1]):
for ia2,n2 in enumerate(sv.atom2s[ia1+2:]-sv.atom2s[ia1+1:-1]):
ia2 += ia1+1
mol2 = gto.Mole(atom=[sv._atom[ia1], sv._atom[ia2]], basis=sv.basis, unit='bohr').build()
bs = get_atom2bas_s(mol2._bas)
ss = (bs[0],bs[1], bs[1],bs[2], bs[0],bs[1], bs[1],bs[2])
eri = mol2.intor('cint2e_sph', shls_slice=ss).reshape(n1,n2,n1,n2)
eri = conv_yzx2xyz_c(mol2).conv_yzx2xyz_4d(eri, 'pyscf2nao', ss).reshape(n1*n2,n1*n2)
ee,xx = np.linalg.eigh(eri) # This the simplest way. TODO: diag in each m-channel separately
mu2d = [domi for domi,eva in enumerate(ee) if eva>tol_biloc] # The choice of important linear combinations is here
nprod=len(mu2d)
if nprod<1: continue # Skip the rest of operations in case there is no large linear combinations.
# add new vertex
vrtx = zeros([nprod,n1,n2])
for p,d in enumerate(mu2d): vrtx[p,:,:] = xx[:,d].reshape(n1,n2)
#print(ia1,ia2,nprod,abs(einsum('pab,qab->pq', lambdx, lambdx).reshape(nprod,nprod)-np.identity(nprod)).sum())
lc2c = ls_part_centers(sv, ia1, ia2, ac_rcut_ratio) # list of participating centers
lc2s = zeros((len(lc2c)+1), dtype=int64) # local product center -> start for the current bilocal pair
for lc,c in enumerate(lc2c): lc2s[lc+1]=lc2s[lc]+self.prod_log.sp2norbs[sv.atom2sp[c]]
npbp = lc2s[-1] # size of the functions which will contribute to the given pair ia1,ia2
hkernel_bp = np.zeros((npbp, npbp)) # this is local kernel for the current bilocal pair
for lc1,c1 in enumerate(lc2c):
for lc2,c2 in enumerate(lc2c):
for i1 in range(lc2s[lc1+1]-lc2s[lc1]):
for i2 in range(lc2s[lc2+1]-lc2s[lc2]):
hkernel_bp[i1+lc2s[lc1],i2+lc2s[lc2]] = self.hkernel_csr[i1+c2s[c1],i2+c2s[c2]] # element-by-element construction here
inv_hk = np.linalg.inv(hkernel_bp)
llp = np.zeros((npbp, nprod))
for c,s,f in zip(lc2c,lc2s,lc2s[1:]):
n3 = sv.atom2s[c+1]-sv.atom2s[c]
lcd = self.prod_log.sp2lambda[sv.atom2sp[c]]
mol3 = gto.Mole(atom=[sv._atom[ia1], sv._atom[ia2], sv._atom[c]], basis=sv.basis, unit='bohr', spin=1).build()
bs = get_atom2bas_s(mol3._bas)
ss = (bs[2],bs[3], bs[2],bs[3], bs[0],bs[1], bs[1],bs[2])
tci_ao = mol3.intor('cint2e_sph', shls_slice=ss).reshape(n3,n3,n1,n2)
tci_ao = conv_yzx2xyz_c(mol3).conv_yzx2xyz_4d(tci_ao, 'pyscf2nao', ss)
lp = einsum('lcd,cdp->lp', lcd,einsum('cdab,pab->cdp', tci_ao, vrtx))
llp[s:f,:] = lp
cc = einsum('ab,bc->ac', inv_hk, llp)
pbiloc = prod_biloc_c(atoms=array([ia1,ia2]), vrtx=vrtx, cc2a=lc2c, cc2s=lc2s, cc=cc.T)
self.bp2info.append(pbiloc)
#print(ia1, ia2, len(mu2d), lc2c, hkernel_bp.sum(), inv_hk.sum())
self.dpc2s,self.dpc2t,self.dpc2sp = self.init_c2s_domiprod() # dominant product's counting
return self