def _gamma2_intermediates(cc, t1, t2, l1, l2):
d2 = ccsd_rdm._gamma2_intermediates(cc, t1, t2, l1, l2)
nocc, nvir = t1.shape
if cc.frozen is None or cc.frozen is 0:
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
dvvov = dovvv.transpose(2,3,0,1)
dvvvv = ao2mo.restore(1, d2[1], nvir)
return dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov
nocc0 = numpy.count_nonzero(cc.mo_occ>0)
nvir0 = cc.mo_occ.size - nocc0
OA, VA, OF, VF = index_frozen_active(cc)
dovov = numpy.zeros((nocc0,nvir0,nocc0,nvir0))
dvvvv = numpy.zeros((nvir0,nvir0,nvir0,nvir0))
doooo = numpy.zeros((nocc0,nocc0,nocc0,nocc0))
doovv = numpy.zeros((nocc0,nocc0,nvir0,nvir0))
dovvo = numpy.zeros((nocc0,nvir0,nvir0,nocc0))
dovvv = numpy.zeros((nocc0,nvir0,nvir0,nvir0))
dooov = numpy.zeros((nocc0,nocc0,nocc0,nvir0))
dovov[OA[:,None,None,None],VA[:,None,None],OA[:,None],VA] = d2[0]
dvvvv[VA[:,None,None,None],VA[:,None,None],VA[:,None],VA] = ao2mo.restore(1, d2[1], nvir)
doooo[OA[:,None,None,None],OA[:,None,None],OA[:,None],OA] = d2[2]
doovv[OA[:,None,None,None],OA[:,None,None],VA[:,None],VA] = d2[3]
dovvo[OA[:,None,None,None],VA[:,None,None],VA[:,None],OA] = d2[4]
dovvv[OA[:,None,None,None],VA[:,None,None],VA[:,None],VA] = d2[6]
dooov[OA[:,None,None,None],OA[:,None,None],OA[:,None],VA] = d2[7]
dvvov = dovvv.transpose(2,3,0,1)
return dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov
def contract_2e(eri, fcivec, nsite, nelec, nphonon):
neleca, nelecb = _unpack_nelec(nelec)
link_indexa = cistring.gen_linkstr_index(range(nsite), neleca)
link_indexb = cistring.gen_linkstr_index(range(nsite), nelecb)
cishape = make_shape(nsite, nelec, nphonon)
ci0 = fcivec.reshape(cishape)
t1a = numpy.zeros((nsite,nsite)+cishape)
t1b = numpy.zeros((nsite,nsite)+cishape)
for str0, tab in enumerate(link_indexa):
for a, i, str1, sign in tab:
t1a[a,i,str1] += sign * ci0[str0]
for str0, tab in enumerate(link_indexb):
for a, i, str1, sign in tab:
t1b[a,i,:,str1] += sign * ci0[:,str0]
g2e_aa = ao2mo.restore(1, eri[0], nsite)
g2e_ab = ao2mo.restore(1, eri[1], nsite)
g2e_bb = ao2mo.restore(1, eri[2], nsite)
t2a = numpy.dot(g2e_aa.reshape(nsite**2,-1), t1a.reshape(nsite**2,-1))
t2a+= numpy.dot(g2e_ab.reshape(nsite**2,-1), t1b.reshape(nsite**2,-1))
t2b = numpy.dot(g2e_ab.reshape(nsite**2,-1).T, t1a.reshape(nsite**2,-1))
t2b+= numpy.dot(g2e_bb.reshape(nsite**2,-1), t1b.reshape(nsite**2,-1))
t2a = t2a.reshape((nsite,nsite)+cishape)
t2b = t2b.reshape((nsite,nsite)+cishape)
fcinew = numpy.zeros(cishape)
for str0, tab in enumerate(link_indexa):
for a, i, str1, sign in tab:
fcinew[str1] += sign * t2a[a,i,str0]
for str0, tab in enumerate(link_indexb):
for a, i, str1, sign in tab:
fcinew[:,str1] += sign * t2b[a,i,:,str0]
return fcinew.reshape(fcivec.shape)
def mp2(mol, h1e, eri, mo, nelec, with_1pdm, with_e2frag):
eri1 = ao2mo.restore(8, eri, mo.shape[1])
hf_energy, mo_energy, mo_coeff, mo_occ = simple_hf(h1e, eri1, mo, nelec)
mf = scf.RHF(mol)
mf.get_hcore = lambda mol: h1e
mf._eri = eri
mymp2 = mp.MP2(mf)
mymp2.nocc = nelec // 2
mymp2.nmo = len(mo_energy)
emp2, t2 = mymp2.kernel(mo_energy, mo_coeff)
if with_1pdm:
rdm1 = mymp2.make_rdm1(t2)
for i in range(nelec // 2):
rdm1[i, i] += 2
rdm1 = reduce(numpy.dot, (mo_coeff, rdm1, mo_coeff.T))
else:
rdm1 = None
if with_e2frag:
norb = mo_coeff.shape[0]
eri1 = part_eri_hermi(eri, norb, with_e2frag)
eri1 = ao2mo.incore.full(eri1, mo_coeff)
eri1 = ao2mo.restore(1, eri1, norb)
rdm2 = mymp2.make_rdm2(t2)
for i in range(nelec // 2):
for j in range(nelec // 2):
rdm2[i, i, j, j] += 4
rdm2[i, j, i, j] += -2
e2frag = 0.5 * numpy.dot(rdm2.reshape(-1), eri1.reshape(-1))
else:
e2frag = None
return hf_energy, emp2 + hf_energy, e2frag, rdm1
def test_nroutcore_eri(self):
ftmp = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
erifile = ftmp.name
eri_ao = ao2mo.restore(1, mol.intor('int2e', aosym='s2kl'), nao)
eriref = numpy.einsum('pjkl,pi->ijkl', eri_ao, mo)
eriref = numpy.einsum('ipkl,pj->ijkl', eriref, mo)
eriref = numpy.einsum('ijpl,pk->ijkl', eriref, mo)
eriref = numpy.einsum('ijkp,pl->ijkl', eriref, mo)
mos = (mo[:,:4], mo[:,:3], mo[:,:3], mo[:,:2])
ao2mo.outcore.general(mol, mos, erifile, dataname='eri_mo',
intor='int2e', aosym=1)
with ao2mo.load(erifile) as eri1:
eri1 = numpy.asarray(eri1).reshape(4,3,3,2)
self.assertTrue(numpy.allclose(eri1, eriref[:4,:3,:3,:2]))
ao2mo.outcore.full(mol, mo, erifile, dataname='eri_mo',
intor='int2e_sph', aosym='s2ij', comp=1)
with ao2mo.load(erifile, 'eri_mo') as eri:
eri1 = ao2mo.restore(1, numpy.array(eri), nao)
eri1 = eri1.reshape(nao,nao,nao,nao)
self.assertTrue(numpy.allclose(eri1, eriref))
mos = (mo[:,:3], mo[:,:3], mo[:,:3], mo[:,:2])
ao2mo.outcore.general(mol, mos, erifile, dataname='eri_mo',
intor='int2e_sph', aosym='s4', comp=1,
compact=False)
with ao2mo.load(erifile, 'eri_mo') as eri1:
eri1 = numpy.asarray(eri1).reshape(3,3,3,2)
self.assertTrue(numpy.allclose(eri1, eriref[:3,:3,:3,:2]))
ao2mo.outcore.full(mol, mo[:,:0], erifile,
intor='int2e', aosym='1', comp=1)
with ao2mo.load(erifile, 'eri_mo') as eri:
self.assertTrue(eri.size == 0)
def writeIntegralFile(shciobj, h1eff, eri_cas, ncas, nelec, ecore=0):
if isinstance(nelec, (int, numpy.integer)):
if shciobj.spin is None:
nelecb = nelec // 2
else:
nelecb = (nelec - shciobj.spin) // 2
neleca = nelec - nelecb
else :
neleca, nelecb = nelec
if shciobj.groupname is not None and shciobj.orbsym is not []:
# First removing the symmetry forbidden integrals. This has been done using
# the pyscf internal irrep-IDs (stored in shciobj.orbsym)
orbsym = numpy.asarray(shciobj.orbsym) % 10
pair_irrep = (orbsym.reshape(-1,1) ^ orbsym)[numpy.tril_indices(ncas)]
sym_forbid = pair_irrep.reshape(-1,1) != pair_irrep.ravel()
eri_cas = ao2mo.restore(4, eri_cas, ncas)
eri_cas[sym_forbid] = 0
eri_cas = ao2mo.restore(8, eri_cas, ncas)
# Convert the pyscf internal irrep-ID to molpro irrep-ID
orbsym = numpy.asarray(symmetry.convert_orbsym(shciobj.groupname, orbsym))
else:
orbsym = []
eri_cas = ao2mo.restore(8, eri_cas, ncas)
if not os.path.exists(shciobj.runtimedir):
os.makedirs(shciobj.runtimedir)
# The name of the FCIDUMP file, default is "FCIDUMP".
integralFile = os.path.join(shciobj.runtimedir, shciobj.integralfile)
tools.fcidump.from_integrals(integralFile, h1eff, eri_cas, ncas,
neleca+nelecb, ecore, ms=abs(neleca-nelecb),
orbsym=orbsym)
return integralFile
def test_mp2_contract_eri_dm(self):
nocc = mol.nelectron//2
nmo = mf.mo_energy.size
nvir = nmo - nocc
pt = mp.mp2.MP2(mf)
emp2, t2 = pt.kernel()
eri = ao2mo.restore(1, ao2mo.kernel(mf._eri, mf.mo_coeff), nmo)
hcore = mf.get_hcore()
rdm1 = pt.make_rdm1()
rdm2 = pt.make_rdm2()
h1 = reduce(numpy.dot, (mf.mo_coeff.T, hcore, mf.mo_coeff))
e1 = numpy.einsum('ij,ji', h1, rdm1)
e1+= numpy.einsum('ijkl,ijkl', eri, rdm2) * .5
e1+= mol.energy_nuc()
self.assertAlmostEqual(e1, pt.e_tot, 9)
pt.frozen = 2
pt.max_memory = 1
emp2, t2 = pt.kernel(with_t2=False)
eri = ao2mo.restore(1, ao2mo.kernel(mf._eri, mf.mo_coeff), nmo)
hcore = mf.get_hcore()
rdm1 = pt.make_rdm1()
rdm2 = pt.make_rdm2()
h1 = reduce(numpy.dot, (mf.mo_coeff.T, hcore, mf.mo_coeff))
e1 = numpy.einsum('ij,ji', h1, rdm1)
e1+= numpy.einsum('ijkl,ijkl', eri, rdm2) * .5
e1+= mol.energy_nuc()
self.assertAlmostEqual(e1, pt.e_tot, 9)
def __init__(self, myci, mo_coeff, method='incore'):
mol = myci.mol
mf = myci._scf
nocc = myci.nocc
nmo = myci.nmo
nvir = nmo - nocc
if mo_coeff is None:
self.mo_coeff = mo_coeff = myci.mo_coeff
if (method == 'incore' and mf._eri is not None):
eri = ao2mo.kernel(mf._eri, mo_coeff, verbose=myci.verbose)
else:
eri = ao2mo.kernel(mol, mo_coeff, verbose=myci.verbose)
eri = ao2mo.restore(1, eri, nmo)
eri = eri.reshape(nmo,nmo,nmo,nmo)
self.oooo = eri[:nocc,:nocc,:nocc,:nocc]
self.vvoo = eri[nocc:,nocc:,:nocc,:nocc]
self.vooo = eri[nocc:,:nocc,:nocc,:nocc]
self.voov = eri[nocc:,:nocc,:nocc,nocc:]
self.vovv = lib.pack_tril(eri[nocc:,:nocc,nocc:,nocc:].reshape(-1,nvir,nvir))
self.vvvv = ao2mo.restore(4, eri[nocc:,nocc:,nocc:,nocc:].copy(), nvir)
dm = mf.make_rdm1()
vhf = mf.get_veff(mol, dm)
h1 = mf.get_hcore(mol)
self.fock = reduce(numpy.dot, (mo_coeff.T, h1 + vhf, mo_coeff))
def writeIntegralFile(DMRGCI, h1eff, eri_cas, ncas, nelec, ecore=0):
if isinstance(nelec, (int, numpy.integer)):
neleca = nelec//2 + nelec%2
nelecb = nelec - neleca
else :
neleca, nelecb = nelec
# The name of the FCIDUMP file, default is "FCIDUMP".
integralFile = os.path.join(DMRGCI.runtimeDir, DMRGCI.integralFile)
if DMRGCI.groupname is not None and DMRGCI.orbsym is not []:
# First removing the symmetry forbidden integrals. This has been done using
# the pyscf internal irrep-IDs (stored in DMRGCI.orbsym)
orbsym = numpy.asarray(DMRGCI.orbsym) % 10
pair_irrep = (orbsym.reshape(-1,1) ^ orbsym)[numpy.tril_indices(ncas)]
sym_forbid = pair_irrep.reshape(-1,1) != pair_irrep.ravel()
eri_cas = ao2mo.restore(4, eri_cas, ncas)
eri_cas[sym_forbid] = 0
eri_cas = ao2mo.restore(8, eri_cas, ncas)
#orbsym = numpy.asarray(dmrg_sym.convert_orbsym(DMRGCI.groupname, DMRGCI.orbsym))
#eri_cas = pyscf.ao2mo.restore(8, eri_cas, ncas)
# Then convert the pyscf internal irrep-ID to molpro irrep-ID
orbsym = numpy.asarray(dmrg_sym.convert_orbsym(DMRGCI.groupname, orbsym))
else:
orbsym = []
eri_cas = ao2mo.restore(8, eri_cas, ncas)
if not os.path.exists(DMRGCI.scratchDirectory):
os.makedirs(DMRGCI.scratchDirectory)
if not os.path.exists(DMRGCI.runtimeDir):
os.makedirs(DMRGCI.runtimeDir)
tools.fcidump.from_integrals(integralFile, h1eff, eri_cas, ncas,
neleca+nelecb, ecore, ms=abs(neleca-nelecb),
orbsym=orbsym)
return integralFile
def pspace(h1e, eri, norb, nelec, hdiag, np=400):
neleca, nelecb = direct_spin1._unpack_nelec(nelec)
h1e_a = numpy.ascontiguousarray(h1e[0])
h1e_b = numpy.ascontiguousarray(h1e[1])
g2e_aa = ao2mo.restore(1, eri[0], norb)
g2e_ab = ao2mo.restore(1, eri[1], norb)
g2e_bb = ao2mo.restore(1, eri[2], norb)
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
nb = link_indexb.shape[0]
addr = numpy.argsort(hdiag)[:np]
addra = addr // nb
addrb = addr % nb
stra = numpy.array([cistring.addr2str(norb,neleca,ia) for ia in addra],
dtype=numpy.long)
strb = numpy.array([cistring.addr2str(norb,nelecb,ib) for ib in addrb],
dtype=numpy.long)
np = len(addr)
h0 = numpy.zeros((np,np))
libfci.FCIpspace_h0tril_uhf(h0.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
g2e_aa.ctypes.data_as(ctypes.c_void_p),
g2e_ab.ctypes.data_as(ctypes.c_void_p),
g2e_bb.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i,i] = hdiag[addr[i]]
h0 = lib.hermi_triu(h0)
return addr, h0
def test_nr_transe1incore(self):
eri_ao = _vhf.int2e_sph(mol._atm, mol._bas, mol._env)
eriref = ao2mo.restore(1, eri_ao, nao)
eriref = numpy.einsum("ijpl,pk->ijkl", eriref, mo)
eriref = numpy.einsum("ijkp,pl->ijkl", eriref, mo)
eriref = ao2mo.restore(4, eriref, nao)
eri_ao = ao2mo.restore(8, eri_ao, nao)
ftrans1 = f1pointer("AO2MOtranse1_incore_s8")
fmmm = f1pointer("AO2MOmmm_nr_s2_s2")
eri1 = numpy.empty((naopair, naopair))
libao2mo1.AO2MOnr_e1incore_drv(
ftrans1,
fmmm,
eri1.ctypes.data_as(ctypes.c_void_p),
eri_ao.ctypes.data_as(ctypes.c_void_p),
mo.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(0),
ctypes.c_int(naopair),
ctypes.c_int(nao),
ctypes.c_int(0),
ctypes.c_int(nao),
ctypes.c_int(0),
ctypes.c_int(nao),
)
self.assertTrue(numpy.allclose(eri1, eriref))
def make_hdiag(h1e, eri, norb, nelec):
neleca, nelecb = direct_spin1._unpack_nelec(nelec)
h1e_a = numpy.ascontiguousarray(h1e[0])
h1e_b = numpy.ascontiguousarray(h1e[1])
g2e_aa = ao2mo.restore(1, eri[0], norb)
g2e_ab = ao2mo.restore(1, eri[1], norb)
g2e_bb = ao2mo.restore(1, eri[2], norb)
strsa = numpy.asarray(cistring.gen_strings4orblist(range(norb), neleca))
strsb = numpy.asarray(cistring.gen_strings4orblist(range(norb), nelecb))
na = len(strsa)
nb = len(strsb)
hdiag = numpy.empty(na*nb)
jdiag_aa = numpy.asarray(numpy.einsum('iijj->ij',g2e_aa), order='C')
jdiag_ab = numpy.asarray(numpy.einsum('iijj->ij',g2e_ab), order='C')
jdiag_bb = numpy.asarray(numpy.einsum('iijj->ij',g2e_bb), order='C')
kdiag_aa = numpy.asarray(numpy.einsum('ijji->ij',g2e_aa), order='C')
kdiag_bb = numpy.asarray(numpy.einsum('ijji->ij',g2e_bb), order='C')
libfci.FCImake_hdiag_uhf(hdiag.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
jdiag_aa.ctypes.data_as(ctypes.c_void_p),
jdiag_ab.ctypes.data_as(ctypes.c_void_p),
jdiag_bb.ctypes.data_as(ctypes.c_void_p),
kdiag_aa.ctypes.data_as(ctypes.c_void_p),
kdiag_bb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(neleca), ctypes.c_int(nelecb),
strsa.ctypes.data_as(ctypes.c_void_p),
strsb.ctypes.data_as(ctypes.c_void_p))
return numpy.asarray(hdiag)
def part_eri_hermi(eri, norb, nimp):
eri1 = ao2mo.restore(4, eri, norb)
for i in range(eri1.shape[0]):
tmp = lib.unpack_tril(eri1[i])
tmp[nimp:] = 0
eri1[i] = lib.pack_tril(tmp + tmp.T)
eri1 = lib.transpose_sum(eri1, inplace=True)
return ao2mo.restore(8, eri1, norb) * 0.25
def contract_2e(eri, civec_strs, norb, nelec, link_index=None):
ci_coeff, nelec, ci_strs = _unpack(civec_strs, nelec)
if link_index is None:
link_index = _all_linkstr_index(ci_strs, norb, nelec)
cd_indexa, dd_indexa, cd_indexb, dd_indexb = link_index
na, nlinka = cd_indexa.shape[:2]
nb, nlinkb = cd_indexb.shape[:2]
eri = ao2mo.restore(1, eri, norb)
eri1 = eri.transpose(0,2,1,3) - eri.transpose(0,2,3,1)
idx,idy = numpy.tril_indices(norb, -1)
idx = idx * norb + idy
eri1 = lib.take_2d(eri1.reshape(norb**2,-1), idx, idx) * 2
fcivec = ci_coeff.reshape(na,nb)
# (bb|bb)
if nelec[1] > 1:
mb, mlinkb = dd_indexb.shape[:2]
fcivecT = lib.transpose(fcivec)
ci1T = numpy.zeros((nb,na))
libfci.SCIcontract_2e_aaaa(eri1.ctypes.data_as(ctypes.c_void_p),
fcivecT.ctypes.data_as(ctypes.c_void_p),
ci1T.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(nb), ctypes.c_int(na),
ctypes.c_int(mb), ctypes.c_int(mlinkb),
dd_indexb.ctypes.data_as(ctypes.c_void_p))
ci1 = lib.transpose(ci1T, out=fcivecT)
else:
ci1 = numpy.zeros_like(fcivec)
# (aa|aa)
if nelec[0] > 1:
ma, mlinka = dd_indexa.shape[:2]
libfci.SCIcontract_2e_aaaa(eri1.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(ma), ctypes.c_int(mlinka),
dd_indexa.ctypes.data_as(ctypes.c_void_p))
h_ps = numpy.einsum('pqqs->ps', eri)
eri1 = eri * 2
for k in range(norb):
eri1[:,:,k,k] += h_ps/nelec[0]
eri1[k,k,:,:] += h_ps/nelec[1]
eri1 = ao2mo.restore(4, eri1, norb)
# (bb|aa)
libfci.SCIcontract_2e_bbaa(eri1.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
cd_indexa.ctypes.data_as(ctypes.c_void_p),
cd_indexb.ctypes.data_as(ctypes.c_void_p))
return _as_SCIvector(ci1.reshape(ci_coeff.shape), ci_strs)
def test_ccsd(self):
mol = gto.M()
mf = scf.RHF(mol)
mcc = cc.CCSD(mf)
numpy.random.seed(12)
mcc.nocc = nocc = 5
mcc.nmo = nmo = 12
nvir = nmo - nocc
eri0 = numpy.random.random((nmo,nmo,nmo,nmo))
eri0 = ao2mo.restore(1, ao2mo.restore(8, eri0, nmo), nmo)
fock0 = numpy.random.random((nmo,nmo))
fock0 = fock0 + fock0.T + numpy.diag(range(nmo))*2
t1 = numpy.random.random((nocc,nvir))
t2 = numpy.random.random((nocc,nocc,nvir,nvir))
t2 = t2 + t2.transpose(1,0,3,2)
l1 = numpy.random.random((nocc,nvir))
l2 = numpy.random.random((nocc,nocc,nvir,nvir))
l2 = l2 + l2.transpose(1,0,3,2)
eris = cc.ccsd._ChemistsERIs()
eris.oooo = eri0[:nocc,:nocc,:nocc,:nocc].copy()
eris.ovoo = eri0[:nocc,nocc:,:nocc,:nocc].copy()
eris.oovv = eri0[:nocc,:nocc,nocc:,nocc:].copy()
eris.ovvo = eri0[:nocc,nocc:,nocc:,:nocc].copy()
idx = numpy.tril_indices(nvir)
eris.ovvv = eri0[:nocc,nocc:,nocc:,nocc:][:,:,idx[0],idx[1]].copy()
eris.vvvv = ao2mo.restore(4,eri0[nocc:,nocc:,nocc:,nocc:],nvir)
eris.fock = fock0
eris.mo_energy = fock0.diagonal()
saved = ccsd_lambda.make_intermediates(mcc, t1, t2, eris)
l1new, l2new = ccsd_lambda.update_lambda(mcc, t1, t2, l1, l2, eris, saved)
self.assertAlmostEqual(abs(l1new).sum(), 38172.7896467303, 8)
self.assertAlmostEqual(numpy.dot(l1new.flatten(), numpy.arange(35)), 739312.005491083, 8)
self.assertAlmostEqual(numpy.dot(l1new.flatten(), numpy.sin(numpy.arange(35))), 7019.50937051188, 8)
self.assertAlmostEqual(numpy.dot(numpy.sin(l1new.flatten()), numpy.arange(35)), 69.6652346635955, 8)
self.assertAlmostEqual(abs(l2new).sum(), 72035.4931071527, 8)
self.assertAlmostEqual(abs(l2new-l2new.transpose(1,0,3,2)).sum(), 0, 9)
self.assertAlmostEqual(numpy.dot(l2new.flatten(), numpy.arange(35**2)), 48427109.5409886, 7)
self.assertAlmostEqual(numpy.dot(l2new.flatten(), numpy.sin(numpy.arange(35**2))), 137.758016736487, 8)
self.assertAlmostEqual(numpy.dot(numpy.sin(l2new.flatten()), numpy.arange(35**2)), 507.656936701192, 8)
mcc.max_memory = 0
saved = ccsd_lambda.make_intermediates(mcc, t1, t2, eris)
l1new, l2new = ccsd_lambda.update_lambda(mcc, t1, t2, l1, l2, eris, saved)
self.assertAlmostEqual(abs(l1new).sum(), 38172.7896467303, 8)
self.assertAlmostEqual(numpy.dot(l1new.flatten(), numpy.arange(35)), 739312.005491083, 8)
self.assertAlmostEqual(numpy.dot(l1new.flatten(), numpy.sin(numpy.arange(35))), 7019.50937051188, 8)
self.assertAlmostEqual(numpy.dot(numpy.sin(l1new.flatten()), numpy.arange(35)), 69.6652346635955, 8)
self.assertAlmostEqual(abs(l2new).sum(), 72035.4931071527, 8)
self.assertAlmostEqual(abs(l2new-l2new.transpose(1,0,3,2)).sum(), 0, 9)
self.assertAlmostEqual(numpy.dot(l2new.flatten(), numpy.arange(35**2)), 48427109.5409886, 7)
self.assertAlmostEqual(numpy.dot(l2new.flatten(), numpy.sin(numpy.arange(35**2))), 137.758016736487, 8)
self.assertAlmostEqual(numpy.dot(numpy.sin(l2new.flatten()), numpy.arange(35**2)), 507.656936701192, 8)
def gen_hop_uhf_external(mf):
mol = mf.mol
mo_a, mo_b = mf.mo_coeff
mo_ea, mo_eb = mf.mo_energy
mo_occa, mo_occb = mf.mo_occ
nmo = mo_a.shape[1]
nocca = numpy.count_nonzero(mo_occa)
noccb = numpy.count_nonzero(mo_occb)
nvira = nmo - nocca
nvirb = nmo - noccb
eri_aa = ao2mo.restore(1, ao2mo.full(mol, mo_a), nmo)
eri_ab = ao2mo.restore(1, ao2mo.general(mol, [mo_a,mo_a,mo_b,mo_b]), nmo)
eri_bb = ao2mo.restore(1, ao2mo.full(mol, mo_b), nmo)
# alpha -> alpha
haa =-numpy.einsum('abji->iajb', eri_aa[nocca:,nocca:,:nocca,:nocca])
haa+= numpy.einsum('ajbi->iajb', eri_aa[nocca:,:nocca,nocca:,:nocca])
for a in range(nvira):
for i in range(nocca):
haa[i,a,i,a] += mo_ea[nocca+a] - mo_ea[i]
# beta -> beta
hbb =-numpy.einsum('abji->iajb', eri_bb[noccb:,noccb:,:noccb,:noccb])
hbb+= numpy.einsum('ajbi->iajb', eri_bb[noccb:,:noccb,noccb:,:noccb])
for a in range(nvirb):
for i in range(noccb):
hbb[i,a,i,a] += mo_eb[noccb+a] - mo_eb[i]
nova = nocca * nvira
novb = noccb * nvirb
h1 = numpy.zeros((nova+novb,nova+novb))
h1[:nova,:nova] = haa.transpose(1,0,3,2).reshape(nova,nova)
h1[nova:,nova:] = hbb.transpose(1,0,3,2).reshape(novb,novb)
def hop1(x):
return h1.dot(x)
h11 =-numpy.einsum('abji->iajb', eri_ab[nocca:,nocca:,:noccb,:noccb])
for a in range(nvira):
for i in range(noccb):
h11[i,a,i,a] += mo_ea[nocca+a] - mo_eb[i]
h22 =-numpy.einsum('jiab->iajb', eri_ab[:nocca,:nocca,noccb:,noccb:])
for a in range(nvirb):
for i in range(nocca):
h22[i,a,i,a] += mo_eb[noccb+a] - mo_ea[i]
h12 =-numpy.einsum('ajbi->iajb', eri_ab[nocca:,:nocca,noccb:,:noccb])
h21 =-numpy.einsum('biaj->iajb', eri_ab[nocca:,:nocca,noccb:,:noccb])
n1 = noccb * nvira
n2 = nocca * nvirb
h2 = numpy.empty((n1+n2,n1+n2))
h2[:n1,:n1] = h11.transpose(1,0,3,2).reshape(n1,n1)
h2[n1:,n1:] = h22.transpose(1,0,3,2).reshape(n2,n2)
h2[:n1,n1:] = h12.transpose(1,0,3,2).reshape(n1,n2)
h2[n1:,:n1] = h21.transpose(1,0,3,2).reshape(n2,n1)
def hop2(x):
return h2.dot(x)
return hop1, hop2
def _get_VVVV(eris):
if eris.VVVV is None and getattr(eris, 'VVL', None) is not None: # DF eris
VVL = np.asarray(eris.VVL)
nvir = int(np.sqrt(eris.VVL.shape[0]*2))
return ao2mo.restore(1, lib.dot(VVL, VVL.T), nvir)
elif len(eris.VVVV.shape) == 2:
nvir = int(np.sqrt(eris.VVVV.shape[0]*2))
return ao2mo.restore(1, np.asarray(eris.VVVV), nvir)
else:
return eris.VVVV
def test_kernel(self):
h1 = h1e + h1e.T
eri = .5* ao2mo.restore(1, ao2mo.restore(8, h2e, norb), norb)
h = fci.direct_spin1.pspace(h1, eri, norb, nelec, np=5000)[1]
eref, c0 = numpy.linalg.eigh(h)
sol = fci.direct_nosym.FCI()
e, c1 = sol.kernel(h1, eri, norb, nelec, max_space=40)
self.assertAlmostEqual(eref[0], e, 9)
self.assertAlmostEqual(abs(c0[:,0].dot(c1.ravel())), 1, 9)
def absorb_h1e(h1e, eri, norb, nelec, fac=1):
'''Modify 2e Hamiltonian to include 1e Hamiltonian contribution.
'''
if not isinstance(nelec, (int, numpy.number)):
nelec = sum(nelec)
h2e = ao2mo.restore(1, eri.copy(), norb)
f1e = h1e - numpy.einsum('jiik->jk', h2e) * .5
f1e = f1e * (1./(nelec+1e-100))
for k in range(norb):
h2e[k,k,:,:] += f1e
h2e[:,:,k,k] += f1e
return ao2mo.restore(4, h2e, norb) * fac
def contract_2e(eri, civec_strs, norb, nelec, link_index=None, orbsym=None):
ci_coeff, nelec, ci_strs = selected_ci._unpack(civec_strs, nelec)
if link_index is None:
link_index = selected_ci._all_linkstr_index(ci_strs, norb, nelec)
cd_indexa, dd_indexa, cd_indexb, dd_indexb = link_index
na, nlinka = nb, nlinkb = cd_indexa.shape[:2]
eri = ao2mo.restore(1, eri, norb)
eri1 = eri.transpose(0,2,1,3) - eri.transpose(0,2,3,1)
idx,idy = numpy.tril_indices(norb, -1)
idx = idx * norb + idy
eri1 = lib.take_2d(eri1.reshape(norb**2,-1), idx, idx) * 2
lib.transpose_sum(eri1, inplace=True)
eri1 *= .5
eri1, dd_indexa, dimirrep = selected_ci_symm.reorder4irrep(eri1, norb, dd_indexa, orbsym, -1)
fcivec = ci_coeff.reshape(na,nb)
ci1 = numpy.zeros_like(fcivec)
# (aa|aa)
if nelec[0] > 1:
ma, mlinka = mb, mlinkb = dd_indexa.shape[:2]
libfci.SCIcontract_2e_aaaa_symm(eri1.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(ma), ctypes.c_int(mlinka),
dd_indexa.ctypes.data_as(ctypes.c_void_p),
dimirrep.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(dimirrep)))
h_ps = numpy.einsum('pqqs->ps', eri) * (.5/nelec[0])
eri1 = eri.copy()
for k in range(norb):
eri1[:,:,k,k] += h_ps
eri1[k,k,:,:] += h_ps
eri1 = ao2mo.restore(4, eri1, norb)
lib.transpose_sum(eri1, inplace=True)
eri1 *= .5
eri1, cd_indexa, dimirrep = selected_ci_symm.reorder4irrep(eri1, norb, cd_indexa, orbsym)
# (bb|aa)
libfci.SCIcontract_2e_bbaa_symm(eri1.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
cd_indexa.ctypes.data_as(ctypes.c_void_p),
cd_indexa.ctypes.data_as(ctypes.c_void_p),
dimirrep.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(dimirrep)))
lib.transpose_sum(ci1, inplace=True)
return selected_ci._as_SCIvector(ci1.reshape(ci_coeff.shape), ci_strs)
def test_large_ci(self):
norb = 6
nelec = (3,3)
numpy.random.seed(10)
h1e = numpy.random.random((norb,norb))
h1e = h1e + h1e.T
g2e = numpy.random.random((norb,norb,norb,norb))
eri = .5* ao2mo.restore(1, ao2mo.restore(8, g2e, norb), norb)
sol = fci.direct_spin1.FCI(mol)
e, c1 = sol.kernel(h1e, eri, norb, nelec)
self.assertAlmostEqual(e, -4.742664117996546, 9)
val = sol.large_ci(c1, norb, nelec)
self.assertAlmostEqual(val[0][0], c1[0,0], 9)
def test_restore4(self):
self.assertTrue(numpy.allclose(a4, ao2mo.restore(4, a1, n)))
self.assertTrue(numpy.allclose(a4, ao2mo.restore('4', a4, n)))
self.assertTrue(numpy.allclose(a4, ao2mo.restore('s4', a8, n)))
self.assertTrue(numpy.allclose(a4, ao2mo.restore('s4', a2ij, n)))
self.assertTrue(numpy.allclose(a4, ao2mo.restore('s4', a2kl, n)))
self.assertTrue(numpy.allclose(b4, ao2mo.restore(4, b1, n)))
self.assertTrue(numpy.allclose(b4, ao2mo.restore('4', b4, n)))
self.assertTrue(numpy.allclose(b4, ao2mo.restore('4', b2ij, n)))
self.assertTrue(numpy.allclose(b4, ao2mo.restore('4', b2kl, n)))
def test_uccsd_rdm2_mo2ao(self):
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
[8 , (0. , 0. , 0.)],
[1 , (0. , -0.757 , 0.587)],
[1 , (0. , 0.757 , 0.587)]]
mol.spin = 2
mol.basis = '631g'
mol.build(0, 0)
mf = scf.UHF(mol)
mf.conv_tol_grad = 1e-8
mf.kernel()
mycc = cc.UCCSD(mf)
mycc.diis_start_cycle = 1
mycc.conv_tol = 1e-10
eris = mycc.ao2mo()
ecc, t1, t2 = mycc.kernel(eris=eris)
l1, l2 = mycc.solve_lambda(eris=eris)
fdm2 = lib.H5TmpFile()
d2 = cc.uccsd_rdm._gamma2_outcore(mycc, t1, t2, l1, l2, fdm2, True)
nao = mycc.mo_coeff[0].shape[0]
ref = cc.uccsd_rdm._make_rdm2(mycc, None, d2, with_dm1=False)
aa = lib.einsum('ijkl,pi,qj,rk,sl->pqrs', ref[0], mycc.mo_coeff[0],
mycc.mo_coeff[0], mycc.mo_coeff[0], mycc.mo_coeff[0])
ab = lib.einsum('ijkl,pi,qj,rk,sl->pqrs', ref[1], mycc.mo_coeff[0],
mycc.mo_coeff[0], mycc.mo_coeff[1], mycc.mo_coeff[1])
bb = lib.einsum('ijkl,pi,qj,rk,sl->pqrs', ref[2], mycc.mo_coeff[1],
mycc.mo_coeff[1], mycc.mo_coeff[1], mycc.mo_coeff[1])
aa = aa + aa.transpose(0,1,3,2)
aa = aa + aa.transpose(1,0,2,3)
aa = ao2mo.restore(4, aa, nao) * .5
bb = bb + bb.transpose(0,1,3,2)
bb = bb + bb.transpose(1,0,2,3)
bb = ao2mo.restore(4, bb, nao) * .5
ab = ab + ab.transpose(0,1,3,2)
ab = ab + ab.transpose(1,0,2,3)
ab = ao2mo.restore(4, ab, nao) * .5
ref = (aa+ab, bb+ab.T)
rdm2 = uccsd_grad._rdm2_mo2ao(mycc, d2, mycc.mo_coeff)
self.assertAlmostEqual(abs(ref[0]-rdm2[0]).max(), 0, 10)
self.assertAlmostEqual(abs(ref[1]-rdm2[1]).max(), 0, 10)
uccsd_grad._rdm2_mo2ao(mycc, d2, mycc.mo_coeff, fdm2)
self.assertAlmostEqual(abs(ref[0]-fdm2['dm2aa+ab'].value).max(), 0, 10)
self.assertAlmostEqual(abs(ref[1]-fdm2['dm2bb+ab'].value).max(), 0, 10)
self.assertAlmostEqual(lib.finger(rdm2[0]), -1.6247203743431637, 7)
self.assertAlmostEqual(lib.finger(rdm2[1]), -0.44062825991527471, 7)
def pspace(h1e, eri, norb, nelec, hdiag, np=400):
'''pspace Hamiltonian to improve Davidson preconditioner. See, CPL, 169, 463
'''
neleca, nelecb = _unpack_nelec(nelec)
h1e = numpy.ascontiguousarray(h1e)
eri = ao2mo.restore(1, eri, norb)
nb = cistring.num_strings(norb, nelecb)
if hdiag.size < np:
addr = numpy.arange(hdiag.size)
else:
try:
addr = numpy.argpartition(hdiag, np-1)[:np]
except AttributeError:
addr = numpy.argsort(hdiag)[:np]
addra, addrb = divmod(addr, nb)
stra = numpy.array([cistring.addr2str(norb,neleca,ia) for ia in addra],
dtype=numpy.uint64)
strb = numpy.array([cistring.addr2str(norb,nelecb,ib) for ib in addrb],
dtype=numpy.uint64)
np = len(addr)
h0 = numpy.zeros((np,np))
libfci.FCIpspace_h0tril(h0.ctypes.data_as(ctypes.c_void_p),
h1e.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i,i] = hdiag[addr[i]]
h0 = lib.hermi_triu(h0)
return addr, h0
def test_eris_contract_vvvv_t2(self):
mol = gto.Mole()
nocc, nvir = 5, 12
nvir_pair = nvir*(nvir+1)//2
numpy.random.seed(9)
t2 = numpy.random.random((nocc,nocc,nvir,nvir)) - .5
t2 = t2 + t2.transpose(1,0,3,2)
eris = ccsd._ChemistsERIs()
vvvv = numpy.random.random((nvir_pair,nvir_pair)) - .5
eris.vvvv = vvvv + vvvv.T
eris.mol = mol
mycc.max_memory, bak = 0, mycc.max_memory
vt2 = eris._contract_vvvv_t2(mycc, t2, eris.vvvv)
mycc.max_memory = bak
self.assertAlmostEqual(lib.finger(vt2), -39.572579908080087, 11)
vvvv = ao2mo.restore(1, eris.vvvv, nvir)
ref = lib.einsum('acbd,ijcd->ijab', vvvv, t2)
self.assertAlmostEqual(abs(vt2 - ref).max(), 0, 11)
# _contract_s1vvvv_t2, testing complex and real mixed contraction
vvvv =(numpy.random.random((nvir,nvir,nvir,nvir)) +
numpy.random.random((nvir,nvir,nvir,nvir))*1j - (.5+.5j))
vvvv = vvvv + vvvv.transpose(1,0,3,2).conj()
vvvv = vvvv + vvvv.transpose(2,3,0,1)
eris.vvvv = vvvv
eris.mol = mol
mycc.max_memory, bak = 0, mycc.max_memory
vt2 = eris._contract_vvvv_t2(mycc, t2, eris.vvvv)
mycc.max_memory = bak
self.assertAlmostEqual(lib.finger(vt2), 23.502736435296871+113.90422480013488j, 11)
ref = lib.einsum('acbd,ijcd->ijab', eris.vvvv, t2)
self.assertAlmostEqual(abs(vt2 - ref).max(), 0, 11)
def Srs(mc, dms, eris=None, verbose=None):
#Subspace S_rs^{(-2)}
mo_core, mo_cas, mo_virt = _extract_orbs(mc, mc.mo_coeff)
dm1 = dms['1']
dm2 = dms['2']
dm3 = dms['3']
ncore = mo_core.shape[1]
ncas = mo_cas.shape[1]
nocc = ncore + ncas
if mo_virt.shape[1] ==0:
return 0, 0
if eris is None:
h1e = mc.h1e_for_cas()[0]
h2e = ao2mo.restore(1, mc.ao2mo(mo_cas), ncas).transpose(0,2,1,3)
h2e_v = ao2mo.incore.general(mc._scf._eri,[mo_virt,mo_cas,mo_virt,mo_cas],compact=False)
h2e_v = h2e_v.reshape(mo_virt.shape[1],ncas,mo_virt.shape[1],ncas).transpose(0,2,1,3)
else:
h1e = eris['h1eff'][ncore:nocc,ncore:nocc]
h2e = eris['ppaa'][ncore:nocc,ncore:nocc].transpose(0,2,1,3)
h2e_v = eris['papa'][nocc:,:,nocc:].transpose(0,2,1,3)
# a7 is very sensitive to the accuracy of HF orbital and CI wfn
rm2, a7 = make_a7(h1e,h2e,dm1,dm2,dm3)
norm = 0.5*numpy.einsum('rsqp,rsba,pqba->rs',h2e_v,h2e_v,rm2)
h = 0.5*numpy.einsum('rsqp,rsba,pqab->rs',h2e_v,h2e_v,a7)
diff = mc.mo_energy[nocc:,None] + mc.mo_energy[None,nocc:]
return _norm_to_energy(norm, h, diff)
def Sijr(mc, dms, eris, verbose=None):
#Subspace S_ijr^{(1)}
mo_core, mo_cas, mo_virt = _extract_orbs(mc, mc.mo_coeff)
dm1 = dms['1']
dm2 = dms['2']
ncore = mo_core.shape[1]
ncas = mo_cas.shape[1]
nocc = ncore + ncas
if eris is None:
h1e = mc.h1e_for_cas()[0]
h2e = ao2mo.restore(1, mc.ao2mo(mo_cas), ncas).transpose(0,2,1,3)
h2e_v = ao2mo.incore.general(mc._scf._eri,[mo_virt,mo_core,mo_cas,mo_core],compact=False)
h2e_v = h2e_v.reshape(mo_virt.shape[1],ncore,ncas,ncore).transpose(0,2,1,3)
else:
h1e = eris['h1eff'][ncore:nocc,ncore:nocc]
h2e = eris['ppaa'][ncore:nocc,ncore:nocc].transpose(0,2,1,3)
h2e_v = eris['pacv'][:ncore].transpose(3,1,2,0)
if 'h1' in dms:
hdm1 = dms['h1']
else:
hdm1 = make_hdm1(dm1)
a3 = make_a3(h1e,h2e,dm1,dm2,hdm1)
norm = 2.0*numpy.einsum('rpji,raji,pa->rji',h2e_v,h2e_v,hdm1)\
- 1.0*numpy.einsum('rpji,raij,pa->rji',h2e_v,h2e_v,hdm1)
h = 2.0*numpy.einsum('rpji,raji,pa->rji',h2e_v,h2e_v,a3)\
- 1.0*numpy.einsum('rpji,raij,pa->rji',h2e_v,h2e_v,a3)
diff = mc.mo_energy[nocc:,None,None] - mc.mo_energy[None,:ncore,None] - mc.mo_energy[None,None,:ncore]
return _norm_to_energy(norm, h, diff)
def Srsi(mc, dms, eris, verbose=None):
#Subspace S_ijr^{(1)}
mo_core, mo_cas, mo_virt = _extract_orbs(mc, mc.mo_coeff)
dm1 = dms['1']
dm2 = dms['2']
ncore = mo_core.shape[1]
ncas = mo_cas.shape[1]
nocc = ncore + ncas
if eris is None:
h1e = mc.h1e_for_cas()[0]
h2e = ao2mo.restore(1, mc.ao2mo(mo_cas), ncas).transpose(0,2,1,3)
h2e_v = ao2mo.incore.general(mc._scf._eri,[mo_virt,mo_core,mo_virt,mo_cas],compact=False)
h2e_v = h2e_v.reshape(mo_virt.shape[1],ncore,mo_virt.shape[1],ncas).transpose(0,2,1,3)
else:
h1e = eris['h1eff'][ncore:nocc,ncore:nocc]
h2e = eris['ppaa'][ncore:nocc,ncore:nocc].transpose(0,2,1,3)
h2e_v = eris['pacv'][nocc:].transpose(3,0,2,1)
k27 = make_k27(h1e,h2e,dm1,dm2)
norm = 2.0*numpy.einsum('rsip,rsia,pa->rsi',h2e_v,h2e_v,dm1)\
- 1.0*numpy.einsum('rsip,sria,pa->rsi',h2e_v,h2e_v,dm1)
h = 2.0*numpy.einsum('rsip,rsia,pa->rsi',h2e_v,h2e_v,k27)\
- 1.0*numpy.einsum('rsip,sria,pa->rsi',h2e_v,h2e_v,k27)
diff = mc.mo_energy[nocc:,None,None] + mc.mo_energy[None,nocc:,None] - mc.mo_energy[None,None,:ncore]
return _norm_to_energy(norm, h, diff)
def make_hdiag(h1e, eri, norb, nelec):
'''Diagonal Hamiltonian for Davidson preconditioner
'''
neleca, nelecb = _unpack_nelec(nelec)
h1e = numpy.asarray(h1e, order='C')
eri = ao2mo.restore(1, eri, norb)
strsa = numpy.asarray(cistring.gen_strings4orblist(range(norb), neleca))
strsb = numpy.asarray(cistring.gen_strings4orblist(range(norb), nelecb))
na = len(strsa)
nb = len(strsb)
hdiag = numpy.empty(na*nb)
jdiag = numpy.asarray(numpy.einsum('iijj->ij',eri), order='C')
kdiag = numpy.asarray(numpy.einsum('ijji->ij',eri), order='C')
c_h1e = h1e.ctypes.data_as(ctypes.c_void_p)
c_jdiag = jdiag.ctypes.data_as(ctypes.c_void_p)
c_kdiag = kdiag.ctypes.data_as(ctypes.c_void_p)
libfci.FCImake_hdiag_uhf(hdiag.ctypes.data_as(ctypes.c_void_p),
c_h1e, c_h1e, c_jdiag, c_jdiag, c_jdiag, c_kdiag, c_kdiag,
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(neleca), ctypes.c_int(nelecb),
strsa.ctypes.data_as(ctypes.c_void_p),
strsb.ctypes.data_as(ctypes.c_void_p))
return hdiag
def make_hdiag(h1e, g2e, ci_strs, norb, nelec):
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
strsa, strsb = ci_strs
strsa = numpy.asarray(strsa)
strsb = numpy.asarray(strsb)
occslista = [[i for i in range(norb) if str0 & (1 << i)] for str0 in strsa]
occslistb = [[i for i in range(norb) if str0 & (1 << i)] for str0 in strsb]
g2e = ao2mo.restore(1, g2e, norb)
diagj = numpy.einsum("iijj->ij", g2e)
diagk = numpy.einsum("ijji->ij", g2e)
hdiag = []
for aocc in occslista:
for bocc in occslistb:
e1 = h1e[aocc, aocc].sum() + h1e[bocc, bocc].sum()
e2 = (
diagj[aocc][:, aocc].sum()
+ diagj[aocc][:, bocc].sum()
+ diagj[bocc][:, aocc].sum()
+ diagj[bocc][:, bocc].sum()
- diagk[aocc][:, aocc].sum()
- diagk[bocc][:, bocc].sum()
)
hdiag.append(e1 + e2 * 0.5)
return numpy.array(hdiag)
def make_diagonal(mol, mo_energy, eris, nocc):
nmo = mo_energy.size
nvir = nmo - nocc
jdiag = numpy.zeros((nmo,nmo))
kdiag = numpy.zeros((nmo,nmo))
eris_vvvv = ao2mo.restore(1, eris.vvvv, nvir)
jdiag[:nocc,:nocc] = numpy.einsum('iijj->ij', eris.oooo)
kdiag[:nocc,:nocc] = numpy.einsum('jiij->ij', eris.oooo)
jdiag[nocc:,nocc:] = numpy.einsum('iijj->ij', eris_vvvv)
kdiag[nocc:,nocc:] = numpy.einsum('jiij->ij', eris_vvvv)
jdiag[:nocc,nocc:] = numpy.einsum('iijj->ji', eris.vvoo)
kdiag[:nocc,nocc:] = numpy.einsum('jiij->ij', eris.voov)
jksum = (jdiag[:nocc,:nocc] * 2 - kdiag[:nocc,:nocc]).sum()
ehf = mo_energy[:nocc].sum() * 2 - jksum
e1diag = numpy.empty((nocc,nvir))
e2diag = numpy.empty((nocc,nocc,nvir,nvir))
for i in range(nocc):
for a in range(nocc, nmo):
e1diag[i,a-nocc] = ehf - mo_energy[i] + mo_energy[a] \
- jdiag[i,a] + kdiag[i,a]
for j in range(nocc):
for b in range(nocc, nmo):
e2diag[i,j,a-nocc,b-nocc] = ehf \
- mo_energy[i] - mo_energy[j] \
+ mo_energy[a] + mo_energy[b] \
+ jdiag[i,j] - jdiag[i,a] + kdiag[i,a] \
- jdiag[j,a] - jdiag[i,b] - jdiag[j,b] \
+ kdiag[j,b] + jdiag[a,b]
return numpy.hstack((ehf, e1diag.reshape(-1), e2diag.reshape(-1)))
def test_get_veff(self):
nao = mol.nao_nr()*2
numpy.random.seed(1)
d1 = numpy.random.random((nao,nao)) + numpy.random.random((nao,nao)) * 1j
d2 = numpy.random.random((nao,nao)) + numpy.random.random((nao,nao)) * 1j
d = numpy.array((d1+d1.conj().T, d2+d2.conj().T))
eri = numpy.zeros((nao, nao, nao, nao))
n = nao // 2
eri[:n,:n,:n,:n] = \
eri[n:,n:,n:,n:] = \
eri[:n,:n,n:,n:] = \
eri[n:,n:,:n,:n] = ao2mo.restore(1, mf._eri, n)
vj = numpy.einsum('ijkl,xji->xkl', eri, d)
vk = numpy.einsum('ijkl,xjk->xil', eri, d)
ref = vj - vk
v = mf.get_veff(mol, d)
self.assertAlmostEqual(abs(ref - v).max(), 0, 12)
self.assertAlmostEqual(numpy.linalg.norm(v), 560.3785699368684, 9)
def test_general(self):
numpy.random.seed(15)
nmo = 12
mo = numpy.random.random((nao,nmo))
eriref = ao2mo.incore.full(eri, mo)
tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
io_size = nao**2*4e-5
semi_incore.general(eri, [mo]*4, tmpfile.name, ioblk_size=io_size)
with ao2mo.load(tmpfile) as eri_mo:
self.assertAlmostEqual(abs(eriref - eri_mo.value).max(), 0, 9)
semi_incore.general(eri, [mo]*4, tmpfile.name, ioblk_size=io_size,
compact=False)
with ao2mo.load(tmpfile) as eri_mo:
eriref = ao2mo.restore(1, eriref, nmo).reshape(nmo**2,nmo**2)
self.assertAlmostEqual(abs(eriref - eri_mo.value).max(), 0, 9)
def test_select_strs(self):
myci = selected_ci.SCI()
myci.select_cutoff = 1e-3
norb, nelec = 10, 4
strs = cistring.make_strings(range(norb), nelec)
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .8
strs = strs[mask]
nn = norb*(norb+1)//2
eri = (numpy.random.random(nn*(nn+1)//2)-.2)**3
eri[eri<.1] *= 3e-3
eri = ao2mo.restore(1, eri, norb)
eri_pq_max = abs(eri.reshape(norb**2,-1)).max(axis=1).reshape(norb,norb)
civec_max = numpy.random.random(len(strs))
strs_add0 = select_strs(myci, eri, eri_pq_max, civec_max, strs, norb, nelec)
strs_add1 = selected_ci.select_strs(myci, eri, eri_pq_max, civec_max,
strs, norb, nelec)
self.assertTrue(numpy.all(strs_add0 == strs_add1))
def contract_2e(eri, fcivec, norb, nelec, link_index=None):
fcivec = numpy.asarray(fcivec, order='C')
eri = ao2mo.restore(4, eri, norb)
lib.transpose_sum(eri, inplace=True)
eri *= .5
link_index = _unpack(norb, nelec, link_index)
na, nlink = link_index.shape[:2]
assert(fcivec.size == na**2)
ci1 = numpy.empty((na,na))
libfci.FCIcontract_2e_spin0(eri.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(na),
ctypes.c_int(nlink),
link_index.ctypes.data_as(ctypes.c_void_p))
# no *.5 because FCIcontract_2e_spin0 only compute half of the contraction
return lib.transpose_sum(ci1, inplace=True).reshape(fcivec.shape)
def Sijr(mc, dms, eris, verbose=None):
#Subspace S_ijr^{(1)}
mo_core, mo_cas, mo_virt = _extract_orbs(mc, mc.mo_coeff)
dm1 = dms['1']
dm2 = dms['2']
ncore = mo_core.shape[1]
ncas = mo_cas.shape[1]
nocc = ncore + ncas
if eris is None:
h1e = mc.h1e_for_cas()[0]
h2e = ao2mo.restore(1, mc.ao2mo(mo_cas), ncas).transpose(0,2,1,3)
h2e_v = ao2mo.incore.general(mc._scf._eri,[mo_virt,mo_core,mo_cas,mo_core],compact=False)
h2e_v = h2e_v.reshape(mo_virt.shape[1],ncore,ncas,ncore).transpose(0,2,1,3)
else:
h1e = eris['h1eff'][ncore:nocc,ncore:nocc]
h2e = eris['ppaa'][ncore:nocc,ncore:nocc].transpose(0,2,1,3)
h2e_v = eris['pacv'][:ncore].transpose(3,1,2,0)
if 'h1' in dms:
hdm1 = dms['h1']
else:
hdm1 = make_hdm1(dm1)
a3 = make_a3(h1e,h2e,dm1,dm2,hdm1)
# We sum norm and h only over i <= j (or j <= i instead).
# See Eq. (13) and (A2) in https://doi.org/10.1063/1.1515317
# This implementation is still somewhat wasteful in terms of memory,
# as we only need about half of norm and h in the end.
ci_diag = numpy.diag_indices(ncore)
ci_triu = numpy.triu_indices(ncore)
norm = 2.0*numpy.einsum('rpji,raji,pa->rji',h2e_v,h2e_v,hdm1)\
- 1.0*numpy.einsum('rpji,raij,pa->rji',h2e_v,h2e_v,hdm1)
norm += norm.transpose(0, 2, 1)
norm[:, ci_diag[0], ci_diag[1]] *= 0.5
h = 2.0*numpy.einsum('rpji,raji,pa->rji',h2e_v,h2e_v,a3)\
- 1.0*numpy.einsum('rpji,raij,pa->rji',h2e_v,h2e_v,a3)
h += h.transpose(0, 2, 1)
h[:, ci_diag[0], ci_diag[1]] *= 0.5
diff = mc.mo_energy[nocc:,None,None] - mc.mo_energy[None,:ncore,None] - mc.mo_energy[None,None,:ncore]
norm_tri = norm[:, ci_triu[0], ci_triu[1]]
h_tri = h[:, ci_triu[0], ci_triu[1]]
diff_tri = diff[:, ci_triu[0], ci_triu[1]]
return _norm_to_energy(norm_tri, h_tri, diff_tri)
def _make_eris_incore(mycc, mo_coeff=None, ao2mofn=None):
cput0 = (time.clock(), time.time())
eris = _PhysicistsERIs()
eris._common_init_(mycc, mo_coeff)
nocc = eris.nocc
nao, nmo = eris.mo_coeff.shape
if callable(ao2mofn):
eri = ao2mofn(eris.mo_coeff).reshape([nmo]*4)
else:
assert(eris.mo_coeff.dtype == np.double)
mo_a = eris.mo_coeff[:nao//2]
mo_b = eris.mo_coeff[nao//2:]
orbspin = eris.orbspin
if orbspin is None:
eri = ao2mo.kernel(mycc._scf._eri, mo_a)
eri += ao2mo.kernel(mycc._scf._eri, mo_b)
eri1 = ao2mo.kernel(mycc._scf._eri, (mo_a,mo_a,mo_b,mo_b))
eri += eri1
eri += eri1.T
else:
mo = mo_a + mo_b
eri = ao2mo.kernel(mycc._scf._eri, mo)
if eri.size == nmo**4: # if mycc._scf._eri is a complex array
sym_forbid = (orbspin[:,None] != orbspin).ravel()
else: # 4-fold symmetry
sym_forbid = (orbspin[:,None] != orbspin)[np.tril_indices(nmo)]
eri[sym_forbid,:] = 0
eri[:,sym_forbid] = 0
if eri.dtype == np.double:
eri = ao2mo.restore(1, eri, nmo)
eri = eri.reshape(nmo,nmo,nmo,nmo)
eri = eri.transpose(0,2,1,3) - eri.transpose(0,2,3,1)
eris.oooo = eri[:nocc,:nocc,:nocc,:nocc].copy()
eris.ooov = eri[:nocc,:nocc,:nocc,nocc:].copy()
eris.oovv = eri[:nocc,:nocc,nocc:,nocc:].copy()
eris.ovov = eri[:nocc,nocc:,:nocc,nocc:].copy()
eris.ovvo = eri[:nocc,nocc:,nocc:,:nocc].copy()
eris.ovvv = eri[:nocc,nocc:,nocc:,nocc:].copy()
eris.vvvv = eri[nocc:,nocc:,nocc:,nocc:].copy()
return eris
def enlarge_space(myci, civec_strs, eri, norb, nelec):
if isinstance(civec_strs, (tuple, list)):
nelec, (strsa, strsb) = selected_ci._unpack(civec_strs[0], nelec)[1:]
ci_coeff = lib.asarray(civec_strs)
else:
ci_coeff, nelec, (strsa,
strsb) = selected_ci._unpack(civec_strs, nelec)
na = nb = len(strsa)
ci0 = ci_coeff.reshape(-1, na, nb)
abs_ci = abs(ci0).max(axis=0)
eri = ao2mo.restore(1, eri, norb)
eri_pq_max = abs(eri.reshape(norb**2, -1)).max(axis=1).reshape(norb, norb)
civec_a_max = abs_ci.max(axis=1)
ci_aidx = numpy.where(civec_a_max > myci.ci_coeff_cutoff)[0]
civec_a_max = civec_a_max[ci_aidx]
strsa = strsa[ci_aidx]
strsa_add = selected_ci.select_strs(myci, eri, eri_pq_max, civec_a_max,
strsa, norb, nelec[0])
strsa = numpy.append(strsa, strsa_add)
aidx = numpy.argsort(strsa)
strsa = strsa[aidx]
aidx = numpy.where(aidx < len(ci_aidx))[0]
ci_bidx = ci_aidx
strsb = strsa
bidx = aidx
ma = mb = len(strsa)
cs = []
for i in range(ci0.shape[0]):
ci1 = numpy.zeros((ma, mb))
tmp = lib.take_2d(ci0[i], ci_aidx, ci_bidx)
lib.takebak_2d(ci1, tmp, aidx, bidx)
cs.append(selected_ci._as_SCIvector(ci1, (strsa, strsb)))
if ci_coeff[0].ndim == 0 or ci_coeff[0].shape[-1] != nb:
cs = [c.ravel() for c in cs]
if (isinstance(ci_coeff, numpy.ndarray) and ci_coeff.shape[0] == na
or ci_coeff.shape[0] == na * nb):
cs = cs[0]
return cs
def Sr(mc,ci,dms, eris=None, verbose=None):
#The subspace S_r^{(-1)}
mo_core, mo_cas, mo_virt = _extract_orbs(mc, mc.mo_coeff)
dm1 = dms['1']
dm2 = dms['2']
dm3 = dms['3']
#dm4 = dms['4']
ncore = mo_core.shape[1]
nvirt = mo_virt.shape[1]
ncas = mo_cas.shape[1]
nocc = ncore + ncas
if eris is None:
h1e = mc.h1e_for_cas()[0]
h2e = ao2mo.restore(1, mc.ao2mo(mo_cas), ncas).transpose(0,2,1,3)
h2e_v = ao2mo.incore.general(mc._scf._eri,[mo_virt,mo_cas,mo_cas,mo_cas],compact=False)
h2e_v = h2e_v.reshape(mo_virt.shape[1],ncas,ncas,ncas).transpose(0,2,1,3)
core_dm = numpy.dot(mo_core,mo_core.T) *2
core_vhf = mc.get_veff(mc.mol,core_dm)
h1e_v = reduce(numpy.dot, (mo_virt.T, mc.get_hcore()+core_vhf , mo_cas))
h1e_v -= numpy.einsum('mbbn->mn',h2e_v)
else:
h1e = eris['h1eff'][ncore:nocc,ncore:nocc]
h2e = eris['ppaa'][ncore:nocc,ncore:nocc].transpose(0,2,1,3)
h2e_v = eris['ppaa'][nocc:,ncore:nocc].transpose(0,2,1,3)
h1e_v = eris['h1eff'][nocc:,ncore:nocc] - numpy.einsum('mbbn->mn',h2e_v)
if getattr(mc.fcisolver, 'nevpt_intermediate', None):
a16 = mc.fcisolver.nevpt_intermediate('A16',ncas,mc.nelecas,ci)
else:
a16 = make_a16(h1e,h2e, dms, ci, ncas, mc.nelecas)
a17 = make_a17(h1e,h2e,dm2,dm3)
a19 = make_a19(h1e,h2e,dm1,dm2)
ener = numpy.einsum('ipqr,pqrabc,iabc->i',h2e_v,a16,h2e_v)\
+ numpy.einsum('ipqr,pqra,ia->i',h2e_v,a17,h1e_v)*2.0\
+ numpy.einsum('ip,pa,ia->i',h1e_v,a19,h1e_v)
norm = numpy.einsum('ipqr,rpqbac,iabc->i',h2e_v,dm3,h2e_v)\
+ numpy.einsum('ipqr,rpqa,ia->i',h2e_v,dm2,h1e_v)*2.0\
+ numpy.einsum('ip,pa,ia->i',h1e_v,dm1,h1e_v)
return _norm_to_energy(norm, ener, mc.mo_energy[nocc:])
def test_rdm_real(self):
nocc = 6
nvir = 10
mf = scf.GHF(mol)
nmo = nocc + nvir
npair = nmo * (nmo // 2 + 1) // 4
numpy.random.seed(12)
mf._eri = numpy.random.random(npair * (npair + 1) // 2) * .3
hcore = numpy.random.random((nmo, nmo)) * .5
hcore = hcore + hcore.T + numpy.diag(range(nmo)) * 2
mf.get_hcore = lambda *args: hcore
mf.get_ovlp = lambda *args: numpy.eye(nmo)
mf.mo_coeff = numpy.eye(nmo)
mf.mo_occ = numpy.zeros(nmo)
mf.mo_occ[:nocc] = 1
mycc = gccsd.GCCSD(mf)
ecc, t1, t2 = mycc.kernel()
l1, l2 = mycc.solve_lambda()
dm1 = gccsd_rdm.make_rdm1(mycc, t1, t2, l1, l2)
dm2 = gccsd_rdm.make_rdm2(mycc, t1, t2, l1, l2)
nao = nmo // 2
mo_a = mf.mo_coeff[:nao]
mo_b = mf.mo_coeff[nao:]
eri = ao2mo.kernel(mf._eri, mo_a)
eri += ao2mo.kernel(mf._eri, mo_b)
eri1 = ao2mo.kernel(mf._eri, (mo_a, mo_a, mo_b, mo_b))
eri += eri1
eri += eri1.T
eri = ao2mo.restore(1, eri, nmo)
h1 = reduce(numpy.dot, (mf.mo_coeff.T.conj(), hcore, mf.mo_coeff))
e1 = numpy.einsum('ij,ji', h1, dm1)
e1 += numpy.einsum('ijkl,ijkl', eri, dm2) * .5
e1 += mol.energy_nuc()
self.assertAlmostEqual(e1, mycc.e_tot, 7)
self.assertAlmostEqual(
abs(dm2 - dm2.transpose(1, 0, 3, 2).conj()).max(), 0, 9)
self.assertAlmostEqual(
abs(dm2 - dm2.transpose(2, 3, 0, 1)).max(), 0, 9)
self.assertAlmostEqual(
abs(dm2 + dm2.transpose(2, 1, 0, 3)).max(), 0, 9)
self.assertAlmostEqual(
abs(dm2 + dm2.transpose(0, 3, 2, 1)).max(), 0, 9)
def test_mp2_dm(self):
nocc = mol.nelectron//2
nmo = mf.mo_energy.size
nvir = nmo - nocc
co = mf.mo_coeff[:,:nocc]
cv = mf.mo_coeff[:,nocc:]
g = ao2mo.incore.general(mf._eri, (co,cv,co,cv)).ravel()
eia = mf.mo_energy[:nocc,None] - mf.mo_energy[nocc:]
t2ref0 = g/(eia.reshape(-1,1)+eia.reshape(-1)).ravel()
t2ref0 = t2ref0.reshape(nocc,nvir,nocc,nvir).transpose(0,2,3,1)
pt = mp.mp2.MP2(mf)
emp2, t2 = pt.kernel()
t2s = numpy.zeros((nocc*2,nocc*2,nvir*2,nvir*2))
t2s[ ::2, ::2, ::2, ::2] = t2ref0 - t2ref0.transpose(0,1,3,2)
t2s[1::2,1::2,1::2,1::2] = t2ref0 - t2ref0.transpose(0,1,3,2)
t2s[ ::2,1::2,1::2, ::2] = t2ref0
t2s[1::2, ::2, ::2,1::2] = t2ref0
t2s[ ::2,1::2, ::2,1::2] = -t2ref0.transpose(0,1,3,2)
t2s[1::2, ::2,1::2, ::2] = -t2ref0.transpose(0,1,3,2)
dm1occ =-.5 * numpy.einsum('ikab,jkab->ij', t2s, t2s)
dm1vir = .5 * numpy.einsum('ijac,ijbc->ab', t2s, t2s)
dm1ref = numpy.zeros((nmo,nmo))
dm1ref[:nocc,:nocc] = dm1occ[ ::2, ::2]+dm1occ[1::2,1::2]
dm1ref[nocc:,nocc:] = dm1vir[ ::2, ::2]+dm1vir[1::2,1::2]
for i in range(nocc):
dm1ref[i,i] += 2
dm1refao = reduce(numpy.dot, (mf.mo_coeff, dm1ref, mf.mo_coeff.T))
rdm1 = mp.mp2.make_rdm1(pt, t2ref0, ao_repr=True)
self.assertTrue(numpy.allclose(rdm1, dm1refao))
self.assertTrue(numpy.allclose(pt.make_rdm1(), dm1ref))
rdm1 = mp.mp2.make_rdm1(pt, ao_repr=True)
self.assertTrue(numpy.allclose(rdm1, dm1refao))
dm2ref = numpy.zeros((nmo*2,)*4)
dm2ref[:nocc*2,nocc*2:,:nocc*2,nocc*2:] = t2s.transpose(0,3,1,2) * .5
dm2ref[nocc*2:,:nocc*2,nocc*2:,:nocc*2] = t2s.transpose(3,0,2,1) * .5
dm2ref = dm2ref[ ::2, ::2, ::2, ::2] + dm2ref[1::2,1::2,1::2,1::2] \
+ dm2ref[ ::2, ::2,1::2,1::2] + dm2ref[1::2,1::2, ::2, ::2]
eris = ao2mo.restore(1, ao2mo.full(mf._eri, mf.mo_coeff), mf.mo_coeff.shape[1])
self.assertAlmostEqual(numpy.einsum('iajb,iajb', eris, dm2ref)*.5, emp2, 9)
def solve_ERI(OEI, TEI, DMguess, numPairs):
mol = gto.Mole()
mol.build(verbose=3)
mol.atom.append(('C', (0, 0, 0)))
mol.nelectron = 2 * numPairs
L = OEI.shape[0]
mf = scf.RHF(mol)
mf.get_hcore = lambda *args: OEI
mf.get_ovlp = lambda *args: np.eye(L)
mf._eri = ao2mo.restore(8, TEI, L)
mf.scf(DMguess)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
if (mf.converged == False):
mf = rhf_newtonraphson.solve(mf, dm_guess=DMloc)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
return DMloc
def Sij(mc, dms, eris, verbose=None):
#Subspace S_ij^{(-2)}
mo_core, mo_cas, mo_virt = _extract_orbs(mc, mc.mo_coeff)
dm1 = dms['1']
dm2 = dms['2']
dm3 = dms['3']
ncore = mo_core.shape[1]
ncas = mo_cas.shape[1]
nocc = ncore + ncas
if mo_core.size == 0:
return 0.0, 0
if eris is None:
h1e = mc.h1e_for_cas()[0]
h2e = ao2mo.restore(1, mc.ao2mo(mo_cas), ncas).transpose(0, 2, 1, 3)
h2e_v = ao2mo.incore.general(mc._scf._eri,
[mo_cas, mo_core, mo_cas, mo_core],
compact=False)
h2e_v = h2e_v.reshape(ncas, ncore, ncas, ncore).transpose(0, 2, 1, 3)
else:
h1e = eris['h1eff'][ncore:nocc, ncore:nocc]
h2e = eris['ppaa'][ncore:nocc, ncore:nocc].transpose(0, 2, 1, 3)
h2e_v = eris['papa'][:ncore, :, :ncore].transpose(1, 3, 0, 2)
if 'h1' in dms:
hdm1 = dms['h1']
else:
hdm1 = make_hdm1(dm1)
if 'h2' in dms:
hdm2 = dms['h2']
else:
hdm2 = make_hdm2(dm1, dm2)
if 'h3' in dms:
hdm3 = dms['h3']
else:
hdm3 = make_hdm3(dm1, dm2, dm3, hdm1, hdm2)
# a9 is very sensitive to the accuracy of HF orbital and CI wfn
a9 = make_a9(h1e, h2e, hdm1, hdm2, hdm3)
norm = 0.5 * numpy.einsum('qpij,baij,pqab->ij', h2e_v, h2e_v, hdm2)
h = 0.5 * numpy.einsum('qpij,baij,pqab->ij', h2e_v, h2e_v, a9)
diff = mc.mo_energy[:ncore, None] + mc.mo_energy[None, :ncore]
return _norm_to_energy(norm, h, -diff)
def get_init_guess (fci, norb, nelec, norb_f, h1, h2, nelec_f=None, smult_f=None):
if nelec_f is None:
nelec_f = _guess_nelec_f (fci, norb, nelec, norb_f, h1, h2)
if smult_f is None:
smult_f = [abs(n[0]-n[1])+1 for n in nelec_f]
h2 = ao2mo.restore (1, h2, norb)
i = 0
ci0_f = []
for no, ne, s in zip (norb_f, nelec_f, smult_f):
j = i + no
h1_i = h1[i:j,i:j]
h2_i = h2[i:j,i:j,i:j,i:j]
i = j
csf = csf_solver (fci.mol, smult=s)
hdiag = csf.make_hdiag_csf (h1_i, h2_i, no, ne)
ci = csf.get_init_guess (no, ne, 1, hdiag)[0]
ci = np.squeeze (fockspace.hilbert2fock (ci, no, ne))
ci0_f.append (ci)
return ci0_f
def enlarge_space(myci, civec_strs, eri, norb, nelec):
if isinstance(civec_strs, (tuple, list)):
nelec, (strsa, strsb) = _unpack(civec_strs[0], nelec)[1:]
ci_coeff = lib.asarray(civec_strs)
else:
ci_coeff, nelec, (strsa, strsb) = _unpack(civec_strs, nelec)
na = len(strsa)
nb = len(strsb)
ci0 = ci_coeff.reshape(-1,na,nb)
civec_a_max = lib.norm(ci0, axis=2).max(axis=0)
civec_b_max = lib.norm(ci0, axis=1).max(axis=0)
ci_aidx = numpy.where(civec_a_max > myci.ci_coeff_cutoff)[0]
ci_bidx = numpy.where(civec_b_max > myci.ci_coeff_cutoff)[0]
civec_a_max = civec_a_max[ci_aidx]
civec_b_max = civec_b_max[ci_bidx]
strsa = strsa[ci_aidx]
strsb = strsb[ci_bidx]
eri = ao2mo.restore(1, eri, norb)
eri_pq_max = abs(eri.reshape(norb**2,-1)).max(axis=1).reshape(norb,norb)
strsa_add = select_strs(myci, eri, eri_pq_max, civec_a_max, strsa, norb, nelec[0])
strsb_add = select_strs(myci, eri, eri_pq_max, civec_b_max, strsb, norb, nelec[1])
strsa = numpy.append(strsa, strsa_add)
strsb = numpy.append(strsb, strsb_add)
aidx = numpy.argsort(strsa)
bidx = numpy.argsort(strsb)
ci_strs = (strsa[aidx], strsb[bidx])
aidx = numpy.where(aidx < len(ci_aidx))[0]
bidx = numpy.where(bidx < len(ci_bidx))[0]
ma = len(strsa)
mb = len(strsb)
cs = []
for i in range(ci0.shape[0]):
ci1 = numpy.zeros((ma,mb))
tmp = lib.take_2d(ci0[i], ci_aidx, ci_bidx)
lib.takebak_2d(ci1, tmp, aidx, bidx)
cs.append(_as_SCIvector(ci1, ci_strs))
if not isinstance(civec_strs, (tuple, list)) and civec_strs.ndim < 3:
cs = cs[0]
return cs
def TestRestore():
for sym in [1, 4, 8]:
print("\n symmetry = ", sym)
norb = 8
g2e = np.zeros((norb, norb, norb, norb))
#g2e[4,4,5,5] = 2*U;
g2e[4, 4, 5, 5] = U
g2e[5, 5, 4, 4] = U
for i1 in range(norb):
for i2 in range(norb):
for i3 in range(norb):
for i4 in range(norb):
if g2e[i1, i2, i3, i4] != 0:
print("g2e[", i1, i2, i3, i4, "] = ", g2e[i1, i2,
i3, i4])
g2e2 = ao2mo.restore(sym, g2e, norb)
del g2e
if (sym == 1):
print(sym, np.shape(g2e2))
for i1 in range(norb):
for i2 in range(norb):
for i3 in range(norb):
for i4 in range(norb):
if g2e2[i1, i2, i3, i4] != 0:
print("--> g2e2[", i1, i2, i3, i4, "] = ",
g2e2[i1, i2, i3, i4])
elif (sym == 4):
print(sym, np.shape(g2e2))
for i1 in range(np.shape(g2e2)[0]):
for i2 in range(np.shape(g2e2)[1]):
if g2e2[i1, i2] != 0:
print("--> g2e2[", i1, i2, "] = ", g2e2[i1, i2])
elif (sym == 8):
print(sym, np.shape(g2e2))
for i1 in range(np.shape(g2e2)[0]):
if g2e2[i1] != 0:
print("--> g2e2[", i1, "] = ", g2e2[i1])
def test_ccsd_rdm(self):
mcc = cc.ccsd.CC(mf)
mcc.max_memory = 0
mcc.conv_tol = 1e-9
mcc.conv_tol_normt = 1e-7
mcc.kernel()
mcc.solve_lambda()
dm1 = mcc.make_rdm1()
dm2 = mcc.make_rdm2()
self.assertAlmostEqual(numpy.linalg.norm(dm1), 4.4227785269355078, 3)
self.assertAlmostEqual(numpy.linalg.norm(dm2), 20.074587448789089, 3)
nmo = mf.mo_coeff.shape[1]
eri = ao2mo.restore(1, ao2mo.kernel(mf._eri, mf.mo_coeff), nmo)
h1 = reduce(numpy.dot, (mf.mo_coeff.T.conj(), mf.get_hcore(), mf.mo_coeff))
e1 = numpy.einsum('ij,ji', h1, dm1)
e1+= numpy.einsum('ijkl,ijkl', eri, dm2) * .5
e1+= mf.energy_nuc()
self.assertAlmostEqual(e1, mcc.e_tot, 7)
def kernel(self, h1, h2, norb, nelec, ci0=None, ecore=0, **kwargs):
fakemol = gto.M(verbose=0)
nelec = numpy.sum(nelec)
fakemol.nelectron = nelec
fake_hf = scf.RHF(fakemol)
fake_hf._eri = ao2mo.restore(8, h2, norb)
fake_hf.get_hcore = lambda *args: h1
fake_hf.get_ovlp = lambda *args: numpy.eye(norb)
fake_hf.kernel()
self.myci = ci.CISD(fake_hf)
self.myci.conv_tol = 1e-7
self.myci.max_cycle = 150
self.myci.max_space = 12
self.myci.lindep = 1e-10
self.myci.nroots = 1
self.myci.level_shift = 0.2 # in precond
e_corr, civec = self.myci.kernel()
e = fake_hf.e_tot + e_corr
return e + ecore, civec
def contract_2e(eri, fcivec, norb, nelec, link_index=None, orbsym=None, wfnsym=0):
if orbsym is None:
return direct_spin0.contract_2e(eri, fcivec, norb, nelec, link_index)
eri = ao2mo.restore(4, eri, norb)
neleca, nelecb = direct_spin1._unpack_nelec(nelec)
assert(neleca == nelecb)
link_indexa = direct_spin0._unpack(norb, nelec, link_index)
na, nlinka = link_indexa.shape[:2]
eri_irs, rank_eri, irrep_eri = direct_spin1_symm.reorder_eri(eri, norb, orbsym)
strsa = numpy.asarray(cistring.gen_strings4orblist(range(norb), neleca))
aidx, link_indexa = direct_spin1_symm.gen_str_irrep(strsa, orbsym, link_indexa,
rank_eri, irrep_eri)
Tirrep = ctypes.c_void_p*TOTIRREPS
linka_ptr = Tirrep(*[x.ctypes.data_as(ctypes.c_void_p) for x in link_indexa])
eri_ptrs = Tirrep(*[x.ctypes.data_as(ctypes.c_void_p) for x in eri_irs])
dimirrep = (ctypes.c_int*TOTIRREPS)(*[x.shape[0] for x in eri_irs])
fcivec_shape = fcivec.shape
fcivec = fcivec.reshape((na,na), order='C')
ci1new = numpy.zeros_like(fcivec)
nas = (ctypes.c_int*TOTIRREPS)(*[x.size for x in aidx])
ci0 = []
ci1 = []
for ir in range(TOTIRREPS):
ma, mb = aidx[ir].size, aidx[wfnsym^ir].size
ci0.append(numpy.zeros((ma,mb)))
ci1.append(numpy.zeros((ma,mb)))
if ma > 0 and mb > 0:
lib.take_2d(fcivec, aidx[ir], aidx[wfnsym^ir], out=ci0[ir])
ci0_ptrs = Tirrep(*[x.ctypes.data_as(ctypes.c_void_p) for x in ci0])
ci1_ptrs = Tirrep(*[x.ctypes.data_as(ctypes.c_void_p) for x in ci1])
libfci.FCIcontract_2e_symm1(eri_ptrs, ci0_ptrs, ci1_ptrs,
ctypes.c_int(norb), nas, nas,
ctypes.c_int(nlinka), ctypes.c_int(nlinka),
linka_ptr, linka_ptr, dimirrep,
ctypes.c_int(wfnsym))
for ir in range(TOTIRREPS):
if ci0[ir].size > 0:
lib.takebak_2d(ci1new, ci1[ir], aidx[ir], aidx[wfnsym^ir])
return lib.transpose_sum(ci1new, inplace=True).reshape(fcivec_shape)
def contract_2e(eri, fcivec, norb, nelec, link_index=None):
r'''Contract the 2-electron Hamiltonian with a FCI vector to get a new FCI
vector.
Note the input arg eri is NOT the 2e hamiltonian matrix, the 2e hamiltonian is
.. math::
h2e &= eri_{pq,rs} p^+ q r^+ s \\
&= (pq|rs) p^+ r^+ s q - (pq|rs) \delta_{qr} p^+ s
So eri is defined as
.. math::
eri_{pq,rs} = (pq|rs) - (1/Nelec) \sum_q (pq|qs)
to restore the symmetry between pq and rs,
.. math::
eri_{pq,rs} = (pq|rs) - (.5/Nelec) [\sum_q (pq|qs) + \sum_p (pq|rp)]
See also :func:`direct_spin1.absorb_h1e`
'''
fcivec = numpy.asarray(fcivec, order='C')
eri = ao2mo.restore(4, eri, norb)
link_indexa, link_indexb = _unpack(norb, nelec, link_index)
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
assert(fcivec.size == na*nb)
ci1 = numpy.empty_like(fcivec)
libfci.FCIcontract_2e_spin1(eri.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p))
return ci1
def v2rdm_pyscf():
# pyscf reference
np.set_printoptions(linewidth=500)
basis = 'STO-3G'
mol = pyscf.M(
atom='B 0 0 0; H 0 0 {}'.format(1.1),
basis=basis)
mf = mol.RHF()
mf.verbose = 3
mf.run()
# make h1 and spatial integrals in MO basis
eri = ao2mo.kernel(mol, mf.mo_coeff)
eri = ao2mo.restore(1, eri, mf.mo_coeff.shape[1])
# this produces spatial MO h1 integrals
h1 = reduce(np.dot, (mf.mo_coeff.T, mf.get_hcore(), mf.mo_coeff))
# these parameters are hard-coded for now
nalpha = 3
nbeta = 3
nmo = 6
# hilbert options
psi4.set_module_options('hilbert', {
#'sdp_solver': 'rrsdp',
'positivity': 'dqg',
'r_convergence': 1e-5,
'e_convergence': 1e-4,
'maxiter': 20000,
})
# grab options object
options = psi4.core.get_options()
options.set_current_module('HILBERT')
v2rdm_pyscf = hilbert.v2RDMHelper(nalpha,nbeta,nmo,h1.flatten(),eri.flatten(),options)
current_energy = v2rdm_pyscf.compute_energy()
return current_energy
def rhf_external(mf, verbose=None):
log = logger.new_logger(mf, verbose)
mol = mf.mol
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nmo = mo_coeff.shape[1]
nocc = numpy.count_nonzero(mo_occ)
nvir = nmo - nocc
nov = nocc * nvir
eri_mo = ao2mo.full(mol, mo_coeff)
eri_mo = ao2mo.restore(1, eri_mo, nmo)
eai = lib.direct_sum('a-i->ai', mo_energy[nocc:], mo_energy[:nocc])
# A
h = numpy.einsum('ckld->kcld', eri_mo[nocc:,:nocc,:nocc,nocc:]) * 2
h-= numpy.einsum('cdlk->kcld', eri_mo[nocc:,nocc:,:nocc,:nocc])
for a in range(nvir):
for i in range(nocc):
h[i,a,i,a] += eai[a,i]
# B
h-= numpy.einsum('ckdl->kcld', eri_mo[nocc:,:nocc,nocc:,:nocc]) * 2
h+= numpy.einsum('cldk->kcld', eri_mo[nocc:,:nocc,nocc:,:nocc])
e1 = scipy.linalg.eigh(h.reshape(nov,nov))[0]
log.debug('rhf_external: lowest eigs = %s', e1[e1<=max(e1[0],1e-5)])
if e1[0] < -1e-5:
log.log('RHF wavefunction has an RHF real -> complex instablity')
else:
log.log('RHF wavefunction is stable in the RHF real -> complex stablity analysis')
h =-numpy.einsum('cdlk->kcld', eri_mo[nocc:,nocc:,:nocc,:nocc])
for a in range(nvir):
for i in range(nocc):
h[i,a,i,a] += eai[a,i]
h-= numpy.einsum('cldk->kcld', eri_mo[nocc:,:nocc,nocc:,:nocc])
e3 = scipy.linalg.eigh(h.reshape(nov,nov))[0]
log.debug('rhf_external: lowest eigs of H = %s', e3[e3<=max(e3[0],1e-5)])
if e3[0] < -1e-5:
log.log('RHF wavefunction has an RHF -> UHF instablity.')
else:
log.log('RHF wavefunction is stable in the RHF -> UHF stablity analysis')
def test_rdm(self):
mol = gto.Mole()
mol.verbose = 5
mol.output = '/dev/null'
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.RHF(mol).run(conv_tol=1e-14)
myci = ci.CISD(mf)
myci.frozen = 1
eris = myci.ao2mo()
ecisd, civec = myci.kernel(eris=eris)
self.assertAlmostEqual(ecisd, -0.048800218694077746, 8)
nmo = myci.nmo
nocc = myci.nocc
strs = fci.cistring.gen_strings4orblist(range(nmo+1), nocc+1)
mask = (strs & 1) != 0
sub_strs = strs[mask]
addrs = fci.cistring.strs2addr(nmo+1, nocc+1, sub_strs)
na = len(strs)
ci0 = numpy.zeros((na,na))
ci0[addrs[:,None],addrs] = myci.to_fcivec(civec, nmo, nocc*2)
ref1, ref2 = fci.direct_spin1.make_rdm12(ci0, (nmo+1), (nocc+1)*2)
rdm1 = myci.make_rdm1(civec)
rdm2 = myci.make_rdm2(civec)
self.assertTrue(numpy.allclose(rdm2, ref2))
self.assertAlmostEqual(abs(rdm2-rdm2.transpose(2,3,0,1)).sum(), 0, 9)
self.assertAlmostEqual(abs(rdm2-rdm2.transpose(1,0,3,2)).sum(), 0, 9)
dm1 = numpy.einsum('ijkk->ij', rdm2)/(mol.nelectron-1)
self.assertAlmostEqual(abs(rdm1 - dm1).sum(), 0, 9)
h1 = reduce(numpy.dot, (mf.mo_coeff.T, mf.get_hcore(), mf.mo_coeff))
eri = ao2mo.restore(1, ao2mo.kernel(mf._eri, mf.mo_coeff), nmo+1)
e1 = numpy.einsum('ij,ji', h1, rdm1)
e1+= numpy.einsum('ijkl,ijkl', eri, rdm2) * .5
e1+= mol.energy_nuc()
self.assertAlmostEqual(e1, myci.e_tot, 7)
def Sir(mc, dms, eris, verbose=None):
#Subspace S_il^{(0)}
mo_core, mo_cas, mo_virt = _extract_orbs(mc, mc.mo_coeff)
dm1 = dms['1']
dm2 = dms['2']
dm3 = dms['3']
ncore = mo_core.shape[1]
ncas = mo_cas.shape[1]
nocc = ncore + ncas
if eris is None:
h1e = mc.h1e_for_cas()[0]
h2e = ao2mo.restore(1, mc.ao2mo(mo_cas), ncas).transpose(0,2,1,3)
h2e_v1 = ao2mo.incore.general(mc._scf._eri,[mo_virt,mo_core,mo_cas,mo_cas],compact=False)
h2e_v1 = h2e_v1.reshape(mo_virt.shape[1],ncore,ncas,ncas).transpose(0,2,1,3)
h2e_v2 = ao2mo.incore.general(mc._scf._eri,[mo_virt,mo_cas,mo_cas,mo_core],compact=False)
h2e_v2 = h2e_v2.reshape(mo_virt.shape[1],ncas,ncas,ncore).transpose(0,2,1,3)
else:
h1e = eris['h1eff'][ncore:nocc,ncore:nocc]
h2e = eris['ppaa'][ncore:nocc,ncore:nocc].transpose(0,2,1,3)
h2e_v1 = eris['ppaa'][nocc:,:ncore].transpose(0,2,1,3)
h2e_v2 = eris['papa'][nocc:,:,:ncore].transpose(0,3,1,2)
h1e_v = eris['h1eff'][nocc:,:ncore]
norm = numpy.einsum('rpiq,raib,qpab->ir',h2e_v1,h2e_v1,dm2)*2.0\
- numpy.einsum('rpiq,rabi,qpab->ir',h2e_v1,h2e_v2,dm2)\
- numpy.einsum('rpqi,raib,qpab->ir',h2e_v2,h2e_v1,dm2)\
+ numpy.einsum('raqi,rabi,qb->ir',h2e_v2,h2e_v2,dm1)*2.0\
- numpy.einsum('rpqi,rabi,qbap->ir',h2e_v2,h2e_v2,dm2)\
+ numpy.einsum('rpqi,raai,qp->ir',h2e_v2,h2e_v2,dm1)\
+ numpy.einsum('rpiq,ri,qp->ir',h2e_v1,h1e_v,dm1)*4.0\
- numpy.einsum('rpqi,ri,qp->ir',h2e_v2,h1e_v,dm1)*2.0\
+ numpy.einsum('ri,ri->ir',h1e_v,h1e_v)*2.0
a12 = make_a12(h1e,h2e,dm1,dm2,dm3)
a13 = make_a13(h1e,h2e,dm1,dm2,dm3)
h = numpy.einsum('rpiq,raib,pqab->ir',h2e_v1,h2e_v1,a12)*2.0\
- numpy.einsum('rpiq,rabi,pqab->ir',h2e_v1,h2e_v2,a12)\
- numpy.einsum('rpqi,raib,pqab->ir',h2e_v2,h2e_v1,a12)\
+ numpy.einsum('rpqi,rabi,pqab->ir',h2e_v2,h2e_v2,a13)
diff = mc.mo_energy[:ncore,None] - mc.mo_energy[None,nocc:]
return _norm_to_energy(norm, h, -diff)
def general(mydf, mo_coeffs, kpts=None, compact=False):
'''General MO integral transformation'''
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2:
mo_coeffs = (mo_coeffs,) * 4
mo_coeffs = [numpy.asarray(mo, order='F') for mo in mo_coeffs]
allreal = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs)
q = kptj - kpti
coulG = tools.get_coulG(cell, q, gs=mydf.gs)
coords = cell.gen_uniform_grids(mydf.gs)
max_memory = mydf.max_memory - lib.current_memory()[0]
if gamma_point(kptijkl) and allreal:
ao = mydf._numint.eval_ao(cell, coords, kpti)[0]
if ((iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and
iden_coeffs(mo_coeffs[1], mo_coeffs[3]))):
moiT = mojT = numpy.asarray(lib.dot(mo_coeffs[0].T,ao.T), order='C')
ao = None
max_memory = max_memory - moiT.nbytes*1e-6
eri = _contract_compact(mydf, (moiT,mojT), coulG, max_memory=max_memory)
if not compact:
nmo = moiT.shape[0]
eri = ao2mo.restore(1, eri, nmo).reshape(nmo**2,nmo**2)
else:
mos = [numpy.asarray(lib.dot(c.T, ao.T), order='C') for c in mo_coeffs]
ao = None
fac = numpy.array(1.)
max_memory = max_memory - sum([x.nbytes for x in mos])*1e-6
eri = _contract_plain(mydf, mos, coulG, fac, max_memory=max_memory).real
return eri
else:
aos = mydf._numint.eval_ao(cell, coords, kptijkl)
mos = [numpy.asarray(lib.dot(c.T, aos[i].T), order='C')
for i,c in enumerate(mo_coeffs)]
aos = None
fac = numpy.exp(-1j * numpy.dot(coords, q))
max_memory = max_memory - sum([x.nbytes for x in mos])*1e-6
eri = _contract_plain(mydf, mos, coulG, fac, max_memory=max_memory)
return eri
def test_eri0000(self):
with_df = mdf.MDF(cell)
with_df.kpts = numpy.zeros((4,3))
mo =(numpy.random.random((nao,nao)) +
numpy.random.random((nao,nao))*1j)
eri = ao2mo.restore(1, with_df.get_eri(with_df.kpts), nao)
eri0 = numpy.einsum('pjkl,pi->ijkl', eri , mo.conj())
eri0 = numpy.einsum('ipkl,pj->ijkl', eri0, mo )
eri0 = numpy.einsum('ijpl,pk->ijkl', eri0, mo.conj())
eri0 = numpy.einsum('ijkp,pl->ijkl', eri0, mo )
eri1 = with_df.ao2mo(mo, with_df.kpts)
self.assertAlmostEqual(abs(eri1.reshape(eri0.shape)-eri0).sum(), 0, 9)
mo = mo.real
eri0 = numpy.einsum('pjkl,pi->ijkl', eri , mo.conj())
eri0 = numpy.einsum('ipkl,pj->ijkl', eri0, mo )
eri0 = numpy.einsum('ijpl,pk->ijkl', eri0, mo.conj())
eri0 = numpy.einsum('ijkp,pl->ijkl', eri0, mo )
eri1 = with_df.ao2mo(mo, with_df.kpts, compact=False)
self.assertAlmostEqual(abs(eri1.reshape(eri0.shape)-eri0).sum(), 0, 9)
def get_ES(n, na, nb, Enuc, h1, h2):
mol_FC = gto.M(verbose=0)
mol_FC.charge = 0
mol_FC.nelectron = na + nb
mol_FC.spin = na - nb
mol_FC.incore_anyway = True
mol_FC.nao_nr = lambda *args: n
mol_FC.energy_nuc = lambda *args: Enuc
mf_FC = scf.RHF(mol_FC)
mf_FC.get_hcore = lambda *args: h1
mf_FC.get_ovlp = lambda *args: np.eye(n)
mf_FC._eri = ao2mo.restore(8, h2, n)
rho = np.zeros((n, n))
for i in range(na):
rho[i, i] = 2.0
Ehf = mf_FC.kernel(rho) + Enuc
Ecc = (cc.CCSD(mf_FC)).kernel()[0]
return Ehf, Ecc, mol_FC, mf_FC
def kernel(self, h1e, eri, norb, nelec, ci0=None, ecore=0, **kwargs):
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
h2e = self.absorb_h1e(h1e, eri, norb, nelec, .5)
h2e = ao2mo.restore(1, h2e, norb)
hdiag = self.make_hdiag(h1e, eri, norb, nelec)
nroots = 1
if ci0 is None:
ci0 = self.get_init_guess(norb, nelec, nroots, hdiag)
def hop(c):
return self.contract_2e(h2e, c, norb, nelec)
precond = lambda x, e, *args: x / (hdiag - e + 1e-4)
e, c = lib.davidson(hop, ci0, precond, **kwargs)
return e + ecore, c
def make_hdiag(h1e, eri, norb, nelec, opt=None):
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
occslista = cistring._gen_occslst(range(norb), neleca)
eri = ao2mo.restore(1, eri, norb)
diagj = numpy.einsum('iijj->ij', eri)
diagk = numpy.einsum('ijji->ij', eri)
hdiag = []
for aocc in occslista:
bocc = aocc
e1 = h1e[aocc, aocc].sum() + h1e[bocc, bocc].sum()
e2 = diagj[aocc][:,aocc].sum() + diagj[aocc][:,bocc].sum() \
+ diagj[bocc][:,aocc].sum() + diagj[bocc][:,bocc].sum() \
- diagk[aocc][:,aocc].sum() - diagk[bocc][:,bocc].sum()
hdiag.append(e1 + e2 * .5)
return numpy.array(hdiag)
def _make_eris_incore(mycc, mo_coeff=None, ao2mofn=None):
cput0 = (time.clock(), time.time())
eris = _ChemistsERIs()
eris._common_init_(mycc, mo_coeff)
nocc = eris.nocc
nmo = eris.fock.shape[0]
if callable(ao2mofn):
eri1 = ao2mofn(eris.mo_coeff).reshape([nmo] * 4)
else:
eri1 = ao2mo.incore.full(mycc._scf._eri, eris.mo_coeff)
eri1 = ao2mo.restore(1, eri1, nmo)
eris.oooo = eri1[:nocc, :nocc, :nocc, :nocc].copy()
eris.ovoo = eri1[:nocc, nocc:, :nocc, :nocc].copy()
eris.ovov = eri1[:nocc, nocc:, :nocc, nocc:].copy()
eris.oovv = eri1[:nocc, :nocc, nocc:, nocc:].copy()
eris.ovvo = eri1[:nocc, nocc:, nocc:, :nocc].copy()
eris.ovvv = eri1[:nocc, nocc:, nocc:, nocc:].copy()
logger.timer(mycc, 'GW integral transformation', *cput0)
return eris
def two_body_integrals(self):
"""A 4-dimension array for electron repulsion integrals in the MO
representation. The integrals are computed as
h[p,q,r,s]=\int \phi_p(x)* \phi_q(y)* V_{elec-elec} \phi_r(y) \phi_s(x) dxdy
"""
if self._two_body_integrals is None:
mol = self._pyscf_data.get('mol', None)
mo = self.canonical_orbitals
n_orbitals = mo.shape[1]
eri = ao2mo.kernel(mol, mo)
eri = ao2mo.restore(
1, # no permutation symmetry
eri,
n_orbitals)
# See PQRS convention in OpenFermion.hamiltonians.molecular_data
# h[p,q,r,s] = (ps|qr) = pyscf_eri[p,s,q,r]
self._two_body_integrals = numpy.asarray(eri.transpose(0, 2, 3, 1),
order='C')
return self._two_body_integrals