def spin2spatial(tx, orbspin):
if tx.ndim == 2: # t1
nocc, nvir = tx.shape
else:
nocc, nvir = tx.shape[1:3]
idxoa = numpy.where(orbspin[:nocc] == 0)[0]
idxob = numpy.where(orbspin[:nocc] == 1)[0]
idxva = numpy.where(orbspin[nocc:] == 0)[0]
idxvb = numpy.where(orbspin[nocc:] == 1)[0]
nocc_a = len(idxoa)
nocc_b = len(idxob)
nvir_a = len(idxva)
nvir_b = len(idxvb)
if tx.ndim == 2: # t1
t1a = lib.take_2d(tx, idxoa, idxva)
t1b = lib.take_2d(tx, idxob, idxvb)
return t1a, t1b
else:
idxoaa = idxoa[:,None] * nocc + idxoa
idxoab = idxoa[:,None] * nocc + idxob
idxobb = idxob[:,None] * nocc + idxob
idxvaa = idxva[:,None] * nvir + idxva
idxvab = idxva[:,None] * nvir + idxvb
idxvbb = idxvb[:,None] * nvir + idxvb
t2 = tx.reshape(nocc**2,nvir**2)
t2aa = lib.take_2d(t2, idxoaa.ravel(), idxvaa.ravel())
t2bb = lib.take_2d(t2, idxobb.ravel(), idxvbb.ravel())
t2ab = lib.take_2d(t2, idxoab.ravel(), idxvab.ravel())
t2aa = t2aa.reshape(nocc_a,nocc_a,nvir_a,nvir_a)
t2bb = t2bb.reshape(nocc_b,nocc_b,nvir_b,nvir_b)
t2ab = t2ab.reshape(nocc_a,nocc_b,nvir_a,nvir_b)
return t2aa,t2ab,t2bb
def trans(ci1, aindex, bindex):
if aindex is None or bindex is None:
return None
ma = len(aindex)
mb = len(bindex)
t1 = numpy.zeros((ma,mb))
for i in range(norb):
signa = aindex[:,i,1]
signb = bindex[:,i,1]
maska = numpy.where(signa!=0)[0]
maskb = numpy.where(signb!=0)[0]
addra = aindex[maska,i,0]
addrb = bindex[maskb,i,0]
citmp = lib.take_2d(ci_coeff, addra, addrb)
citmp *= signa[maska].reshape(-1,1)
citmp *= signb[maskb]
#: t1[addra.reshape(-1,1),addrb] += citmp
lib.takebak_2d(t1, citmp, maska, maskb)
for i in range(norb):
signa = aindex[:,i,1]
signb = bindex[:,i,1]
maska = numpy.where(signa!=0)[0]
maskb = numpy.where(signb!=0)[0]
addra = aindex[maska,i,0]
addrb = bindex[maskb,i,0]
citmp = lib.take_2d(t1, maska, maskb)
citmp *= signa[maska].reshape(-1,1)
citmp *= signb[maskb]
#: ci1[maska.reshape(-1,1), maskb] += citmp
lib.takebak_2d(ci1, citmp, addra, addrb)
def trans(ci1, aindex, bindex, nea, neb):
if aindex is None or bindex is None:
return None
t1 = numpy.zeros((cistring.num_strings(norb,nea),
cistring.num_strings(norb,neb)))
for i in range(norb):
signa = aindex[:,i,1]
signb = bindex[:,i,1]
maska = numpy.where(signa!=0)[0]
maskb = numpy.where(signb!=0)[0]
addra = aindex[maska,i,0]
addrb = bindex[maskb,i,0]
citmp = lib.take_2d(fcivec, maska, maskb)
citmp *= signa[maska].reshape(-1,1)
citmp *= signb[maskb]
#: t1[addra.reshape(-1,1),addrb] += citmp
lib.takebak_2d(t1, citmp, addra, addrb)
for i in range(norb):
signa = aindex[:,i,1]
signb = bindex[:,i,1]
maska = numpy.where(signa!=0)[0]
maskb = numpy.where(signb!=0)[0]
addra = aindex[maska,i,0]
addrb = bindex[maskb,i,0]
citmp = lib.take_2d(t1, addra, addrb)
citmp *= signa[maska].reshape(-1,1)
citmp *= signb[maskb]
#: ci1[maska.reshape(-1,1), maskb] += citmp
lib.takebak_2d(ci1, citmp, maska, maskb)
def test_take_2d(self):
a = numpy.arange(49.).reshape(7,7)
idx = [3,0,5]
idy = [5,4,1]
ref = a[idx][:,idy]
self.assertTrue(numpy.array_equal(ref, lib.take_2d(a, idx, idy)))
a = numpy.arange(49, dtype=numpy.int32).reshape(7,7)
ref = a[idx][:,idy]
self.assertTrue(numpy.array_equal(ref, lib.take_2d(a, idx, idy)))
self.assertTrue(lib.take_2d(a, idx, idy).dtype == numpy.int32)
def _sort_t2_vooo_(mycc, orbsym, t1, t2, eris):
assert(t2.flags.c_contiguous)
vooo = numpy.asarray(eris.ovoo).transpose(1,0,3,2).conj().copy()
nocc, nvir = t1.shape
if mycc.mol.symmetry:
orbsym = numpy.asarray(orbsym, dtype=numpy.int32)
o_sorted = _irrep_argsort(orbsym[:nocc])
v_sorted = _irrep_argsort(orbsym[nocc:])
mo_energy = eris.mo_energy
mo_energy = numpy.hstack((mo_energy[:nocc][o_sorted],
mo_energy[nocc:][v_sorted]))
t1T = numpy.asarray(t1.T[v_sorted][:,o_sorted], order='C')
fvo = eris.fock[nocc:,:nocc]
fvo = numpy.asarray(fvo[v_sorted][:,o_sorted], order='C')
o_sym = orbsym[o_sorted]
oo_sym = (o_sym[:,None] ^ o_sym).ravel()
oo_sorted = _irrep_argsort(oo_sym)
#:vooo = eris.ovoo.transpose(1,0,2,3)
#:vooo = vooo[v_sorted][:,o_sorted][:,:,o_sorted][:,:,:,o_sorted]
#:vooo = vooo.reshape(nvir,-1,nocc)[:,oo_sorted]
oo_idx = numpy.arange(nocc**2).reshape(nocc,nocc)[o_sorted][:,o_sorted]
oo_idx = oo_idx.ravel()[oo_sorted]
oo_idx = (oo_idx[:,None]*nocc+o_sorted).ravel()
vooo = lib.take_2d(vooo.reshape(nvir,-1), v_sorted, oo_idx)
vooo = vooo.reshape(nvir,nocc,nocc,nocc)
#:t2T = t2.transpose(2,3,1,0)
#:t2T = ref_t2T[v_sorted][:,v_sorted][:,:,o_sorted][:,:,:,o_sorted]
#:t2T = ref_t2T.reshape(nvir,nvir,-1)[:,:,oo_sorted]
t2T = lib.transpose(t2.reshape(nocc**2,-1))
oo_idx = numpy.arange(nocc**2).reshape(nocc,nocc).T[o_sorted][:,o_sorted]
oo_idx = oo_idx.ravel()[oo_sorted]
vv_idx = (v_sorted[:,None]*nvir+v_sorted).ravel()
t2T = lib.take_2d(t2T.reshape(nvir**2,nocc**2), vv_idx, oo_idx, out=t2)
t2T = t2T.reshape(nvir,nvir,nocc,nocc)
def restore_t2_inplace(t2T):
tmp = numpy.zeros((nvir**2,nocc**2), dtype=t2T.dtype)
lib.takebak_2d(tmp, t2T.reshape(nvir**2,nocc**2), vv_idx, oo_idx)
t2 = lib.transpose(tmp.reshape(nvir**2,nocc**2), out=t2T)
return t2.reshape(nocc,nocc,nvir,nvir)
else:
fvo = eris.fock[nocc:,:nocc].copy()
t1T = t1.T.copy()
t2T = lib.transpose(t2.reshape(nocc**2,nvir**2))
t2T = lib.transpose(t2T.reshape(nvir**2,nocc,nocc), axes=(0,2,1), out=t2)
mo_energy = numpy.asarray(eris.mo_energy, order='C')
def restore_t2_inplace(t2T):
tmp = lib.transpose(t2T.reshape(nvir**2,nocc,nocc), axes=(0,2,1))
t2 = lib.transpose(tmp.reshape(nvir**2,nocc**2), out=t2T)
return t2.reshape(nocc,nocc,nvir,nvir)
t2T = t2T.reshape(nvir,nvir,nocc,nocc)
return mo_energy, t1T, t2T, vooo, fvo, restore_t2_inplace
def amplitudes_to_cisdvec(c0, c1, c2):
nocc, nvir = c1.shape
ooidx = numpy.tril_indices(nocc, -1)
vvidx = numpy.tril_indices(nvir, -1)
c2tril = lib.take_2d(c2.reshape(nocc**2,nvir**2),
ooidx[0]*nocc+ooidx[1], vvidx[0]*nvir+vvidx[1])
return numpy.hstack((c0, c1.ravel(), c2tril.ravel()))
def reorder_eri(eri, norb, orbsym):
if orbsym is None:
return [eri], numpy.arange(norb), numpy.zeros(norb,dtype=numpy.int32)
# map irrep IDs of Dooh or Coov to D2h, C2v
# see symm.basis.linearmole_symm_descent
orbsym = numpy.asarray(orbsym) % 10
# irrep of (ij| pair
trilirrep = (orbsym[:,None]^orbsym)[numpy.tril_indices(norb)]
# and the number of occurence for each irrep
dimirrep = numpy.asarray(numpy.bincount(trilirrep), dtype=numpy.int32)
# we sort the irreps of (ij| pair, to group the pairs which have same irreps
# "order" is irrep-id-sorted index. The (ij| paired is ordered that the
# pair-id given by order[0] comes first in the sorted pair
# "rank" is a sorted "order". Given nth (ij| pair, it returns the place(rank)
# of the sorted pair
old_eri_irrep = numpy.asarray(trilirrep, dtype=numpy.int32)
rank_in_irrep = numpy.empty_like(old_eri_irrep)
p0 = 0
eri_irs = [numpy.zeros((0,0))] * TOTIRREPS
for ir, nnorb in enumerate(dimirrep):
idx = numpy.asarray(numpy.where(trilirrep == ir)[0], dtype=numpy.int32)
rank_in_irrep[idx] = numpy.arange(nnorb, dtype=numpy.int32)
eri_irs[ir] = lib.take_2d(eri, idx, idx)
p0 += nnorb
return eri_irs, rank_in_irrep, old_eri_irrep
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 from_fci(fcivec, ci_strs, norb, nelec):
fcivec, nelec, ci_strs = _unpack(fcivec, nelec, ci_strs)
addrsa = [cistring.str2addr(norb, nelec[0], x) for x in ci_strs[0]]
addrsb = [cistring.str2addr(norb, nelec[1], x) for x in ci_strs[1]]
na = cistring.num_strings(norb, nelec[0])
nb = cistring.num_strings(norb, nelec[1])
fcivec = fcivec.reshape(na,nb)
civec = lib.take_2d(fcivec, addrsa, addrsb)
return _as_SCIvector(civec, ci_strs)
def _make_eris_outcore(mycc, mo_coeff=None):
cput0 = (time.clock(), time.time())
log = logger.Logger(mycc.stdout, mycc.verbose)
eris = _ChemistsERIs()
eris._common_init_(mycc, mo_coeff)
mol = mycc.mol
mo_coeff = eris.mo_coeff
nocc = eris.nocc
nao, nmo = mo_coeff.shape
nvir = nmo - nocc
orbo = mo_coeff[:,:nocc]
orbv = mo_coeff[:,nocc:]
nvpair = nvir * (nvir+1) // 2
eris.feri1 = lib.H5TmpFile()
eris.oooo = eris.feri1.create_dataset('oooo', (nocc,nocc,nocc,nocc), 'f8')
eris.ovoo = eris.feri1.create_dataset('ovoo', (nocc,nvir,nocc,nocc), 'f8', chunks=(nocc,1,nocc,nocc))
eris.ovov = eris.feri1.create_dataset('ovov', (nocc,nvir,nocc,nvir), 'f8', chunks=(nocc,1,nocc,nvir))
eris.ovvo = eris.feri1.create_dataset('ovvo', (nocc,nvir,nvir,nocc), 'f8', chunks=(nocc,1,nvir,nocc))
eris.ovvv = eris.feri1.create_dataset('ovvv', (nocc,nvir,nvir,nvir), 'f8')
eris.oovv = eris.feri1.create_dataset('oovv', (nocc,nocc,nvir,nvir), 'f8', chunks=(nocc,nocc,1,nvir))
eris.vvvv = eris.feri1.create_dataset('vvvv', (nvir,nvir,nvir,nvir), 'f8')
max_memory = max(MEMORYMIN, mycc.max_memory-lib.current_memory()[0])
ftmp = lib.H5TmpFile()
ao2mo.full(mol, mo_coeff, ftmp, max_memory=max_memory, verbose=log)
eri = ftmp['eri_mo']
nocc_pair = nocc*(nocc+1)//2
tril2sq = lib.square_mat_in_trilu_indices(nmo)
oo = eri[:nocc_pair]
eris.oooo[:] = ao2mo.restore(1, oo[:,:nocc_pair], nocc)
oovv = lib.take_2d(oo, tril2sq[:nocc,:nocc].ravel(), tril2sq[nocc:,nocc:].ravel())
eris.oovv[:] = oovv.reshape(nocc,nocc,nvir,nvir)
oo = oovv = None
tril2sq = lib.square_mat_in_trilu_indices(nmo)
blksize = min(nvir, max(BLKMIN, int(max_memory*1e6/8/nmo**3/2)))
for p0, p1 in lib.prange(0, nvir, blksize):
q0, q1 = p0+nocc, p1+nocc
off0 = q0*(q0+1)//2
off1 = q1*(q1+1)//2
buf = lib.unpack_tril(eri[off0:off1])
tmp = buf[ tril2sq[q0:q1,:nocc] - off0 ]
eris.ovoo[:,p0:p1] = tmp[:,:,:nocc,:nocc].transpose(1,0,2,3)
eris.ovvo[:,p0:p1] = tmp[:,:,nocc:,:nocc].transpose(1,0,2,3)
eris.ovov[:,p0:p1] = tmp[:,:,:nocc,nocc:].transpose(1,0,2,3)
eris.ovvv[:,p0:p1] = tmp[:,:,nocc:,nocc:].transpose(1,0,2,3)
tmp = buf[ tril2sq[q0:q1,nocc:q1] - off0 ]
eris.vvvv[p0:p1,:p1] = tmp[:,:,nocc:,nocc:]
if p0 > 0:
eris.vvvv[:p0,p0:p1] = tmp[:,:p0,nocc:,nocc:].transpose(1,0,2,3)
buf = tmp = None
log.timer('CCSD integral transformation', *cput0)
return eris
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)
totirrep = len(eri_irs)
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, totirrep)
Tirrep = ctypes.c_void_p*totirrep
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*totirrep)(*[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*8)(*[x.size for x in aidx])
ci0 = []
ci1 = []
for ir in range(totirrep):
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(totirrep), ctypes.c_int(wfnsym))
for ir in range(totirrep):
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 spin2spatial(tx, orbspin, kconserv):
if tx.ndim == 3: # t1
nocc, nvir = tx.shape[1:]
else:
nocc, nvir = tx.shape[4:6]
nkpts = len(tx)
idxoa = [numpy.where(orbspin[k][:nocc] == 0)[0] for k in range(nkpts)]
idxob = [numpy.where(orbspin[k][:nocc] == 1)[0] for k in range(nkpts)]
idxva = [numpy.where(orbspin[k][nocc:] == 0)[0] for k in range(nkpts)]
idxvb = [numpy.where(orbspin[k][nocc:] == 1)[0] for k in range(nkpts)]
nocc_a = len(idxoa[0])
nocc_b = len(idxob[0])
nvir_a = len(idxva[0])
nvir_b = len(idxvb[0])
if tx.ndim == 3: # t1
t1a = numpy.zeros((nkpts,nocc_a,nvir_a), dtype=tx.dtype)
t1b = numpy.zeros((nkpts,nocc_b,nvir_b), dtype=tx.dtype)
for k in range(nkpts):
lib.take_2d(tx[k], idxoa[k], idxva[k], out=t1a[k])
lib.take_2d(tx[k], idxob[k], idxvb[k], out=t1b[k])
return t1a, t1b
else:
t2aa = numpy.zeros((nkpts,nkpts,nkpts,nocc_a,nocc_a,nvir_a,nvir_a), dtype=tx.dtype)
t2ab = numpy.zeros((nkpts,nkpts,nkpts,nocc_a,nocc_b,nvir_a,nvir_b), dtype=tx.dtype)
t2bb = numpy.zeros((nkpts,nkpts,nkpts,nocc_b,nocc_b,nvir_b,nvir_b), dtype=tx.dtype)
t2 = tx.reshape(nkpts,nkpts,nkpts,nocc**2,nvir**2)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki,ka,kj]
idxoaa = idxoa[ki][:,None] * nocc + idxoa[kj]
idxoab = idxoa[ki][:,None] * nocc + idxob[kj]
idxobb = idxob[ki][:,None] * nocc + idxob[kj]
idxvaa = idxva[ka][:,None] * nvir + idxva[kb]
idxvab = idxva[ka][:,None] * nvir + idxvb[kb]
idxvbb = idxvb[ka][:,None] * nvir + idxvb[kb]
lib.take_2d(t2[ki,kj,ka], idxoaa.ravel(), idxvaa.ravel(), out=t2aa[ki,kj,ka])
lib.take_2d(t2[ki,kj,ka], idxobb.ravel(), idxvbb.ravel(), out=t2bb[ki,kj,ka])
lib.take_2d(t2[ki,kj,ka], idxoab.ravel(), idxvab.ravel(), out=t2ab[ki,kj,ka])
return t2aa, t2ab, t2bb
def reorder4irrep_minors(eri, norb, link_index, orbsym):
if orbsym is None:
return eri, link_index, numpy.array(norb, dtype=numpy.int32)
orbsym = numpy.asarray(orbsym) % 10
trilirrep = (orbsym[:,None]^orbsym)[numpy.tril_indices(norb,-1)]
dimirrep = numpy.array(numpy.bincount(trilirrep), dtype=numpy.int32)
order = numpy.argsort(trilirrep)
rank = order.argsort()
eri = lib.take_2d(eri, order, order)
link_index_irrep = link_index.copy()
link_index_irrep[:,:,0] = rank[link_index[:,:,0]]
return numpy.asarray(eri, order='C'), link_index_irrep, dimirrep
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 spin2spatial_ip_doublet(r1, r2, kconserv, kshift, orbspin):
'''Convert R1/R2 of spin orbital representation to R1/R2 of
spatial orbital representation '''
nkpts, nocc, nvir = np.array(r2.shape)[[1, 3, 4]]
idxoa = [np.where(orbspin[k][:nocc] == 0)[0] for k in range(nkpts)]
idxob = [np.where(orbspin[k][:nocc] == 1)[0] for k in range(nkpts)]
idxva = [np.where(orbspin[k][nocc:] == 0)[0] for k in range(nkpts)]
idxvb = [np.where(orbspin[k][nocc:] == 1)[0] for k in range(nkpts)]
nocc_a = len(idxoa[0]) # Assume nocc/nvir same for each k-point
nocc_b = len(idxob[0])
nvir_a = len(idxva[0])
nvir_b = len(idxvb[0])
r1a = r1[idxoa[kshift]]
r1b = r1[idxob[kshift]]
r2aaa = np.zeros((nkpts,nkpts,nocc_a,nocc_a,nvir_a), dtype=r2.dtype)
r2baa = np.zeros((nkpts,nkpts,nocc_b,nocc_a,nvir_a), dtype=r2.dtype)
r2abb = np.zeros((nkpts,nkpts,nocc_a,nocc_b,nvir_b), dtype=r2.dtype)
r2bbb = np.zeros((nkpts,nkpts,nocc_b,nocc_b,nvir_b), dtype=r2.dtype)
for ki, kj in itertools.product(range(nkpts), repeat=2):
ka = kconserv[ki, kshift, kj]
idxoaa = idxoa[ki][:,None] * nocc + idxoa[kj]
idxoab = idxoa[ki][:,None] * nocc + idxob[kj]
idxoba = idxob[ki][:,None] * nocc + idxoa[kj]
idxobb = idxob[ki][:,None] * nocc + idxob[kj]
r2_tmp = r2[ki, kj].reshape(nocc**2, nvir)
r2aaa_tmp = lib.take_2d(r2_tmp, idxoaa.ravel(), idxva[ka])
r2baa_tmp = lib.take_2d(r2_tmp, idxoba.ravel(), idxva[ka])
r2abb_tmp = lib.take_2d(r2_tmp, idxoab.ravel(), idxvb[ka])
r2bbb_tmp = lib.take_2d(r2_tmp, idxobb.ravel(), idxvb[ka])
r2aaa[ki, kj] = r2aaa_tmp.reshape(nocc_a, nocc_a, nvir_a)
r2baa[ki, kj] = r2baa_tmp.reshape(nocc_b, nocc_a, nvir_a)
r2abb[ki, kj] = r2abb_tmp.reshape(nocc_a, nocc_b, nvir_b)
r2bbb[ki, kj] = r2bbb_tmp.reshape(nocc_b, nocc_b, nvir_b)
return [r1a, r1b], [r2aaa, r2baa, r2abb, r2bbb]
def spin2spatial_ea_doublet(r1, r2, kconserv, kshift, orbspin):
'''Convert R1/R2 of spin orbital representation to R1/R2 of
spatial orbital representation'''
nkpts, nocc, nvir = np.array(r2.shape)[[1, 2, 3]]
idxoa = [np.where(orbspin[k][:nocc] == 0)[0] for k in range(nkpts)]
idxob = [np.where(orbspin[k][:nocc] == 1)[0] for k in range(nkpts)]
idxva = [np.where(orbspin[k][nocc:] == 0)[0] for k in range(nkpts)]
idxvb = [np.where(orbspin[k][nocc:] == 1)[0] for k in range(nkpts)]
nocc_a = len(idxoa[0])
nocc_b = len(idxob[0])
nvir_a = len(idxva[0])
nvir_b = len(idxvb[0])
r1a = r1[idxva[kshift]]
r1b = r1[idxvb[kshift]]
r2aaa = np.zeros((nkpts,nkpts,nocc_a,nvir_a,nvir_a), dtype=r2.dtype)
r2aba = np.zeros((nkpts,nkpts,nocc_a,nvir_b,nvir_a), dtype=r2.dtype)
r2bab = np.zeros((nkpts,nkpts,nocc_b,nvir_a,nvir_b), dtype=r2.dtype)
r2bbb = np.zeros((nkpts,nkpts,nocc_b,nvir_b,nvir_b), dtype=r2.dtype)
for kj, ka in itertools.product(range(nkpts), repeat=2):
kb = kconserv[kshift, ka, kj]
idxvaa = idxva[ka][:,None] * nvir + idxva[kb]
idxvab = idxva[ka][:,None] * nvir + idxvb[kb]
idxvba = idxvb[ka][:,None] * nvir + idxva[kb]
idxvbb = idxvb[ka][:,None] * nvir + idxvb[kb]
r2_tmp = r2[kj, ka].reshape(nocc, nvir**2)
r2aaa_tmp = lib.take_2d(r2_tmp, idxoa[kj], idxvaa.ravel())
r2aba_tmp = lib.take_2d(r2_tmp, idxoa[kj], idxvba.ravel())
r2bab_tmp = lib.take_2d(r2_tmp, idxob[kj], idxvab.ravel())
r2bbb_tmp = lib.take_2d(r2_tmp, idxob[kj], idxvbb.ravel())
r2aaa[kj, ka] = r2aaa_tmp.reshape(nocc_a, nvir_a, nvir_a)
r2aba[kj, ka] = r2aba_tmp.reshape(nocc_a, nvir_b, nvir_a)
r2bab[kj, ka] = r2bab_tmp.reshape(nocc_b, nvir_a, nvir_b)
r2bbb[kj, ka] = r2bbb_tmp.reshape(nocc_b, nvir_b, nvir_b)
return [r1a, r1b], [r2aaa, r2aba, r2bab, r2bbb]
def amplitudes_to_cisdvec(c0, c1, c2):
c1a, c1b = c1
c2aa, c2ab, c2bb = c2
nocca, nvira = c1a.shape
noccb, nvirb = c1b.shape
def trilidx(n):
idx = numpy.tril_indices(n, -1)
return idx[0] * n + idx[1]
ooidxa = trilidx(nocca)
vvidxa = trilidx(nvira)
ooidxb = trilidx(noccb)
vvidxb = trilidx(nvirb)
size = (1, nocca*nvira, noccb*nvirb, nocca*noccb*nvira*nvirb,
len(ooidxa)*len(vvidxa), len(ooidxb)*len(vvidxb))
loc = numpy.cumsum(size)
civec = numpy.empty(loc[-1], dtype=c2ab.dtype)
civec[0] = c0
civec[loc[0]:loc[1]] = c1a.ravel()
civec[loc[1]:loc[2]] = c1b.ravel()
civec[loc[2]:loc[3]] = c2ab.ravel()
lib.take_2d(c2aa.reshape(nocca**2,nvira**2), ooidxa, vvidxa, out=civec[loc[3]:loc[4]])
lib.take_2d(c2bb.reshape(noccb**2,nvirb**2), ooidxb, vvidxb, out=civec[loc[4]:loc[5]])
return civec
def rotate_mo(self, mo_coeff, u, log=None):
#from pyscf.lo import orth
#s = self._scf.get_ovlp()
#if self._scf.mol.symmetry:
# s = symm.symmetrize_matrix(s, self._scf._scf.mol.symm_orb)
#return orth.vec_lowdin(numpy.dot(mo_coeff, u), s)
mo = numpy.dot(mo_coeff, u)
if log is not None and log.verbose >= logger.DEBUG:
idx = numpy.where(self.mo_occ > 0)[0]
s = reduce(numpy.dot, (mo[:,idx].T, self._scf.get_ovlp(),
self.mo_coeff[:,idx]))
log.debug('Overlap to initial guess, SVD = %s',
_effective_svd(s, 1e-5))
log.debug('Overlap to last step, SVD = %s',
_effective_svd(lib.take_2d(u,idx,idx), 1e-5))
return mo
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 overlap(string1, string2, norb, s=None):
'''Determinants overlap on non-orthogonal one-particle basis'''
if s is None: # orthogonal basis with s_ij = delta_ij
return string1 == string2
else:
if isinstance(string1, str):
nelec = string1.count('1')
string1 = int(string1, 2)
else:
nelec = bin(string1).count('1')
if isinstance(string2, str):
assert(string2.count('1') == nelec)
string2 = int(string2, 2)
else:
assert(bin(string2).count('1') == nelec)
idx1 = [i for i in range(norb) if (1<<i & string1)]
idx2 = [i for i in range(norb) if (1<<i & string2)]
s1 = lib.take_2d(s, idx1, idx2)
return numpy.linalg.det(s1)
def reorder(ci, nelec, orbidxa, orbidxb=None):
'''Reorder the CI coefficients, to adapt the reordered orbitals (The relation
of the reordered orbitals and original orbitals is new = old[idx]). Eg.
The orbital ordering indices ``orbidx = [2,0,1]`` indicates the map
old orbital a b c -> new orbital c a b. The strings are reordered as
old-strings 0b011, 0b101, 0b110 == (1,2), (1,3), (2,3) <= apply orbidx to get orb-strings
orb-strings (3,1), (3,2), (1,2) == 0B101, 0B110, 0B011 <= by gen_strings4orblist
then argsort to translate the string representation to the address
[2(=0B011), 0(=0B101), 1(=0B110)]
'''
neleca, nelecb = _unpack(nelec)
if orbidxb is None:
orbidxb = orbidxa
guide_stringsa = cistring.gen_strings4orblist(orbidxa, neleca)
guide_stringsb = cistring.gen_strings4orblist(orbidxb, nelecb)
old_det_idxa = numpy.argsort(guide_stringsa)
old_det_idxb = numpy.argsort(guide_stringsb)
return lib.take_2d(ci, old_det_idxa, old_det_idxb)
def enlarge_space(myci, civec_strs, eri, norb, nelec):
if isinstance(civec_strs, (tuple, list)):
nelec, (strsa, strsb) = select_ci._unpack(civec_strs[0], nelec)[1:]
ci_coeff = lib.asarray(civec_strs)
else:
ci_coeff, nelec, (strsa, strsb) = select_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 = select_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(select_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 _gamma2_intermediates(mycc, t1, t2, l1, l2, eris=None,
compress_vvvv=False):
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
ccsd_rdm._gamma2_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = mycc.ao2mo()
nocc, nvir = t1.shape
eris_ovvv = numpy.asarray(eris.get_ovvv())
eris_ovoo = numpy.asarray(eris.ovoo)
eris_ovov = numpy.asarray(eris.ovov)
mo_e = eris.mo_energy
eia = lib.direct_sum('i-a->ia', mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
w =(numpy.einsum('iafb,kjcf->ijkabc', eris_ovvv.conj(), t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo.conj(), t2)) / d3
v =(numpy.einsum('iajb,kc->ijkabc', eris_ovov.conj(), t1)
+ numpy.einsum('ck,ijab->ijkabc', eris.fock[nocc:,:nocc], t2)) / d3
w = p6(w)
v = p6(v)
rw = r6(w)
rwv = r6(w * 2 + v * .5)
dovov += numpy.einsum('kc,ijkabc->iajb', t1, rw.conj()) * .5
dooov -= numpy.einsum('mkbc,ijkabc->jmia', t2, rwv.conj())
# Note "dovvv +=" also changes the value of dvvov
dovvv += numpy.einsum('kjcf,ijkabc->iafb', t2, rwv.conj())
dvvov = dovvv.transpose(2,3,0,1)
if compress_vvvv:
nvir = mycc.nmo - mycc.nocc
idx = numpy.tril_indices(nvir)
vidx = idx[0] * nvir + idx[1]
dvvvv = dvvvv + dvvvv.transpose(1,0,2,3)
dvvvv = dvvvv + dvvvv.transpose(0,1,3,2)
dvvvv = lib.take_2d(dvvvv.reshape(nvir**2,nvir**2), vidx, vidx)
dvvvv *= .25
return dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov
def reorder4irrep(eri, norb, link_index, orbsym, offdiag=0):
if orbsym is None:
return eri, link_index, numpy.array(norb, dtype=numpy.int32)
orbsym = numpy.asarray(orbsym)
# map irrep IDs of Dooh or Coov to D2h, C2v
# see symm.basis.linearmole_symm_descent
orbsym = orbsym % 10
# irrep of (ij| pair
trilirrep = (orbsym[:,None]^orbsym)[numpy.tril_indices(norb, offdiag)]
# and the number of occurence for each irrep
dimirrep = numpy.array(numpy.bincount(trilirrep), dtype=numpy.int32)
# we sort the irreps of (ij| pair, to group the pairs which have same irreps
# "order" is irrep-id-sorted index. The (ij| paired is ordered that the
# pair-id given by order[0] comes first in the sorted pair
# "rank" is a sorted "order". Given nth (ij| pair, it returns the place(rank)
# of the sorted pair
order = numpy.asarray(trilirrep.argsort(), dtype=numpy.int32)
rank = numpy.asarray(order.argsort(), dtype=numpy.int32)
eri = lib.take_2d(eri, order, order)
link_index_irrep = link_index.copy()
link_index_irrep[:,:,0] = rank[link_index[:,:,0]]
return numpy.asarray(eri, order='C'), link_index_irrep, dimirrep
def _make_eris_incore(mycc, mo_coeff=None, ao2mofn=None):
cput0 = (time.clock(), time.time())
eris = _ChemistsERIs()
eris._common_init_(mycc, mo_coeff)
nocca, noccb = mycc.nocc
nmoa, nmob = mycc.nmo
nvira, nvirb = nmoa - nocca, nmob - noccb
moa = eris.mo_coeff[0]
mob = eris.mo_coeff[1]
nmoa = moa.shape[1]
nmob = mob.shape[1]
if callable(ao2mofn):
eri_aa = ao2mofn(moa).reshape([nmoa] * 4)
eri_bb = ao2mofn(mob).reshape([nmob] * 4)
eri_ab = ao2mofn((moa, moa, mob, mob))
else:
eri_aa = ao2mo.restore(1, ao2mo.full(mycc._scf._eri, moa), nmoa)
eri_bb = ao2mo.restore(1, ao2mo.full(mycc._scf._eri, mob), nmob)
eri_ab = ao2mo.general(mycc._scf._eri, (moa, moa, mob, mob),
compact=False)
eri_ba = eri_ab.reshape(nmoa, nmoa, nmob, nmob).transpose(2, 3, 0, 1)
eri_aa = eri_aa.reshape(nmoa, nmoa, nmoa, nmoa)
eri_ab = eri_ab.reshape(nmoa, nmoa, nmob, nmob)
eri_ba = eri_ba.reshape(nmob, nmob, nmoa, nmoa)
eri_bb = eri_bb.reshape(nmob, nmob, nmob, nmob)
eris.oooo = eri_aa[:nocca, :nocca, :nocca, :nocca].copy()
eris.ovoo = eri_aa[:nocca, nocca:, :nocca, :nocca].copy()
eris.ovov = eri_aa[:nocca, nocca:, :nocca, nocca:].copy()
eris.oovv = eri_aa[:nocca, :nocca, nocca:, nocca:].copy()
eris.ovvo = eri_aa[:nocca, nocca:, nocca:, :nocca].copy()
eris.ovvv = eri_aa[:nocca, nocca:, nocca:, nocca:].copy()
eris.vvvv = eri_aa[nocca:, nocca:, nocca:, nocca:].copy()
eris.OOOO = eri_bb[:noccb, :noccb, :noccb, :noccb].copy()
eris.OVOO = eri_bb[:noccb, noccb:, :noccb, :noccb].copy()
eris.OVOV = eri_bb[:noccb, noccb:, :noccb, noccb:].copy()
eris.OOVV = eri_bb[:noccb, :noccb, noccb:, noccb:].copy()
eris.OVVO = eri_bb[:noccb, noccb:, noccb:, :noccb].copy()
eris.OVVV = eri_bb[:noccb, noccb:, noccb:, noccb:].copy()
eris.VVVV = eri_bb[noccb:, noccb:, noccb:, noccb:].copy()
eris.ooOO = eri_ab[:nocca, :nocca, :noccb, :noccb].copy()
eris.ovOO = eri_ab[:nocca, nocca:, :noccb, :noccb].copy()
eris.ovOV = eri_ab[:nocca, nocca:, :noccb, noccb:].copy()
eris.ooVV = eri_ab[:nocca, :nocca, noccb:, noccb:].copy()
eris.ovVO = eri_ab[:nocca, nocca:, noccb:, :noccb].copy()
eris.ovVV = eri_ab[:nocca, nocca:, noccb:, noccb:].copy()
eris.vvVV = eri_ab[nocca:, nocca:, noccb:, noccb:].copy()
#eris.OOoo = eri_ba[:noccb,:noccb,:nocca,:nocca].copy()
eris.OVoo = eri_ba[:noccb, noccb:, :nocca, :nocca].copy()
#eris.OVov = eri_ba[:noccb,noccb:,:nocca,nocca:].copy()
eris.OOvv = eri_ba[:noccb, :noccb, nocca:, nocca:].copy()
eris.OVvo = eri_ba[:noccb, noccb:, nocca:, :nocca].copy()
eris.OVvv = eri_ba[:noccb, noccb:, nocca:, nocca:].copy()
#eris.VVvv = eri_ba[noccb:,noccb:,nocca:,nocca:].copy()
if not callable(ao2mofn):
ovvv = eris.ovvv.reshape(nocca * nvira, nvira, nvira)
eris.ovvv = lib.pack_tril(ovvv).reshape(nocca, nvira,
nvira * (nvira + 1) // 2)
eris.vvvv = ao2mo.restore(4, eris.vvvv, nvira)
OVVV = eris.OVVV.reshape(noccb * nvirb, nvirb, nvirb)
eris.OVVV = lib.pack_tril(OVVV).reshape(noccb, nvirb,
nvirb * (nvirb + 1) // 2)
eris.VVVV = ao2mo.restore(4, eris.VVVV, nvirb)
ovVV = eris.ovVV.reshape(nocca * nvira, nvirb, nvirb)
eris.ovVV = lib.pack_tril(ovVV).reshape(nocca, nvira,
nvirb * (nvirb + 1) // 2)
vvVV = eris.vvVV.reshape(nvira**2, nvirb**2)
idxa = np.tril_indices(nvira)
idxb = np.tril_indices(nvirb)
eris.vvVV = lib.take_2d(vvVV, idxa[0] * nvira + idxa[1],
idxb[0] * nvirb + idxb[1])
OVvv = eris.OVvv.reshape(noccb * nvirb, nvira, nvira)
eris.OVvv = lib.pack_tril(OVvv).reshape(noccb, nvirb,
nvira * (nvira + 1) // 2)
return eris
def overlap(cibra, ciket, nmo, nocc, s=None):
'''Overlap between two CISD wavefunctions.
Args:
s : 2D array
The overlap matrix of non-orthogonal one-particle basis
'''
if s is None:
return dot(cibra, ciket, nmo, nocc)
DEBUG = True
nvir = nmo - nocc
nov = nocc * nvir
bra0, bra1, bra2 = cisdvec_to_amplitudes(cibra, nmo, nocc)
ket0, ket1, ket2 = cisdvec_to_amplitudes(ciket, nmo, nocc)
# Sort the ket orbitals to make the orbitals in bra one-one mapt to orbitals
# in ket.
if ((not DEBUG) and abs(numpy.linalg.det(s[:nocc, :nocc]) - 1) < 1e-2
and abs(numpy.linalg.det(s[nocc:, nocc:]) - 1) < 1e-2):
ket_orb_idx = numpy.where(abs(s) > 0.9)[1]
s = s[:, ket_orb_idx]
oidx = ket_orb_idx[:nocc]
vidx = ket_orb_idx[nocc:] - nocc
ket1 = ket1[oidx[:, None], vidx]
ket2 = ket2[oidx[:, None, None, None], oidx[:, None, None],
vidx[:, None], vidx]
ooidx = numpy.tril_indices(nocc, -1)
vvidx = numpy.tril_indices(nvir, -1)
bra2aa = bra2 - bra2.transpose(1, 0, 2, 3)
bra2aa = lib.take_2d(bra2aa.reshape(nocc**2,
nvir**2), ooidx[0] * nocc + ooidx[1],
vvidx[0] * nvir + vvidx[1])
ket2aa = ket2 - ket2.transpose(1, 0, 2, 3)
ket2aa = lib.take_2d(ket2aa.reshape(nocc**2,
nvir**2), ooidx[0] * nocc + ooidx[1],
vvidx[0] * nvir + vvidx[1])
occlist0 = numpy.arange(nocc).reshape(1, nocc)
occlists = numpy.repeat(occlist0, 1 + nov + bra2aa.size, axis=0)
occlist0 = occlists[:1]
occlist1 = occlists[1:1 + nov]
occlist2 = occlists[1 + nov:]
ia = 0
for i in range(nocc):
for a in range(nocc, nmo):
occlist1[ia, i] = a
ia += 1
ia = 0
for i in range(nocc):
for j in range(i):
for a in range(nocc, nmo):
for b in range(nocc, a):
occlist2[ia, i] = a
occlist2[ia, j] = b
ia += 1
na = len(occlists)
if DEBUG:
trans = numpy.empty((na, na))
for i, idx in enumerate(occlists):
s_sub = s[idx].T.copy()
minors = s_sub[occlists]
trans[i, :] = numpy.linalg.det(minors)
# Mimic the transformation einsum('ab,ap->pb', FCI, trans).
# The wavefunction FCI has the [excitation_alpha,excitation_beta]
# representation. The zero blocks like FCI[S_alpha,D_beta],
# FCI[D_alpha,D_beta], are explicitly excluded.
bra_mat = numpy.zeros((na, na))
bra_mat[0, 0] = bra0
bra_mat[0, 1:1 + nov] = bra_mat[1:1 + nov, 0] = bra1.ravel()
bra_mat[0, 1 + nov:] = bra_mat[1 + nov:, 0] = bra2aa.ravel()
bra_mat[1:1 + nov, 1:1 + nov] = bra2.transpose(0, 2, 1,
3).reshape(nov, nov)
ket_mat = numpy.zeros((na, na))
ket_mat[0, 0] = ket0
ket_mat[0, 1:1 + nov] = ket_mat[1:1 + nov, 0] = ket1.ravel()
ket_mat[0, 1 + nov:] = ket_mat[1 + nov:, 0] = ket2aa.ravel()
ket_mat[1:1 + nov, 1:1 + nov] = ket2.transpose(0, 2, 1,
3).reshape(nov, nov)
ovlp = lib.einsum('ab,ap,bq,pq->', bra_mat, trans, trans, ket_mat)
else:
nov1 = 1 + nov
noovv = bra2aa.size
bra_SS = numpy.zeros((nov1, nov1))
bra_SS[0, 0] = bra0
bra_SS[0, 1:] = bra_SS[1:, 0] = bra1.ravel()
bra_SS[1:, 1:] = bra2.transpose(0, 2, 1, 3).reshape(nov, nov)
ket_SS = numpy.zeros((nov1, nov1))
ket_SS[0, 0] = ket0
ket_SS[0, 1:] = ket_SS[1:, 0] = ket1.ravel()
ket_SS[1:, 1:] = ket2.transpose(0, 2, 1, 3).reshape(nov, nov)
trans_SS = numpy.empty((nov1, nov1))
trans_SD = numpy.empty((nov1, noovv))
trans_DS = numpy.empty((noovv, nov1))
occlist01 = occlists[:nov1]
for i, idx in enumerate(occlist01):
s_sub = s[idx].T.copy()
minors = s_sub[occlist01]
trans_SS[i, :] = numpy.linalg.det(minors)
minors = s_sub[occlist2]
trans_SD[i, :] = numpy.linalg.det(minors)
s_sub = s[:, idx].copy()
minors = s_sub[occlist2]
trans_DS[:, i] = numpy.linalg.det(minors)
ovlp = lib.einsum('ab,ap,bq,pq->', bra_SS, trans_SS, trans_SS, ket_SS)
ovlp += lib.einsum('ab,a ,bq, q->', bra_SS, trans_SS[:, 0], trans_SD,
ket2aa.ravel())
ovlp += lib.einsum('ab,ap,b ,p ->', bra_SS, trans_SD, trans_SS[:, 0],
ket2aa.ravel())
ovlp += lib.einsum(' b, p,bq,pq->', bra2aa.ravel(), trans_SS[0, :],
trans_DS, ket_SS)
ovlp += lib.einsum(' b, p,b ,p ->', bra2aa.ravel(), trans_SD[0, :],
trans_DS[:, 0], ket2aa.ravel())
ovlp += lib.einsum('a ,ap, q,pq->', bra2aa.ravel(), trans_DS,
trans_SS[0, :], ket_SS)
ovlp += lib.einsum('a ,a , q, q->', bra2aa.ravel(), trans_DS[:, 0],
trans_SD[0, :], ket2aa.ravel())
# FIXME: whether to approximate the overlap between double excitation coefficients
if numpy.linalg.norm(bra2aa) * numpy.linalg.norm(ket2aa) < 1e-4:
# Skip the overlap if coefficients of double excitation are small enough
pass
if (abs(numpy.linalg.det(s[:nocc, :nocc]) - 1) < 1e-2
and abs(numpy.linalg.det(s[nocc:, nocc:]) - 1) < 1e-2):
# If the overlap matrix close to identity enough, use the <D|D'> overlap
# for orthogonal single-particle basis to approximate the overlap
# for non-orthogonal basis.
ovlp += numpy.dot(bra2aa.ravel(), ket2aa.ravel()) * trans_SS[0,
0] * 2
else:
from multiprocessing import sharedctypes, Process
buf_ctypes = sharedctypes.RawArray('d', noovv)
trans_ket = numpy.ndarray(noovv, buffer=buf_ctypes)
def trans_dot_ket(i0, i1):
for i in range(i0, i1):
s_sub = s[occlist2[i]].T.copy()
minors = s_sub[occlist2]
trans_ket[i] = numpy.linalg.det(minors).dot(ket2aa.ravel())
nproc = lib.num_threads()
if nproc > 1:
seg = (noovv + nproc - 1) // nproc
ps = []
for i0, i1 in lib.prange(0, noovv, seg):
p = Process(target=trans_dot_ket, args=(i0, i1))
ps.append(p)
p.start()
[p.join() for p in ps]
else:
trans_dot_ket(0, noovv)
ovlp += numpy.dot(bra2aa.ravel(), trans_ket) * trans_SS[0, 0] * 2
return ovlp
def _gamma2_outcore(cc, t1, t2, l1, l2, h5fobj, compress_vvvv=False):
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
l1a, l1b = l1
l2aa, l2ab, l2bb = l2
tauaa = t2aa + numpy.einsum('ia,jb->ijab', 2 * t1a, t1a)
tauab = t2ab + numpy.einsum('ia,jb->ijab', t1a, t1b)
taubb = t2bb + numpy.einsum('ia,jb->ijab', 2 * t1b, t1b)
miajb = einsum('ikac,kjcb->iajb', l2aa, t2aa)
miajb += einsum('ikac,jkbc->iajb', l2ab, t2ab)
miaJB = einsum('ikac,kjcb->iajb', l2aa, t2ab)
miaJB += einsum('ikac,kjcb->iajb', l2ab, t2bb)
mIAjb = einsum('kica,jkbc->iajb', l2bb, t2ab)
mIAjb += einsum('kica,kjcb->iajb', l2ab, t2aa)
mIAJB = einsum('ikac,kjcb->iajb', l2bb, t2bb)
mIAJB += einsum('kica,kjcb->iajb', l2ab, t2ab)
miAjB = einsum('ikca,jkcb->iajb', l2ab, t2ab)
mIaJb = einsum('kiac,kjbc->iajb', l2ab, t2ab)
goovv = (l2aa.conj() + tauaa) * .25
goOvV = (l2ab.conj() + tauab) * .5
gOOVV = (l2bb.conj() + taubb) * .25
tmpa = einsum('kc,kica->ia', l1a, t2aa)
tmpa += einsum('kc,ikac->ia', l1b, t2ab)
tmpb = einsum('kc,kica->ia', l1b, t2bb)
tmpb += einsum('kc,kica->ia', l1a, t2ab)
goovv += einsum('ia,jb->ijab', tmpa, t1a)
goOvV += einsum('ia,jb->ijab', tmpa, t1b) * .5
goOvV += einsum('ia,jb->jiba', tmpb, t1a) * .5
gOOVV += einsum('ia,jb->ijab', tmpb, t1b)
tmpa = einsum('kc,kb->cb', l1a, t1a)
tmpb = einsum('kc,kb->cb', l1b, t1b)
goovv += einsum('cb,ijca->ijab', tmpa, t2aa) * .5
goOvV -= einsum('cb,ijac->ijab', tmpb, t2ab) * .5
goOvV -= einsum('cb,jica->jiba', tmpa, t2ab) * .5
gOOVV += einsum('cb,ijca->ijab', tmpb, t2bb) * .5
tmpa = einsum('kc,jc->kj', l1a, t1a)
tmpb = einsum('kc,jc->kj', l1b, t1b)
goovv += einsum('kiab,kj->ijab', tauaa, tmpa) * .5
goOvV -= einsum('ikab,kj->ijab', tauab, tmpb) * .5
goOvV -= einsum('kiba,kj->jiba', tauab, tmpa) * .5
gOOVV += einsum('kiab,kj->ijab', taubb, tmpb) * .5
tmpa = numpy.einsum('ldjd->lj', miajb)
tmpa += numpy.einsum('ldjd->lj', miAjB)
tmpb = numpy.einsum('ldjd->lj', mIAJB)
tmpb += numpy.einsum('ldjd->lj', mIaJb)
goovv -= einsum('lj,liba->ijab', tmpa, tauaa) * .25
goOvV -= einsum('lj,ilab->ijab', tmpb, tauab) * .25
goOvV -= einsum('lj,liba->jiba', tmpa, tauab) * .25
gOOVV -= einsum('lj,liba->ijab', tmpb, taubb) * .25
tmpa = numpy.einsum('ldlb->db', miajb)
tmpa += numpy.einsum('ldlb->db', mIaJb)
tmpb = numpy.einsum('ldlb->db', mIAJB)
tmpb += numpy.einsum('ldlb->db', miAjB)
goovv -= einsum('db,jida->ijab', tmpa, tauaa) * .25
goOvV -= einsum('db,ijad->ijab', tmpb, tauab) * .25
goOvV -= einsum('db,jida->jiba', tmpa, tauab) * .25
gOOVV -= einsum('db,jida->ijab', tmpb, taubb) * .25
goovv -= einsum('ldia,ljbd->ijab', miajb, tauaa) * .5
goovv += einsum('LDia,jLbD->ijab', mIAjb, t2ab) * .5
gOOVV -= einsum('ldia,ljbd->ijab', mIAJB, taubb) * .5
gOOVV += einsum('ldia,ljdb->ijab', miaJB, t2ab) * .5
goOvV -= einsum('LDia,LJBD->iJaB', mIAjb, taubb) * .25
goOvV += einsum('ldia,lJdB->iJaB', miajb, t2ab) * .25
goOvV -= einsum('ldIA,ljbd->jIbA', miaJB, tauaa) * .25
goOvV += einsum('LDIA,jLbD->jIbA', mIAJB, t2ab) * .25
goOvV += einsum('lDiA,lJbD->iJbA', miAjB, tauab) * .5
goOvV += einsum('LdIa,jd,LB->jIaB', mIaJb, t1a, t1b) * .5
tmpaa = einsum('klcd,ijcd->ijkl', l2aa, tauaa) * .25**2
tmpbb = einsum('klcd,ijcd->ijkl', l2bb, taubb) * .25**2
tmpabab = einsum('kLcD,iJcD->iJkL', l2ab, tauab) * .5
goovv += einsum('ijkl,klab->ijab', tmpaa, tauaa)
goOvV += einsum('ijkl,klab->ijab', tmpabab, tauab)
gOOVV += einsum('ijkl,klab->ijab', tmpbb, taubb)
goovv = goovv.conj()
goOvV = goOvV.conj()
gOOVV = gOOVV.conj()
gvvvv = einsum('ijab,ijcd->abcd', tauaa, l2aa) * .125
gvVvV = einsum('ijab,ijcd->abcd', tauab, l2ab) * .25
gVVVV = einsum('ijab,ijcd->abcd', taubb, l2bb) * .125
goooo = einsum('ijab,klab->ijkl', l2aa, tauaa) * .125
goOoO = einsum('ijab,klab->ijkl', l2ab, tauab) * .25
gOOOO = einsum('ijab,klab->ijkl', l2bb, taubb) * .125
gooov = einsum('jkba,ib->jkia', tauaa, -0.25 * l1a)
goOoV = einsum('jkba,ib->jkia', tauab, -0.5 * l1a)
gOoOv = einsum('kjab,ib->jkia', tauab, -0.5 * l1b)
gOOOV = einsum('jkba,ib->jkia', taubb, -0.25 * l1b)
gooov += einsum('iljk,la->jkia', goooo, t1a)
goOoV += einsum('iljk,la->jkia', goOoO, t1b) * 2
gOoOv += einsum('likj,la->jkia', goOoO, t1a) * 2
gOOOV += einsum('iljk,la->jkia', gOOOO, t1b)
tmpa = numpy.einsum('icjc->ij', miajb) * .25
tmpa += numpy.einsum('icjc->ij', miAjB) * .25
tmpb = numpy.einsum('icjc->ij', mIAJB) * .25
tmpb += numpy.einsum('icjc->ij', mIaJb) * .25
gooov -= einsum('ij,ka->jkia', tmpa, t1a)
goOoV -= einsum('ij,ka->jkia', tmpa, t1b)
gOoOv -= einsum('ij,ka->jkia', tmpb, t1a)
gOOOV -= einsum('ij,ka->jkia', tmpb, t1b)
gooov += einsum('icja,kc->jkia', miajb, .5 * t1a)
goOoV += einsum('icja,kc->jkia', miAjB, .5 * t1b)
goOoV -= einsum('icJA,kc->kJiA', miaJB, .5 * t1a)
gOoOv += einsum('icja,kc->jkia', mIaJb, .5 * t1a)
gOoOv -= einsum('ICja,KC->KjIa', mIAjb, .5 * t1b)
gOOOV += einsum('icja,kc->jkia', mIAJB, .5 * t1b)
gooov = gooov.conj()
goOoV = goOoV.conj()
gOoOv = gOoOv.conj()
gOOOV = gOOOV.conj()
gooov += einsum('jkab,ib->jkia', l2aa, .25 * t1a)
goOoV -= einsum('jkba,ib->jkia', l2ab, .5 * t1a)
gOoOv -= einsum('kjab,ib->jkia', l2ab, .5 * t1b)
gOOOV += einsum('jkab,ib->jkia', l2bb, .25 * t1b)
govvv = einsum('ja,ijcb->iacb', .25 * l1a, tauaa)
goVvV = einsum('ja,ijcb->iacb', .5 * l1b, tauab)
gOvVv = einsum('ja,jibc->iacb', .5 * l1a, tauab)
gOVVV = einsum('ja,ijcb->iacb', .25 * l1b, taubb)
govvv += einsum('bcad,id->iabc', gvvvv, t1a)
goVvV -= einsum('bcda,id->iabc', gvVvV, t1a) * 2
gOvVv -= einsum('cbad,id->iabc', gvVvV, t1b) * 2
gOVVV += einsum('bcad,id->iabc', gVVVV, t1b)
tmpa = numpy.einsum('kakb->ab', miajb) * .25
tmpa += numpy.einsum('kakb->ab', mIaJb) * .25
tmpb = numpy.einsum('kakb->ab', mIAJB) * .25
tmpb += numpy.einsum('kakb->ab', miAjB) * .25
govvv += einsum('ab,ic->iacb', tmpa, t1a)
goVvV += einsum('ab,ic->iacb', tmpb, t1a)
gOvVv += einsum('ab,ic->iacb', tmpa, t1b)
gOVVV += einsum('ab,ic->iacb', tmpb, t1b)
govvv += einsum('kaib,kc->iabc', miajb, .5 * t1a)
goVvV += einsum('KAib,KC->iAbC', mIAjb, .5 * t1b)
goVvV -= einsum('kAiB,kc->iAcB', miAjB, .5 * t1a)
gOvVv += einsum('kaIB,kc->IaBc', miaJB, .5 * t1a)
gOvVv -= einsum('KaIb,KC->IaCb', mIaJb, .5 * t1b)
gOVVV += einsum('kaib,kc->iabc', mIAJB, .5 * t1b)
govvv = govvv.conj()
goVvV = goVvV.conj()
gOvVv = gOvVv.conj()
gOVVV = gOVVV.conj()
govvv += einsum('ijbc,ja->iabc', l2aa, .25 * t1a)
goVvV += einsum('iJbC,JA->iAbC', l2ab, .5 * t1b)
gOvVv += einsum('jIcB,ja->IaBc', l2ab, .5 * t1a)
gOVVV += einsum('ijbc,ja->iabc', l2bb, .25 * t1b)
govvo = einsum('ia,jb->ibaj', l1a, t1a)
goVvO = einsum('ia,jb->ibaj', l1a, t1b)
gOvVo = einsum('ia,jb->ibaj', l1b, t1a)
gOVVO = einsum('ia,jb->ibaj', l1b, t1b)
govvo += numpy.einsum('iajb->ibaj', miajb)
goVvO += numpy.einsum('iajb->ibaj', miaJB)
gOvVo += numpy.einsum('iajb->ibaj', mIAjb)
gOVVO += numpy.einsum('iajb->ibaj', mIAJB)
goVoV = numpy.einsum('iajb->ibja', miAjB)
gOvOv = numpy.einsum('iajb->ibja', mIaJb)
govvo -= einsum('ikac,jc,kb->ibaj', l2aa, t1a, t1a)
goVvO -= einsum('iKaC,JC,KB->iBaJ', l2ab, t1b, t1b)
gOvVo -= einsum('kIcA,jc,kb->IbAj', l2ab, t1a, t1a)
gOVVO -= einsum('ikac,jc,kb->ibaj', l2bb, t1b, t1b)
goVoV += einsum('iKcA,jc,KB->iBjA', l2ab, t1a, t1b)
gOvOv += einsum('kIaC,JC,kb->IbJa', l2ab, t1b, t1a)
dovov = goovv.transpose(0, 2, 1, 3) - goovv.transpose(0, 3, 1, 2)
dvvvv = gvvvv.transpose(0, 2, 1, 3) - gvvvv.transpose(0, 3, 1, 2)
doooo = goooo.transpose(0, 2, 1, 3) - goooo.transpose(0, 3, 1, 2)
dovvv = govvv.transpose(0, 2, 1, 3) - govvv.transpose(0, 3, 1, 2)
dooov = gooov.transpose(0, 2, 1, 3) - gooov.transpose(1, 2, 0, 3)
dovvo = govvo.transpose(0, 2, 1, 3)
dovov = (dovov + dovov.transpose(2, 3, 0, 1)) * .5
dvvvv = dvvvv + dvvvv.transpose(1, 0, 3, 2).conj()
doooo = doooo + doooo.transpose(1, 0, 3, 2).conj()
dovvo = (dovvo + dovvo.transpose(3, 2, 1, 0).conj()) * .5
doovv = -dovvo.transpose(0, 3, 2, 1)
dvvov = None
dOVOV = gOOVV.transpose(0, 2, 1, 3) - gOOVV.transpose(0, 3, 1, 2)
dVVVV = gVVVV.transpose(0, 2, 1, 3) - gVVVV.transpose(0, 3, 1, 2)
dOOOO = gOOOO.transpose(0, 2, 1, 3) - gOOOO.transpose(0, 3, 1, 2)
dOVVV = gOVVV.transpose(0, 2, 1, 3) - gOVVV.transpose(0, 3, 1, 2)
dOOOV = gOOOV.transpose(0, 2, 1, 3) - gOOOV.transpose(1, 2, 0, 3)
dOVVO = gOVVO.transpose(0, 2, 1, 3)
dOVOV = (dOVOV + dOVOV.transpose(2, 3, 0, 1)) * .5
dVVVV = dVVVV + dVVVV.transpose(1, 0, 3, 2).conj()
dOOOO = dOOOO + dOOOO.transpose(1, 0, 3, 2).conj()
dOVVO = (dOVVO + dOVVO.transpose(3, 2, 1, 0).conj()) * .5
dOOVV = -dOVVO.transpose(0, 3, 2, 1)
dVVOV = None
dovOV = goOvV.transpose(0, 2, 1, 3)
dvvVV = gvVvV.transpose(0, 2, 1, 3) * 2
dooOO = goOoO.transpose(0, 2, 1, 3) * 2
dovVV = goVvV.transpose(0, 2, 1, 3)
dooOV = goOoV.transpose(0, 2, 1, 3)
dovVO = goVvO.transpose(0, 2, 1, 3)
dOVvv = gOvVv.transpose(0, 2, 1, 3)
dOOov = gOoOv.transpose(0, 2, 1, 3)
dOVvo = gOvVo.transpose(0, 2, 1, 3)
dooVV = goVoV.transpose(0, 2, 1, 3)
dOOvv = gOvOv.transpose(0, 2, 1, 3)
dvvVV = dvvVV + dvvVV.transpose(1, 0, 3, 2).conj()
dooOO = dooOO + dooOO.transpose(1, 0, 3, 2).conj()
dovVO = (dovVO + dOVvo.transpose(3, 2, 1, 0).conj()) * .5
dooVV = -(dooVV + dooVV.transpose(1, 0, 3, 2).conj()) * .5
dvvOV = None
dOVov = None
dVVvv = None
dOOoo = None
dOVvo = dovVO.transpose(3, 2, 1, 0).conj()
dOOvv = -(dOOvv + dOOvv.transpose(1, 0, 3, 2).conj()) * .5
dVVov = None
if compress_vvvv:
nocca, noccb, nvira, nvirb = t2ab.shape
idxa = numpy.tril_indices(nvira)
idxa = idxa[0] * nvira + idxa[1]
idxb = numpy.tril_indices(nvirb)
idxb = idxb[0] * nvirb + idxb[1]
dvvvv = dvvvv + dvvvv.transpose(1, 0, 2, 3)
dvvvv = lib.take_2d(dvvvv.reshape(nvira**2, nvira**2), idxa, idxa)
dvvvv *= .5
dvvVV = dvvVV + dvvVV.transpose(1, 0, 2, 3)
dvvVV = lib.take_2d(dvvVV.reshape(nvira**2, nvirb**2), idxa, idxb)
dvvVV *= .5
dVVVV = dVVVV + dVVVV.transpose(1, 0, 2, 3)
dVVVV = lib.take_2d(dVVVV.reshape(nvirb**2, nvirb**2), idxb, idxb)
dVVVV *= .5
return ((dovov, dovOV, dOVov, dOVOV), (dvvvv, dvvVV, dVVvv, dVVVV),
(doooo, dooOO, dOOoo, dOOOO), (doovv, dooVV, dOOvv, dOOVV),
(dovvo, dovVO, dOVvo, dOVVO), (dvvov, dvvOV, dVVov, dVVOV),
(dovvv, dovVV, dOVvv, dOVVV), (dooov, dooOV, dOOov, dOOOV))
def contract_2e(eri, fcivec, norb, nelec, link_index=None, orbsym=None, wfnsym=0):
if orbsym is None:
return direct_spin1.contract_2e(eri, fcivec, norb, nelec, link_index)
eri = ao2mo.restore(4, eri, norb)
neleca, nelecb = _unpack_nelec(nelec)
link_indexa, link_indexb = direct_spin1._unpack(norb, nelec, link_index)
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
eri_irs, rank_eri, irrep_eri = reorder_eri(eri, norb, orbsym)
strsa = cistring.gen_strings4orblist(range(norb), neleca)
aidx, link_indexa = gen_str_irrep(strsa, orbsym, link_indexa, rank_eri, irrep_eri)
if neleca == nelecb:
bidx, link_indexb = aidx, link_indexa
else:
strsb = cistring.gen_strings4orblist(range(norb), nelecb)
bidx, link_indexb = gen_str_irrep(strsb, orbsym, link_indexb, 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])
linkb_ptr = Tirrep(*[x.ctypes.data_as(ctypes.c_void_p) for x in link_indexb])
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,nb), order='C')
ci1new = numpy.zeros_like(fcivec)
nas = (ctypes.c_int*TOTIRREPS)(*[x.size for x in aidx])
nbs = (ctypes.c_int*TOTIRREPS)(*[x.size for x in bidx])
# aa, ab
ci0 = []
ci1 = []
for ir in range(TOTIRREPS):
ma, mb = aidx[ir].size, bidx[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], bidx[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, nbs,
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
linka_ptr, linkb_ptr, dimirrep,
ctypes.c_int(wfnsym))
for ir in range(TOTIRREPS):
if ci0[ir].size > 0:
lib.takebak_2d(ci1new, ci1[ir], aidx[ir], bidx[wfnsym^ir])
# bb, ba
ci0T = []
for ir in range(TOTIRREPS):
mb, ma = bidx[ir].size, aidx[wfnsym^ir].size
ci0T.append(numpy.zeros((mb,ma)))
if ma > 0 and mb > 0:
lib.transpose(ci0[wfnsym^ir], out=ci0T[ir])
ci0, ci0T = ci0T, None
ci1 = [numpy.zeros_like(x) for x in ci0]
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), nbs, nas,
ctypes.c_int(nlinkb), ctypes.c_int(nlinka),
linkb_ptr, linka_ptr, dimirrep,
ctypes.c_int(wfnsym))
for ir in range(TOTIRREPS):
if ci0[ir].size > 0:
lib.takebak_2d(ci1new, lib.transpose(ci1[ir]), aidx[wfnsym^ir], bidx[ir])
return ci1new.reshape(fcivec_shape)
def _make_eris_incore(myci, mo_coeff=None):
cput0 = (time.clock(), time.time())
eris = _UCISD_ERIs(myci, mo_coeff)
nocca = eris.nocca
noccb = eris.noccb
nmoa = eris.focka.shape[0]
nmob = eris.fockb.shape[0]
nvira = nmoa - nocca
nvirb = nmob - noccb
moa, mob = eris.mo_coeff
eri_aa = ao2mo.restore(1, ao2mo.full(myci._scf._eri, moa), nmoa)
eris.oooo = eri_aa[:nocca, :nocca, :nocca, :nocca].copy()
eris.ooov = eri_aa[:nocca, :nocca, :nocca, nocca:].copy()
eris.vooo = eri_aa[nocca:, :nocca, :nocca, :nocca].copy()
eris.oovo = eri_aa[:nocca, :nocca, nocca:, :nocca].copy()
eris.voov = eri_aa[nocca:, :nocca, :nocca, nocca:].copy()
eris.vvoo = eri_aa[nocca:, nocca:, :nocca, :nocca].copy()
eris.oovv = eri_aa[:nocca, :nocca, nocca:, nocca:].copy()
eris.vovo = eri_aa[nocca:, :nocca, nocca:, :nocca].copy()
eris.vovv = eri_aa[nocca:, :nocca, nocca:, nocca:].copy()
#vovv = eri_aa[nocca:,:nocca,nocca:,nocca:].reshape(-1,nvira,nvira)
#eris.vovv = lib.pack_tril(vovv).reshape(nvira,nocca,nvira*(nvira+1)//2)
eris.vvvv = ao2mo.restore(4, eri_aa[nocca:, nocca:, nocca:, nocca:].copy(),
nvira)
vovv = eri_aa = None
eri_bb = ao2mo.restore(1, ao2mo.full(myci._scf._eri, mob), nmob)
eris.OOOO = eri_bb[:noccb, :noccb, :noccb, :noccb].copy()
eris.OOOV = eri_bb[:noccb, :noccb, :noccb, noccb:].copy()
eris.VOOO = eri_bb[noccb:, :noccb, :noccb, :noccb].copy()
eris.OOVO = eri_bb[:noccb, :noccb, noccb:, :noccb].copy()
eris.VOOV = eri_bb[noccb:, :noccb, :noccb, noccb:].copy()
eris.VVOO = eri_bb[noccb:, noccb:, :noccb, :noccb].copy()
eris.OOVV = eri_bb[:noccb, :noccb, noccb:, noccb:].copy()
eris.VOVO = eri_bb[noccb:, :noccb, noccb:, :noccb].copy()
eris.VOVV = eri_bb[noccb:, :noccb, noccb:, noccb:].copy()
#VOVV = eri_bb[noccb:,:noccb,noccb:,noccb:].reshape(-1,nvirb,nvirb)
#eris.VOVV = lib.pack_tril(VOVV).reshape(nvirb,noccb,nvirb*(nvirb+1)//2)
eris.VVVV = ao2mo.restore(4, eri_bb[noccb:, noccb:, noccb:, noccb:].copy(),
nvirb)
VOVV = eri_bb = None
eri_ab = ao2mo.general(myci._scf._eri, (moa, moa, mob, mob), compact=False)
eri_ab = eri_ab.reshape(nmoa, nmoa, nmob, nmob)
eris.ooOO = eri_ab[:nocca, :nocca, :noccb, :noccb].copy()
eris.ooOV = eri_ab[:nocca, :nocca, :noccb, noccb:].copy()
eris.voOO = eri_ab[nocca:, :nocca, :noccb, :noccb].copy()
eris.ooVO = eri_ab[:nocca, :nocca, noccb:, :noccb].copy()
eris.voOV = eri_ab[nocca:, :nocca, :noccb, noccb:].copy()
eris.ooVV = eri_ab[:nocca, :nocca, noccb:, noccb:].copy()
eris.vvOO = eri_ab[nocca:, nocca:, :noccb, :noccb].copy()
eris.voVO = eri_ab[nocca:, :nocca, noccb:, :noccb].copy()
eris.voVV = eri_ab[nocca:, :nocca, noccb:, noccb:].copy()
#voVV = eri_ab[nocca:,:nocca,noccb:,noccb:].reshape(nocca*nvira,nvirb,nvirb)
#eris.voVV = lib.pack_tril(voVV).reshape(nvira,nocca,nvirb*(nvirb+1)//2)
voVV = None
vvVV = eri_ab[nocca:, nocca:, noccb:, noccb:].reshape(nvira**2, nvirb**2)
idxa = numpy.tril_indices(nvira)
idxb = numpy.tril_indices(nvirb)
eris.vvVV = lib.take_2d(vvVV, idxa[0] * nvira + idxa[1],
idxb[0] * nvirb + idxb[1])
eri_ba = lib.transpose(eri_ab.reshape(nmoa**2, nmob**2))
eri_ba = eri_ba.reshape(nmob, nmob, nmoa, nmoa)
eris.OOoo = eri_ba[:noccb, :noccb, :nocca, :nocca].copy()
eris.OOov = eri_ba[:noccb, :noccb, :nocca, nocca:].copy()
eris.VOoo = eri_ba[noccb:, :noccb, :nocca, :nocca].copy()
eris.OOvo = eri_ba[:noccb, :noccb, nocca:, :nocca].copy()
eris.VOov = eri_ba[noccb:, :noccb, :nocca, nocca:].copy()
eris.VVoo = eri_ba[noccb:, noccb:, :nocca, :nocca].copy()
eris.VOvo = eri_ba[noccb:, :noccb, nocca:, :nocca].copy()
eris.VOvv = eri_ba[noccb:, :noccb, nocca:, nocca:].copy()
#VOvv = eri_ba[noccb:,:noccb,nocca:,nocca:].reshape(noccb*nvirb,nvira,nvira)
#eris.VOvv = lib.pack_tril(VOvv).reshape(nvirb,noccb,nvira*(nvira+1)//2)
VOvv = None
eris.VVvv = eri_ba[noccb:, noccb:, nocca:, nocca:].copy()
return eris
def _ao2mo_ovov(mp, orbo, orbv, feri, max_memory=2000, verbose=None):
time0 = (time.clock(), time.time())
log = logger.new_logger(mp, verbose)
mol = mp.mol
int2e = mol._add_suffix('int2e')
ao2mopt = _ao2mo.AO2MOpt(mol, int2e, 'CVHFnr_schwarz_cond',
'CVHFsetnr_direct_scf')
nao, nocc = orbo.shape
nvir = orbv.shape[1]
nbas = mol.nbas
assert(nvir <= nao)
ao_loc = mol.ao_loc_nr()
dmax = max(4, min(nao/3, numpy.sqrt(max_memory*.95e6/8/(nao+nocc)**2)))
sh_ranges = ao2mo.outcore.balance_partition(ao_loc, dmax)
dmax = max(x[2] for x in sh_ranges)
eribuf = numpy.empty((nao,dmax,dmax,nao))
ftmp = lib.H5TmpFile()
log.debug('max_memory %s MB (dmax = %s) required disk space %g MB',
max_memory, dmax, nocc**2*(nao*(nao+dmax)/2+nvir**2)*8/1e6)
buf_i = numpy.empty((nocc*dmax**2*nao))
buf_li = numpy.empty((nocc**2*dmax**2))
buf1 = numpy.empty_like(buf_li)
fint = gto.moleintor.getints4c
jk_blk_slices = []
count = 0
time1 = time0
with lib.call_in_background(ftmp.__setitem__) as save:
for ip, (ish0, ish1, ni) in enumerate(sh_ranges):
for jsh0, jsh1, nj in sh_ranges[:ip+1]:
i0, i1 = ao_loc[ish0], ao_loc[ish1]
j0, j1 = ao_loc[jsh0], ao_loc[jsh1]
jk_blk_slices.append((i0,i1,j0,j1))
eri = fint(int2e, mol._atm, mol._bas, mol._env,
shls_slice=(0,nbas,ish0,ish1, jsh0,jsh1,0,nbas),
aosym='s1', ao_loc=ao_loc, cintopt=ao2mopt._cintopt,
out=eribuf)
tmp_i = numpy.ndarray((nocc,(i1-i0)*(j1-j0)*nao), buffer=buf_i)
tmp_li = numpy.ndarray((nocc,nocc*(i1-i0)*(j1-j0)), buffer=buf_li)
lib.ddot(orbo.T, eri.reshape(nao,(i1-i0)*(j1-j0)*nao), c=tmp_i)
lib.ddot(orbo.T, tmp_i.reshape(nocc*(i1-i0)*(j1-j0),nao).T, c=tmp_li)
tmp_li = tmp_li.reshape(nocc,nocc,(i1-i0),(j1-j0))
save(str(count), tmp_li.transpose(1,0,2,3))
buf_li, buf1 = buf1, buf_li
count += 1
time1 = log.timer_debug1('partial ao2mo [%d:%d,%d:%d]' %
(ish0,ish1,jsh0,jsh1), *time1)
time1 = time0 = log.timer('mp2 ao2mo_ovov pass1', *time0)
eri = eribuf = tmp_i = tmp_li = buf_i = buf_li = buf1 = None
chunks = (nvir,nvir)
h5dat = feri.create_dataset('ovov', (nocc*nvir,nocc*nvir), 'f8',
chunks=chunks)
# jk_where is the sorting indices for the stacked (oO|pP) integrals in pass 2
jk_where = []
aoao_idx = numpy.arange(nao*nao).reshape(nao,nao)
for i0, i1, j0, j1 in jk_blk_slices:
# idx of pP in <oO|pP>
jk_where.append(aoao_idx[i0:i1,j0:j1].ravel())
if i0 != j0:
# idx of pP in (<oO|pP>).transpose(1,0,3,2)
jk_where.append(aoao_idx[j0:j1,i0:i1].ravel())
jk_where = numpy.argsort(numpy.hstack(jk_where)).astype(numpy.int32)
orbv = numpy.asarray(orbv, order='F')
occblk = int(min(nocc, max(4, 250/nocc, max_memory*.9e6/8/(nao**2*nocc)/5)))
def load(i0, eri):
if i0 >= nocc:
return
i1 = min(i0+occblk, nocc)
eri = eri[:(i1-i0)*nocc]
p1 = 0
for k, jk_slice in enumerate(jk_blk_slices):
dat = numpy.asarray(ftmp[str(k)][i0:i1]).reshape((i1-i0)*nocc,-1)
p0, p1 = p1, p1 + dat.shape[1]
eri[:,p0:p1] = dat
if jk_slice[0] != jk_slice[2]:
dat = numpy.asarray(ftmp[str(k)][:,i0:i1])
dat = dat.transpose(1,0,3,2).reshape((i1-i0)*nocc,-1)
p0, p1 = p1, p1 + dat.shape[1]
eri[:,p0:p1] = dat
def save(i0, i1, dat):
for i in range(i0, i1):
h5dat[i*nvir:(i+1)*nvir] = dat[i-i0].reshape(nvir,nocc*nvir)
buf_prefecth = numpy.empty((occblk*nocc,nao**2))
buf = numpy.empty_like(buf_prefecth)
buf1 = numpy.empty_like(buf_prefecth)
bufw = numpy.empty((occblk*nocc,nvir**2))
bufw1 = numpy.empty_like(bufw)
with lib.call_in_background(load) as prefetch:
with lib.call_in_background(save) as bsave:
load(0, buf_prefecth)
for i0, i1 in lib.prange(0, nocc, occblk):
buf, buf_prefecth = buf_prefecth, buf
eri = buf[:(i1-i0)*nocc]
prefetch(i1, buf_prefecth)
idx = numpy.arange(eri.shape[0], dtype=numpy.int32)
dat = lib.take_2d(eri, idx, jk_where, out=buf1)
dat = _ao2mo.nr_e2(dat, orbv, (0,nvir,0,nvir), 's1', 's1', out=bufw)
bsave(i0, i1, dat.reshape(i1-i0,nocc,nvir,nvir).transpose(0,2,1,3))
bufw, bufw1 = bufw1, bufw
time1 = log.timer_debug1('pass2 ao2mo [%d:%d]' % (i0,i1), *time1)
time0 = log.timer('mp2 ao2mo_ovov pass2', *time0)
return h5dat
def restore(symmetry, eri, norb, tao=None):
r'''Convert the 2e integrals (in Chemist's notation) between different
level of permutation symmetry (8-fold, 4-fold, or no symmetry)
Args:
symmetry : int or str
code to present the target symmetry of 2e integrals
| 's8' or '8' or 8 : 8-fold symmetry
| 's4' or '4' or 4 : 4-fold symmetry
| 's1' or '1' or 1 : no symmetry
| 's2ij' or '2ij' : symmetric ij pair for (ij|kl) (TODO)
| 's2ij' or '2kl' : symmetric kl pair for (ij|kl) (TODO)
Note the 4-fold symmetry requires (ij|kl) == (ij|lk) == (ij|lk)
while (ij|kl) != (kl|ij) is not required.
eri : ndarray
The symmetry of eri is determined by the size of eri and norb
norb : int
The symmetry of eri is determined by the size of eri and norb
Returns:
ndarray. The shape depends on the target symmetry.
| 8 : (norb*(norb+1)/2)*(norb*(norb+1)/2+1)/2
| 4 : (norb*(norb+1)/2, norb*(norb+1)/2)
| 1 : (norb, norb, norb, norb)
Examples:
>>> from pyscf import gto
>>> from pyscf.scf import _vhf
>>> from pyscf import ao2mo
>>> mol = gto.M(atom='O 0 0 0; H 0 1 0; H 0 0 1', basis='sto3g')
>>> eri = mol.intor('int2e')
>>> eri1 = ao2mo.restore(1, eri, mol.nao_nr())
>>> eri4 = ao2mo.restore(4, eri, mol.nao_nr())
>>> eri8 = ao2mo.restore(8, eri, mol.nao_nr())
>>> print(eri1.shape)
(7, 7, 7, 7)
>>> print(eri1.shape)
(28, 28)
>>> print(eri1.shape)
(406,)
'''
targetsym = _stand_sym_code(symmetry)
if targetsym not in ('8', '4', '1', '2kl', '2ij'):
raise ValueError('symmetry = %s' % symmetry)
if eri.dtype != numpy.double:
raise RuntimeError('Complex integrals not supported')
eri = numpy.asarray(eri, order='C')
npair = norb*(norb+1)//2
if eri.size == norb**4: # s1
if targetsym == '1':
return eri.reshape(norb,norb,norb,norb)
elif targetsym == '2kl':
eri = lib.pack_tril(eri.reshape(norb**2,norb,norb))
return eri.reshape(norb,norb,npair)
elif targetsym == '2ij':
eri = lib.pack_tril(eri.reshape(norb,norb,norb**2), axis=0)
return eri.reshape(npair,norb,norb)
else:
return _convert('1', targetsym, eri, norb)
elif eri.size == npair**2: # s4
if targetsym == '4':
return eri.reshape(npair,npair)
elif targetsym == '8':
return lib.pack_tril(eri.reshape(npair,npair))
elif targetsym == '2kl':
return lib.unpack_tril(eri, lib.SYMMETRIC, axis=0)
elif targetsym == '2ij':
return lib.unpack_tril(eri, lib.SYMMETRIC, axis=-1)
else:
return _convert('4', targetsym, eri, norb)
elif eri.size == npair*(npair+1)//2: # 8-fold
if targetsym == '8':
return eri.ravel()
elif targetsym == '4':
return lib.unpack_tril(eri.ravel(), lib.SYMMETRIC)
elif targetsym == '2kl':
return lib.unpack_tril(lib.unpack_tril(eri.ravel()), lib.SYMMETRIC, axis=0)
elif targetsym == '2ij':
return lib.unpack_tril(lib.unpack_tril(eri.ravel()), lib.SYMMETRIC, axis=-1)
else:
return _convert('8', targetsym, eri, norb)
elif eri.size == npair*norb**2 and eri.shape[0] == npair: # s2ij
if targetsym == '2ij':
return eri.reshape(npair,norb,norb)
elif targetsym == '8':
eri = lib.pack_tril(eri.reshape(npair,norb,norb))
return lib.pack_tril(eri)
elif targetsym == '4':
return lib.pack_tril(eri.reshape(npair,norb,norb))
elif targetsym == '1':
eri = lib.unpack_tril(eri.reshape(npair,norb**2), lib.SYMMETRIC, axis=0)
return eri.reshape(norb,norb,norb,norb)
elif targetsym == '2kl':
tril2sq = lib.square_mat_in_trilu_indices(norb)
trilidx = numpy.tril_indices(norb)
eri = lib.take_2d(eri.reshape(npair,norb**2), tril2sq.ravel(),
trilidx[0]*norb+trilidx[1])
return eri.reshape(norb,norb,npair)
elif eri.size == npair*norb**2 and eri.shape[-1] == npair: # s2kl
if targetsym == '2kl':
return eri.reshape(norb,norb,npair)
elif targetsym == '8':
eri = lib.pack_tril(eri.reshape(norb,norb,npair), axis=0)
return lib.pack_tril(eri)
elif targetsym == '4':
return lib.pack_tril(eri.reshape(norb,norb,npair), axis=0)
elif targetsym == '1':
eri = lib.unpack_tril(eri.reshape(norb**2,npair), lib.SYMMETRIC, axis=-1)
return eri.reshape(norb,norb,norb,norb)
elif targetsym == '2ij':
tril2sq = lib.square_mat_in_trilu_indices(norb)
trilidx = numpy.tril_indices(norb)
eri = lib.take_2d(eri.reshape(norb**2,npair),
trilidx[0]*norb+trilidx[1], tril2sq.ravel())
return eri.reshape(npair,norb,norb)
else:
raise RuntimeError('eri.size = %d, norb = %d' % (eri.size, norb))
def overlap(cibra, ciket, nmo, nocc, s=None):
'''Overlap between two CISD wavefunctions.
Args:
s : a list of 2D arrays
The overlap matrix of non-orthogonal one-particle basis
'''
if s is None:
return dot(cibra, ciket, nmo, nocc)
if isinstance(nmo, (int, numpy.integer)):
nmoa = nmob = nmo
else:
nmoa, nmob = nmo
nocca, noccb = nocc
nvira, nvirb = nmoa - nocca, nmob - noccb
bra0, bra1, bra2 = cisdvec_to_amplitudes(cibra, (nmoa, nmob), nocc)
ket0, ket1, ket2 = cisdvec_to_amplitudes(ciket, (nmoa, nmob), nocc)
ooidx = numpy.tril_indices(nocca, -1)
vvidx = numpy.tril_indices(nvira, -1)
bra2aa = lib.take_2d(bra2[0].reshape(nocca**2, nvira**2),
ooidx[0] * nocca + ooidx[1],
vvidx[0] * nvira + vvidx[1])
ket2aa = lib.take_2d(ket2[0].reshape(nocca**2, nvira**2),
ooidx[0] * nocca + ooidx[1],
vvidx[0] * nvira + vvidx[1])
ooidx = numpy.tril_indices(noccb, -1)
vvidx = numpy.tril_indices(nvirb, -1)
bra2bb = lib.take_2d(bra2[2].reshape(noccb**2, nvirb**2),
ooidx[0] * noccb + ooidx[1],
vvidx[0] * nvirb + vvidx[1])
ket2bb = lib.take_2d(ket2[2].reshape(noccb**2, nvirb**2),
ooidx[0] * noccb + ooidx[1],
vvidx[0] * nvirb + vvidx[1])
nova = nocca * nvira
novb = noccb * nvirb
occlist0a = numpy.arange(nocca).reshape(1, nocca)
occlist0b = numpy.arange(noccb).reshape(1, noccb)
occlistsa = numpy.repeat(occlist0a, 1 + nova + bra2aa.size, axis=0)
occlistsb = numpy.repeat(occlist0b, 1 + novb + bra2bb.size, axis=0)
occlist0a = occlistsa[:1]
occlist1a = occlistsa[1:1 + nova]
occlist2a = occlistsa[1 + nova:]
occlist0b = occlistsb[:1]
occlist1b = occlistsb[1:1 + novb]
occlist2b = occlistsb[1 + novb:]
ia = 0
for i in range(nocca):
for a in range(nocca, nmoa):
occlist1a[ia, i] = a
ia += 1
ia = 0
for i in range(noccb):
for a in range(noccb, nmob):
occlist1b[ia, i] = a
ia += 1
ia = 0
for i in range(nocca):
for j in range(i):
for a in range(nocca, nmoa):
for b in range(nocca, a):
occlist2a[ia, i] = a
occlist2a[ia, j] = b
ia += 1
ia = 0
for i in range(noccb):
for j in range(i):
for a in range(noccb, nmob):
for b in range(noccb, a):
occlist2b[ia, i] = a
occlist2b[ia, j] = b
ia += 1
na = len(occlistsa)
trans_a = numpy.empty((na, na))
for i, idx in enumerate(occlistsa):
s_sub = s[0][idx].T.copy()
minors = s_sub[occlistsa]
trans_a[i, :] = numpy.linalg.det(minors)
nb = len(occlistsb)
trans_b = numpy.empty((nb, nb))
for i, idx in enumerate(occlistsb):
s_sub = s[1][idx].T.copy()
minors = s_sub[occlistsb]
trans_b[i, :] = numpy.linalg.det(minors)
# Mimic the transformation einsum('ab,ap->pb', FCI, trans).
# The wavefunction FCI has the [excitation_alpha,excitation_beta]
# representation. The zero blocks like FCI[S_alpha,D_beta],
# FCI[D_alpha,D_beta], are explicitly excluded.
bra_mat = numpy.zeros((na, nb))
bra_mat[0, 0] = bra0
bra_mat[1:1 + nova, 0] = bra1[0].ravel()
bra_mat[0, 1:1 + novb] = bra1[1].ravel()
bra_mat[1 + nova:, 0] = bra2aa.ravel()
bra_mat[0, 1 + novb:] = bra2bb.ravel()
bra_mat[1:1 + nova, 1:1 + novb] = bra2[1].transpose(0, 2, 1,
3).reshape(nova, novb)
c_s = lib.einsum('ab,ap,bq->pq', bra_mat, trans_a, trans_b)
ovlp = c_s[0, 0] * ket0
ovlp += numpy.dot(c_s[1:1 + nova, 0], ket1[0].ravel())
ovlp += numpy.dot(c_s[0, 1:1 + novb], ket1[1].ravel())
ovlp += numpy.dot(c_s[1 + nova:, 0], ket2aa.ravel())
ovlp += numpy.dot(c_s[0, 1 + novb:], ket2bb.ravel())
ovlp += numpy.einsum(
'ijab,iajb->', ket2[1],
c_s[1:1 + nova, 1:1 + novb].reshape(nocca, nvira, noccb, nvirb))
return ovlp
def contract_2e(eri,
fcivec,
norb,
nelec,
link_index=None,
orbsym=None,
wfnsym=0):
if orbsym is None:
return direct_spin1.contract_2e(eri, fcivec, norb, nelec, link_index)
eri = ao2mo.restore(4, eri, norb)
neleca, nelecb = _unpack_nelec(nelec)
link_indexa, link_indexb = direct_spin1._unpack(norb, nelec, link_index)
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
eri_irs, rank_eri, irrep_eri = reorder_eri(eri, norb, orbsym)
strsa = cistring.gen_strings4orblist(range(norb), neleca)
aidx, link_indexa = gen_str_irrep(strsa, orbsym, link_indexa, rank_eri,
irrep_eri)
if neleca == nelecb:
bidx, link_indexb = aidx, link_indexa
else:
strsb = cistring.gen_strings4orblist(range(norb), nelecb)
bidx, link_indexb = gen_str_irrep(strsb, orbsym, link_indexb, 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])
linkb_ptr = Tirrep(
*[x.ctypes.data_as(ctypes.c_void_p) for x in link_indexb])
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, nb), order='C')
ci1new = numpy.zeros_like(fcivec)
nas = (ctypes.c_int * TOTIRREPS)(*[x.size for x in aidx])
nbs = (ctypes.c_int * TOTIRREPS)(*[x.size for x in bidx])
# aa, ab
ci0 = []
ci1 = []
for ir in range(TOTIRREPS):
ma, mb = aidx[ir].size, bidx[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], bidx[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, nbs,
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
linka_ptr, linkb_ptr, dimirrep,
ctypes.c_int(wfnsym))
for ir in range(TOTIRREPS):
if ci0[ir].size > 0:
lib.takebak_2d(ci1new, ci1[ir], aidx[ir], bidx[wfnsym ^ ir])
# bb, ba
ci0T = []
for ir in range(TOTIRREPS):
mb, ma = bidx[ir].size, aidx[wfnsym ^ ir].size
ci0T.append(numpy.zeros((mb, ma)))
if ma > 0 and mb > 0:
lib.transpose(ci0[wfnsym ^ ir], out=ci0T[ir])
ci0, ci0T = ci0T, None
ci1 = [numpy.zeros_like(x) for x in ci0]
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), nbs, nas,
ctypes.c_int(nlinkb), ctypes.c_int(nlinka),
linkb_ptr, linka_ptr, dimirrep,
ctypes.c_int(wfnsym))
for ir in range(TOTIRREPS):
if ci0[ir].size > 0:
lib.takebak_2d(ci1new, lib.transpose(ci1[ir]), aidx[wfnsym ^ ir],
bidx[ir])
return ci1new.reshape(fcivec_shape)
def overlap(cibra, ciket, nmo, nocc, s=None):
'''Overlap between two CISD wavefunctions.
Args:
s : a list of 2D arrays
The overlap matrix of non-orthogonal one-particle basis
'''
if s is None:
return dot(cibra, ciket, nmo, nocc)
if isinstance(nmo, (int, numpy.integer)):
nmoa = nmob = nmo
else:
nmoa, nmob = nmo
nocca, noccb = nocc
nvira, nvirb = nmoa - nocca, nmob - noccb
bra0, bra1, bra2 = cisdvec_to_amplitudes(cibra, (nmoa,nmob), nocc)
ket0, ket1, ket2 = cisdvec_to_amplitudes(ciket, (nmoa,nmob), nocc)
ooidx = numpy.tril_indices(nocca, -1)
vvidx = numpy.tril_indices(nvira, -1)
bra2aa = lib.take_2d(bra2[0].reshape(nocca**2,nvira**2),
ooidx[0]*nocca+ooidx[1], vvidx[0]*nvira+vvidx[1])
ket2aa = lib.take_2d(ket2[0].reshape(nocca**2,nvira**2),
ooidx[0]*nocca+ooidx[1], vvidx[0]*nvira+vvidx[1])
ooidx = numpy.tril_indices(noccb, -1)
vvidx = numpy.tril_indices(nvirb, -1)
bra2bb = lib.take_2d(bra2[2].reshape(noccb**2,nvirb**2),
ooidx[0]*noccb+ooidx[1], vvidx[0]*nvirb+vvidx[1])
ket2bb = lib.take_2d(ket2[2].reshape(noccb**2,nvirb**2),
ooidx[0]*noccb+ooidx[1], vvidx[0]*nvirb+vvidx[1])
nova = nocca * nvira
novb = noccb * nvirb
occlist0a = numpy.arange(nocca).reshape(1,nocca)
occlist0b = numpy.arange(noccb).reshape(1,noccb)
occlistsa = numpy.repeat(occlist0a, 1+nova+bra2aa.size, axis=0)
occlistsb = numpy.repeat(occlist0b, 1+novb+bra2bb.size, axis=0)
occlist0a = occlistsa[:1]
occlist1a = occlistsa[1:1+nova]
occlist2a = occlistsa[1+nova:]
occlist0b = occlistsb[:1]
occlist1b = occlistsb[1:1+novb]
occlist2b = occlistsb[1+novb:]
ia = 0
for i in range(nocca):
for a in range(nocca, nmoa):
occlist1a[ia,i] = a
ia += 1
ia = 0
for i in range(noccb):
for a in range(noccb, nmob):
occlist1b[ia,i] = a
ia += 1
ia = 0
for i in range(nocca):
for j in range(i):
for a in range(nocca, nmoa):
for b in range(nocca, a):
occlist2a[ia,i] = a
occlist2a[ia,j] = b
ia += 1
ia = 0
for i in range(noccb):
for j in range(i):
for a in range(noccb, nmob):
for b in range(noccb, a):
occlist2b[ia,i] = a
occlist2b[ia,j] = b
ia += 1
na = len(occlistsa)
trans_a = numpy.empty((na,na))
for i, idx in enumerate(occlistsa):
s_sub = s[0][idx].T.copy()
minors = s_sub[occlistsa]
trans_a[i,:] = numpy.linalg.det(minors)
nb = len(occlistsb)
trans_b = numpy.empty((nb,nb))
for i, idx in enumerate(occlistsb):
s_sub = s[1][idx].T.copy()
minors = s_sub[occlistsb]
trans_b[i,:] = numpy.linalg.det(minors)
# Mimic the transformation einsum('ab,ap->pb', FCI, trans).
# The wavefunction FCI has the [excitation_alpha,excitation_beta]
# representation. The zero blocks like FCI[S_alpha,D_beta],
# FCI[D_alpha,D_beta], are explicitly excluded.
bra_mat = numpy.zeros((na,nb))
bra_mat[0,0] = bra0
bra_mat[1:1+nova,0] = bra1[0].ravel()
bra_mat[0,1:1+novb] = bra1[1].ravel()
bra_mat[1+nova:,0] = bra2aa.ravel()
bra_mat[0,1+novb:] = bra2bb.ravel()
bra_mat[1:1+nova,1:1+novb] = bra2[1].transpose(0,2,1,3).reshape(nova,novb)
c_s = lib.einsum('ab,ap,bq->pq', bra_mat, trans_a, trans_b)
ovlp = c_s[0,0] * ket0
ovlp += numpy.dot(c_s[1:1+nova,0], ket1[0].ravel())
ovlp += numpy.dot(c_s[0,1:1+novb], ket1[1].ravel())
ovlp += numpy.dot(c_s[1+nova:,0] , ket2aa.ravel())
ovlp += numpy.dot(c_s[0,1+novb:] , ket2bb.ravel())
ovlp += numpy.einsum('ijab,iajb->', ket2[1],
c_s[1:1+nova,1:1+novb].reshape(nocca,nvira,noccb,nvirb))
return ovlp
def _gamma2_outcore(cc, t1, t2, l1, l2, h5fobj, compress_vvvv=False):
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
l1a, l1b = l1
l2aa, l2ab, l2bb = l2
tauaa = t2aa + numpy.einsum('ia,jb->ijab', 2*t1a, t1a)
tauab = t2ab + numpy.einsum('ia,jb->ijab', t1a, t1b)
taubb = t2bb + numpy.einsum('ia,jb->ijab', 2*t1b, t1b)
miajb = einsum('ikac,kjcb->iajb', l2aa, t2aa)
miajb+= einsum('ikac,jkbc->iajb', l2ab, t2ab)
miaJB = einsum('ikac,kjcb->iajb', l2aa, t2ab)
miaJB+= einsum('ikac,kjcb->iajb', l2ab, t2bb)
mIAjb = einsum('kica,jkbc->iajb', l2bb, t2ab)
mIAjb+= einsum('kica,kjcb->iajb', l2ab, t2aa)
mIAJB = einsum('ikac,kjcb->iajb', l2bb, t2bb)
mIAJB+= einsum('kica,kjcb->iajb', l2ab, t2ab)
miAjB = einsum('ikca,jkcb->iajb', l2ab, t2ab)
mIaJb = einsum('kiac,kjbc->iajb', l2ab, t2ab)
goovv = (l2aa.conj() + tauaa) * .25
goOvV = (l2ab.conj() + tauab) * .5
gOOVV = (l2bb.conj() + taubb) * .25
tmpa = einsum('kc,kica->ia', l1a, t2aa)
tmpa += einsum('kc,ikac->ia', l1b, t2ab)
tmpb = einsum('kc,kica->ia', l1b, t2bb)
tmpb += einsum('kc,kica->ia', l1a, t2ab)
goovv += einsum('ia,jb->ijab', tmpa, t1a)
goOvV += einsum('ia,jb->ijab', tmpa, t1b) * .5
goOvV += einsum('ia,jb->jiba', tmpb, t1a) * .5
gOOVV += einsum('ia,jb->ijab', tmpb, t1b)
tmpa = einsum('kc,kb->cb', l1a, t1a)
tmpb = einsum('kc,kb->cb', l1b, t1b)
goovv += einsum('cb,ijca->ijab', tmpa, t2aa) * .5
goOvV -= einsum('cb,ijac->ijab', tmpb, t2ab) * .5
goOvV -= einsum('cb,jica->jiba', tmpa, t2ab) * .5
gOOVV += einsum('cb,ijca->ijab', tmpb, t2bb) * .5
tmpa = einsum('kc,jc->kj', l1a, t1a)
tmpb = einsum('kc,jc->kj', l1b, t1b)
goovv += einsum('kiab,kj->ijab', tauaa, tmpa) * .5
goOvV -= einsum('ikab,kj->ijab', tauab , tmpb) * .5
goOvV -= einsum('kiba,kj->jiba', tauab , tmpa) * .5
gOOVV += einsum('kiab,kj->ijab', taubb, tmpb) * .5
tmpa = numpy.einsum('ldjd->lj', miajb)
tmpa += numpy.einsum('ldjd->lj', miAjB)
tmpb = numpy.einsum('ldjd->lj', mIAJB)
tmpb += numpy.einsum('ldjd->lj', mIaJb)
goovv -= einsum('lj,liba->ijab', tmpa, tauaa) * .25
goOvV -= einsum('lj,ilab->ijab', tmpb, tauab) * .25
goOvV -= einsum('lj,liba->jiba', tmpa, tauab) * .25
gOOVV -= einsum('lj,liba->ijab', tmpb, taubb) * .25
tmpa = numpy.einsum('ldlb->db', miajb)
tmpa += numpy.einsum('ldlb->db', mIaJb)
tmpb = numpy.einsum('ldlb->db', mIAJB)
tmpb += numpy.einsum('ldlb->db', miAjB)
goovv -= einsum('db,jida->ijab', tmpa, tauaa) * .25
goOvV -= einsum('db,ijad->ijab', tmpb, tauab) * .25
goOvV -= einsum('db,jida->jiba', tmpa, tauab) * .25
gOOVV -= einsum('db,jida->ijab', tmpb, taubb) * .25
goovv -= einsum('ldia,ljbd->ijab', miajb, tauaa) * .5
goovv += einsum('LDia,jLbD->ijab', mIAjb, t2ab ) * .5
gOOVV -= einsum('ldia,ljbd->ijab', mIAJB, taubb) * .5
gOOVV += einsum('ldia,ljdb->ijab', miaJB, t2ab ) * .5
goOvV -= einsum('LDia,LJBD->iJaB', mIAjb, taubb) * .25
goOvV += einsum('ldia,lJdB->iJaB', miajb, t2ab ) * .25
goOvV -= einsum('ldIA,ljbd->jIbA', miaJB, tauaa) * .25
goOvV += einsum('LDIA,jLbD->jIbA', mIAJB, t2ab ) * .25
goOvV += einsum('lDiA,lJbD->iJbA', miAjB, tauab) * .5
goOvV += einsum('LdIa,jd,LB->jIaB', mIaJb, t1a, t1b) * .5
tmpaa = einsum('klcd,ijcd->ijkl', l2aa, tauaa) * .25**2
tmpbb = einsum('klcd,ijcd->ijkl', l2bb, taubb) * .25**2
tmpabab = einsum('kLcD,iJcD->iJkL', l2ab, tauab) * .5
goovv += einsum('ijkl,klab->ijab', tmpaa, tauaa)
goOvV += einsum('ijkl,klab->ijab', tmpabab, tauab)
gOOVV += einsum('ijkl,klab->ijab', tmpbb, taubb)
goovv = goovv.conj()
goOvV = goOvV.conj()
gOOVV = gOOVV.conj()
gvvvv = einsum('ijab,ijcd->abcd', tauaa, l2aa) * .125
gvVvV = einsum('ijab,ijcd->abcd', tauab, l2ab) * .25
gVVVV = einsum('ijab,ijcd->abcd', taubb, l2bb) * .125
goooo = einsum('ijab,klab->ijkl', l2aa, tauaa) * .125
goOoO = einsum('ijab,klab->ijkl', l2ab, tauab) * .25
gOOOO = einsum('ijab,klab->ijkl', l2bb, taubb) * .125
gooov = einsum('jkba,ib->jkia', tauaa, -0.25 * l1a)
goOoV = einsum('jkba,ib->jkia', tauab, -0.5 * l1a)
gOoOv = einsum('kjab,ib->jkia', tauab, -0.5 * l1b)
gOOOV = einsum('jkba,ib->jkia', taubb, -0.25 * l1b)
gooov += einsum('iljk,la->jkia', goooo, t1a)
goOoV += einsum('iljk,la->jkia', goOoO, t1b) * 2
gOoOv += einsum('likj,la->jkia', goOoO, t1a) * 2
gOOOV += einsum('iljk,la->jkia', gOOOO, t1b)
tmpa = numpy.einsum('icjc->ij', miajb) * .25
tmpa += numpy.einsum('icjc->ij', miAjB) * .25
tmpb = numpy.einsum('icjc->ij', mIAJB) * .25
tmpb += numpy.einsum('icjc->ij', mIaJb) * .25
gooov -= einsum('ij,ka->jkia', tmpa, t1a)
goOoV -= einsum('ij,ka->jkia', tmpa, t1b)
gOoOv -= einsum('ij,ka->jkia', tmpb, t1a)
gOOOV -= einsum('ij,ka->jkia', tmpb, t1b)
gooov += einsum('icja,kc->jkia', miajb, .5 * t1a)
goOoV += einsum('icja,kc->jkia', miAjB, .5 * t1b)
goOoV -= einsum('icJA,kc->kJiA', miaJB, .5 * t1a)
gOoOv += einsum('icja,kc->jkia', mIaJb, .5 * t1a)
gOoOv -= einsum('ICja,KC->KjIa', mIAjb, .5 * t1b)
gOOOV += einsum('icja,kc->jkia', mIAJB, .5 * t1b)
gooov = gooov.conj()
goOoV = goOoV.conj()
gOoOv = gOoOv.conj()
gOOOV = gOOOV.conj()
gooov += einsum('jkab,ib->jkia', l2aa, .25*t1a)
goOoV -= einsum('jkba,ib->jkia', l2ab, .5 *t1a)
gOoOv -= einsum('kjab,ib->jkia', l2ab, .5 *t1b)
gOOOV += einsum('jkab,ib->jkia', l2bb, .25*t1b)
govvv = einsum('ja,ijcb->iacb', .25 * l1a, tauaa)
goVvV = einsum('ja,ijcb->iacb', .5 * l1b, tauab)
gOvVv = einsum('ja,jibc->iacb', .5 * l1a, tauab)
gOVVV = einsum('ja,ijcb->iacb', .25 * l1b, taubb)
govvv += einsum('bcad,id->iabc', gvvvv, t1a)
goVvV -= einsum('bcda,id->iabc', gvVvV, t1a) * 2
gOvVv -= einsum('cbad,id->iabc', gvVvV, t1b) * 2
gOVVV += einsum('bcad,id->iabc', gVVVV, t1b)
tmpa = numpy.einsum('kakb->ab', miajb) * .25
tmpa += numpy.einsum('kakb->ab', mIaJb) * .25
tmpb = numpy.einsum('kakb->ab', mIAJB) * .25
tmpb += numpy.einsum('kakb->ab', miAjB) * .25
govvv += einsum('ab,ic->iacb', tmpa, t1a)
goVvV += einsum('ab,ic->iacb', tmpb, t1a)
gOvVv += einsum('ab,ic->iacb', tmpa, t1b)
gOVVV += einsum('ab,ic->iacb', tmpb, t1b)
govvv += einsum('kaib,kc->iabc', miajb, .5 * t1a)
goVvV += einsum('KAib,KC->iAbC', mIAjb, .5 * t1b)
goVvV -= einsum('kAiB,kc->iAcB', miAjB, .5 * t1a)
gOvVv += einsum('kaIB,kc->IaBc', miaJB, .5 * t1a)
gOvVv -= einsum('KaIb,KC->IaCb', mIaJb, .5 * t1b)
gOVVV += einsum('kaib,kc->iabc', mIAJB, .5 * t1b)
govvv = govvv.conj()
goVvV = goVvV.conj()
gOvVv = gOvVv.conj()
gOVVV = gOVVV.conj()
govvv += einsum('ijbc,ja->iabc', l2aa, .25*t1a)
goVvV += einsum('iJbC,JA->iAbC', l2ab, .5 *t1b)
gOvVv += einsum('jIcB,ja->IaBc', l2ab, .5 *t1a)
gOVVV += einsum('ijbc,ja->iabc', l2bb, .25*t1b)
govvo = einsum('ia,jb->ibaj', l1a, t1a)
goVvO = einsum('ia,jb->ibaj', l1a, t1b)
gOvVo = einsum('ia,jb->ibaj', l1b, t1a)
gOVVO = einsum('ia,jb->ibaj', l1b, t1b)
govvo += numpy.einsum('iajb->ibaj', miajb)
goVvO += numpy.einsum('iajb->ibaj', miaJB)
gOvVo += numpy.einsum('iajb->ibaj', mIAjb)
gOVVO += numpy.einsum('iajb->ibaj', mIAJB)
goVoV = numpy.einsum('iajb->ibja', miAjB)
gOvOv = numpy.einsum('iajb->ibja', mIaJb)
govvo -= einsum('ikac,jc,kb->ibaj', l2aa, t1a, t1a)
goVvO -= einsum('iKaC,JC,KB->iBaJ', l2ab, t1b, t1b)
gOvVo -= einsum('kIcA,jc,kb->IbAj', l2ab, t1a, t1a)
gOVVO -= einsum('ikac,jc,kb->ibaj', l2bb, t1b, t1b)
goVoV += einsum('iKcA,jc,KB->iBjA', l2ab, t1a, t1b)
gOvOv += einsum('kIaC,JC,kb->IbJa', l2ab, t1b, t1a)
dovov = goovv.transpose(0,2,1,3) - goovv.transpose(0,3,1,2)
dvvvv = gvvvv.transpose(0,2,1,3) - gvvvv.transpose(0,3,1,2)
doooo = goooo.transpose(0,2,1,3) - goooo.transpose(0,3,1,2)
dovvv = govvv.transpose(0,2,1,3) - govvv.transpose(0,3,1,2)
dooov = gooov.transpose(0,2,1,3) - gooov.transpose(1,2,0,3)
dovvo = govvo.transpose(0,2,1,3)
dovov =(dovov + dovov.transpose(2,3,0,1)) * .5
dvvvv = dvvvv + dvvvv.transpose(1,0,3,2).conj()
doooo = doooo + doooo.transpose(1,0,3,2).conj()
dovvo =(dovvo + dovvo.transpose(3,2,1,0).conj()) * .5
doovv =-dovvo.transpose(0,3,2,1)
dvvov = None
dOVOV = gOOVV.transpose(0,2,1,3) - gOOVV.transpose(0,3,1,2)
dVVVV = gVVVV.transpose(0,2,1,3) - gVVVV.transpose(0,3,1,2)
dOOOO = gOOOO.transpose(0,2,1,3) - gOOOO.transpose(0,3,1,2)
dOVVV = gOVVV.transpose(0,2,1,3) - gOVVV.transpose(0,3,1,2)
dOOOV = gOOOV.transpose(0,2,1,3) - gOOOV.transpose(1,2,0,3)
dOVVO = gOVVO.transpose(0,2,1,3)
dOVOV =(dOVOV + dOVOV.transpose(2,3,0,1)) * .5
dVVVV = dVVVV + dVVVV.transpose(1,0,3,2).conj()
dOOOO = dOOOO + dOOOO.transpose(1,0,3,2).conj()
dOVVO =(dOVVO + dOVVO.transpose(3,2,1,0).conj()) * .5
dOOVV =-dOVVO.transpose(0,3,2,1)
dVVOV = None
dovOV = goOvV.transpose(0,2,1,3)
dvvVV = gvVvV.transpose(0,2,1,3) * 2
dooOO = goOoO.transpose(0,2,1,3) * 2
dovVV = goVvV.transpose(0,2,1,3)
dooOV = goOoV.transpose(0,2,1,3)
dovVO = goVvO.transpose(0,2,1,3)
dOVvv = gOvVv.transpose(0,2,1,3)
dOOov = gOoOv.transpose(0,2,1,3)
dOVvo = gOvVo.transpose(0,2,1,3)
dooVV = goVoV.transpose(0,2,1,3)
dOOvv = gOvOv.transpose(0,2,1,3)
dvvVV = dvvVV + dvvVV.transpose(1,0,3,2).conj()
dooOO = dooOO + dooOO.transpose(1,0,3,2).conj()
dovVO = (dovVO + dOVvo.transpose(3,2,1,0).conj()) * .5
dooVV =-(dooVV + dooVV.transpose(1,0,3,2).conj()) * .5
dvvOV = None
dOVov = None
dVVvv = None
dOOoo = None
dOVvo = dovVO.transpose(3,2,1,0).conj()
dOOvv =-(dOOvv + dOOvv.transpose(1,0,3,2).conj()) * .5
dVVov = None
if compress_vvvv:
nocca, noccb, nvira, nvirb = t2ab.shape
idxa = numpy.tril_indices(nvira)
idxa = idxa[0] * nvira + idxa[1]
idxb = numpy.tril_indices(nvirb)
idxb = idxb[0] * nvirb + idxb[1]
dvvvv = dvvvv + dvvvv.transpose(1,0,2,3)
dvvvv = lib.take_2d(dvvvv.reshape(nvira**2,nvira**2), idxa, idxa)
dvvvv *= .5
dvvVV = dvvVV + dvvVV.transpose(1,0,2,3)
dvvVV = lib.take_2d(dvvVV.reshape(nvira**2,nvirb**2), idxa, idxb)
dvvVV *= .5
dVVVV = dVVVV + dVVVV.transpose(1,0,2,3)
dVVVV = lib.take_2d(dVVVV.reshape(nvirb**2,nvirb**2), idxb, idxb)
dVVVV *= .5
return ((dovov, dovOV, dOVov, dOVOV),
(dvvvv, dvvVV, dVVvv, dVVVV),
(doooo, dooOO, dOOoo, dOOOO),
(doovv, dooVV, dOOvv, dOOVV),
(dovvo, dovVO, dOVvo, dOVVO),
(dvvov, dvvOV, dVVov, dVVOV),
(dovvv, dovVV, dOVvv, dOVVV),
(dooov, dooOV, dOOov, dOOOV))
def _make_eris_incore(mycc, mo_coeff=None, ao2mofn=None):
cput0 = (time.clock(), time.time())
eris = _ChemistsERIs()
eris._common_init_(mycc, mo_coeff)
nocca, noccb = mycc.nocc
nmoa, nmob = mycc.nmo
nvira, nvirb = nmoa-nocca, nmob-noccb
moa = eris.mo_coeff[0]
mob = eris.mo_coeff[1]
nmoa = moa.shape[1]
nmob = mob.shape[1]
if callable(ao2mofn):
eri_aa = ao2mofn(moa).reshape([nmoa]*4)
eri_bb = ao2mofn(mob).reshape([nmob]*4)
eri_ab = ao2mofn((moa,moa,mob,mob))
else:
eri_aa = ao2mo.restore(1, ao2mo.full(mycc._scf._eri, moa), nmoa)
eri_bb = ao2mo.restore(1, ao2mo.full(mycc._scf._eri, mob), nmob)
eri_ab = ao2mo.general(mycc._scf._eri, (moa,moa,mob,mob), compact=False)
eri_ba = eri_ab.reshape(nmoa,nmoa,nmob,nmob).transpose(2,3,0,1)
eri_aa = eri_aa.reshape(nmoa,nmoa,nmoa,nmoa)
eri_ab = eri_ab.reshape(nmoa,nmoa,nmob,nmob)
eri_ba = eri_ba.reshape(nmob,nmob,nmoa,nmoa)
eri_bb = eri_bb.reshape(nmob,nmob,nmob,nmob)
eris.oooo = eri_aa[:nocca,:nocca,:nocca,:nocca].copy()
eris.ovoo = eri_aa[:nocca,nocca:,:nocca,:nocca].copy()
eris.ovov = eri_aa[:nocca,nocca:,:nocca,nocca:].copy()
eris.oovv = eri_aa[:nocca,:nocca,nocca:,nocca:].copy()
eris.ovvo = eri_aa[:nocca,nocca:,nocca:,:nocca].copy()
eris.ovvv = eri_aa[:nocca,nocca:,nocca:,nocca:].copy()
eris.vvvv = eri_aa[nocca:,nocca:,nocca:,nocca:].copy()
eris.OOOO = eri_bb[:noccb,:noccb,:noccb,:noccb].copy()
eris.OVOO = eri_bb[:noccb,noccb:,:noccb,:noccb].copy()
eris.OVOV = eri_bb[:noccb,noccb:,:noccb,noccb:].copy()
eris.OOVV = eri_bb[:noccb,:noccb,noccb:,noccb:].copy()
eris.OVVO = eri_bb[:noccb,noccb:,noccb:,:noccb].copy()
eris.OVVV = eri_bb[:noccb,noccb:,noccb:,noccb:].copy()
eris.VVVV = eri_bb[noccb:,noccb:,noccb:,noccb:].copy()
eris.ooOO = eri_ab[:nocca,:nocca,:noccb,:noccb].copy()
eris.ovOO = eri_ab[:nocca,nocca:,:noccb,:noccb].copy()
eris.ovOV = eri_ab[:nocca,nocca:,:noccb,noccb:].copy()
eris.ooVV = eri_ab[:nocca,:nocca,noccb:,noccb:].copy()
eris.ovVO = eri_ab[:nocca,nocca:,noccb:,:noccb].copy()
eris.ovVV = eri_ab[:nocca,nocca:,noccb:,noccb:].copy()
eris.vvVV = eri_ab[nocca:,nocca:,noccb:,noccb:].copy()
#eris.OOoo = eri_ba[:noccb,:noccb,:nocca,:nocca].copy()
eris.OVoo = eri_ba[:noccb,noccb:,:nocca,:nocca].copy()
#eris.OVov = eri_ba[:noccb,noccb:,:nocca,nocca:].copy()
eris.OOvv = eri_ba[:noccb,:noccb,nocca:,nocca:].copy()
eris.OVvo = eri_ba[:noccb,noccb:,nocca:,:nocca].copy()
eris.OVvv = eri_ba[:noccb,noccb:,nocca:,nocca:].copy()
#eris.VVvv = eri_ba[noccb:,noccb:,nocca:,nocca:].copy()
if not callable(ao2mofn):
ovvv = eris.ovvv.reshape(nocca*nvira,nvira,nvira)
eris.ovvv = lib.pack_tril(ovvv).reshape(nocca,nvira,nvira*(nvira+1)//2)
eris.vvvv = ao2mo.restore(4, eris.vvvv, nvira)
OVVV = eris.OVVV.reshape(noccb*nvirb,nvirb,nvirb)
eris.OVVV = lib.pack_tril(OVVV).reshape(noccb,nvirb,nvirb*(nvirb+1)//2)
eris.VVVV = ao2mo.restore(4, eris.VVVV, nvirb)
ovVV = eris.ovVV.reshape(nocca*nvira,nvirb,nvirb)
eris.ovVV = lib.pack_tril(ovVV).reshape(nocca,nvira,nvirb*(nvirb+1)//2)
vvVV = eris.vvVV.reshape(nvira**2,nvirb**2)
idxa = np.tril_indices(nvira)
idxb = np.tril_indices(nvirb)
eris.vvVV = lib.take_2d(vvVV, idxa[0]*nvira+idxa[1], idxb[0]*nvirb+idxb[1])
OVvv = eris.OVvv.reshape(noccb*nvirb,nvira,nvira)
eris.OVvv = lib.pack_tril(OVvv).reshape(noccb,nvirb,nvira*(nvira+1)//2)
return eris
def _make_eris_outcore(mycc, mo_coeff=None):
cput0 = (time.clock(), time.time())
log = logger.Logger(mycc.stdout, mycc.verbose)
eris = _ChemistsERIs()
eris._common_init_(mycc, mo_coeff)
mol = mycc.mol
mo_coeff = eris.mo_coeff
nocc = eris.nocc
nao, nmo = mo_coeff.shape
nvir = nmo - nocc
orbo = mo_coeff[:, :nocc]
orbv = mo_coeff[:, nocc:]
nvpair = nvir * (nvir + 1) // 2
eris.feri1 = lib.H5TmpFile()
eris.oooo = eris.feri1.create_dataset('oooo', (nocc, nocc, nocc, nocc),
'f8')
eris.ovoo = eris.feri1.create_dataset('ovoo', (nocc, nvir, nocc, nocc),
'f8',
chunks=(nocc, 1, nocc, nocc))
eris.ovov = eris.feri1.create_dataset('ovov', (nocc, nvir, nocc, nvir),
'f8',
chunks=(nocc, 1, nocc, nvir))
eris.ovvo = eris.feri1.create_dataset('ovvo', (nocc, nvir, nvir, nocc),
'f8',
chunks=(nocc, 1, nvir, nocc))
eris.ovvv = eris.feri1.create_dataset('ovvv', (nocc, nvir, nvir, nvir),
'f8',
chunks=(nocc, 1, nvir, nvir))
eris.oovv = eris.feri1.create_dataset('oovv', (nocc, nocc, nvir, nvir),
'f8',
chunks=(nocc, nocc, 1, nvir))
eris.vvvv = eris.feri1.create_dataset('vvvv', (nvir, nvir, nvir, nvir),
'f8')
max_memory = max(MEMORYMIN, mycc.max_memory - lib.current_memory()[0])
ftmp = lib.H5TmpFile()
ao2mo.full(mol, mo_coeff, ftmp, max_memory=max_memory, verbose=log)
eri = ftmp['eri_mo']
nocc_pair = nocc * (nocc + 1) // 2
tril2sq = lib.square_mat_in_trilu_indices(nmo)
oo = eri[:nocc_pair]
eris.oooo[:] = ao2mo.restore(1, oo[:, :nocc_pair], nocc)
oovv = lib.take_2d(oo, tril2sq[:nocc, :nocc].ravel(),
tril2sq[nocc:, nocc:].ravel())
eris.oovv[:] = oovv.reshape(nocc, nocc, nvir, nvir)
oo = oovv = None
tril2sq = lib.square_mat_in_trilu_indices(nmo)
blksize = min(nvir, max(BLKMIN, int(max_memory * 1e6 / 8 / nmo**3 / 2)))
for p0, p1 in lib.prange(0, nvir, blksize):
q0, q1 = p0 + nocc, p1 + nocc
off0 = q0 * (q0 + 1) // 2
off1 = q1 * (q1 + 1) // 2
buf = lib.unpack_tril(eri[off0:off1])
tmp = buf[tril2sq[q0:q1, :nocc] - off0]
eris.ovoo[:, p0:p1] = tmp[:, :, :nocc, :nocc].transpose(1, 0, 2, 3)
eris.ovvo[:, p0:p1] = tmp[:, :, nocc:, :nocc].transpose(1, 0, 2, 3)
eris.ovov[:, p0:p1] = tmp[:, :, :nocc, nocc:].transpose(1, 0, 2, 3)
eris.ovvv[:, p0:p1] = tmp[:, :, nocc:, nocc:].transpose(1, 0, 2, 3)
tmp = buf[tril2sq[q0:q1, nocc:q1] - off0]
eris.vvvv[p0:p1, :p1] = tmp[:, :, nocc:, nocc:]
if p0 > 0:
eris.vvvv[:p0, p0:p1] = tmp[:, :p0, nocc:,
nocc:].transpose(1, 0, 2, 3)
buf = tmp = None
log.timer('CCSD integral transformation', *cput0)
return eris
def _gamma2_intermediates(mycc, t1, t2, l1, l2, eris=None,
compress_vvvv=False):
d2 = uccsd_rdm._gamma2_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = mycc.ao2mo()
dovov, dovOV, dOVov, dOVOV = d2[0]
dvvvv, dvvVV, dVVvv, dVVVV = d2[1]
doooo, dooOO, dOOoo, dOOOO = d2[2]
doovv, dooVV, dOOvv, dOOVV = d2[3]
dovvo, dovVO, dOVvo, dOVVO = d2[4]
dvvov, dvvOV, dVVov, dVVOV = d2[5]
dovvv, dovVV, dOVvv, dOVVV = d2[6]
dooov, dooOV, dOOov, dOOOV = d2[7]
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb, nvira, nvirb = t2ab.shape
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
wvd = r6(p6(w * 2 + v)) / d3
dovov += numpy.einsum('ia,ijkabc->jbkc', t1a, rw.conj()) * 0.25
# *(1/8) instead of (1/4) because ooov appears 4 times in the 2pdm tensor due
# to symmetrization, and its contribution is scaled by 1/2 in Tr(H,2pdm)
dooov -= numpy.einsum('mkbc,ijkabc->jmia', t2aa, wvd.conj()) * .125
dovvv += numpy.einsum('kjcf,ijkabc->iafb', t2aa, wvd.conj()) * .125
# 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
wvd = r6(p6(w * 2 + v)) / d3
dOVOV += numpy.einsum('ia,ijkabc->jbkc', t1b, rw.conj()) * .25
dOOOV -= numpy.einsum('mkbc,ijkabc->jmia', t2bb, wvd.conj()) * .125
dOVVV += numpy.einsum('kjcf,ijkabc->iafb', t2bb, wvd.conj()) * .125
# baa
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
wvd = r4(w * 2 + v) / d3
dovvv += numpy.einsum('jiea,ijkabc->kceb', t2ab, wvd.conj()) * .25
dovVV += numpy.einsum('jibe,ijkabc->kcea', t2ab, wvd.conj()) * .25
dOVvv += numpy.einsum('jkbe,ijkabc->iaec', t2aa, wvd.conj()) * .125
dooov -= numpy.einsum('miba,ijkabc->jmkc', t2ab, wvd.conj()) * .25
dOOov -= numpy.einsum('jmba,ijkabc->imkc', t2ab, wvd.conj()) * .25
dooOV -= numpy.einsum('jmbc,ijkabc->kmia', t2aa, wvd.conj()) * .125
dovov += numpy.einsum('ia,ijkabc->jbkc', t1b, rw.conj()) * .25
#dOVov += numpy.einsum('jb,ijkabc->iakc', t1a, rw.conj()) * .25
dovOV += numpy.einsum('jb,ijkabc->kcia', t1a, rw.conj()) * .25
# 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
wvd = r4(w * 2 + v) / d3
dOVVV += numpy.einsum('ijae,ijkabc->kceb', t2ab, wvd.conj()) * .25
dOVvv += numpy.einsum('ijeb,ijkabc->kcea', t2ab, wvd.conj()) * .25
dovVV += numpy.einsum('jkbe,ijkabc->iaec', t2bb, wvd.conj()) * .125
dOOOV -= numpy.einsum('imab,ijkabc->jmkc', t2ab, wvd.conj()) * .25
dooOV -= numpy.einsum('mjab,ijkabc->imkc', t2ab, wvd.conj()) * .25
dOOov -= numpy.einsum('jmbc,ijkabc->kmia', t2bb, wvd.conj()) * .125
dOVOV += numpy.einsum('ia,ijkabc->jbkc', t1a, rw.conj()) * .25
dovOV += numpy.einsum('jb,ijkabc->iakc', t1b, rw.conj()) * .25
#dOVov += numpy.einsum('jb,ijkabc->kcia', t1b, rw.conj()) * .25
if compress_vvvv:
nmoa, nmob = mycc.nmo
nocca, noccb, nvira, nvirb = t2ab.shape
idxa = numpy.tril_indices(nvira)
idxa = idxa[0] * nvira + idxa[1]
idxb = numpy.tril_indices(nvirb)
idxb = idxb[0] * nvirb + idxb[1]
dvvvv = dvvvv + dvvvv.transpose(1,0,2,3)
dvvvv = lib.take_2d(dvvvv.reshape(nvira**2,nvira**2), idxa, idxa)
dvvvv *= .5
dvvVV = dvvVV + dvvVV.transpose(1,0,2,3)
dvvVV = lib.take_2d(dvvVV.reshape(nvira**2,nvirb**2), idxa, idxb)
dVVVV = dVVVV + dVVVV.transpose(1,0,2,3)
dVVVV = lib.take_2d(dVVVV.reshape(nvirb**2,nvirb**2), idxb, idxb)
dVVVV *= .5
d2 = ((dovov, dovOV, dOVov, dOVOV),
(dvvvv, dvvVV, dVVvv, dVVVV),
(doooo, dooOO, dOOoo, dOOOO),
(doovv, dooVV, dOOvv, dOOVV),
(dovvo, dovVO, dOVvo, dOVVO),
(dvvov, dvvOV, dVVov, dVVOV),
(dovvv, dovVV, dOVvv, dOVVV),
(dooov, dooOV, dOOov, dOOOV))
return d2
def restore(symmetry, eri, norb, tao=None):
r'''Convert the 2e integrals (in Chemist's notation) between different
level of permutation symmetry (8-fold, 4-fold, or no symmetry)
Args:
symmetry : int or str
code to present the target symmetry of 2e integrals
| 's8' or '8' or 8 : 8-fold symmetry
| 's4' or '4' or 4 : 4-fold symmetry
| 's1' or '1' or 1 : no symmetry
| 's2ij' or '2ij' : symmetric ij pair for (ij|kl) (TODO)
| 's2ij' or '2kl' : symmetric kl pair for (ij|kl) (TODO)
Note the 4-fold symmetry requires (ij|kl) == (ij|lk) == (ij|lk)
while (ij|kl) != (kl|ij) is not required.
eri : ndarray
The symmetry of eri is determined by the size of eri and norb
norb : int
The symmetry of eri is determined by the size of eri and norb
Returns:
ndarray. The shape depends on the target symmetry.
| 8 : (norb*(norb+1)/2)*(norb*(norb+1)/2+1)/2
| 4 : (norb*(norb+1)/2, norb*(norb+1)/2)
| 1 : (norb, norb, norb, norb)
Examples:
>>> from pyscf import gto
>>> from pyscf.scf import _vhf
>>> from pyscf import ao2mo
>>> mol = gto.M(atom='O 0 0 0; H 0 1 0; H 0 0 1', basis='sto3g')
>>> eri = mol.intor('int2e')
>>> eri1 = ao2mo.restore(1, eri, mol.nao_nr())
>>> eri4 = ao2mo.restore(4, eri, mol.nao_nr())
>>> eri8 = ao2mo.restore(8, eri, mol.nao_nr())
>>> print(eri1.shape)
(7, 7, 7, 7)
>>> print(eri1.shape)
(28, 28)
>>> print(eri1.shape)
(406,)
'''
targetsym = _stand_sym_code(symmetry)
if targetsym not in ('8', '4', '1', '2kl', '2ij'):
raise ValueError('symmetry = %s' % symmetry)
if eri.dtype != numpy.double:
raise RuntimeError('Complex integrals not supported')
eri = numpy.asarray(eri, order='C')
npair = norb*(norb+1)//2
if eri.size == norb**4: # s1
if targetsym == '1':
return eri.reshape(norb,norb,norb,norb)
elif targetsym == '2kl':
eri = lib.pack_tril(eri.reshape(norb**2,norb,norb))
return eri.reshape(norb,norb,npair)
elif targetsym == '2ij':
eri = lib.pack_tril(eri.reshape(norb,norb,norb**2), axis=0)
return eri.reshape(npair,norb,norb)
else:
return _convert('1', targetsym, eri, norb)
elif eri.size == npair**2: # s4
if targetsym == '4':
return eri.reshape(npair,npair)
elif targetsym == '8':
return lib.pack_tril(eri.reshape(npair,npair))
elif targetsym == '2kl':
return lib.unpack_tril(eri, lib.SYMMETRIC, axis=0)
elif targetsym == '2ij':
return lib.unpack_tril(eri, lib.SYMMETRIC, axis=-1)
else:
return _convert('4', targetsym, eri, norb)
elif eri.size == npair*(npair+1)//2: # 8-fold
if targetsym == '8':
return eri.ravel()
elif targetsym == '4':
return lib.unpack_tril(eri.ravel(), lib.SYMMETRIC)
elif targetsym == '2kl':
return lib.unpack_tril(lib.unpack_tril(eri.ravel()), lib.SYMMETRIC, axis=0)
elif targetsym == '2ij':
return lib.unpack_tril(lib.unpack_tril(eri.ravel()), lib.SYMMETRIC, axis=-1)
else:
return _convert('8', targetsym, eri, norb)
elif eri.size == npair*norb**2 and eri.shape[0] == npair: # s2ij
if targetsym == '2ij':
return eri.reshape(npair,norb,norb)
elif targetsym == '8':
eri = lib.pack_tril(eri.reshape(npair,norb,norb))
return lib.pack_tril(eri)
elif targetsym == '4':
return lib.pack_tril(eri.reshape(npair,norb,norb))
elif targetsym == '1':
eri = lib.unpack_tril(eri.reshape(npair,norb**2), lib.SYMMETRIC, axis=0)
return eri.reshape(norb,norb,norb,norb)
elif targetsym == '2kl':
tril2sq = lib.square_mat_in_trilu_indices(norb)
trilidx = numpy.tril_indices(norb)
eri = lib.take_2d(eri.reshape(npair,norb**2), tril2sq.ravel(),
trilidx[0]*norb+trilidx[1])
return eri.reshape(norb,norb,npair)
elif eri.size == npair*norb**2 and eri.shape[-1] == npair: # s2kl
if targetsym == '2kl':
return eri.reshape(norb,norb,npair)
elif targetsym == '8':
eri = lib.pack_tril(eri.reshape(norb,norb,npair), axis=0)
return lib.pack_tril(eri)
elif targetsym == '4':
return lib.pack_tril(eri.reshape(norb,norb,npair), axis=0)
elif targetsym == '1':
eri = lib.unpack_tril(eri.reshape(norb**2,npair), lib.SYMMETRIC, axis=-1)
return eri.reshape(norb,norb,norb,norb)
elif targetsym == '2ij':
tril2sq = lib.square_mat_in_trilu_indices(norb)
trilidx = numpy.tril_indices(norb)
eri = lib.take_2d(eri.reshape(norb**2,npair),
trilidx[0]*norb+trilidx[1], tril2sq.ravel())
return eri.reshape(npair,norb,norb)
else:
raise RuntimeError('eri.size = %d, norb = %d' % (eri.size, norb))
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))
# Adding h_ps below to because contract_2e function computes the
# contraction "E_{pq}E_{rs} V_{pqrs} |CI>" (~ p^+ q r^+ s |CI>) while
# the actual contraction for (aa|aa) and (bb|bb) part is
# "p^+ r^+ s q V_{pqrs} |CI>". To make (aa|aa) and (bb|bb) code reproduce
# "p^+ q r^+ s |CI>", we employ the identity
# p^+ q r^+ s = p^+ r^+ s q + delta(qr) p^+ s
# the second term is the source of h_ps
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)
