def from_fcivec(ci0, norb, nelec, frozen=0):
'''Extract CISD coefficients from FCI coefficients'''
if frozen is not 0:
raise NotImplementedError
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
norba = norbb = norb
nocc = nocca, noccb = neleca, nelecb
nvira = norba - nocca
nvirb = norbb - noccb
t1addra, t1signa = cisd.tn_addrs_signs(norba, nocca, 1)
t1addrb, t1signb = cisd.tn_addrs_signs(norbb, noccb, 1)
na = cistring.num_strings(norba, nocca)
nb = cistring.num_strings(norbb, noccb)
ci0 = ci0.reshape(na,nb)
c0 = ci0[0,0]
c1a = (ci0[t1addra,0] * t1signa).reshape(nocca,nvira)
c1b = (ci0[0,t1addrb] * t1signb).reshape(noccb,nvirb)
c2ab = numpy.einsum('i,j,ij->ij', t1signa, t1signb, ci0[t1addra[:,None],t1addrb])
c2ab = c2ab.reshape(nocca,nvira,noccb,nvirb).transpose(0,2,1,3)
t2addra, t2signa = cisd.tn_addrs_signs(norba, nocca, 2)
t2addrb, t2signb = cisd.tn_addrs_signs(norbb, noccb, 2)
c2aa = (ci0[t2addra,0] * t2signa).reshape(nocca*(nocca-1)//2, nvira*(nvira-1)//2)
c2aa = _unpack_4fold(c2aa, nocca, nvira)
c2bb = (ci0[0,t2addrb] * t2signb).reshape(noccb*(noccb-1)//2, nvirb*(nvirb-1)//2)
c2bb = _unpack_4fold(c2bb, noccb, nvirb)
return amplitudes_to_cisdvec(c0, (c1a,c1b), (c2aa,c2ab,c2bb))
def from_fcivec(ci0, norb, nelec, frozen=0):
'''Extract CISD coefficients from FCI coefficients'''
if frozen is not 0:
raise NotImplementedError
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
norba = norbb = norb
nocc = nocca, noccb = neleca, nelecb
nvira = norba - nocca
nvirb = norbb - noccb
t1addra, t1signa = cisd.tn_addrs_signs(norba, nocca, 1)
t1addrb, t1signb = cisd.tn_addrs_signs(norbb, noccb, 1)
na = cistring.num_strings(norba, nocca)
nb = cistring.num_strings(norbb, noccb)
ci0 = ci0.reshape(na,nb)
c0 = ci0[0,0]
c1a = (ci0[t1addra,0] * t1signa).reshape(nocca,nvira)
c1b = (ci0[0,t1addrb] * t1signb).reshape(noccb,nvirb)
c2ab = numpy.einsum('i,j,ij->ij', t1signa, t1signb, ci0[t1addra[:,None],t1addrb])
c2ab = c2ab.reshape(nocca,nvira,noccb,nvirb).transpose(0,2,1,3)
t2addra, t2signa = cisd.tn_addrs_signs(norba, nocca, 2)
t2addrb, t2signb = cisd.tn_addrs_signs(norbb, noccb, 2)
c2aa = (ci0[t2addra,0] * t2signa).reshape(nocca*(nocca-1)//2, nvira*(nvira-1)//2)
c2aa = _unpack_4fold(c2aa, nocca, nvira)
c2bb = (ci0[0,t2addrb] * t2signb).reshape(noccb*(noccb-1)//2, nvirb*(nvirb-1)//2)
c2bb = _unpack_4fold(c2bb, noccb, nvirb)
return amplitudes_to_cisdvec(c0, (c1a,c1b), (c2aa,c2ab,c2bb))
def to_fcivec(cisdvec, norb, nelec, frozen=0):
'''Convert CISD coefficients to FCI coefficients'''
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
frozena_mask = numpy.zeros(norb, dtype=bool)
frozenb_mask = numpy.zeros(norb, dtype=bool)
if isinstance(frozen, (int, numpy.integer)):
nfroza = nfrozb = frozen
frozena_mask[:frozen] = True
frozenb_mask[:frozen] = True
else:
nfroza = len(frozen[0])
nfrozb = len(frozen[1])
frozena_mask[frozen[0]] = True
frozenb_mask[frozen[1]] = True
# if nfroza != nfrozb:
# raise NotImplementedError
nocca = numpy.count_nonzero(~frozena_mask[:neleca])
noccb = numpy.count_nonzero(~frozenb_mask[:nelecb])
nmo = nmoa, nmob = norb - nfroza, norb - nfrozb
nocc = nocca, noccb
nvira, nvirb = nmoa - nocca, nmob - noccb
c0, c1, c2 = cisdvec_to_amplitudes(cisdvec, nmo, nocc)
c1a, c1b = c1
c2aa, c2ab, c2bb = c2
t1addra, t1signa = cisd.tn_addrs_signs(nmoa, nocca, 1)
t1addrb, t1signb = cisd.tn_addrs_signs(nmob, noccb, 1)
na = cistring.num_strings(nmoa, nocca)
nb = cistring.num_strings(nmob, noccb)
fcivec = numpy.zeros((na,nb))
fcivec[0,0] = c0
fcivec[t1addra,0] = c1a.ravel() * t1signa
fcivec[0,t1addrb] = c1b.ravel() * t1signb
c2ab = c2ab.transpose(0,2,1,3).reshape(nocca*nvira,-1)
c2ab = numpy.einsum('i,j,ij->ij', t1signa, t1signb, c2ab)
fcivec[t1addra[:,None],t1addrb] = c2ab
if nocca > 1 and nvira > 1:
ooidx = numpy.tril_indices(nocca, -1)
vvidx = numpy.tril_indices(nvira, -1)
c2aa = c2aa[ooidx][:,vvidx[0],vvidx[1]]
t2addra, t2signa = cisd.tn_addrs_signs(nmoa, nocca, 2)
fcivec[t2addra,0] = c2aa.ravel() * t2signa
if noccb > 1 and nvirb > 1:
ooidx = numpy.tril_indices(noccb, -1)
vvidx = numpy.tril_indices(nvirb, -1)
c2bb = c2bb[ooidx][:,vvidx[0],vvidx[1]]
t2addrb, t2signb = cisd.tn_addrs_signs(nmob, noccb, 2)
fcivec[0,t2addrb] = c2bb.ravel() * t2signb
if nfroza == nfrozb == 0:
return fcivec
assert(norb < 63)
strsa = cistring.gen_strings4orblist(range(norb), neleca)
strsb = cistring.gen_strings4orblist(range(norb), nelecb)
na = len(strsa)
nb = len(strsb)
count_a = numpy.zeros(na, dtype=int)
count_b = numpy.zeros(nb, dtype=int)
parity_a = numpy.zeros(na, dtype=bool)
parity_b = numpy.zeros(nb, dtype=bool)
core_a_mask = numpy.ones(na, dtype=bool)
core_b_mask = numpy.ones(nb, dtype=bool)
for i in range(norb):
if frozena_mask[i]:
if i < neleca:
core_a_mask &= (strsa & (1<<i)) != 0
parity_a ^= (count_a & 1) == 1
else:
core_a_mask &= (strsa & (1<<i)) == 0
else:
count_a += (strsa & (1<<i)) != 0
if frozenb_mask[i]:
if i < nelecb:
core_b_mask &= (strsb & (1<<i)) != 0
parity_b ^= (count_b & 1) == 1
else:
core_b_mask &= (strsb & (1<<i)) == 0
else:
count_b += (strsb & (1<<i)) != 0
sub_strsa = strsa[core_a_mask & (count_a == nocca)]
sub_strsb = strsb[core_b_mask & (count_b == noccb)]
addrsa = cistring.strs2addr(norb, neleca, sub_strsa)
addrsb = cistring.strs2addr(norb, nelecb, sub_strsb)
fcivec1 = numpy.zeros((na,nb))
fcivec1[addrsa[:,None],addrsb] = fcivec
fcivec1[parity_a,:] *= -1
fcivec1[:,parity_b] *= -1
return fcivec1
from pyscf.ci.cisd import tn_addrs_signs
mol = gto.Mole()
mol.atom = [
['O', ( 0., 0. , 0. )],
['H', ( 0., -0.857, 0.587)],
['H', ( 0., 0.757 , 0.687)],]
mol.basis = '321g'
mol.build()
mf = scf.RHF(mol).run()
e, fcivec = fci.FCI(mf).kernel(verbose=5)
nmo = mol.nao
nocc = mol.nelectron // 2
t1addrs, t1signs = tn_addrs_signs(nmo, nocc, 1)
t2addrs, t2signs = tn_addrs_signs(nmo, nocc, 2)
t3addrs, t3signs = tn_addrs_signs(nmo, nocc, 3)
t4addrs, t4signs = tn_addrs_signs(nmo, nocc, 4)
# CIS includes two types of amplitudes: alpha -> alpha and beta -> beta
cis_a = fcivec[t1addrs, 0] * t1signs
cis_b = fcivec[0, t1addrs] * t1signs
# CID has:
# alpha,alpha -> alpha,alpha
# alpha,beta -> alpha,beta
# beta ,beta -> beta ,beta
# For alpha,alpha -> alpha,alpha excitations, the redundant coefficients are
# excluded. The number of coefficients is nocc*(nocc-1)//2 * nvir*(nvir-1)//2,
# which corresponds to C2_{ijab}, i > j and a > b.
def to_fcivec(cisdvec, norb, nelec, frozen=0):
'''Convert CISD coefficients to FCI coefficients'''
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
frozena_mask = numpy.zeros(norb, dtype=bool)
frozenb_mask = numpy.zeros(norb, dtype=bool)
if isinstance(frozen, (int, numpy.integer)):
nfroza = nfrozb = frozen
frozena_mask[:frozen] = True
frozenb_mask[:frozen] = True
else:
nfroza = len(frozen[0])
nfrozb = len(frozen[1])
frozena_mask[frozen[0]] = True
frozenb_mask[frozen[1]] = True
# if nfroza != nfrozb:
# raise NotImplementedError
nocca = numpy.count_nonzero(~frozena_mask[:neleca])
noccb = numpy.count_nonzero(~frozenb_mask[:nelecb])
nmo = nmoa, nmob = norb - nfroza, norb - nfrozb
nocc = nocca, noccb
nvira, nvirb = nmoa - nocca, nmob - noccb
c0, c1, c2 = cisdvec_to_amplitudes(cisdvec, nmo, nocc)
c1a, c1b = c1
c2aa, c2ab, c2bb = c2
t1addra, t1signa = cisd.tn_addrs_signs(nmoa, nocca, 1)
t1addrb, t1signb = cisd.tn_addrs_signs(nmob, noccb, 1)
na = cistring.num_strings(nmoa, nocca)
nb = cistring.num_strings(nmob, noccb)
fcivec = numpy.zeros((na,nb))
fcivec[0,0] = c0
fcivec[t1addra,0] = c1a.ravel() * t1signa
fcivec[0,t1addrb] = c1b.ravel() * t1signb
c2ab = c2ab.transpose(0,2,1,3).reshape(nocca*nvira,-1)
c2ab = numpy.einsum('i,j,ij->ij', t1signa, t1signb, c2ab)
fcivec[t1addra[:,None],t1addrb] = c2ab
if nocca > 1 and nvira > 1:
ooidx = numpy.tril_indices(nocca, -1)
vvidx = numpy.tril_indices(nvira, -1)
c2aa = c2aa[ooidx][:,vvidx[0],vvidx[1]]
t2addra, t2signa = cisd.tn_addrs_signs(nmoa, nocca, 2)
fcivec[t2addra,0] = c2aa.ravel() * t2signa
if noccb > 1 and nvirb > 1:
ooidx = numpy.tril_indices(noccb, -1)
vvidx = numpy.tril_indices(nvirb, -1)
c2bb = c2bb[ooidx][:,vvidx[0],vvidx[1]]
t2addrb, t2signb = cisd.tn_addrs_signs(nmob, noccb, 2)
fcivec[0,t2addrb] = c2bb.ravel() * t2signb
if nfroza == nfrozb == 0:
return fcivec
assert(norb < 63)
strsa = cistring.gen_strings4orblist(range(norb), neleca)
strsb = cistring.gen_strings4orblist(range(norb), nelecb)
na = len(strsa)
nb = len(strsb)
count_a = numpy.zeros(na, dtype=int)
count_b = numpy.zeros(nb, dtype=int)
parity_a = numpy.zeros(na, dtype=bool)
parity_b = numpy.zeros(nb, dtype=bool)
core_a_mask = numpy.ones(na, dtype=bool)
core_b_mask = numpy.ones(nb, dtype=bool)
for i in range(norb):
if frozena_mask[i]:
if i < neleca:
core_a_mask &= (strsa & (1<<i)) != 0
parity_a ^= (count_a & 1) == 1
else:
core_a_mask &= (strsa & (1<<i)) == 0
else:
count_a += (strsa & (1<<i)) != 0
if frozenb_mask[i]:
if i < nelecb:
core_b_mask &= (strsb & (1<<i)) != 0
parity_b ^= (count_b & 1) == 1
else:
core_b_mask &= (strsb & (1<<i)) == 0
else:
count_b += (strsb & (1<<i)) != 0
sub_strsa = strsa[core_a_mask & (count_a == nocca)]
sub_strsb = strsb[core_b_mask & (count_b == noccb)]
addrsa = cistring.strs2addr(norb, neleca, sub_strsa)
addrsb = cistring.strs2addr(norb, nelecb, sub_strsb)
fcivec1 = numpy.zeros((na,nb))
fcivec1[addrsa[:,None],addrsb] = fcivec
fcivec1[parity_a,:] *= -1
fcivec1[:,parity_b] *= -1
return fcivec1