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ucisd_slow.py
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ucisd_slow.py
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#!/usr/bin/env python
#
# Author: Qiming Sun <osirpt.sun@gmail.com>
#
'''
Unrestricted CISD
'''
import time
from functools import reduce
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf import ao2mo
from pyscf.ci import cisd
from pyscf.cc import uccsd
einsum = lib.einsum
def kernel(myci, eris, ci0=None, max_cycle=50, tol=1e-8,
verbose=logger.INFO):
mol = myci.mol
diag = myci.make_diagonal(eris)
ehf = diag[0]
diag -= ehf
if ci0 is None:
ci0 = myci.get_init_guess(eris)[1]
def op(xs):
return [myci.contract(x, eris) for x in xs]
def precond(x, e, *args):
diagd = diag - (e-myci.level_shift)
diagd[abs(diagd)<1e-8] = 1e-8
return x / diagd
conv, ecisd, ci = lib.davidson1(op, ci0, precond, tol=tol,
max_cycle=max_cycle, max_space=myci.max_space,
lindep=myci.lindep, nroots=myci.nroots,
verbose=verbose)
if myci.nroots == 1:
conv = conv[0]
ecisd = ecisd[0]
ci = ci[0]
return conv, ecisd, ci
def make_diagonal(myci, eris):
nocca = eris.nocca
noccb = eris.noccb
nmoa = eris.focka.shape[0]
nmob = eris.focka.shape[1]
nvira = nmoa - nocca
nvirb = nmob - noccb
jdiag_aa = numpy.zeros((nmoa,nmoa))
jdiag_ab = numpy.zeros((nmoa,nmob))
jdiag_bb = numpy.zeros((nmob,nmob))
def diag_idx(n):
idx = numpy.arange(n)
return idx * (idx + 1) // 2 + idx
jdiag_aa[:nocca,:nocca] = numpy.einsum('iijj->ij', eris.oooo)
jdiag_aa[nocca:,nocca:] = eris.vvvv[diag_idx(nvira)[:,None],diag_idx(nvira)]
jdiag_aa[:nocca,nocca:] = numpy.einsum('iijj->ij', eris.oovv)
jdiag_aa[nocca:,:nocca] = jdiag_aa[:nocca,nocca:].T
jdiag_ab[:nocca,:noccb] = numpy.einsum('iijj->ij', eris.ooOO)
jdiag_ab[nocca:,noccb:] = eris.vvVV[diag_idx(nvira)[:,None],diag_idx(nvirb)]
jdiag_ab[:nocca,noccb:] = numpy.einsum('iijj->ij', eris.ooVV)
jdiag_ab[nocca:,:noccb] = numpy.einsum('iijj->ij', eris.vvOO)
jdiag_bb[:noccb,:noccb] = numpy.einsum('iijj->ij', eris.OOOO)
jdiag_bb[noccb:,noccb:] = eris.VVVV[diag_idx(nvirb)[:,None],diag_idx(nvirb)]
jdiag_bb[:noccb,noccb:] = numpy.einsum('iijj->ij', eris.OOVV)
jdiag_bb[noccb:,:noccb] = jdiag_bb[:noccb,noccb:].T
kdiag_aa = numpy.zeros((nmoa,nmoa))
kdiag_bb = numpy.zeros((nmob,nmob))
kdiag_aa[:nocca,:nocca] = numpy.einsum('ijji->ij', eris.oooo)
kdiag_aa[nocca:,nocca:] = lib.unpack_tril(eris.vvvv.diagonal())
kdiag_aa[:nocca,nocca:] = numpy.einsum('ijji->ji', eris.voov)
kdiag_aa[nocca:,:nocca] = kdiag_aa[:nocca,nocca:].T
kdiag_bb[:noccb,:noccb] = numpy.einsum('ijji->ij', eris.OOOO)
kdiag_bb[noccb:,noccb:] = lib.unpack_tril(eris.VVVV.diagonal())
kdiag_bb[:noccb,noccb:] = numpy.einsum('ijji->ji', eris.VOOV)
kdiag_bb[noccb:,:noccb] = kdiag_bb[:noccb,noccb:].T
jkdiag_aa = jdiag_aa - kdiag_aa
jkdiag_ab = jdiag_ab
jkdiag_bb = jdiag_bb - kdiag_bb
mo_ea = eris.focka.diagonal()
mo_eb = eris.fockb.diagonal()
ehf = (mo_ea[:nocca].sum() + mo_eb[:noccb].sum()
- (jdiag_aa[:nocca,:nocca].sum() - kdiag_aa[:nocca,:nocca].sum()) * .5
- jdiag_ab[:nocca,:noccb].sum()
- (jdiag_bb[:noccb,:noccb].sum() - kdiag_bb[:noccb,:noccb].sum()) * .5)
e1diag_a = numpy.empty((nocca,nvira))
e1diag_b = numpy.empty((noccb,nvirb))
e2diag_aa = numpy.empty((nocca,nocca,nvira,nvira))
e2diag_ab = numpy.empty((nocca,noccb,nvira,nvirb))
e2diag_bb = numpy.empty((noccb,noccb,nvirb,nvirb))
for i in range(nocca):
for a in range(nocca, nmoa):
e1diag_a[i,a-nocca] = ehf - mo_ea[i] + mo_ea[a] - jkdiag_aa[i,a]
for j in range(nocca):
for b in range(nocca, nmoa):
e2diag_aa[i,j,a-nocca,b-nocca] = ehf \
- mo_ea[i] - mo_ea[j] \
+ mo_ea[a] + mo_ea[b] \
+ jkdiag_aa[i,j] + jkdiag_aa[a,b] \
- jkdiag_aa[i,a] - jkdiag_aa[j,a] \
- jkdiag_aa[i,b] - jkdiag_aa[j,b]
for i in range(nocca):
for a in range(nocca, nmoa):
for j in range(noccb):
for b in range(noccb, nmob):
e2diag_ab[i,j,a-nocca,b-noccb] = ehf \
- mo_ea[i] - mo_eb[j] \
+ mo_ea[a] + mo_eb[b] \
+ jdiag_ab[i,j] + jdiag_ab[a,b] \
- jkdiag_aa[i,a] - jkdiag_bb[j,b] \
- jdiag_ab[i,b] - jdiag_ab[a,j]
for i in range(noccb):
for a in range(noccb, nmob):
e1diag_b[i,a-noccb] = ehf - mo_eb[i] + mo_eb[a] - jkdiag_bb[i,a]
for j in range(noccb):
for b in range(noccb, nmob):
e2diag_bb[i,j,a-noccb,b-noccb] = ehf \
- mo_eb[i] - mo_eb[j] \
+ mo_eb[a] + mo_eb[b] \
+ jkdiag_bb[i,j] + jkdiag_bb[a,b] \
- jkdiag_bb[i,a] - jkdiag_bb[j,a] \
- jkdiag_bb[i,b] - jkdiag_bb[j,b]
return amplitudes_to_cisdvec(ehf, (e1diag_a, e1diag_b),
(e2diag_aa, e2diag_ab, e2diag_bb))
def contract(myci, civec, eris):
nocca = eris.nocca
noccb = eris.noccb
nmoa = eris.focka.shape[0]
nmob = eris.fockb.shape[0]
nvira = nmoa - nocca
nvirb = nmob - noccb
c0, (c1a,c1b), (c2aa,c2ab,c2bb) = \
cisdvec_to_amplitudes(civec, (nmoa,nmob), (nocca,noccb))
fooa = eris.focka[:nocca,:nocca]
foob = eris.fockb[:noccb,:noccb]
fova = eris.focka[:nocca,nocca:]
fovb = eris.fockb[:noccb,noccb:]
fvva = eris.focka[nocca:,nocca:]
fvvb = eris.fockb[noccb:,noccb:]
#:t1 = einsum('ie,ae->ia', c1, fvv)
t1a = einsum('ie,ae->ia', c1a, fvva)
t1b = einsum('ie,ae->ia', c1b, fvvb)
#:t1 -= einsum('ma,mi->ia', c1, foo)
t1a -= einsum('ma,mi->ia', c1a, fooa)
t1b -= einsum('ma,mi->ia', c1b, foob)
#:t1 += einsum('imae,me->ia', c2, fov)
t1a += numpy.einsum('imae,me->ia', c2aa, fova)
t1a += numpy.einsum('imae,me->ia', c2ab, fovb)
t1b += numpy.einsum('imae,me->ia', c2bb, fovb)
t1b += numpy.einsum('miea,me->ia', c2ab, fova)
#:t1 += einsum('nf,nafi->ia', c1, eris.ovvo)
t1a += numpy.einsum('nf,ainf->ia', c1a, eris.voov)
t1a -= numpy.einsum('nf,nifa->ia', c1a, eris.oovv)
t1b += numpy.einsum('nf,ainf->ia', c1b, eris.VOOV)
t1b -= numpy.einsum('nf,nifa->ia', c1b, eris.OOVV)
t1b += numpy.einsum('nf,ainf->ia', c1a, eris.VOov)
t1a += numpy.einsum('nf,ainf->ia', c1b, eris.voOV)
#:t1 -= 0.5*einsum('imef,maef->ia', c2, eris.ovvv)
eris_Hovvv = _cp(eris.vovv).transpose(1,0,2,3)
eris_HOVVV = _cp(eris.VOVV).transpose(1,0,2,3)
eris_HovVV = _cp(eris.voVV).transpose(1,0,2,3)
eris_HOVvv = _cp(eris.VOvv).transpose(1,0,2,3)
ovvv = eris_Hovvv - eris_Hovvv.transpose(0,3,2,1)
OVVV = eris_HOVVV - eris_HOVVV.transpose(0,3,2,1)
t1a += 0.5*lib.einsum('mief,meaf->ia', c2aa, ovvv)
t1b += 0.5*lib.einsum('MIEF,MEAF->IA', c2bb, OVVV)
t1a += lib.einsum('iMfE,MEaf->ia', c2ab, eris_HOVvv)
t1b += lib.einsum('mIeF,meAF->IA', c2ab, eris_HovVV)
#:t1 -= 0.5*einsum('mnae,mnie->ia', c2, eris.ooov)
eris_Hooov = _cp(eris.ooov)
eris_HOOOV = _cp(eris.OOOV)
eris_HooOV = _cp(eris.ooOV)
eris_HOOov = _cp(eris.OOov)
ooov = eris_Hooov - eris_Hooov.transpose(2,1,0,3)
OOOV = eris_HOOOV - eris_HOOOV.transpose(2,1,0,3)
t1a += 0.5*lib.einsum('mnae,nime->ia', c2aa, ooov)
t1b += 0.5*lib.einsum('mnae,nime->ia', c2bb, OOOV)
t1a -= lib.einsum('nMaE,niME->ia', c2ab, eris_HooOV)
t1b -= lib.einsum('mNeA,NIme->IA', c2ab, eris_HOOov)
#:tmp = einsum('ijae,be->ijab', c2, fvv)
#:t2 = tmp - tmp.transpose(0,1,3,2)
t2aa = lib.einsum('ijae,be->ijab', c2aa, fvva)
t2aa = t2aa - t2aa.transpose(0,1,3,2)
t2bb = lib.einsum('ijae,be->ijab', c2bb, fvvb)
t2bb = t2bb - t2bb.transpose(0,1,3,2)
t2ab = lib.einsum('iJaE,BE->iJaB', c2ab, fvvb)
t2ab+= lib.einsum('iJeA,be->iJbA', c2ab, fvva)
#:tmp = einsum('imab,mj->ijab', c2, foo)
#:t2 -= tmp - tmp.transpose(1,0,2,3)
tmp = lib.einsum('imab,mj->ijab', c2aa, fooa)
t2aa-= tmp - tmp.transpose(1,0,2,3)
tmp = lib.einsum('imab,mj->ijab', c2bb, foob)
t2bb-= tmp - tmp.transpose(1,0,2,3)
t2ab-= lib.einsum('iMaB,MJ->iJaB', c2ab, foob)
t2ab-= lib.einsum('mIaB,mj->jIaB', c2ab, fooa)
#:t2 += 0.5*einsum('mnab,mnij->ijab', c2, eris.oooo)
Woooo = _cp(eris.oooo).transpose(0,2,1,3)
WOOOO = _cp(eris.OOOO).transpose(0,2,1,3)
WoOoO = _cp(eris.ooOO).transpose(0,2,1,3)
Woooo = Woooo - Woooo.transpose(1,0,2,3)
WOOOO = WOOOO - WOOOO.transpose(1,0,2,3)
t2aa += 0.5*lib.einsum('mnab,mnij->ijab', c2aa, Woooo)
t2bb += 0.5*lib.einsum('mnab,mnij->ijab', c2bb, WOOOO)
t2ab += lib.einsum('mNaB,mNiJ->iJaB', c2ab, WoOoO)
#:t2 += 0.5*einsum('ijef,abef->ijab', c2, eris.vvvv)
eris_Hvvvv = ao2mo.restore(1, eris.vvvv, nvira)
eris_HvvVV = _restore(eris.vvVV, nvira, nvirb)
eris_HVVVV = ao2mo.restore(1, eris.VVVV, nvirb)
t2aa += lib.einsum('ijef,aebf->ijab', c2aa, eris_Hvvvv)
t2bb += lib.einsum('ijef,aebf->ijab', c2bb, eris_HVVVV)
t2ab += lib.einsum('iJeF,aeBF->iJaB', c2ab, eris_HvvVV)
#:tmp = einsum('imae,mbej->ijab', c2, eris.ovvo)
#:tmp = tmp - tmp.transpose(0,1,3,2)
#:t2 += tmp - tmp.transpose(1,0,2,3)
eris_Hoovv = _cp(eris.oovv)
eris_HooVV = _cp(eris.ooVV)
eris_HOOvv = _cp(eris.vvOO).transpose(2,3,0,1)
eris_HOOVV = _cp(eris.OOVV)
wovvo = -eris_Hoovv.transpose(0,2,3,1)
woVVo = -eris_HooVV.transpose(0,2,3,1)
wOvvO = -eris_HOOvv.transpose(0,2,3,1)
wOVVO = -eris_HOOVV.transpose(0,2,3,1)
eris_Hovvo = _cp(eris.voov).transpose(2,3,0,1)
eris_HovVO = _cp(eris.VOov).transpose(2,3,0,1)
eris_HOVvo = _cp(eris.voOV).transpose(2,3,0,1)
eris_HOVVO = _cp(eris.VOOV).transpose(2,3,0,1)
oovv = eris_Hoovv - eris_Hovvo.transpose(0,3,2,1)
OOVV = eris_HOOVV - eris_HOVVO.transpose(0,3,2,1)
wovvo = wovvo + eris_Hovvo.transpose(0,2,1,3)
wOVVO = wOVVO + eris_HOVVO.transpose(0,2,1,3)
woVvO = eris_HovVO.transpose(0,2,1,3)
wOvVo = eris_HOVvo.transpose(0,2,1,3)
tmpaa = lib.einsum('imae,mbej->ijab', c2aa, wovvo)
tmpaa+= lib.einsum('iMaE,MbEj->ijab', c2ab, wOvVo)
tmpbb = lib.einsum('imae,mbej->ijab', c2bb, wOVVO)
tmpbb+= lib.einsum('mIeA,mBeJ->IJAB', c2ab, woVvO)
tmpab = lib.einsum('imae,mBeJ->iJaB', c2aa, woVvO)
tmpab+= lib.einsum('iMaE,MBEJ->iJaB', c2ab, wOVVO)
tmpba = lib.einsum('IMAE,MbEj->IjAb', c2bb, wOvVo)
tmpba+= lib.einsum('mIeA,mbej->IjAb', c2ab, wovvo)
tmpabba =-lib.einsum('iMeA,MbeJ->iJAb', c2ab, wOvvO)
tmpbaab =-lib.einsum('mIaE,mBEj->IjaB', c2ab, woVVo)
tmpaa = tmpaa - tmpaa.transpose(0,1,3,2)
t2aa += tmpaa - tmpaa.transpose(1,0,2,3)
tmpbb = tmpbb - tmpbb.transpose(0,1,3,2)
t2bb += tmpbb - tmpbb.transpose(1,0,2,3)
tmpab -= tmpabba.transpose(0,1,3,2)
tmpab -= tmpbaab.transpose(1,0,2,3)
tmpab += tmpba.transpose(1,0,3,2)
t2ab += tmpab
#:tmp = numpy.einsum('ia,jb->ijab', c1, fov)
#:tmp = tmp - tmp.transpose(0,1,3,2)
#:t2 += tmp - tmp.transpose(1,0,2,3)
tmpaa = numpy.einsum('ia,jb->ijab', c1a, fova)
tmpab = numpy.einsum('ia,jb->ijab', c1a, fovb)
tmpba = numpy.einsum('ia,jb->ijab', c1b, fova)
tmpbb = numpy.einsum('ia,jb->ijab', c1b, fovb)
tmpaa = tmpaa - tmpaa.transpose(0,1,3,2)
t2aa += tmpaa - tmpaa.transpose(1,0,2,3)
tmpbb = tmpbb - tmpbb.transpose(0,1,3,2)
t2bb += tmpbb - tmpbb.transpose(1,0,2,3)
t2ab += tmpab + tmpba.transpose(1,0,3,2)
#:tmp = einsum('ie,jeba->ijab', c1, numpy.asarray(eris.ovvv).conj())
#:t2 += tmp - tmp.transpose(1,0,2,3)
tmpaa = lib.einsum('ie,mbea->imab', c1a, ovvv.conj())
t2aa += tmpaa - tmpaa.transpose(1,0,2,3)
tmpbb = lib.einsum('ie,mbea->imab', c1b, OVVV.conj())
t2bb += tmpbb - tmpbb.transpose(1,0,2,3)
t2ab += lib.einsum('ie,MBea->iMaB', c1a, eris_HOVvv.conj())
t2ab += lib.einsum('IE,maEB->mIaB', c1b, eris_HovVV.conj())
#:tmp = einsum('ma,mbij->ijab', c1, eris.ovoo)
#:t2 -= tmp - tmp.transpose(0,1,3,2)
eris_Hoovo = _cp(eris.oovo)
eris_HOOVO = _cp(eris.OOVO)
eris_HooVO = _cp(eris.ooVO)
eris_HOOvo = _cp(eris.OOvo)
oovo = eris_Hoovo - eris_Hoovo.transpose(0,3,2,1)
OOVO = eris_HOOVO - eris_HOOVO.transpose(0,3,2,1)
tmpaa = lib.einsum('ma,mibj->ijab', c1a, oovo)
t2aa -= tmpaa - tmpaa.transpose(0,1,3,2)
tmpbb = lib.einsum('ma,mibj->ijab', c1b, OOVO)
t2bb -= tmpbb - tmpbb.transpose(0,1,3,2)
t2ab -= lib.einsum('ma,miBJ->iJaB', c1a, eris_HooVO)
t2ab -= lib.einsum('MA,MJbi->iJbA', c1b, eris_HOOvo)
#:t1 += fov * c0
t1a += fova * c0
t1b += fovb * c0
#:t2 += eris.oovv * c0
t2aa += eris.voov.transpose(1,2,0,3) * c0
t2aa -= eris.voov.transpose(1,2,3,0) * c0
t2bb += eris.VOOV.transpose(1,2,0,3) * c0
t2bb -= eris.VOOV.transpose(1,2,3,0) * c0
t2ab += eris.voOV.transpose(1,2,0,3) * c0
#:t0 = numpy.einsum('ia,ia', fov, c1)
#:t0 += numpy.einsum('ijab,ijab', eris.oovv, c2) * .25
t0 = numpy.einsum('ia,ia', fova, c1a)
t0 += numpy.einsum('ia,ia', fovb, c1b)
t0 += numpy.einsum('aijb,ijab', eris.voov, c2aa) * .25
t0 -= numpy.einsum('ajib,ijab', eris.voov, c2aa) * .25
t0 += numpy.einsum('aijb,ijab', eris.VOOV, c2bb) * .25
t0 -= numpy.einsum('ajib,ijab', eris.VOOV, c2bb) * .25
t0 += numpy.einsum('aijb,ijab', eris.voOV, c2ab)
return amplitudes_to_cisdvec(t0, (t1a,t1b), (t2aa,t2ab,t2bb))
def amplitudes_to_cisdvec(c0, c1, c2):
c1a, c1b = c1
c2aa, c2ab, c2bb = c2
nocca, nvira = c1a.shape
noccb, nvirb = c1b.shape
def trilidx(n):
idx = numpy.tril_indices(n, -1)
return idx[0] * n + idx[1]
ooidxa = trilidx(nocca)
vvidxa = trilidx(nvira)
ooidxb = trilidx(noccb)
vvidxb = trilidx(nvirb)
size = (1, nocca*nvira, noccb*nvirb, nocca*noccb*nvira*nvirb,
len(ooidxa)*len(vvidxa), len(ooidxb)*len(vvidxb))
loc = numpy.cumsum(size)
civec = numpy.empty(loc[-1])
civec[0] = c0
civec[loc[0]:loc[1]] = c1a.ravel()
civec[loc[1]:loc[2]] = c1b.ravel()
civec[loc[2]:loc[3]] = c2ab.ravel()
lib.take_2d(c2aa.reshape(nocca**2,nvira**2), ooidxa, vvidxa, out=civec[loc[3]:loc[4]])
lib.take_2d(c2bb.reshape(noccb**2,nvirb**2), ooidxb, vvidxb, out=civec[loc[4]:loc[5]])
return civec
def cisdvec_to_amplitudes(civec, nmoa_nmob, nocca_noccb):
norba, norbb = nmoa_nmob
nocca, noccb = nocca_noccb
nvira = norba - nocca
nvirb = norbb - noccb
nooa = nocca * (nocca-1) // 2
nvva = nvira * (nvira-1) // 2
noob = noccb * (noccb-1) // 2
nvvb = nvirb * (nvirb-1) // 2
size = (1, nocca*nvira, noccb*nvirb, nocca*noccb*nvira*nvirb,
nooa*nvva, noob*nvvb)
loc = numpy.cumsum(size)
c0 = civec[0]
c1a = civec[loc[0]:loc[1]].reshape(nocca,nvira)
c1b = civec[loc[1]:loc[2]].reshape(noccb,nvirb)
c2ab = civec[loc[2]:loc[3]].reshape(nocca,noccb,nvira,nvirb)
c2aa = _unpack_4fold(civec[loc[3]:loc[4]], nocca, nvira)
c2bb = _unpack_4fold(civec[loc[4]:loc[5]], noccb, nvirb)
return c0, (c1a,c1b), (c2aa,c2ab,c2bb)
def _unpack_4fold(c2vec, nocc, nvir):
ooidx = numpy.tril_indices(nocc, -1)
vvidx = numpy.tril_indices(nvir, -1)
c2tmp = numpy.zeros((nocc,nocc,nvir*(nvir-1)//2))
c2tmp[ooidx] = c2vec.reshape(nocc*(nocc-1)//2, nvir*(nvir-1)//2)
c2tmp = c2tmp - c2tmp.transpose(1,0,2)
c2 = numpy.zeros((nocc,nocc,nvir,nvir))
c2[:,:,vvidx[0],vvidx[1]] = c2tmp
c2 = c2 - c2.transpose(0,1,3,2)
return c2
def to_fci(cisdvec, nmoa_nmob, nocca_noccb):
from pyscf import fci
from pyscf.ci.cisd_slow import t2strs
norba, norbb = nmoa_nmob
nocca, noccb = nocca_noccb
nvira = norba - nocca
nvirb = norbb - noccb
c0, c1, c2 = cisdvec_to_amplitudes(cisdvec, nmoa_nmob, nocca_noccb)
c1a, c1b = c1
c2aa, c2ab, c2bb = c2
t1addra, t1signa = cisd.t1strs(norba, nocca)
t1addrb, t1signb = cisd.t1strs(norbb, noccb)
na = fci.cistring.num_strings(norba, nocca)
nb = fci.cistring.num_strings(norbb, noccb)
fcivec = numpy.zeros((na,nb))
fcivec[0,0] = c0
fcivec[t1addra,0] = c1a[::-1].T.ravel() * t1signa
fcivec[0,t1addrb] = c1b[::-1].T.ravel() * t1signb
c2ab = c2ab[::-1,::-1].transpose(2,0,3,1).reshape(nocca*nvira,-1)
c2ab = numpy.einsum('i,j,ij->ij', t1signa, t1signb, c2ab)
lib.takebak_2d(fcivec, c2ab, t1addra, t1addrb)
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 = t2strs(norba, nocca)
fcivec[t2addra,0] = c2aa[::-1].T.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 = t2strs(norbb, noccb)
fcivec[0,t2addrb] = c2bb[::-1].T.ravel() * t2signb
return fcivec
def from_fci(ci0, nmoa_nmob, nocca_noccb):
from pyscf import fci
from pyscf.ci.cisd_slow import t2strs
norba, norbb = nmoa_nmob
nocca, noccb = nocca_noccb
nvira = norba - nocca
nvirb = norbb - noccb
t1addra, t1signa = cisd.t1strs(norba, nocca)
t1addrb, t1signb = cisd.t1strs(norbb, noccb)
na = fci.cistring.num_strings(norba, nocca)
nb = fci.cistring.num_strings(norbb, noccb)
ci0 = ci0.reshape(na,nb)
c0 = ci0[0,0]
c1a = ((ci0[t1addra,0] * t1signa).reshape(nvira,nocca).T)[::-1]
c1b = ((ci0[0,t1addrb] * t1signb).reshape(nvirb,noccb).T)[::-1]
c2ab = numpy.einsum('i,j,ij->ij', t1signa, t1signb, ci0[t1addra][:,t1addrb])
c2ab = c2ab.reshape(nvira,nocca,nvirb,noccb).transpose(1,3,0,2)
c2ab = c2ab[::-1,::-1]
t2addra, t2signa = t2strs(norba, nocca)
c2aa = (ci0[t2addra,0] * t2signa).reshape(nvira*(nvira-1)//2,-1).T
c2aa = _unpack_4fold(c2aa[::-1], nocca, nvira)
t2addrb, t2signb = t2strs(norbb, noccb)
c2bb = (ci0[0,t2addrb] * t2signb).reshape(nvirb*(nvirb-1)//2,-1).T
c2bb = _unpack_4fold(c2bb[::-1], noccb, nvirb)
return amplitudes_to_cisdvec(c0, (c1a,c1b), (c2aa,c2ab,c2bb))
def make_rdm1(ci, nmoa_nmob, nocca_noccb):
nmoa, nmob = nmoa_nmob
nocca, noccb = nocca_noccb
c0, c1, c2 = cisdvec_to_amplitudes(ci, nmoa_nmob, nocca_noccb)
c1a, c1b = c1
c2aa, c2ab, c2bb = c2
dova = c0 * c1a
dovb = c0 * c1b
dova += numpy.einsum('jb,ijab->ia', c1a, c2aa)
dova += numpy.einsum('jb,ijab->ia', c1b, c2ab)
dovb += numpy.einsum('jb,ijab->ia', c1b, c2bb)
dovb += numpy.einsum('jb,jiba->ia', c1a, c2ab)
dooa =-numpy.einsum('ia,ka->ik', c1a, c1a)
doob =-numpy.einsum('ia,ka->ik', c1b, c1b)
dooa -= numpy.einsum('ijab,ikab->jk', c2aa, c2aa) * .5
dooa -= numpy.einsum('jiab,kiab->jk', c2ab, c2ab)
doob -= numpy.einsum('ijab,ikab->jk', c2bb, c2bb) * .5
doob -= numpy.einsum('ijab,ikab->jk', c2ab, c2ab)
dvva = numpy.einsum('ia,ic->ca', c1a, c1a)
dvvb = numpy.einsum('ia,ic->ca', c1b, c1b)
dvva += numpy.einsum('ijab,ijac->cb', c2aa, c2aa) * .5
dvva += numpy.einsum('ijba,ijca->cb', c2ab, c2ab)
dvvb += numpy.einsum('ijba,ijca->cb', c2bb, c2bb) * .5
dvvb += numpy.einsum('ijab,ijac->cb', c2ab, c2ab)
dm1a = numpy.empty((nmoa,nmoa))
dm1b = numpy.empty((nmob,nmob))
dm1a[:nocca,nocca:] = dova
dm1b[:noccb,noccb:] = dovb
dm1a[nocca:,:nocca] = dova.T.conj()
dm1b[noccb:,:noccb] = dovb.T.conj()
dm1a[:nocca,:nocca] = dooa
dm1b[:noccb,:noccb] = doob
dm1a[nocca:,nocca:] = dvva
dm1b[noccb:,noccb:] = dvvb
dm1a[numpy.diag_indices(nocca)] += 1
dm1b[numpy.diag_indices(noccb)] += 1
return dm1a, dm1b
def make_rdm2(ci, nmoa_nmob, nocca_noccb):
'''spin-orbital 2pdm in chemist's notation
'''
nmoa, nmob = nmoa_nmob
nocca, noccb = nocca_noccb
c0, c1, c2 = cisdvec_to_amplitudes(ci, nmoa_nmob, nocca_noccb)
c1a, c1b = c1
c2aa, c2ab, c2bb = c2
d2oovv = c0 * c2aa * .5
d2oOvV = c0 * c2ab
d2OOVV = c0 * c2bb * .5
#:dvvvo = numpy.einsum('ia,ikcd->cdak', c1, c2) * .5
d2vvvo = numpy.einsum('ia,ikcd->cdak', c1a, c2aa) * .5
d2vVvO = numpy.einsum('ia,ikcd->cdak', c1a, c2ab)
d2VvVo = numpy.einsum('ia,kidc->cdak', c1b, c2ab)
d2VVVO = numpy.einsum('ia,ikcd->cdak', c1b, c2bb) * .5
#:dovoo = numpy.einsum('ia,klac->ickl', c1, c2) *-.5
d2ovoo = numpy.einsum('ia,klac->ickl', c1a, c2aa) *-.5
d2oVoO =-numpy.einsum('ia,klac->ickl', c1a, c2ab)
d2OvOo =-numpy.einsum('ia,lkca->ickl', c1b, c2ab)
d2OVOO = numpy.einsum('ia,klac->ickl', c1b, c2bb) *-.5
#:doooo = numpy.einsum('klab,ijab->klij', c2, c2) * .25
d2oooo = numpy.einsum('klab,ijab->klij', c2aa, c2aa) * .25
d2oOoO = numpy.einsum('klab,ijab->klij', c2ab, c2ab)
d2OOOO = numpy.einsum('klab,ijab->klij', c2bb, c2bb) * .25
#:dvvvv = numpy.einsum('ijcd,ijab->cdab', c2, c2) * .25
d2vvvv = numpy.einsum('ijcd,ijab->cdab', c2aa, c2aa) * .25
d2vVvV = numpy.einsum('ijcd,ijab->cdab', c2ab, c2ab)
d2VVVV = numpy.einsum('ijcd,ijab->cdab', c2bb, c2bb) * .25
#:dovov =-numpy.einsum('ijab,ikac->jckb', c2, c2)
#:dovov-= numpy.einsum('ia,jb->jaib', c1, c1)
d2ovov =-numpy.einsum('ijab,ikac->jckb', c2aa, c2aa)
d2ovov-= numpy.einsum('jiba,kica->jckb', c2ab, c2ab)
d2oVoV =-numpy.einsum('jIaB,kIaC->jCkB', c2ab, c2ab)
d2OvOv =-numpy.einsum('iJbA,iKcA->JcKb', c2ab, c2ab)
d2OVOV =-numpy.einsum('ijab,ikac->jckb', c2bb, c2bb)
d2OVOV-= numpy.einsum('ijab,ikac->jckb', c2ab, c2ab)
d2ovov-= numpy.einsum('ia,jb->jaib', c1a, c1a)
d2OVOV-= numpy.einsum('ia,jb->jaib', c1b, c1b)
#:dvoov = numpy.einsum('ijab,ikac->cjkb', c2, c2)
#:dvoov+= numpy.einsum('ia,jb->ajib', c1, c1)
d2voov = numpy.einsum('ijab,ikac->cjkb', c2aa, c2aa)
d2voov+= numpy.einsum('jIbA,kIcA->cjkb', c2ab, c2ab)
d2vOoV = numpy.einsum('iJaB,ikac->cJkB', c2ab, c2aa)
d2vOoV+= numpy.einsum('IJAB,kIcA->cJkB', c2bb, c2ab)
d2VOOV = numpy.einsum('ijab,ikac->cjkb', c2bb, c2bb)
d2VOOV+= numpy.einsum('iJaB,iKaC->CJKB', c2ab, c2ab)
d2voov+= numpy.einsum('ia,jb->ajib', c1a, c1a)
d2vOoV+= numpy.einsum('ia,jb->ajib', c1a, c1b)
d2VOOV+= numpy.einsum('ia,jb->ajib', c1b, c1b)
dm2aa = numpy.zeros((nmoa,nmoa,nmoa,nmoa))
dm2ab = numpy.zeros((nmoa,nmoa,nmob,nmob))
dm2bb = numpy.zeros((nmob,nmob,nmob,nmob))
dm2aa[:nocca,:nocca,:nocca,:nocca] = d2oooo - d2oooo.transpose(1,0,2,3)
dm2ab[:nocca,:noccb,:nocca,:noccb] = d2oOoO
dm2bb[:noccb,:noccb,:noccb,:noccb] = d2OOOO - d2OOOO.transpose(1,0,2,3)
dm2aa[:nocca,nocca:,:nocca,:nocca] = d2ovoo - d2ovoo.transpose(0,1,3,2)
dm2aa[nocca:,:nocca,:nocca,:nocca] = dm2aa[:nocca,nocca:,:nocca,:nocca].transpose(1,0,3,2)
dm2aa[:nocca,:nocca,:nocca,nocca:] = dm2aa[:nocca,nocca:,:nocca,:nocca].transpose(2,3,0,1)
dm2aa[:nocca,:nocca,nocca:,:nocca] = dm2aa[:nocca,nocca:,:nocca,:nocca].transpose(3,2,1,0)
dm2ab[:nocca,noccb:,:nocca,:noccb] = d2oVoO
dm2ab[nocca:,:noccb,:nocca,:noccb] = d2OvOo.transpose(1,0,3,2)
dm2ab[:nocca,:noccb,:nocca,noccb:] = dm2ab[:nocca,noccb:,:nocca,:noccb].transpose(2,3,0,1)
dm2ab[:nocca,:noccb,nocca:,:noccb] = dm2ab[nocca:,:noccb,:nocca,:noccb].transpose(2,3,0,1)
dm2bb[:noccb,noccb:,:noccb,:noccb] = d2OVOO - d2OVOO.transpose(0,1,3,2)
dm2bb[noccb:,:noccb,:noccb,:noccb] = dm2bb[:noccb,noccb:,:noccb,:noccb].transpose(1,0,3,2)
dm2bb[:noccb,:noccb,:noccb,noccb:] = dm2bb[:noccb,noccb:,:noccb,:noccb].transpose(2,3,0,1)
dm2bb[:noccb,:noccb,noccb:,:noccb] = dm2bb[:noccb,noccb:,:noccb,:noccb].transpose(3,2,1,0)
dm2aa[:nocca,:nocca,nocca:,nocca:] = d2oovv - d2oovv.transpose(1,0,2,3)
dm2ab[:nocca,:noccb,nocca:,noccb:] = d2oOvV
dm2bb[:noccb,:noccb,noccb:,noccb:] = d2OOVV - d2OOVV.transpose(1,0,2,3)
dm2aa[nocca:,nocca:,:nocca,:nocca] = dm2aa[:nocca,:nocca,nocca:,nocca:].transpose(2,3,0,1)
dm2ab[nocca:,noccb:,:nocca,:noccb] = dm2ab[:nocca,:noccb,nocca:,noccb:].transpose(2,3,0,1)
dm2bb[noccb:,noccb:,:noccb,:noccb] = dm2bb[:noccb,:noccb,noccb:,noccb:].transpose(2,3,0,1)
dm2aa[nocca:,nocca:,nocca:,:nocca] = d2vvvo - d2vvvo.transpose(1,0,2,3)
dm2aa[nocca:,nocca:,:nocca,nocca:] = dm2aa[nocca:,nocca:,nocca:,:nocca].transpose(1,0,3,2)
dm2aa[nocca:,:nocca,nocca:,nocca:] = dm2aa[nocca:,nocca:,nocca:,:nocca].transpose(2,3,0,1)
dm2aa[:nocca,nocca:,nocca:,nocca:] = dm2aa[nocca:,nocca:,nocca:,:nocca].transpose(3,2,1,0)
dm2ab[nocca:,noccb:,nocca:,:noccb] = d2vVvO
dm2ab[nocca:,noccb:,:nocca,noccb:] = d2VvVo.transpose(1,0,3,2)
dm2ab[nocca:,:noccb,nocca:,noccb:] = dm2ab[nocca:,noccb:,nocca:,:noccb].transpose(2,3,0,1)
dm2ab[:nocca,noccb:,nocca:,noccb:] = dm2ab[nocca:,noccb:,:nocca,noccb:].transpose(2,3,0,1)
dm2bb[noccb:,noccb:,noccb:,:noccb] = d2VVVO - d2VVVO.transpose(1,0,2,3)
dm2bb[noccb:,noccb:,:noccb,noccb:] = dm2bb[noccb:,noccb:,noccb:,:noccb].transpose(1,0,3,2)
dm2bb[noccb:,:noccb,noccb:,noccb:] = dm2bb[noccb:,noccb:,noccb:,:noccb].transpose(2,3,0,1)
dm2bb[:noccb,noccb:,noccb:,noccb:] = dm2bb[noccb:,noccb:,noccb:,:noccb].transpose(3,2,1,0)
dm2aa[nocca:,nocca:,nocca:,nocca:] = d2vvvv - d2vvvv.transpose(1,0,2,3)
dm2ab[nocca:,noccb:,nocca:,noccb:] = d2vVvV
dm2bb[noccb:,noccb:,noccb:,noccb:] = d2VVVV - d2VVVV.transpose(1,0,2,3)
dm2aa[:nocca,nocca:,:nocca,nocca:] = d2ovov
dm2aa[nocca:,:nocca,nocca:,:nocca] = dm2aa[:nocca,nocca:,:nocca,nocca:].transpose(1,0,3,2)
dm2ab[:nocca,noccb:,:nocca,noccb:] = d2oVoV
dm2ab[nocca:,:noccb,nocca:,:noccb] = d2OvOv.transpose(1,0,3,2)
dm2bb[:noccb,noccb:,:noccb,noccb:] = d2OVOV
dm2bb[noccb:,:noccb,noccb:,:noccb] = dm2bb[:noccb,noccb:,:noccb,noccb:].transpose(1,0,3,2)
dm2aa[nocca:,:nocca,:nocca,nocca:] = d2voov
dm2aa[:nocca,nocca:,nocca:,:nocca] = dm2aa[nocca:,:nocca,:nocca,nocca:].transpose(1,0,3,2)
dm2ab[nocca:,:noccb,:nocca,noccb:] = d2vOoV
dm2ab[:nocca,noccb:,nocca:,:noccb] = d2vOoV.transpose(2,3,0,1)
dm2bb[noccb:,:noccb,:noccb,noccb:] = d2VOOV
dm2bb[:noccb,noccb:,noccb:,:noccb] = dm2bb[noccb:,:noccb,:noccb,noccb:].transpose(1,0,3,2)
dm1a, dm1b = make_rdm1(ci, nmoa_nmob, nocca_noccb)
dm1a[numpy.diag_indices(nocca)] -= 1
dm1b[numpy.diag_indices(noccb)] -= 1
for i in range(nocca):
for j in range(nocca):
dm2aa[i,j,i,j] += 1
dm2aa[i,j,j,i] -= 1
dm2aa[i,:,i,:] += dm1a
dm2aa[:,i,:,i] += dm1a
dm2aa[:,i,i,:] -= dm1a
dm2aa[i,:,:,i] -= dm1a
for i in range(noccb):
for j in range(noccb):
dm2bb[i,j,i,j] += 1
dm2bb[i,j,j,i] -= 1
dm2bb[i,:,i,:] += dm1b
dm2bb[:,i,:,i] += dm1b
dm2bb[:,i,i,:] -= dm1b
dm2bb[i,:,:,i] -= dm1b
for i in range(nocca):
for j in range(noccb):
dm2ab[i,j,i,j] += 1
dm2ab[i,:,i,:] += dm1b
for i in range(noccb):
dm2ab[:,i,:,i] += dm1a
# To chemist's convention
dm2aa = dm2aa.transpose(0,2,1,3)
dm2ab = dm2ab.transpose(0,2,1,3)
dm2bb = dm2bb.transpose(0,2,1,3)
return dm2aa, dm2ab, dm2bb
class CISD(cisd.CISD):
@property
def nocc(self):
nocca, noccb = self.get_nocc()
return nocca + noccb
@property
def nmo(self):
nmoa, nmob = self.get_nmo()
return nmoa + nmob
get_nocc = uccsd.get_nocc
get_nmo = uccsd.get_nmo
def kernel(self, ci0=None, mo_coeff=None, eris=None):
if eris is None:
eris = self.ao2mo(mo_coeff)
self.converged, self.e_corr, self.ci = \
kernel(self, eris, ci0, max_cycle=self.max_cycle,
tol=self.conv_tol, verbose=self.verbose)
if numpy.all(self.converged):
logger.info(self, 'CISD converged')
else:
logger.info(self, 'CISD not converged')
if self.nroots > 1:
for i,e in enumerate(self.e_tot):
logger.note(self, 'CISD root %d E = %.16g', i, e)
else:
logger.note(self, 'E(CISD) = %.16g E_corr = %.16g',
self.e_tot, self.e_corr)
return self.e_corr, self.ci
def get_init_guess(self, eris=None):
if eris is None:
eris = self.ao2mo(self.mo_coeff)
nocca = eris.nocca
noccb = eris.noccb
mo_ea = eris.focka.diagonal()
mo_eb = eris.fockb.diagonal()
eia_a = mo_ea[:nocca,None] - mo_ea[None,nocca:]
eia_b = mo_eb[:noccb,None] - mo_eb[None,noccb:]
t1a = eris.focka[:nocca,nocca:] / eia_a
t1b = eris.fockb[:noccb,noccb:] / eia_b
eris_voov = _cp(eris.voov)
eris_voOV = _cp(eris.voOV)
eris_VOOV = _cp(eris.VOOV)
t2aa = eris_voov.transpose(1,2,0,3) - eris_voov.transpose(2,1,0,3)
t2bb = eris_VOOV.transpose(1,2,0,3) - eris_VOOV.transpose(2,1,0,3)
t2ab = eris_voOV.transpose(1,2,0,3).copy()
t2aa /= lib.direct_sum('ia+jb->ijab', eia_a, eia_a)
t2ab /= lib.direct_sum('ia+jb->ijab', eia_a, eia_b)
t2bb /= lib.direct_sum('ia+jb->ijab', eia_b, eia_b)
emp2 = numpy.einsum('ia,ia', eris.focka[:nocca,nocca:], t1a)
emp2 += numpy.einsum('ia,ia', eris.fockb[:noccb,noccb:], t1b)
emp2 += numpy.einsum('aijb,ijab', eris_voov, t2aa) * .25
emp2 -= numpy.einsum('ajib,ijab', eris_voov, t2aa) * .25
emp2 += numpy.einsum('aijb,ijab', eris_VOOV, t2bb) * .25
emp2 -= numpy.einsum('ajib,ijab', eris_VOOV, t2bb) * .25
emp2 += numpy.einsum('aijb,ijab', eris_voOV, t2ab)
self.emp2 = emp2
logger.info(self, 'Init t2, MP2 energy = %.15g', self.emp2)
return self.emp2, amplitudes_to_cisdvec(1, (t1a,t1b), (t2aa,t2ab,t2bb))
contract = contract
make_diagonal = make_diagonal
def ao2mo(self, mo_coeff=None):
return _make_eris_incore(self, mo_coeff)
def to_fci(self, cisdvec, nmoa_nmob=None, nocca_noccb=None):
return to_fci(cisdvec, nmoa_nmob, nocca_noccb)
def from_fci(self, fcivec, nmoa_nmob=None, nocca_noccb=None):
return from_fci(fcivec, nmoa_nmob, nocca_noccb)
def make_rdm1(self, ci=None, nmoa_nmob=None, nocca_noccb=None):
if ci is None: ci = self.ci
if nmoa_nmob is None: nmoa_nmob = self.get_nmo()
if nocca_noccb is None: nocca_noccb = self.get_nocc()
return make_rdm1(ci, nmoa_nmob, nocca_noccb)
def make_rdm2(self, ci=None, nmoa_nmob=None, nocca_noccb=None):
if ci is None: ci = self.ci
if nmoa_nmob is None: nmoa_nmob = self.get_nmo()
if nocca_noccb is None: nocca_noccb = self.get_nocc()
return make_rdm2(ci, nmoa_nmob, nocca_noccb)
class _UCISD_ERIs:
def __init__(self, myci, mo_coeff=None):
moidx = uccsd.get_umoidx(myci)
if mo_coeff is None:
mo_coeff = (myci.mo_coeff[0][:,moidx[0]], myci.mo_coeff[1][:,moidx[1]])
else:
mo_coeff = (mo_coeff[0][:,moidx[0]], mo_coeff[1][:,moidx[1]])
# Note: Always recompute the fock matrix in UCISD because the mf object may be
# converted from ROHF object in which orbital energies are eigenvalues of
# Roothaan Fock rather than the true alpha, beta orbital energies.
dm = myci._scf.make_rdm1(myci.mo_coeff, myci.mo_occ)
fockao = myci._scf.get_hcore() + myci._scf.get_veff(myci.mol, dm)
self.focka = reduce(numpy.dot, (mo_coeff[0].T, fockao[0], mo_coeff[0]))
self.fockb = reduce(numpy.dot, (mo_coeff[1].T, fockao[1], mo_coeff[1]))
self.mo_coeff = mo_coeff
self.nocca, self.noccb = myci.get_nocc()
self.oooo = None
self.vooo = None
self.voov = None
self.vvoo = None
self.vovv = None
self.vvvv = None
self.OOOO = None
self.VOOO = None
self.VOOV = None
self.VVOO = None
self.VOVV = None
self.VVVV = None
self.ooOO = None
self.voOO = None
self.voOV = None
self.vvOO = None
self.voVV = None
self.vvVV = None
self.VOoo = None
self.VVoo = None
self.VOvv = None
self.OVvv = None
def _make_eris_incore(myci, mo_coeff=None):
cput0 = (time.clock(), time.time())
eris = _UCISD_ERIs(myci, mo_coeff)
nocca = eris.nocca
noccb = eris.noccb
nmoa = eris.focka.shape[0]
nmob = eris.fockb.shape[0]
nvira = nmoa - nocca
nvirb = nmob - noccb
moa, mob = eris.mo_coeff
eri_aa = ao2mo.restore(1, ao2mo.full(myci._scf._eri, moa), nmoa)
eris.oooo = eri_aa[:nocca,:nocca,:nocca,:nocca].copy()
eris.ooov = eri_aa[:nocca,:nocca,:nocca,nocca:].copy()
eris.vooo = eri_aa[nocca:,:nocca,:nocca,:nocca].copy()
eris.oovo = eri_aa[:nocca,:nocca,nocca:,:nocca].copy()
eris.voov = eri_aa[nocca:,:nocca,:nocca,nocca:].copy()
eris.vvoo = eri_aa[nocca:,nocca:,:nocca,:nocca].copy()
eris.oovv = eri_aa[:nocca,:nocca,nocca:,nocca:].copy()
eris.vovo = eri_aa[nocca:,:nocca,nocca:,:nocca].copy()
eris.vovv = eri_aa[nocca:,:nocca,nocca:,nocca:].copy()
#vovv = eri_aa[nocca:,:nocca,nocca:,nocca:].reshape(-1,nvira,nvira)
#eris.vovv = lib.pack_tril(vovv).reshape(nvira,nocca,nvira*(nvira+1)//2)
eris.vvvv = ao2mo.restore(4, eri_aa[nocca:,nocca:,nocca:,nocca:].copy(), nvira)
vovv = eri_aa = None
eri_bb = ao2mo.restore(1, ao2mo.full(myci._scf._eri, mob), nmob)
eris.OOOO = eri_bb[:noccb,:noccb,:noccb,:noccb].copy()
eris.OOOV = eri_bb[:noccb,:noccb,:noccb,noccb:].copy()
eris.VOOO = eri_bb[noccb:,:noccb,:noccb,:noccb].copy()
eris.OOVO = eri_bb[:noccb,:noccb,noccb:,:noccb].copy()
eris.VOOV = eri_bb[noccb:,:noccb,:noccb,noccb:].copy()
eris.VVOO = eri_bb[noccb:,noccb:,:noccb,:noccb].copy()
eris.OOVV = eri_bb[:noccb,:noccb,noccb:,noccb:].copy()
eris.VOVO = eri_bb[noccb:,:noccb,noccb:,:noccb].copy()
eris.VOVV = eri_bb[noccb:,:noccb,noccb:,noccb:].copy()
#VOVV = eri_bb[noccb:,:noccb,noccb:,noccb:].reshape(-1,nvirb,nvirb)
#eris.VOVV = lib.pack_tril(VOVV).reshape(nvirb,noccb,nvirb*(nvirb+1)//2)
eris.VVVV = ao2mo.restore(4, eri_bb[noccb:,noccb:,noccb:,noccb:].copy(), nvirb)
VOVV = eri_bb = None
eri_ab = ao2mo.general(myci._scf._eri, (moa,moa,mob,mob), compact=False)
eri_ab = eri_ab.reshape(nmoa,nmoa,nmob,nmob)
eris.ooOO = eri_ab[:nocca,:nocca,:noccb,:noccb].copy()
eris.ooOV = eri_ab[:nocca,:nocca,:noccb,noccb:].copy()
eris.voOO = eri_ab[nocca:,:nocca,:noccb,:noccb].copy()
eris.ooVO = eri_ab[:nocca,:nocca,noccb:,:noccb].copy()
eris.voOV = eri_ab[nocca:,:nocca,:noccb,noccb:].copy()
eris.ooVV = eri_ab[:nocca,:nocca,noccb:,noccb:].copy()
eris.vvOO = eri_ab[nocca:,nocca:,:noccb,:noccb].copy()
eris.voVO = eri_ab[nocca:,:nocca,noccb:,:noccb].copy()
eris.voVV = eri_ab[nocca:,:nocca,noccb:,noccb:].copy()
#voVV = eri_ab[nocca:,:nocca,noccb:,noccb:].reshape(nocca*nvira,nvirb,nvirb)
#eris.voVV = lib.pack_tril(voVV).reshape(nvira,nocca,nvirb*(nvirb+1)//2)
voVV = None
vvVV = eri_ab[nocca:,nocca:,noccb:,noccb:].reshape(nvira**2,nvirb**2)
idxa = numpy.tril_indices(nvira)
idxb = numpy.tril_indices(nvirb)
eris.vvVV = lib.take_2d(vvVV, idxa[0]*nvira+idxa[1], idxb[0]*nvirb+idxb[1])
eri_ba = lib.transpose(eri_ab.reshape(nmoa**2,nmob**2))
eri_ba = eri_ba.reshape(nmob,nmob,nmoa,nmoa)
eris.OOoo = eri_ba[:noccb,:noccb,:nocca,:nocca].copy()
eris.OOov = eri_ba[:noccb,:noccb,:nocca,nocca:].copy()
eris.VOoo = eri_ba[noccb:,:noccb,:nocca,:nocca].copy()
eris.OOvo = eri_ba[:noccb,:noccb,nocca:,:nocca].copy()
eris.VOov = eri_ba[noccb:,:noccb,:nocca,nocca:].copy()
eris.VVoo = eri_ba[noccb:,noccb:,:nocca,:nocca].copy()
eris.VOvo = eri_ba[noccb:,:noccb,nocca:,:nocca].copy()
eris.VOvv = eri_ba[noccb:,:noccb,nocca:,nocca:].copy()
#VOvv = eri_ba[noccb:,:noccb,nocca:,nocca:].reshape(noccb*nvirb,nvira,nvira)
#eris.VOvv = lib.pack_tril(VOvv).reshape(nvirb,noccb,nvira*(nvira+1)//2)
VOvv = None
eris.VVvv = eri_ba[noccb:,noccb:,nocca:,nocca:].copy()
return eris
def _cp(a):
return numpy.array(a, copy=False, order='C')
def _restore(mat, nvira, nvirb):
mat1 = numpy.zeros((nvira*nvira,nvirb*nvirb))
idxa = numpy.tril_indices(nvira)
idxb = numpy.tril_indices(nvirb)
lib.takebak_2d(mat1, mat, idxa[0]*nvira+idxa[1], idxb[0]*nvirb+idxb[1])
lib.takebak_2d(mat1, mat, idxa[0]*nvira+idxa[1], idxb[1]*nvirb+idxb[0])
lib.takebak_2d(mat1, mat, idxa[1]*nvira+idxa[0], idxb[0]*nvirb+idxb[1])
lib.takebak_2d(mat1, mat, idxa[1]*nvira+idxa[0], idxb[1]*nvirb+idxb[0])
mat1 = mat1.reshape(nvira,nvira,nvirb,nvirb)
idxa = numpy.arange(nvira)
idxb = numpy.arange(nvirb)
mat1[idxa,idxa] *= .5
mat1[:,:,idxb,idxb] *= .5
return mat1
if __name__ == '__main__':
from pyscf import gto
from pyscf import scf
from pyscf import fci
numpy.random.seed(12)
nocc = 3
nvir = 5
nmo = nocc + nvir
c1a = numpy.random.random((nocc,nvir))
c1b = numpy.random.random((nocc,nvir))
c2aa = numpy.random.random((nocc,nocc,nvir,nvir))
c2bb = numpy.random.random((nocc,nocc,nvir,nvir))
c2ab = numpy.random.random((nocc,nocc,nvir,nvir))
c1 = (c1a, c1b)
c2 = (c2aa, c2ab, c2bb)
cisdvec = amplitudes_to_cisdvec(1., c1, c2)
fcivec = to_fci(cisdvec, (nmo,nmo), (nocc,nocc))
cisdvec1 = from_fci(fcivec, (nmo,nmo), (nocc,nocc))
print(abs(cisdvec-cisdvec1).sum())
ci1 = to_fci(cisdvec1, (nmo,nmo), (nocc,nocc))
print(abs(fcivec-ci1).sum())
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
['H', ( 1.,-1. , 0. )],
['H', ( 0.,-1. ,-1. )],
['H', ( 1.,-0.5 , 0. )],
['H', ( 0.,-1. , 1. )],
]
mol.charge = -2
mol.spin = 2
mol.basis = '3-21g'
mol.build()
mf = scf.UHF(mol).run(conv_tol=1e-14)
ehf0 = mf.e_tot - mol.energy_nuc()
myci = CISD(mf)
numpy.random.seed(10)
mo = numpy.random.random(myci.mo_coeff.shape)
eris = myci.ao2mo(mo)
numpy.random.seed(12)
nocca, noccb = mol.nelec
nmo = mf.mo_occ[0].size
nvira = nmo - nocca
nvirb = nmo - noccb
c1a = .1 * numpy.random.random((nocca,nvira))
c1b = .1 * numpy.random.random((noccb,nvirb))
c2aa = .1 * numpy.random.random((nocca,nocca,nvira,nvira))
c2bb = .1 * numpy.random.random((noccb,noccb,nvirb,nvirb))
c2ab = .1 * numpy.random.random((nocca,noccb,nvira,nvirb))
cisdvec = amplitudes_to_cisdvec(1., (c1a, c1b), (c2aa, c2ab, c2bb))
hcisd0 = contract(myci, amplitudes_to_cisdvec(1., (c1a,c1b), (c2aa,c2ab,c2bb)), eris)
# from pyscf.ci import gcisd_slow
# res = cisdvec_to_amplitudes(hcisd0, nmoa_nmob, nocca_noccb)
# res = (res[0],
# uccsd.spatial2spin(res[1], eris.orbspin),
# uccsd.spatial2spin(res[2], eris.orbspin))
# print(lib.finger(gcisd_slow.amplitudes_to_cisdvec(*res)) - 187.10206473716548)
print(lib.finger(hcisd0) - 466.56620234351681)
eris = myci.ao2mo(mf.mo_coeff)
hcisd0 = contract(myci, cisdvec, eris)
eri_aa = ao2mo.kernel(mf._eri, mf.mo_coeff[0])
eri_bb = ao2mo.kernel(mf._eri, mf.mo_coeff[1])
eri_ab = ao2mo.kernel(mf._eri, [mf.mo_coeff[0], mf.mo_coeff[0],
mf.mo_coeff[1], mf.mo_coeff[1]])
h1a = reduce(numpy.dot, (mf.mo_coeff[0].T, mf.get_hcore(), mf.mo_coeff[0]))
h1b = reduce(numpy.dot, (mf.mo_coeff[1].T, mf.get_hcore(), mf.mo_coeff[1]))
h2e = fci.direct_uhf.absorb_h1e((h1a,h1b), (eri_aa,eri_ab,eri_bb),
h1a.shape[0], mol.nelec, .5)
nmo = (mf.mo_coeff[0].shape[1],mf.mo_coeff[1].shape[1])
fcivec = to_fci(cisdvec, nmo, mol.nelec)
hci1 = fci.direct_uhf.contract_2e(h2e, fcivec, h1a.shape[0], mol.nelec)
hci1 -= ehf0 * fcivec
hcisd1 = from_fci(hci1, nmo, mol.nelec)
print(numpy.linalg.norm(hcisd1-hcisd0) / numpy.linalg.norm(hcisd0))
hdiag0 = make_diagonal(myci, eris)
hdiag0 = to_fci(hdiag0, nmo, mol.nelec).ravel()
hdiag0 = from_fci(hdiag0, nmo, mol.nelec).ravel()
hdiag1 = fci.direct_uhf.make_hdiag((h1a,h1b), (eri_aa,eri_ab,eri_bb),
h1a.shape[0], mol.nelec)
hdiag1 = from_fci(hdiag1, nmo, mol.nelec).ravel()
print(numpy.linalg.norm(abs(hdiag0)-abs(hdiag1)))
ecisd = myci.kernel(eris=eris)[0]
efci = fci.direct_uhf.kernel((h1a,h1b), (eri_aa,eri_ab,eri_bb),
h1a.shape[0], mol.nelec)[0]
print(ecisd, ecisd - -0.037067274690894436, '> E(fci)', efci-ehf0)
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
['H', ( 1.,-1. , 0. )],
['H', ( 0.,-1. ,-1. )],
['H', ( 1.,-0.5 , 0. )],
['H', ( 0.,-1. , 1. )],
]
mol.charge = 2
mol.spin = 2
mol.basis = '6-31g'
mol.build()
mf = scf.UHF(mol).run(conv_tol=1e-14)
ehf0 = mf.e_tot - mol.energy_nuc()
myci = CISD(mf)
eris = myci.ao2mo()
ecisd = myci.kernel(eris=eris)[0]
eri_aa = ao2mo.kernel(mf._eri, mf.mo_coeff[0])
eri_bb = ao2mo.kernel(mf._eri, mf.mo_coeff[1])
eri_ab = ao2mo.kernel(mf._eri, [mf.mo_coeff[0], mf.mo_coeff[0],
mf.mo_coeff[1], mf.mo_coeff[1]])
h1a = reduce(numpy.dot, (mf.mo_coeff[0].T, mf.get_hcore(), mf.mo_coeff[0]))
h1b = reduce(numpy.dot, (mf.mo_coeff[1].T, mf.get_hcore(), mf.mo_coeff[1]))
efci, fcivec = fci.direct_uhf.kernel((h1a,h1b), (eri_aa,eri_ab,eri_bb),
h1a.shape[0], mol.nelec)
print(ecisd, '== E(fci)', efci-ehf0)
dm1ref, dm2ref = fci.direct_uhf.make_rdm12s(fcivec, h1a.shape[0], mol.nelec)
rdm1 = make_rdm1(myci.ci, myci.get_nmo(), myci.get_nocc())
rdm2 = make_rdm2(myci.ci, myci.get_nmo(), myci.get_nocc())
print('dm1a', abs(dm1ref[0] - rdm1[0]).max())
print('dm1b', abs(dm1ref[1] - rdm1[1]).max())
print('dm2aa', abs(dm2ref[0] - rdm2[0]).max())
print('dm2ab', abs(dm2ref[1] - rdm2[1]).max())
print('dm2bb', abs(dm2ref[2] - rdm2[2]).max())
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
['O', ( 0., 0. , 0. )],
['H', ( 0., -0.757, 0.587)],
['H', ( 0., 0.757 , 0.587)],]
mol.basis = {'H': 'sto-3g',
'O': 'sto-3g',}
mol.build()
mf = scf.UHF(mol).run(conv_tol=1e-14)
myci = CISD(mf)
eris = myci.ao2mo()
ecisd, civec = myci.kernel(eris=eris)