def test_update_lambda_real(self):
numpy.random.seed(21)
eris = mycc.ao2mo()
gcc1 = gccsd.GCCSD(scf.addons.convert_to_ghf(mf))
eri1 = gcc1.ao2mo()
orbspin = eri1.orbspin
nocc = mol.nelectron
nvir = mol.nao_nr() * 2 - nocc
t1r = numpy.random.random((nocc, nvir)) * .1
t2r = numpy.random.random((nocc, nocc, nvir, nvir)) * .1
t2r = t2r - t2r.transpose(1, 0, 2, 3)
t2r = t2r - t2r.transpose(0, 1, 3, 2)
l1r = numpy.random.random((nocc, nvir)) * .1
l2r = numpy.random.random((nocc, nocc, nvir, nvir)) * .1
l2r = l2r - l2r.transpose(1, 0, 2, 3)
l2r = l2r - l2r.transpose(0, 1, 3, 2)
t1r = addons.spin2spatial(t1r, orbspin)
t2r = addons.spin2spatial(t2r, orbspin)
t1r = addons.spatial2spin(t1r, orbspin)
t2r = addons.spatial2spin(t2r, orbspin)
l1r = addons.spin2spatial(l1r, orbspin)
l2r = addons.spin2spatial(l2r, orbspin)
l1r = addons.spatial2spin(l1r, orbspin)
l2r = addons.spatial2spin(l2r, orbspin)
imds = gccsd_lambda.make_intermediates(gcc1, t1r, t2r, eri1)
l1ref, l2ref = gccsd_lambda.update_lambda(gcc1, t1r, t2r, l1r, l2r,
eri1, imds)
t1 = addons.spin2spatial(t1r, orbspin)
t2 = addons.spin2spatial(t2r, orbspin)
l1 = addons.spin2spatial(l1r, orbspin)
l2 = addons.spin2spatial(l2r, orbspin)
imds = uccsd_lambda.make_intermediates(mycc, t1, t2, eris)
l1, l2 = uccsd_lambda.update_lambda(mycc, t1, t2, l1, l2, eris, imds)
self.assertAlmostEqual(
float(abs(addons.spatial2spin(l1, orbspin) - l1ref).max()), 0, 8)
self.assertAlmostEqual(
float(abs(addons.spatial2spin(l2, orbspin) - l2ref).max()), 0, 8)
l1ref = addons.spin2spatial(l1ref, orbspin)
l2ref = addons.spin2spatial(l2ref, orbspin)
self.assertAlmostEqual(abs(l1[0] - l1ref[0]).max(), 0, 8)
self.assertAlmostEqual(abs(l1[1] - l1ref[1]).max(), 0, 8)
self.assertAlmostEqual(abs(l2[0] - l2ref[0]).max(), 0, 8)
self.assertAlmostEqual(abs(l2[1] - l2ref[1]).max(), 0, 8)
self.assertAlmostEqual(abs(l2[2] - l2ref[2]).max(), 0, 8)
def test_update_lambda_real(self):
numpy.random.seed(21)
eris = mycc.ao2mo()
gcc1 = gccsd.GCCSD(scf.addons.convert_to_ghf(mf))
eri1 = gcc1.ao2mo()
orbspin = eri1.orbspin
nocc = mol.nelectron
nvir = mol.nao_nr()*2 - nocc
t1r = numpy.random.random((nocc,nvir))*.1
t2r = numpy.random.random((nocc,nocc,nvir,nvir))*.1
t2r = t2r - t2r.transpose(1,0,2,3)
t2r = t2r - t2r.transpose(0,1,3,2)
l1r = numpy.random.random((nocc,nvir))*.1
l2r = numpy.random.random((nocc,nocc,nvir,nvir))*.1
l2r = l2r - l2r.transpose(1,0,2,3)
l2r = l2r - l2r.transpose(0,1,3,2)
t1r = addons.spin2spatial(t1r, orbspin)
t2r = addons.spin2spatial(t2r, orbspin)
t1r = addons.spatial2spin(t1r, orbspin)
t2r = addons.spatial2spin(t2r, orbspin)
l1r = addons.spin2spatial(l1r, orbspin)
l2r = addons.spin2spatial(l2r, orbspin)
l1r = addons.spatial2spin(l1r, orbspin)
l2r = addons.spatial2spin(l2r, orbspin)
imds = gccsd_lambda.make_intermediates(gcc1, t1r, t2r, eri1)
l1ref, l2ref = gccsd_lambda.update_lambda(gcc1, t1r, t2r, l1r, l2r, eri1, imds)
t1 = addons.spin2spatial(t1r, orbspin)
t2 = addons.spin2spatial(t2r, orbspin)
l1 = addons.spin2spatial(l1r, orbspin)
l2 = addons.spin2spatial(l2r, orbspin)
imds = uccsd_lambda.make_intermediates(mycc, t1, t2, eris)
l1, l2 = uccsd_lambda.update_lambda(mycc, t1, t2, l1, l2, eris, imds)
self.assertAlmostEqual(float(abs(addons.spatial2spin(l1, orbspin)-l1ref).max()), 0, 8)
self.assertAlmostEqual(float(abs(addons.spatial2spin(l2, orbspin)-l2ref).max()), 0, 8)
l1ref = addons.spin2spatial(l1ref, orbspin)
l2ref = addons.spin2spatial(l2ref, orbspin)
self.assertAlmostEqual(abs(l1[0]-l1ref[0]).max(), 0, 8)
self.assertAlmostEqual(abs(l1[1]-l1ref[1]).max(), 0, 8)
self.assertAlmostEqual(abs(l2[0]-l2ref[0]).max(), 0, 8)
self.assertAlmostEqual(abs(l2[1]-l2ref[1]).max(), 0, 8)
self.assertAlmostEqual(abs(l2[2]-l2ref[2]).max(), 0, 8)
def make_intermediates(mycc, t1, t2, eris):
from pyscf.cc import uccsd_t_slow
def p6(t):
return (t + t.transpose(1,2,0,4,5,3) +
t.transpose(2,0,1,5,3,4) + t.transpose(0,2,1,3,5,4) +
t.transpose(2,1,0,5,4,3) + t.transpose(1,0,2,4,3,5))
def r6(w):
return (w + w.transpose(2,0,1,3,4,5) + w.transpose(1,2,0,3,4,5)
- w.transpose(2,1,0,3,4,5) - w.transpose(0,2,1,3,4,5)
- w.transpose(1,0,2,3,4,5))
imds = uccsd_lambda.make_intermediates(mycc, t1, t2, eris)
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb = t2ab.shape[:2]
nmoa = eris.focka.shape[0]
nmob = eris.fockb.shape[0]
mo_ea = eris.focka.diagonal().real
mo_eb = eris.fockb.diagonal().real
eia = mo_ea[:nocca,None] - mo_ea[nocca:]
eIA = mo_eb[:noccb,None] - mo_eb[noccb:]
fvo = eris.focka[nocca:,:nocca]
fVO = eris.fockb[noccb:,:noccb]
# aaa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
w = numpy.einsum('ijae,kceb->ijkabc', t2aa, numpy.asarray(eris.get_ovvv()).conj())
w-= numpy.einsum('mkbc,iajm->ijkabc', t2aa, numpy.asarray(eris.ovoo.conj()))
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.ovov).conj(), t1a)
v+= numpy.einsum('jkbc,ai->ijkabc', t2aa, fvo) * .5
rw = r6(p6(w)) / d3
imds.l1a_t = numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.ovov)) / eia * .25
wvd = r6(p6(w * 2 + v)) / d3
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_ovvv()).conj())
l2_t -= numpy.einsum('ijkabc,iajm->mkbc', wvd, numpy.asarray(eris.ovoo.conj()))
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fvo)
imds.l2aa_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eia) * .5
# bbb
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2bb, numpy.asarray(eris.get_OVVV()).conj())
w-= numpy.einsum('imab,kcjm->ijkabc', t2bb, numpy.asarray(eris.OVOO.conj()))
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1b)
v+= numpy.einsum('jkbc,ai->ijkabc', t2bb, fVO) * .5
rw = r6(p6(w)) / d3
imds.l1b_t = numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.OVOV)) / eIA * .25
wvd = r6(p6(w * 2 + v)) / d3
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_OVVV()).conj())
l2_t -= numpy.einsum('ijkabc,iajm->mkbc', wvd, numpy.asarray(eris.OVOO.conj()))
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fVO)
imds.l2bb_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eIA, eIA) * .5
# baa
def r4(w):
w = w - w.transpose(0,2,1,3,4,5)
w = w + w.transpose(0,2,1,3,5,4)
return w
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eia, eia)
w = numpy.einsum('jIeA,kceb->IjkAbc', t2ab, numpy.asarray(eris.get_ovvv()).conj()) * 2
w += numpy.einsum('jIbE,kcEA->IjkAbc', t2ab, numpy.asarray(eris.get_ovVV()).conj()) * 2
w += numpy.einsum('jkbe,IAec->IjkAbc', t2aa, numpy.asarray(eris.get_OVvv()).conj())
w -= numpy.einsum('mIbA,kcjm->IjkAbc', t2ab, numpy.asarray(eris.ovoo).conj()) * 2
w -= numpy.einsum('jMbA,kcIM->IjkAbc', t2ab, numpy.asarray(eris.ovOO).conj()) * 2
w -= numpy.einsum('jmbc,IAkm->IjkAbc', t2aa, numpy.asarray(eris.OVoo).conj())
v = numpy.einsum('jbkc,IA->IjkAbc', numpy.asarray(eris.ovov).conj(), t1b)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('jkbc,AI->IjkAbc', t2aa, fVO) * .5
v += numpy.einsum('kIcA,bj->IjkAbc', t2ab, fvo) * 2
rw = r4(w) / d3
imds.l1a_t += numpy.einsum('ijkabc,kcia->jb', rw.conj(),
numpy.asarray(eris.ovOV)) / eia * .5
imds.l1b_t += numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.ovov)) / eIA * .25
wvd = r4(w * 2 + v) / d3
l2_t = numpy.einsum('ijkabc,iaec->jkbe', wvd, numpy.asarray(eris.get_OVvv()).conj())
l2_t -= numpy.einsum('ijkabc,iakm->jmbc', wvd, numpy.asarray(eris.OVoo).conj())
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fVO)
imds.l2aa_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eia) * .5
l2_t = numpy.einsum('ijkabc,kceb->jiea', wvd, numpy.asarray(eris.get_ovvv()).conj())
l2_t += numpy.einsum('ijkabc,kcea->jibe', wvd, numpy.asarray(eris.get_ovVV()).conj())
l2_t -= numpy.einsum('ijkabc,kcjm->miba', wvd, numpy.asarray(eris.ovoo).conj())
l2_t -= numpy.einsum('ijkabc,kcim->jmba', wvd, numpy.asarray(eris.ovOO).conj())
l2_t += numpy.einsum('ijkabc,bj->kica', rw, fvo)
imds.l2ab_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eIA) * .5
# bba
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2ab, numpy.asarray(eris.get_OVVV()).conj()) * 2
w += numpy.einsum('ijeb,kcea->ijkabc', t2ab, numpy.asarray(eris.get_OVvv()).conj()) * 2
w += numpy.einsum('jkbe,iaec->ijkabc', t2bb, numpy.asarray(eris.get_ovVV()).conj())
w -= numpy.einsum('imab,kcjm->ijkabc', t2ab, numpy.asarray(eris.OVOO).conj()) * 2
w -= numpy.einsum('mjab,kcim->ijkabc', t2ab, numpy.asarray(eris.OVoo).conj()) * 2
w -= numpy.einsum('jmbc,iakm->ijkabc', t2bb, numpy.asarray(eris.ovOO).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1a)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('JKBC,ai->iJKaBC', t2bb, fvo) * .5
v += numpy.einsum('iKaC,BJ->iJKaBC', t2ab, fVO) * 2
rw = r4(w) / d3
imds.l1a_t += numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.OVOV)) / eia * .25
imds.l1b_t += numpy.einsum('ijkabc,iakc->jb', rw.conj(),
numpy.asarray(eris.ovOV)) / eIA * .5
wvd = r4(w * 2 + v) / d3
l2_t = numpy.einsum('ijkabc,iaec->jkbe', wvd, numpy.asarray(eris.get_ovVV()).conj())
l2_t -= numpy.einsum('ijkabc,iakm->jmbc', wvd, numpy.asarray(eris.ovOO).conj())
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fvo)
imds.l2bb_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eIA, eIA) * .5
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_OVVV()).conj())
l2_t += numpy.einsum('ijkabc,kcea->ijeb', wvd, numpy.asarray(eris.get_OVvv()).conj())
l2_t -= numpy.einsum('ijkabc,kcjm->imab', wvd, numpy.asarray(eris.OVOO).conj())
l2_t -= numpy.einsum('ijkabc,kcim->mjab', wvd, numpy.asarray(eris.OVoo).conj())
l2_t += numpy.einsum('ijkabc,bj->ikac', rw, fVO)
imds.l2ab_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eIA) * .5
return imds
def test_update_lambda_complex(self):
nocca, noccb = mol.nelec
nmo = mol.nao_nr()
nvira,nvirb = nmo-nocca, nmo-noccb
numpy.random.seed(9)
t1 = [numpy.random.random((nocca,nvira))-.9,
numpy.random.random((noccb,nvirb))-.9]
l1 = [numpy.random.random((nocca,nvira))-.9,
numpy.random.random((noccb,nvirb))-.9]
t2 = [numpy.random.random((nocca,nocca,nvira,nvira))-.9,
numpy.random.random((nocca,noccb,nvira,nvirb))-.9,
numpy.random.random((noccb,noccb,nvirb,nvirb))-.9]
t2[0] = t2[0] - t2[0].transpose(1,0,2,3)
t2[0] = t2[0] - t2[0].transpose(0,1,3,2)
t2[2] = t2[2] - t2[2].transpose(1,0,2,3)
t2[2] = t2[2] - t2[2].transpose(0,1,3,2)
l2 = [numpy.random.random((nocca,nocca,nvira,nvira))-.9,
numpy.random.random((nocca,noccb,nvira,nvirb))-.9,
numpy.random.random((noccb,noccb,nvirb,nvirb))-.9]
l2[0] = l2[0] - l2[0].transpose(1,0,2,3)
l2[0] = l2[0] - l2[0].transpose(0,1,3,2)
l2[2] = l2[2] - l2[2].transpose(1,0,2,3)
l2[2] = l2[2] - l2[2].transpose(0,1,3,2)
# eris = mycc.ao2mo()
# imds = make_intermediates(mycc, t1, t2, eris)
# l1new, l2new = update_lambda(mycc, t1, t2, l1, l2, eris, imds)
# print(lib.finger(l1new[0]) --104.55975252585894)
# print(lib.finger(l1new[1]) --241.12677819375281)
# print(lib.finger(l2new[0]) --0.4957533529669417)
# print(lib.finger(l2new[1]) - 15.46423057451851 )
# print(lib.finger(l2new[2]) - 5.8430776663704407)
nocca, noccb = mol.nelec
mo_a = mf.mo_coeff[0] + numpy.sin(mf.mo_coeff[0]) * .01j
mo_b = mf.mo_coeff[1] + numpy.sin(mf.mo_coeff[1]) * .01j
nao = mo_a.shape[0]
eri = ao2mo.restore(1, mf._eri, nao)
eri0aa = lib.einsum('pqrs,pi,qj,rk,sl->ijkl', eri, mo_a.conj(), mo_a, mo_a.conj(), mo_a)
eri0ab = lib.einsum('pqrs,pi,qj,rk,sl->ijkl', eri, mo_a.conj(), mo_a, mo_b.conj(), mo_b)
eri0bb = lib.einsum('pqrs,pi,qj,rk,sl->ijkl', eri, mo_b.conj(), mo_b, mo_b.conj(), mo_b)
eri0ba = eri0ab.transpose(2,3,0,1)
nvira = nao - nocca
nvirb = nao - noccb
eris = uccsd._ChemistsERIs(mol)
eris.oooo = eri0aa[:nocca,:nocca,:nocca,:nocca].copy()
eris.ovoo = eri0aa[:nocca,nocca:,:nocca,:nocca].copy()
eris.oovv = eri0aa[:nocca,:nocca,nocca:,nocca:].copy()
eris.ovvo = eri0aa[:nocca,nocca:,nocca:,:nocca].copy()
eris.ovov = eri0aa[:nocca,nocca:,:nocca,nocca:].copy()
eris.ovvv = eri0aa[:nocca,nocca:,nocca:,nocca:].copy()
eris.vvvv = eri0aa[nocca:,nocca:,nocca:,nocca:].copy()
eris.OOOO = eri0bb[:noccb,:noccb,:noccb,:noccb].copy()
eris.OVOO = eri0bb[:noccb,noccb:,:noccb,:noccb].copy()
eris.OOVV = eri0bb[:noccb,:noccb,noccb:,noccb:].copy()
eris.OVVO = eri0bb[:noccb,noccb:,noccb:,:noccb].copy()
eris.OVOV = eri0bb[:noccb,noccb:,:noccb,noccb:].copy()
eris.OVVV = eri0bb[:noccb,noccb:,noccb:,noccb:].copy()
eris.VVVV = eri0bb[noccb:,noccb:,noccb:,noccb:].copy()
eris.ooOO = eri0ab[:nocca,:nocca,:noccb,:noccb].copy()
eris.ovOO = eri0ab[:nocca,nocca:,:noccb,:noccb].copy()
eris.ooVV = eri0ab[:nocca,:nocca,noccb:,noccb:].copy()
eris.ovVO = eri0ab[:nocca,nocca:,noccb:,:noccb].copy()
eris.ovOV = eri0ab[:nocca,nocca:,:noccb,noccb:].copy()
eris.ovVV = eri0ab[:nocca,nocca:,noccb:,noccb:].copy()
eris.vvVV = eri0ab[nocca:,nocca:,noccb:,noccb:].copy()
eris.OOoo = eri0ba[:noccb,:noccb,:nocca,:nocca].copy()
eris.OVoo = eri0ba[:noccb,noccb:,:nocca,:nocca].copy()
eris.OOvv = eri0ba[:noccb,:noccb,nocca:,nocca:].copy()
eris.OVvo = eri0ba[:noccb,noccb:,nocca:,:nocca].copy()
eris.OVov = eri0ba[:noccb,noccb:,:nocca,nocca:].copy()
eris.OVvv = eri0ba[:noccb,noccb:,nocca:,nocca:].copy()
eris.VVvv = eri0ba[noccb:,noccb:,nocca:,nocca:].copy()
eris.focka = numpy.diag(mf.mo_energy[0])
eris.fockb = numpy.diag(mf.mo_energy[1])
eris.mo_energy = mf.mo_energy
t1[0] = t1[0] + numpy.sin(t1[0]) * .05j
t1[1] = t1[1] + numpy.sin(t1[1]) * .05j
t2[0] = t2[0] + numpy.sin(t2[0]) * .05j
t2[1] = t2[1] + numpy.sin(t2[1]) * .05j
t2[2] = t2[2] + numpy.sin(t2[2]) * .05j
l1[0] = l1[0] + numpy.sin(l1[0]) * .05j
l1[1] = l1[1] + numpy.sin(l1[1]) * .05j
l2[0] = l2[0] + numpy.sin(l2[0]) * .05j
l2[1] = l2[1] + numpy.sin(l2[1]) * .05j
l2[2] = l2[2] + numpy.sin(l2[2]) * .05j
imds = uccsd_lambda.make_intermediates(mycc, t1, t2, eris)
l1new_ref, l2new_ref = uccsd_lambda.update_lambda(mycc, t1, t2, l1, l2, eris, imds)
nocc = nocca + noccb
orbspin = numpy.zeros(nao*2, dtype=int)
orbspin[1::2] = 1
orbspin[nocc-1] = 0
orbspin[nocc ] = 1
eri1 = numpy.zeros([nao*2]*4, dtype=numpy.complex)
idxa = numpy.where(orbspin == 0)[0]
idxb = numpy.where(orbspin == 1)[0]
eri1[idxa[:,None,None,None],idxa[:,None,None],idxa[:,None],idxa] = eri0aa
eri1[idxa[:,None,None,None],idxa[:,None,None],idxb[:,None],idxb] = eri0ab
eri1[idxb[:,None,None,None],idxb[:,None,None],idxa[:,None],idxa] = eri0ba
eri1[idxb[:,None,None,None],idxb[:,None,None],idxb[:,None],idxb] = eri0bb
eri1 = eri1.transpose(0,2,1,3) - eri1.transpose(0,2,3,1)
erig = gccsd._PhysicistsERIs()
erig.oooo = eri1[:nocc,:nocc,:nocc,:nocc].copy()
erig.ooov = eri1[:nocc,:nocc,:nocc,nocc:].copy()
erig.ovov = eri1[:nocc,nocc:,:nocc,nocc:].copy()
erig.ovvo = eri1[:nocc,nocc:,nocc:,:nocc].copy()
erig.oovv = eri1[:nocc,:nocc,nocc:,nocc:].copy()
erig.ovvv = eri1[:nocc,nocc:,nocc:,nocc:].copy()
erig.vvvv = eri1[nocc:,nocc:,nocc:,nocc:].copy()
mo_e = numpy.empty(nao*2)
mo_e[orbspin==0] = mf.mo_energy[0]
mo_e[orbspin==1] = mf.mo_energy[1]
erig.fock = numpy.diag(mo_e)
erig.mo_energy = mo_e.real
myccg = gccsd.GCCSD(scf.addons.convert_to_ghf(mf))
t1 = myccg.spatial2spin(t1, orbspin)
t2 = myccg.spatial2spin(t2, orbspin)
l1 = myccg.spatial2spin(l1, orbspin)
l2 = myccg.spatial2spin(l2, orbspin)
imds = gccsd_lambda.make_intermediates(myccg, t1, t2, erig)
l1new, l2new = gccsd_lambda.update_lambda(myccg, t1, t2, l1, l2, erig, imds)
l1new = myccg.spin2spatial(l1new, orbspin)
l2new = myccg.spin2spatial(l2new, orbspin)
self.assertAlmostEqual(abs(l1new[0] - l1new_ref[0]).max(), 0, 11)
self.assertAlmostEqual(abs(l1new[1] - l1new_ref[1]).max(), 0, 11)
self.assertAlmostEqual(abs(l2new[0] - l2new_ref[0]).max(), 0, 11)
self.assertAlmostEqual(abs(l2new[1] - l2new_ref[1]).max(), 0, 11)
self.assertAlmostEqual(abs(l2new[2] - l2new_ref[2]).max(), 0, 11)
def test_update_lambda_complex(self):
nocca, noccb = mol.nelec
nmo = mol.nao_nr()
nvira, nvirb = nmo - nocca, nmo - noccb
numpy.random.seed(9)
t1 = [
numpy.random.random((nocca, nvira)) - .9,
numpy.random.random((noccb, nvirb)) - .9
]
l1 = [
numpy.random.random((nocca, nvira)) - .9,
numpy.random.random((noccb, nvirb)) - .9
]
t2 = [
numpy.random.random((nocca, nocca, nvira, nvira)) - .9,
numpy.random.random((nocca, noccb, nvira, nvirb)) - .9,
numpy.random.random((noccb, noccb, nvirb, nvirb)) - .9
]
t2[0] = t2[0] - t2[0].transpose(1, 0, 2, 3)
t2[0] = t2[0] - t2[0].transpose(0, 1, 3, 2)
t2[2] = t2[2] - t2[2].transpose(1, 0, 2, 3)
t2[2] = t2[2] - t2[2].transpose(0, 1, 3, 2)
l2 = [
numpy.random.random((nocca, nocca, nvira, nvira)) - .9,
numpy.random.random((nocca, noccb, nvira, nvirb)) - .9,
numpy.random.random((noccb, noccb, nvirb, nvirb)) - .9
]
l2[0] = l2[0] - l2[0].transpose(1, 0, 2, 3)
l2[0] = l2[0] - l2[0].transpose(0, 1, 3, 2)
l2[2] = l2[2] - l2[2].transpose(1, 0, 2, 3)
l2[2] = l2[2] - l2[2].transpose(0, 1, 3, 2)
# eris = mycc.ao2mo()
# imds = make_intermediates(mycc, t1, t2, eris)
# l1new, l2new = update_lambda(mycc, t1, t2, l1, l2, eris, imds)
# print(lib.finger(l1new[0]) --104.55975252585894)
# print(lib.finger(l1new[1]) --241.12677819375281)
# print(lib.finger(l2new[0]) --0.4957533529669417)
# print(lib.finger(l2new[1]) - 15.46423057451851 )
# print(lib.finger(l2new[2]) - 5.8430776663704407)
nocca, noccb = mol.nelec
mo_a = mf.mo_coeff[0] + numpy.sin(mf.mo_coeff[0]) * .01j
mo_b = mf.mo_coeff[1] + numpy.sin(mf.mo_coeff[1]) * .01j
nao = mo_a.shape[0]
eri = ao2mo.restore(1, mf._eri, nao)
eri0aa = lib.einsum('pqrs,pi,qj,rk,sl->ijkl', eri, mo_a.conj(), mo_a,
mo_a.conj(), mo_a)
eri0ab = lib.einsum('pqrs,pi,qj,rk,sl->ijkl', eri, mo_a.conj(), mo_a,
mo_b.conj(), mo_b)
eri0bb = lib.einsum('pqrs,pi,qj,rk,sl->ijkl', eri, mo_b.conj(), mo_b,
mo_b.conj(), mo_b)
eri0ba = eri0ab.transpose(2, 3, 0, 1)
nvira = nao - nocca
nvirb = nao - noccb
eris = uccsd._ChemistsERIs(mol)
eris.oooo = eri0aa[:nocca, :nocca, :nocca, :nocca].copy()
eris.ovoo = eri0aa[:nocca, nocca:, :nocca, :nocca].copy()
eris.oovv = eri0aa[:nocca, :nocca, nocca:, nocca:].copy()
eris.ovvo = eri0aa[:nocca, nocca:, nocca:, :nocca].copy()
eris.ovov = eri0aa[:nocca, nocca:, :nocca, nocca:].copy()
eris.ovvv = eri0aa[:nocca, nocca:, nocca:, nocca:].copy()
eris.vvvv = eri0aa[nocca:, nocca:, nocca:, nocca:].copy()
eris.OOOO = eri0bb[:noccb, :noccb, :noccb, :noccb].copy()
eris.OVOO = eri0bb[:noccb, noccb:, :noccb, :noccb].copy()
eris.OOVV = eri0bb[:noccb, :noccb, noccb:, noccb:].copy()
eris.OVVO = eri0bb[:noccb, noccb:, noccb:, :noccb].copy()
eris.OVOV = eri0bb[:noccb, noccb:, :noccb, noccb:].copy()
eris.OVVV = eri0bb[:noccb, noccb:, noccb:, noccb:].copy()
eris.VVVV = eri0bb[noccb:, noccb:, noccb:, noccb:].copy()
eris.ooOO = eri0ab[:nocca, :nocca, :noccb, :noccb].copy()
eris.ovOO = eri0ab[:nocca, nocca:, :noccb, :noccb].copy()
eris.ooVV = eri0ab[:nocca, :nocca, noccb:, noccb:].copy()
eris.ovVO = eri0ab[:nocca, nocca:, noccb:, :noccb].copy()
eris.ovOV = eri0ab[:nocca, nocca:, :noccb, noccb:].copy()
eris.ovVV = eri0ab[:nocca, nocca:, noccb:, noccb:].copy()
eris.vvVV = eri0ab[nocca:, nocca:, noccb:, noccb:].copy()
eris.OOoo = eri0ba[:noccb, :noccb, :nocca, :nocca].copy()
eris.OVoo = eri0ba[:noccb, noccb:, :nocca, :nocca].copy()
eris.OOvv = eri0ba[:noccb, :noccb, nocca:, nocca:].copy()
eris.OVvo = eri0ba[:noccb, noccb:, nocca:, :nocca].copy()
eris.OVov = eri0ba[:noccb, noccb:, :nocca, nocca:].copy()
eris.OVvv = eri0ba[:noccb, noccb:, nocca:, nocca:].copy()
eris.VVvv = eri0ba[noccb:, noccb:, nocca:, nocca:].copy()
eris.focka = numpy.diag(mf.mo_energy[0])
eris.fockb = numpy.diag(mf.mo_energy[1])
t1[0] = t1[0] + numpy.sin(t1[0]) * .05j
t1[1] = t1[1] + numpy.sin(t1[1]) * .05j
t2[0] = t2[0] + numpy.sin(t2[0]) * .05j
t2[1] = t2[1] + numpy.sin(t2[1]) * .05j
t2[2] = t2[2] + numpy.sin(t2[2]) * .05j
l1[0] = l1[0] + numpy.sin(l1[0]) * .05j
l1[1] = l1[1] + numpy.sin(l1[1]) * .05j
l2[0] = l2[0] + numpy.sin(l2[0]) * .05j
l2[1] = l2[1] + numpy.sin(l2[1]) * .05j
l2[2] = l2[2] + numpy.sin(l2[2]) * .05j
imds = uccsd_lambda.make_intermediates(mycc, t1, t2, eris)
l1new_ref, l2new_ref = uccsd_lambda.update_lambda(
mycc, t1, t2, l1, l2, eris, imds)
nocc = nocca + noccb
orbspin = numpy.zeros(nao * 2, dtype=int)
orbspin[1::2] = 1
orbspin[nocc - 1] = 0
orbspin[nocc] = 1
eri1 = numpy.zeros([nao * 2] * 4, dtype=numpy.complex)
idxa = numpy.where(orbspin == 0)[0]
idxb = numpy.where(orbspin == 1)[0]
eri1[idxa[:, None, None, None], idxa[:, None, None], idxa[:, None],
idxa] = eri0aa
eri1[idxa[:, None, None, None], idxa[:, None, None], idxb[:, None],
idxb] = eri0ab
eri1[idxb[:, None, None, None], idxb[:, None, None], idxa[:, None],
idxa] = eri0ba
eri1[idxb[:, None, None, None], idxb[:, None, None], idxb[:, None],
idxb] = eri0bb
eri1 = eri1.transpose(0, 2, 1, 3) - eri1.transpose(0, 2, 3, 1)
erig = gccsd._PhysicistsERIs()
erig.oooo = eri1[:nocc, :nocc, :nocc, :nocc].copy()
erig.ooov = eri1[:nocc, :nocc, :nocc, nocc:].copy()
erig.ovov = eri1[:nocc, nocc:, :nocc, nocc:].copy()
erig.ovvo = eri1[:nocc, nocc:, nocc:, :nocc].copy()
erig.oovv = eri1[:nocc, :nocc, nocc:, nocc:].copy()
erig.ovvv = eri1[:nocc, nocc:, nocc:, nocc:].copy()
erig.vvvv = eri1[nocc:, nocc:, nocc:, nocc:].copy()
mo_e = numpy.empty(nao * 2)
mo_e[orbspin == 0] = mf.mo_energy[0]
mo_e[orbspin == 1] = mf.mo_energy[1]
erig.fock = numpy.diag(mo_e)
myccg = gccsd.GCCSD(scf.addons.convert_to_ghf(mf))
t1 = myccg.spatial2spin(t1, orbspin)
t2 = myccg.spatial2spin(t2, orbspin)
l1 = myccg.spatial2spin(l1, orbspin)
l2 = myccg.spatial2spin(l2, orbspin)
imds = gccsd_lambda.make_intermediates(myccg, t1, t2, erig)
l1new, l2new = gccsd_lambda.update_lambda(myccg, t1, t2, l1, l2, erig,
imds)
l1new = myccg.spin2spatial(l1new, orbspin)
l2new = myccg.spin2spatial(l2new, orbspin)
self.assertAlmostEqual(abs(l1new[0] - l1new_ref[0]).max(), 0, 11)
self.assertAlmostEqual(abs(l1new[1] - l1new_ref[1]).max(), 0, 11)
self.assertAlmostEqual(abs(l2new[0] - l2new_ref[0]).max(), 0, 11)
self.assertAlmostEqual(abs(l2new[1] - l2new_ref[1]).max(), 0, 11)
self.assertAlmostEqual(abs(l2new[2] - l2new_ref[2]).max(), 0, 11)
def make_intermediates(mycc, t1, t2, eris):
from pyscf.cc import uccsd_t_slow
def p6(t):
return (t + t.transpose(1,2,0,4,5,3) +
t.transpose(2,0,1,5,3,4) + t.transpose(0,2,1,3,5,4) +
t.transpose(2,1,0,5,4,3) + t.transpose(1,0,2,4,3,5))
def r6(w):
return (w + w.transpose(2,0,1,3,4,5) + w.transpose(1,2,0,3,4,5)
- w.transpose(2,1,0,3,4,5) - w.transpose(0,2,1,3,4,5)
- w.transpose(1,0,2,3,4,5))
imds = uccsd_lambda.make_intermediates(mycc, t1, t2, eris)
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb = t2ab.shape[:2]
nmoa = eris.focka.shape[0]
nmob = eris.fockb.shape[0]
mo_ea, mo_eb = eris.mo_energy
eia = mo_ea[:nocca,None] - mo_ea[nocca:]
eIA = mo_eb[:noccb,None] - mo_eb[noccb:]
fvo = eris.focka[nocca:,:nocca]
fVO = eris.fockb[noccb:,:noccb]
# aaa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
w = numpy.einsum('ijae,kceb->ijkabc', t2aa, numpy.asarray(eris.get_ovvv()).conj())
w-= numpy.einsum('mkbc,iajm->ijkabc', t2aa, numpy.asarray(eris.ovoo.conj()))
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.ovov).conj(), t1a)
v+= numpy.einsum('jkbc,ai->ijkabc', t2aa, fvo) * .5
rw = r6(p6(w)) / d3
imds.l1a_t = numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.ovov)) / eia * .25
wvd = r6(p6(w * 2 + v)) / d3
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_ovvv()).conj())
l2_t -= numpy.einsum('ijkabc,iajm->mkbc', wvd, numpy.asarray(eris.ovoo.conj()))
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fvo)
imds.l2aa_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eia) * .5
# bbb
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2bb, numpy.asarray(eris.get_OVVV()).conj())
w-= numpy.einsum('imab,kcjm->ijkabc', t2bb, numpy.asarray(eris.OVOO.conj()))
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1b)
v+= numpy.einsum('jkbc,ai->ijkabc', t2bb, fVO) * .5
rw = r6(p6(w)) / d3
imds.l1b_t = numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.OVOV)) / eIA * .25
wvd = r6(p6(w * 2 + v)) / d3
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_OVVV()).conj())
l2_t -= numpy.einsum('ijkabc,iajm->mkbc', wvd, numpy.asarray(eris.OVOO.conj()))
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fVO)
imds.l2bb_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eIA, eIA) * .5
# baa
def r4(w):
w = w - w.transpose(0,2,1,3,4,5)
w = w + w.transpose(0,2,1,3,5,4)
return w
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eia, eia)
w = numpy.einsum('jIeA,kceb->IjkAbc', t2ab, numpy.asarray(eris.get_ovvv()).conj()) * 2
w += numpy.einsum('jIbE,kcEA->IjkAbc', t2ab, numpy.asarray(eris.get_ovVV()).conj()) * 2
w += numpy.einsum('jkbe,IAec->IjkAbc', t2aa, numpy.asarray(eris.get_OVvv()).conj())
w -= numpy.einsum('mIbA,kcjm->IjkAbc', t2ab, numpy.asarray(eris.ovoo).conj()) * 2
w -= numpy.einsum('jMbA,kcIM->IjkAbc', t2ab, numpy.asarray(eris.ovOO).conj()) * 2
w -= numpy.einsum('jmbc,IAkm->IjkAbc', t2aa, numpy.asarray(eris.OVoo).conj())
v = numpy.einsum('jbkc,IA->IjkAbc', numpy.asarray(eris.ovov).conj(), t1b)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('jkbc,AI->IjkAbc', t2aa, fVO) * .5
v += numpy.einsum('kIcA,bj->IjkAbc', t2ab, fvo) * 2
rw = r4(w) / d3
imds.l1a_t += numpy.einsum('ijkabc,kcia->jb', rw.conj(),
numpy.asarray(eris.ovOV)) / eia * .5
imds.l1b_t += numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.ovov)) / eIA * .25
wvd = r4(w * 2 + v) / d3
l2_t = numpy.einsum('ijkabc,iaec->jkbe', wvd, numpy.asarray(eris.get_OVvv()).conj())
l2_t -= numpy.einsum('ijkabc,iakm->jmbc', wvd, numpy.asarray(eris.OVoo).conj())
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fVO)
imds.l2aa_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eia) * .5
l2_t = numpy.einsum('ijkabc,kceb->jiea', wvd, numpy.asarray(eris.get_ovvv()).conj())
l2_t += numpy.einsum('ijkabc,kcea->jibe', wvd, numpy.asarray(eris.get_ovVV()).conj())
l2_t -= numpy.einsum('ijkabc,kcjm->miba', wvd, numpy.asarray(eris.ovoo).conj())
l2_t -= numpy.einsum('ijkabc,kcim->jmba', wvd, numpy.asarray(eris.ovOO).conj())
l2_t += numpy.einsum('ijkabc,bj->kica', rw, fvo)
imds.l2ab_t = l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eIA) * .5
# bba
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2ab, numpy.asarray(eris.get_OVVV()).conj()) * 2
w += numpy.einsum('ijeb,kcea->ijkabc', t2ab, numpy.asarray(eris.get_OVvv()).conj()) * 2
w += numpy.einsum('jkbe,iaec->ijkabc', t2bb, numpy.asarray(eris.get_ovVV()).conj())
w -= numpy.einsum('imab,kcjm->ijkabc', t2ab, numpy.asarray(eris.OVOO).conj()) * 2
w -= numpy.einsum('mjab,kcim->ijkabc', t2ab, numpy.asarray(eris.OVoo).conj()) * 2
w -= numpy.einsum('jmbc,iakm->ijkabc', t2bb, numpy.asarray(eris.ovOO).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1a)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('JKBC,ai->iJKaBC', t2bb, fvo) * .5
v += numpy.einsum('iKaC,BJ->iJKaBC', t2ab, fVO) * 2
rw = r4(w) / d3
imds.l1a_t += numpy.einsum('ijkabc,jbkc->ia', rw.conj(),
numpy.asarray(eris.OVOV)) / eia * .25
imds.l1b_t += numpy.einsum('ijkabc,iakc->jb', rw.conj(),
numpy.asarray(eris.ovOV)) / eIA * .5
wvd = r4(w * 2 + v) / d3
l2_t = numpy.einsum('ijkabc,iaec->jkbe', wvd, numpy.asarray(eris.get_ovVV()).conj())
l2_t -= numpy.einsum('ijkabc,iakm->jmbc', wvd, numpy.asarray(eris.ovOO).conj())
l2_t = l2_t + l2_t.transpose(1,0,3,2)
l2_t += numpy.einsum('ijkabc,ai->jkbc', rw, fvo)
imds.l2bb_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eIA, eIA) * .5
l2_t = numpy.einsum('ijkabc,kceb->ijae', wvd, numpy.asarray(eris.get_OVVV()).conj())
l2_t += numpy.einsum('ijkabc,kcea->ijeb', wvd, numpy.asarray(eris.get_OVvv()).conj())
l2_t -= numpy.einsum('ijkabc,kcjm->imab', wvd, numpy.asarray(eris.OVOO).conj())
l2_t -= numpy.einsum('ijkabc,kcim->mjab', wvd, numpy.asarray(eris.OVoo).conj())
l2_t += numpy.einsum('ijkabc,bj->ikac', rw, fVO)
imds.l2ab_t += l2_t.conj() / lib.direct_sum('ia+jb->ijab', eia, eIA) * .5
return imds
