def _make_Lpq(mydf, mol, auxmol):
atm, bas, env, ao_loc = incore._env_and_aoloc('cint3c1e_sph', mol, auxmol)
nao = ao_loc[mol.nbas]
naux = ao_loc[-1] - nao
nao_pair = nao * (nao+1) // 2
if mydf.metric.upper() == 'S':
intor = 'cint3c1e_sph'
s_aux = auxmol.intor_symmetric('cint1e_ovlp_sph')
elif mydf.metric.upper() == 'T':
intor = 'cint3c1e_p2_sph'
s_aux = auxmol.intor_symmetric('cint1e_kin_sph') * 2
else: # metric.upper() == 'J'
intor = 'cint3c2e_sph'
s_aux = incore.fill_2c2e(mol, auxmol)
cintopt = gto.moleintor.make_cintopt(atm, bas, env, intor)
if mydf.charge_constraint:
ovlp = lib.pack_tril(mol.intor_symmetric('cint1e_ovlp_sph'))
aux_loc = auxmol.ao_loc_nr()
s_index = numpy.hstack([range(aux_loc[i],aux_loc[i+1])
for i,l in enumerate(auxmol._bas[:,ANG_OF]) if l == 0])
a = numpy.zeros((naux+1,naux+1))
a[:naux,:naux] = s_aux
a[naux,s_index] = a[s_index,naux] = 1
try:
cd = scipy.linalg.cho_factor(a)
def solve(Lpq):
return scipy.linalg.cho_solve(cd, Lpq)
except scipy.linalg.LinAlgError:
def solve(Lpq):
return scipy.linalg.solve(a, Lpq)
else:
cd = scipy.linalg.cho_factor(s_aux)
def solve(Lpq):
return scipy.linalg.cho_solve(cd, Lpq, overwrite_b=True)
def get_Lpq(shls_slice, col0, col1, buf):
# Be cautious here, _ri.nr_auxe2 assumes buf in F-order
Lpq = _ri.nr_auxe2(intor, atm, bas, env, shls_slice, ao_loc,
's2ij', 1, cintopt, buf).T
if mydf.charge_constraint:
Lpq = numpy.ndarray(shape=(naux+1,col1-col0), buffer=buf)
Lpq[naux,:] = ovlp[col0:col1]
Lpq1 = solve(Lpq)
assert(Lpq1.flags.f_contiguous)
lib.transpose(Lpq1.T, out=Lpq)
return Lpq[:naux]
else:
return solve(Lpq)
return get_Lpq
def cholesky_eri_b(mol, erifile, auxbasis='weigend+etb', dataname='eri_mo',
int3c='cint3c2e_sph', aosym='s2ij', int2c='cint2c2e_sph',
comp=1, ioblk_size=256, verbose=logger.NOTE):
'''3-center 2-electron AO integrals
'''
assert(aosym in ('s1', 's2ij'))
time0 = (time.clock(), time.time())
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mol.stdout, verbose)
auxmol = incore.format_aux_basis(mol, auxbasis)
j2c = incore.fill_2c2e(mol, auxmol, intor=int2c)
log.debug('size of aux basis %d', j2c.shape[0])
time1 = log.timer('2c2e', *time0)
low = scipy.linalg.cholesky(j2c, lower=True)
j2c = None
time1 = log.timer('Cholesky 2c2e', *time1)
if h5py.is_hdf5(erifile):
feri = h5py.File(erifile)
if dataname in feri:
del(feri[dataname])
else:
feri = h5py.File(erifile, 'w')
for icomp in range(comp):
feri.create_group('%s/%d'%(dataname,icomp)) # for h5py old version
def store(b, label):
cderi = scipy.linalg.solve_triangular(low, b, lower=True, overwrite_b=True)
if cderi.flags.f_contiguous:
cderi = lib.transpose(cderi.T)
feri[label] = cderi
atm, bas, env, ao_loc = incore._env_and_aoloc(int3c, mol, auxmol)
nao = ao_loc[mol.nbas]
naoaux = ao_loc[-1] - nao
if aosym == 's1':
nao_pair = nao * nao
buflen = min(max(int(ioblk_size*1e6/8/naoaux/comp), 1), nao_pair)
shranges = _guess_shell_ranges(mol, buflen, 's1')
else:
nao_pair = nao * (nao+1) // 2
buflen = min(max(int(ioblk_size*1e6/8/naoaux/comp), 1), nao_pair)
shranges = _guess_shell_ranges(mol, buflen, 's2ij')
log.debug('erifile %.8g MB, IO buf size %.8g MB',
naoaux*nao_pair*8/1e6, comp*buflen*naoaux*8/1e6)
if log.verbose >= logger.DEBUG1:
log.debug1('shranges = %s', shranges)
cintopt = gto.moleintor.make_cintopt(atm, bas, env, int3c)
bufs1 = numpy.empty((comp*max([x[2] for x in shranges]),naoaux))
for istep, sh_range in enumerate(shranges):
log.debug('int3c2e [%d/%d], AO [%d:%d], nrow = %d', \
istep+1, len(shranges), *sh_range)
bstart, bend, nrow = sh_range
shls_slice = (bstart, bend, 0, mol.nbas, mol.nbas, mol.nbas+auxmol.nbas)
buf = _ri.nr_auxe2(int3c, atm, bas, env, shls_slice, ao_loc,
aosym, comp, cintopt, bufs1)
if comp == 1:
store(buf.T, '%s/0/%d'%(dataname,istep))
else:
for icomp in range(comp):
store(buf[icomp].T, '%s/%d/%d'%(dataname,icomp,istep))
time1 = log.timer('gen CD eri [%d/%d]' % (istep+1,len(shranges)), *time1)
buf = bufs1 = None
feri.close()
return erifile
def _make_j3c(mydf, mol, auxmol):
log = logger.Logger(mydf.stdout, mydf.verbose)
atm, bas, env, ao_loc = incore._env_and_aoloc('cint3c2e_sph', mol, auxmol)
nao = ao_loc[mol.nbas]
naux = ao_loc[-1] - nao
nao_pair = nao * (nao+1) // 2
cintopt = gto.moleintor.make_cintopt(atm, bas, env, 'cint3c2e_sph')
if mydf.approx_sr_level == 0:
get_Lpq = _make_Lpq(mydf, mol, auxmol)
else:
get_Lpq = _make_Lpq_atomic_approx(mydf, mol, auxmol)
feri = h5py.File(mydf._cderi)
chunks = (min(256,naux), min(256,nao_pair)) # 512K
feri.create_dataset('j3c', (naux,nao_pair), 'f8', chunks=chunks)
feri.create_dataset('Lpq', (naux,nao_pair), 'f8', chunks=chunks)
def save(label, dat, col0, col1):
feri[label][:,col0:col1] = dat
Gv, Gvbase, kws = non_uniform_kgrids(mydf.gs)
nxyz = [i*2 for i in mydf.gs]
gxyz = lib.cartesian_prod([range(i) for i in nxyz])
kk = numpy.einsum('ki,ki->k', Gv, Gv)
idx = numpy.argsort(kk)[::-1]
kk = kk[idx]
Gv = Gv[idx]
kws = kws[idx]
gxyz = gxyz[idx]
coulG = .5/numpy.pi**2 * kws / kk
aoaux = ft_ao.ft_ao(auxmol, Gv, None, Gvbase, gxyz, nxyz)
kLR = numpy.asarray(aoaux.real, order='C')
kLI = numpy.asarray(aoaux.imag, order='C')
j2c = auxmol.intor('cint2c2e_sph', hermi=1).T # .T to C-ordr
lib.dot(kLR.T*coulG, kLR, -1, j2c, 1)
lib.dot(kLI.T*coulG, kLI, -1, j2c, 1)
kLR *= coulG.reshape(-1,1)
kLI *= coulG.reshape(-1,1)
aoaux = coulG = kk = kws = idx = None
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
buflen = min(max(int(max_memory*.3*1e6/8/naux), 1), nao_pair)
shranges = outcore._guess_shell_ranges(mol, buflen, 's2ij')
buflen = max([x[2] for x in shranges])
blksize = max(16, int(max_memory*.15*1e6/16/buflen))
pqkbuf = numpy.empty(buflen*blksize)
bufs1 = numpy.empty((buflen*naux))
# bufs2 holds either Lpq and ft_aopair
bufs2 = numpy.empty(max(buflen*(naux+1),buflen*blksize*2)) # *2 for cmplx
col1 = 0
for istep, sh_range in enumerate(shranges):
log.debug('int3c2e [%d/%d], AO [%d:%d], ncol = %d', \
istep+1, len(shranges), *sh_range)
bstart, bend, ncol = sh_range
col0, col1 = col1, col1+ncol
shls_slice = (bstart, bend, 0, bend, mol.nbas, mol.nbas+auxmol.nbas)
Lpq = get_Lpq(shls_slice, col0, col1, bufs2)
save('Lpq', Lpq, col0, col1)
j3c = _ri.nr_auxe2('cint3c2e_sph', atm, bas, env, shls_slice, ao_loc,
's2ij', 1, cintopt, bufs1)
j3c = j3c.T # -> (L|pq) in C-order
lib.dot(j2c, Lpq, -.5, j3c, 1)
Lpq = None
for p0, p1 in lib.prange(0, Gv.shape[0], blksize):
aoao = ft_ao.ft_aopair(mol, Gv[p0:p1], shls_slice[:4], 's2',
Gvbase, gxyz[p0:p1], nxyz, buf=bufs2)
nG = p1 - p0
pqkR = numpy.ndarray((ncol,nG), buffer=pqkbuf)
pqkR[:] = aoao.real.T
lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3c, 1)
pqkI = numpy.ndarray((ncol,nG), buffer=pqkbuf)
pqkI[:] = aoao.imag.T
lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3c, 1)
aoao = aoaux = None
save('j3c', j3c, col0, col1)
feri.close()
def cholesky_eri_b(mol, erifile, auxbasis='weigend+etb', dataname='eri_mo',
int3c='cint3c2e_sph', aosym='s2ij', int2c='cint2c2e_sph',
comp=1, ioblk_size=256, verbose=logger.NOTE):
'''3-center 2-electron AO integrals
'''
assert(aosym in ('s1', 's2ij'))
time0 = (time.clock(), time.time())
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mol.stdout, verbose)
auxmol = incore.format_aux_basis(mol, auxbasis)
j2c = incore.fill_2c2e(mol, auxmol, intor=int2c)
log.debug('size of aux basis %d', j2c.shape[0])
time1 = log.timer('2c2e', *time0)
low = scipy.linalg.cholesky(j2c, lower=True)
j2c = None
time1 = log.timer('Cholesky 2c2e', *time1)
if h5py.is_hdf5(erifile):
feri = h5py.File(erifile)
if dataname in feri:
del(feri[dataname])
else:
feri = h5py.File(erifile, 'w')
for icomp in range(comp):
feri.create_group('%s/%d'%(dataname,icomp)) # for h5py old version
def store(b, label):
cderi = scipy.linalg.solve_triangular(low, b, lower=True, overwrite_b=True)
if cderi.flags.f_contiguous:
cderi = lib.transpose(cderi.T)
feri[label] = cderi
atm, bas, env, ao_loc = incore._env_and_aoloc(int3c, mol, auxmol)
nao = ao_loc[mol.nbas]
naoaux = ao_loc[-1] - nao
if aosym == 's1':
nao_pair = nao * nao
buflen = min(max(int(ioblk_size*1e6/8/naoaux/comp), 1), nao_pair)
shranges = _guess_shell_ranges(mol, buflen, 's1')
else:
nao_pair = nao * (nao+1) // 2
buflen = min(max(int(ioblk_size*1e6/8/naoaux/comp), 1), nao_pair)
shranges = _guess_shell_ranges(mol, buflen, 's2ij')
log.debug('erifile %.8g MB, IO buf size %.8g MB',
naoaux*nao_pair*8/1e6, comp*buflen*naoaux*8/1e6)
if log.verbose >= logger.DEBUG1:
log.debug1('shranges = %s', shranges)
cintopt = gto.moleintor.make_cintopt(atm, bas, env, int3c)
bufs1 = numpy.empty((comp*max([x[2] for x in shranges]),naoaux))
for istep, sh_range in enumerate(shranges):
log.debug('int3c2e [%d/%d], AO [%d:%d], nrow = %d', \
istep+1, len(shranges), *sh_range)
bstart, bend, nrow = sh_range
shls_slice = (bstart, bend, 0, mol.nbas, mol.nbas, mol.nbas+auxmol.nbas)
buf = _ri.nr_auxe2(int3c, atm, bas, env, shls_slice, ao_loc,
aosym, comp, cintopt, bufs1)
if comp == 1:
store(buf.T, '%s/0/%d'%(dataname,istep))
else:
for icomp in range(comp):
store(buf[icomp].T, '%s/%d/%d'%(dataname,icomp,istep))
time1 = log.timer('gen CD eri [%d/%d]' % (istep+1,len(shranges)), *time1)
buf = bufs1 = None
feri.close()
return erifile
