def gen_int3c(job_id, ish0, ish1):
dataname = 'j3c-chunks/%d' % job_id
i0 = ao_loc[ish0]
i1 = ao_loc[ish1]
dii = i1 * (i1 + 1) // 2 - i0 * (i0 + 1) // 2
if j_only:
dij = dii
buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dii + dii)))
else:
dij = (i1 - i0) * nao
buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dij + dij)))
auxranges = balance_segs(aux_loc[1:] - aux_loc[:-1], buflen)
buflen = max([x[2] for x in auxranges])
buf = numpy.empty(nkptij * dij * buflen, dtype=dtype)
buf1 = numpy.empty(dij * buflen, dtype=dtype)
naux = aux_loc[-1]
for kpt_id, kptij in enumerate(kptij_lst):
key = '%s/%d' % (dataname, kpt_id)
if aosym_s2[kpt_id]:
shape = (naux, dii)
else:
shape = (naux, dij)
if gamma_point(kptij):
fswap.create_dataset(key, shape, 'f8')
else:
fswap.create_dataset(key, shape, 'c16')
naux0 = 0
for istep, auxrange in enumerate(auxranges):
log.alldebug2("aux_e1 job_id %d step %d", job_id, istep)
sh0, sh1, nrow = auxrange
sub_slice = (ish0, ish1, 0, cell.nbas, sh0, sh1)
mat = numpy.ndarray((nkptij, dij, nrow), dtype=dtype, buffer=buf)
mat = int3c(sub_slice, mat)
for k, kptij in enumerate(kptij_lst):
h5dat = fswap['%s/%d' % (dataname, k)]
v = lib.transpose(mat[k], out=buf1)
if not j_only and aosym_s2[k]:
idy = idxb[i0 * (i0 + 1) // 2:i1 *
(i1 + 1) // 2] - i0 * nao
out = numpy.ndarray((nrow, dii),
dtype=v.dtype,
buffer=mat[k])
v = numpy.take(v, idy, axis=1, out=out)
if gamma_point(kptij):
h5dat[naux0:naux0 + nrow] = v.real
else:
h5dat[naux0:naux0 + nrow] = v
naux0 += nrow
def gen_int3c(job_id, ish0, ish1):
dataname = 'j3c-chunks/%d' % job_id
i0 = ao_loc[ish0]
i1 = ao_loc[ish1]
dii = i1*(i1+1)//2 - i0*(i0+1)//2
dij = (i1 - i0) * nao
if j_only:
buflen = max(8, int(max_memory*1e6/16/(nkptij*dii+dii)))
else:
buflen = max(8, int(max_memory*1e6/16/(nkptij*dij+dij)))
auxranges = balance_segs(aux_loc[1:]-aux_loc[:-1], buflen)
buflen = max([x[2] for x in auxranges])
buf = numpy.empty(nkptij*dij*buflen, dtype=dtype)
buf1 = numpy.empty(dij*buflen, dtype=dtype)
naux = aux_loc[-1]
for kpt_id, kptij in enumerate(kptij_lst):
key = '%s/%d' % (dataname, kpt_id)
if aosym_s2[kpt_id]:
shape = (naux, dii)
else:
shape = (naux, dij)
if gamma_point(kptij):
fswap.create_dataset(key, shape, 'f8')
else:
fswap.create_dataset(key, shape, 'c16')
naux0 = 0
for istep, auxrange in enumerate(auxranges):
log.alldebug2("aux_e1 job_id %d step %d", job_id, istep)
sh0, sh1, nrow = auxrange
sub_slice = (ish0, ish1, 0, cell.nbas, sh0, sh1)
if j_only:
mat = numpy.ndarray((nkptij,dii,nrow), dtype=dtype, buffer=buf)
else:
mat = numpy.ndarray((nkptij,dij,nrow), dtype=dtype, buffer=buf)
mat = int3c(sub_slice, mat)
for k, kptij in enumerate(kptij_lst):
h5dat = fswap['%s/%d'%(dataname,k)]
v = lib.transpose(mat[k], out=buf1)
if not j_only and aosym_s2[k]:
idy = idxb[i0*(i0+1)//2:i1*(i1+1)//2] - i0 * nao
out = numpy.ndarray((nrow,dii), dtype=v.dtype, buffer=mat[k])
v = numpy.take(v, idy, axis=1, out=out)
if gamma_point(kptij):
h5dat[naux0:naux0+nrow] = v.real
else:
h5dat[naux0:naux0+nrow] = v
naux0 += nrow
def get_j_kpts(mydf, dm_kpts, hermi=1, kpts=numpy.zeros((1,3)),
kpts_band=None):
mydf = _sync_mydf(mydf)
cell = mydf.cell
mesh = mydf.mesh
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
coulG = tools.get_coulG(cell, mesh=mesh)
ngrids = len(coulG)
vR = rhoR = numpy.zeros((nset,ngrids))
for ao_ks_etc, p0, p1 in mydf.mpi_aoR_loop(mydf.grids, kpts):
ao_ks = ao_ks_etc[0]
for k, ao in enumerate(ao_ks):
for i in range(nset):
rhoR[i,p0:p1] += numint.eval_rho(cell, ao, dms[i,k])
ao = ao_ks = None
rhoR = mpi.allreduce(rhoR)
for i in range(nset):
rhoR[i] *= 1./nkpts
rhoG = tools.fft(rhoR[i], mesh)
vG = coulG * rhoG
vR[i] = tools.ifft(vG, mesh).real
kpts_band, input_band = _format_kpts_band(kpts_band, kpts), kpts_band
nband = len(kpts_band)
weight = cell.vol / ngrids
vR *= weight
if gamma_point(kpts_band):
vj_kpts = numpy.zeros((nset,nband,nao,nao))
else:
vj_kpts = numpy.zeros((nset,nband,nao,nao), dtype=numpy.complex128)
for ao_ks_etc, p0, p1 in mydf.mpi_aoR_loop(mydf.grids, kpts_band):
ao_ks = ao_ks_etc[0]
for k, ao in enumerate(ao_ks):
for i in range(nset):
vj_kpts[i,k] += lib.dot(ao.T.conj()*vR[i,p0:p1], ao)
vj_kpts = mpi.reduce(vj_kpts)
if gamma_point(kpts_band):
vj_kpts = vj_kpts.real
return _format_jks(vj_kpts, dm_kpts, input_band, kpts)
def get_j_kpts(mydf, dm_kpts, hermi=1, kpts=np.zeros((1, 3)), kpts_band=None):
'''Get the Coulomb (J) AO matrix at sampled k-points.
Args:
dm_kpts : (nkpts, nao, nao) ndarray or a list of (nkpts,nao,nao) ndarray
Density matrix at each k-point. If a list of k-point DMs, eg,
UHF alpha and beta DM, the alpha and beta DMs are contracted
separately.
kpts : (nkpts, 3) ndarray
Kwargs:
kpts_band : (3,) ndarray or (*,3) ndarray
A list of arbitrary "band" k-points at which to evalute the matrix.
Returns:
vj : (nkpts, nao, nao) ndarray
or list of vj if the input dm_kpts is a list of DMs
'''
cell = mydf.cell
gs = mydf.gs
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
coulG = tools.get_coulG(cell, gs=gs)
ngs = len(coulG)
vR = rhoR = np.zeros((nset, ngs))
for k, aoR in mydf.aoR_loop(gs, kpts):
for i in range(nset):
rhoR[i] += numint.eval_rho(cell, aoR, dms[i, k])
for i in range(nset):
rhoR[i] *= 1. / nkpts
rhoG = tools.fft(rhoR[i], gs)
vG = coulG * rhoG
vR[i] = tools.ifft(vG, gs).real
kpts_band, single_kpt_band = _format_kpts_band(kpts_band, kpts)
nband = len(kpts_band)
vj_kpts = []
weight = cell.vol / ngs
if gamma_point(kpts_band):
vj_kpts = np.empty((nset, nband, nao, nao))
else:
vj_kpts = np.empty((nset, nband, nao, nao), dtype=np.complex128)
for k, aoR in mydf.aoR_loop(gs, kpts_band):
for i in range(nset):
vj_kpts[i, k] = weight * lib.dot(aoR.T.conj() * vR[i], aoR)
return _format_jks(vj_kpts, dm_kpts, kpts_band, kpts, single_kpt_band)
def ft_fuse(job_id, uniq_kptji_id, sh0, sh1):
kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
shls_slice = (auxcell.nbas, fused_cell.nbas)
Gaux = ft_ao.ft_ao(fused_cell, Gv, shls_slice, b, gxyz, Gvbase, kpt)
Gaux *= mydf.weighted_coulG(kpt, False, gs).reshape(-1, 1)
kLR = Gaux.real.copy('C')
kLI = Gaux.imag.copy('C')
j2c = numpy.asarray(feri['j2c/%d' % uniq_kptji_id])
j2ctag = j2ctags[uniq_kptji_id]
naux0 = j2c.shape[0]
if is_zero(kpt):
aosym = 's2'
else:
aosym = 's1'
j3cR = [None] * nkptj
j3cI = [None] * nkptj
i0 = ao_loc[sh0]
i1 = ao_loc[sh1]
for k, idx in enumerate(adapted_ji_idx):
key = 'j3c-chunks/%d/%d' % (job_id, idx)
v = numpy.asarray(feri[key])
if is_zero(kpt):
for i, c in enumerate(vbar):
if c != 0:
v[i] -= c * ovlp[k][i0 * (i0 + 1) // 2:i1 *
(i1 + 1) // 2].ravel()
j3cR[k] = numpy.asarray(v.real, order='C')
if v.dtype == numpy.complex128:
j3cI[k] = numpy.asarray(v.imag, order='C')
v = None
ncol = j3cR[0].shape[1]
Gblksize = max(16, int(max_memory * 1e6 / 16 / ncol /
(nkptj + 1))) # +1 for pqkRbuf/pqkIbuf
Gblksize = min(Gblksize, ngs, 16384)
pqkRbuf = numpy.empty(ncol * Gblksize)
pqkIbuf = numpy.empty(ncol * Gblksize)
buf = numpy.empty(nkptj * ncol * Gblksize, dtype=numpy.complex128)
log.alldebug2(' blksize (%d,%d)', Gblksize, ncol)
shls_slice = (sh0, sh1, 0, cell.nbas)
for p0, p1 in lib.prange(0, ngs, Gblksize):
dat = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
kpt,
adapted_kptjs,
out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = dat[k].reshape(nG, ncol)
pqkR = numpy.ndarray((ncol, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol, nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k][naux:], 1)
lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k][naux:], 1)
if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])):
lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k][naux:], 1)
lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k][naux:], 1)
for k, idx in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
v = fuse(j3cR[k])
else:
v = fuse(j3cR[k] + j3cI[k] * 1j)
if j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c,
v,
lower=True,
overwrite_b=True)
else:
v = lib.dot(j2c, v)
feri['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = v
def get_jk(mydf, dm, hermi=1, kpt=numpy.zeros(3),
kpt_band=None, with_j=True, with_k=True, exxdiv=None):
'''JK for given k-point'''
from pyscf.pbc.df.df_jk import _ewald_exxdiv_for_G0
vj = vk = None
if kpt_band is not None and abs(kpt-kpt_band).sum() > 1e-9:
kpt = numpy.reshape(kpt, (1,3))
if with_k:
vk = get_k_kpts(mydf, dm, hermi, kpt, kpt_band, exxdiv)
if with_j:
vj = get_j_kpts(mydf, dm, hermi, kpt, kpt_band)
return vj, vk
cell = mydf.cell
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = (time.clock(), time.time())
dm = numpy.asarray(dm, order='C')
dms = _format_dms(dm, [kpt])
nset, _, nao = dms.shape[:3]
dms = dms.reshape(nset,nao,nao)
j_real = gamma_point(kpt)
k_real = gamma_point(kpt) and not numpy.iscomplexobj(dms)
kptii = numpy.asarray((kpt,kpt))
kpt_allow = numpy.zeros(3)
if with_j:
vjcoulG = mydf.weighted_coulG(kpt_allow, False, mydf.gs)
vjR = numpy.zeros((nset,nao,nao))
vjI = numpy.zeros((nset,nao,nao))
if with_k:
mydf.exxdiv = exxdiv
vkcoulG = mydf.weighted_coulG(kpt_allow, True, mydf.gs)
vkR = numpy.zeros((nset,nao,nao))
vkI = numpy.zeros((nset,nao,nao))
dmsR = numpy.asarray(dms.real.reshape(nset,nao,nao), order='C')
dmsI = numpy.asarray(dms.imag.reshape(nset,nao,nao), order='C')
mem_now = lib.current_memory()[0]
max_memory = max(2000, (mydf.max_memory - mem_now)) * .8
log.debug1('max_memory = %d MB (%d in use)', max_memory, mem_now)
t2 = t1
# rho_rs(-G+k_rs) is computed as conj(rho_{rs^*}(G-k_rs))
# == conj(transpose(rho_sr(G+k_sr), (0,2,1)))
blksize = max(int(max_memory*.25e6/16/nao**2), 16)
bufR = numpy.empty(blksize*nao**2)
bufI = numpy.empty(blksize*nao**2)
for pqkR, pqkI, p0, p1 in mydf.pw_loop(mydf.gs, kptii, max_memory=max_memory):
t2 = log.timer_debug1('%d:%d ft_aopair'%(p0,p1), *t2)
pqkR = pqkR.reshape(nao,nao,-1)
pqkI = pqkI.reshape(nao,nao,-1)
if with_j:
#:v4 = numpy.einsum('ijL,lkL->ijkl', pqk, pqk.conj())
#:vj += numpy.einsum('ijkl,lk->ij', v4, dm)
for i in range(nset):
rhoR = numpy.einsum('pq,pqk->k', dmsR[i], pqkR)
rhoR+= numpy.einsum('pq,pqk->k', dmsI[i], pqkI)
rhoI = numpy.einsum('pq,pqk->k', dmsI[i], pqkR)
rhoI-= numpy.einsum('pq,pqk->k', dmsR[i], pqkI)
rhoR *= vjcoulG[p0:p1]
rhoI *= vjcoulG[p0:p1]
vjR[i] += numpy.einsum('pqk,k->pq', pqkR, rhoR)
vjR[i] -= numpy.einsum('pqk,k->pq', pqkI, rhoI)
if not j_real:
vjI[i] += numpy.einsum('pqk,k->pq', pqkR, rhoI)
vjI[i] += numpy.einsum('pqk,k->pq', pqkI, rhoR)
#t2 = log.timer_debug1(' with_j', *t2)
if with_k:
coulG = numpy.sqrt(vkcoulG[p0:p1])
pqkR *= coulG
pqkI *= coulG
#:v4 = numpy.einsum('ijL,lkL->ijkl', pqk, pqk.conj())
#:vk += numpy.einsum('ijkl,jk->il', v4, dm)
pLqR = lib.transpose(pqkR, axes=(0,2,1), out=bufR).reshape(-1,nao)
pLqI = lib.transpose(pqkI, axes=(0,2,1), out=bufI).reshape(-1,nao)
iLkR = numpy.ndarray((nao*(p1-p0),nao), buffer=pqkR)
iLkI = numpy.ndarray((nao*(p1-p0),nao), buffer=pqkI)
for i in range(nset):
if k_real:
lib.dot(pLqR, dmsR[i], 1, iLkR)
lib.dot(pLqI, dmsR[i], 1, iLkI)
lib.dot(iLkR.reshape(nao,-1), pLqR.reshape(nao,-1).T, 1, vkR[i], 1)
lib.dot(iLkI.reshape(nao,-1), pLqI.reshape(nao,-1).T, 1, vkR[i], 1)
else:
zdotNN(pLqR, pLqI, dmsR[i], dmsI[i], 1, iLkR, iLkI)
zdotNC(iLkR.reshape(nao,-1), iLkI.reshape(nao,-1),
pLqR.reshape(nao,-1).T, pLqI.reshape(nao,-1).T,
1, vkR[i], vkI[i])
#t2 = log.timer_debug1(' with_k', *t2)
pqkR = pqkI = coulG = pLqR = pLqI = iLkR = iLkI = None
#t2 = log.timer_debug1('%d:%d'%(p0,p1), *t2)
bufR = bufI = None
t1 = log.timer_debug1('aft_jk.get_jk', *t1)
if with_j:
if j_real:
vj = vjR
else:
vj = vjR + vjI * 1j
vj = vj.reshape(dm.shape)
if with_k:
if k_real:
vk = vkR
else:
vk = vkR + vkI * 1j
if cell.dimension != 3 and exxdiv:
assert(exxdiv.lower() == 'ewald')
_ewald_exxdiv_for_G0(cell, kpt, dms, vk)
vk = vk.reshape(dm.shape)
return vj, vk
def get_k_kpts(mydf, dm_kpts, hermi=1, kpts=numpy.zeros((1,3)), kpts_band=None,
exxdiv=None):
cell = mydf.cell
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = (time.clock(), time.time())
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
swap_2e = (kpts_band is None)
kpts_band, single_kpt_band = _format_kpts_band(kpts_band, kpts)
nband = len(kpts_band)
kk_table = kpts_band.reshape(-1,1,3) - kpts.reshape(1,-1,3)
kk_todo = numpy.ones(kk_table.shape[:2], dtype=bool)
vkR = numpy.zeros((nset,nband,nao,nao))
vkI = numpy.zeros((nset,nband,nao,nao))
dmsR = numpy.asarray(dms.real, order='C')
dmsI = numpy.asarray(dms.imag, order='C')
mem_now = lib.current_memory()[0]
max_memory = max(2000, (mydf.max_memory - mem_now)) * .8
log.debug1('max_memory = %d MB (%d in use)', max_memory, mem_now)
# K_pq = ( p{k1} i{k2} | i{k2} q{k1} )
def make_kpt(kpt): # kpt = kptj - kpti
# search for all possible ki and kj that has ki-kj+kpt=0
kk_match = numpy.einsum('ijx->ij', abs(kk_table + kpt)) < 1e-9
kpti_idx, kptj_idx = numpy.where(kk_todo & kk_match)
nkptj = len(kptj_idx)
log.debug1('kpt = %s', kpt)
log.debug2('kpti_idx = %s', kpti_idx)
log.debug2('kptj_idx = %s', kptj_idx)
kk_todo[kpti_idx,kptj_idx] = False
if swap_2e and not is_zero(kpt):
kk_todo[kptj_idx,kpti_idx] = False
max_memory1 = max_memory * (nkptj+1)/(nkptj+5)
blksize = max(int(max_memory1*4e6/(nkptj+5)/16/nao**2), 16)
bufR = numpy.empty((blksize*nao**2))
bufI = numpy.empty((blksize*nao**2))
# Use DF object to mimic KRHF/KUHF object in function get_coulG
mydf.exxdiv = exxdiv
vkcoulG = mydf.weighted_coulG(kpt, True, mydf.gs)
kptjs = kpts[kptj_idx]
# <r|-G+k_rs|s> = conj(<s|G-k_rs|r>) = conj(<s|G+k_sr|r>)
for k, pqkR, pqkI, p0, p1 \
in mydf.ft_loop(mydf.gs, kpt, kptjs, max_memory=max_memory1):
ki = kpti_idx[k]
kj = kptj_idx[k]
coulG = numpy.sqrt(vkcoulG[p0:p1])
# case 1: k_pq = (pi|iq)
#:v4 = numpy.einsum('ijL,lkL->ijkl', pqk, pqk.conj())
#:vk += numpy.einsum('ijkl,jk->il', v4, dm)
pqkR *= coulG
pqkI *= coulG
pLqR = lib.transpose(pqkR.reshape(nao,nao,-1), axes=(0,2,1), out=bufR)
pLqI = lib.transpose(pqkI.reshape(nao,nao,-1), axes=(0,2,1), out=bufI)
iLkR = numpy.empty((nao*(p1-p0),nao))
iLkI = numpy.empty((nao*(p1-p0),nao))
for i in range(nset):
iLkR, iLkI = zdotNN(pLqR.reshape(-1,nao), pLqI.reshape(-1,nao),
dmsR[i,kj], dmsI[i,kj], 1, iLkR, iLkI)
zdotNC(iLkR.reshape(nao,-1), iLkI.reshape(nao,-1),
pLqR.reshape(nao,-1).T, pLqI.reshape(nao,-1).T,
1, vkR[i,ki], vkI[i,ki], 1)
# case 2: k_pq = (iq|pi)
#:v4 = numpy.einsum('iLj,lLk->ijkl', pqk, pqk.conj())
#:vk += numpy.einsum('ijkl,li->kj', v4, dm)
if swap_2e and not is_zero(kpt):
iLkR = iLkR.reshape(nao,-1)
iLkI = iLkI.reshape(nao,-1)
for i in range(nset):
iLkR, iLkI = zdotNN(dmsR[i,ki], dmsI[i,ki], pLqR.reshape(nao,-1),
pLqI.reshape(nao,-1), 1, iLkR, iLkI)
zdotCN(pLqR.reshape(-1,nao).T, pLqI.reshape(-1,nao).T,
iLkR.reshape(-1,nao), iLkI.reshape(-1,nao),
1, vkR[i,kj], vkI[i,kj], 1)
pqkR = pqkI = coulG = pLqR = pLqI = iLkR = iLkI = None
for ki, kpti in enumerate(kpts_band):
for kj, kptj in enumerate(kpts):
if kk_todo[ki,kj]:
make_kpt(kptj-kpti)
if (gamma_point(kpts) and gamma_point(kpts_band) and
not numpy.iscomplexobj(dm_kpts)):
vk_kpts = vkR
else:
vk_kpts = vkR + vkI * 1j
vk_kpts *= 1./nkpts
# G=0 was not included in the non-uniform grids
if cell.dimension != 3 and exxdiv:
assert(exxdiv.lower() == 'ewald')
_ewald_exxdiv_for_G0(cell, kpts_band, dms, vk_kpts, kpts_band)
return _format_jks(vk_kpts, dm_kpts, kpts_band, kpts, single_kpt_band)
def get_jk(mydf, dm, hermi=1, kpt=numpy.zeros(3),
kpt_band=None, with_j=True, with_k=True, exxdiv=None):
'''JK for given k-point'''
from pyscf.pbc.df.df_jk import _ewald_exxdiv_for_G0
vj = vk = None
if kpt_band is not None and abs(kpt-kpt_band).sum() > 1e-9:
kpt = numpy.reshape(kpt, (1,3))
if with_k:
vk = get_k_kpts(mydf, [dm], hermi, kpt, kpt_band, exxdiv)
if with_j:
vj = get_j_kpts(mydf, [dm], hermi, kpt, kpt_band)
return vj, vk
cell = mydf.cell
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = (time.clock(), time.time())
dm = numpy.asarray(dm, order='C')
dms = _format_dms(dm, [kpt])
nset, _, nao = dms.shape[:3]
dms = dms.reshape(nset,nao,nao)
j_real = gamma_point(kpt)
k_real = gamma_point(kpt) and not numpy.iscomplexobj(dms)
kptii = numpy.asarray((kpt,kpt))
kpt_allow = numpy.zeros(3)
if with_j:
vjcoulG = mydf.weighted_coulG(kpt_allow, False, mydf.gs)
vjR = numpy.zeros((nset,nao,nao))
vjI = numpy.zeros((nset,nao,nao))
if with_k:
mydf.exxdiv = exxdiv
vkcoulG = mydf.weighted_coulG(kpt_allow, True, mydf.gs)
vkR = numpy.zeros((nset,nao,nao))
vkI = numpy.zeros((nset,nao,nao))
dmsR = numpy.asarray(dms.real.reshape(nset,nao,nao), order='C')
dmsI = numpy.asarray(dms.imag.reshape(nset,nao,nao), order='C')
mem_now = lib.current_memory()[0]
max_memory = max(2000, (mydf.max_memory - mem_now)) * .8
log.debug1('max_memory = %d MB (%d in use)', max_memory, mem_now)
t2 = t1
# rho_rs(-G+k_rs) is computed as conj(rho_{rs^*}(G-k_rs))
# == conj(transpose(rho_sr(G+k_sr), (0,2,1)))
blksize = max(int(max_memory*.25e6/16/nao**2), 16)
bufR = numpy.empty(blksize*nao**2)
bufI = numpy.empty(blksize*nao**2)
for pqkR, pqkI, p0, p1 in mydf.pw_loop(mydf.gs, kptii, max_memory=max_memory):
t2 = log.timer_debug1('%d:%d ft_aopair'%(p0,p1), *t2)
pqkR = pqkR.reshape(nao,nao,-1)
pqkI = pqkI.reshape(nao,nao,-1)
if with_j:
for i in range(nset):
rhoR = numpy.einsum('pq,pqk->k', dmsR[i], pqkR)
rhoR+= numpy.einsum('pq,pqk->k', dmsI[i], pqkI)
rhoI = numpy.einsum('pq,pqk->k', dmsI[i], pqkR)
rhoI-= numpy.einsum('pq,pqk->k', dmsR[i], pqkI)
rhoR *= vjcoulG[p0:p1]
rhoI *= vjcoulG[p0:p1]
vjR[i] += numpy.einsum('pqk,k->pq', pqkR, rhoR)
vjR[i] -= numpy.einsum('pqk,k->pq', pqkI, rhoI)
if not j_real:
vjI[i] += numpy.einsum('pqk,k->pq', pqkR, rhoI)
vjI[i] += numpy.einsum('pqk,k->pq', pqkI, rhoR)
#t2 = log.timer_debug1(' with_j', *t2)
if with_k:
coulG = numpy.sqrt(vkcoulG[p0:p1])
pqkR *= coulG
pqkI *= coulG
#:v4 = numpy.einsum('ijL,lkL->ijkl', pqk, pqk.conj())
#:vk += numpy.einsum('ijkl,jk->il', v4, dm)
pLqR = lib.transpose(pqkR, axes=(0,2,1), out=bufR).reshape(-1,nao)
pLqI = lib.transpose(pqkI, axes=(0,2,1), out=bufI).reshape(-1,nao)
iLkR = numpy.ndarray((nao*(p1-p0),nao), buffer=pqkR)
iLkI = numpy.ndarray((nao*(p1-p0),nao), buffer=pqkI)
for i in range(nset):
if k_real:
lib.dot(pLqR, dmsR[i], 1, iLkR)
lib.dot(pLqI, dmsR[i], 1, iLkI)
lib.dot(iLkR.reshape(nao,-1), pLqR.reshape(nao,-1).T, 1, vkR[i], 1)
lib.dot(iLkI.reshape(nao,-1), pLqI.reshape(nao,-1).T, 1, vkR[i], 1)
else:
zdotNN(pLqR, pLqI, dmsR[i], dmsI[i], 1, iLkR, iLkI)
zdotNC(iLkR.reshape(nao,-1), iLkI.reshape(nao,-1),
pLqR.reshape(nao,-1).T, pLqI.reshape(nao,-1).T,
1, vkR[i], vkI[i])
#t2 = log.timer_debug1(' with_k', *t2)
pqkR = pqkI = coulG = pLqR = pLqI = iLkR = iLkI = None
#t2 = log.timer_debug1('%d:%d'%(p0,p1), *t2)
bufR = bufI = None
t1 = log.timer_debug1('pwdf_jk.get_jk', *t1)
if with_j:
if j_real:
vj = vjR
else:
vj = vjR + vjI * 1j
vj = vj.reshape(dm.shape)
if with_k:
if k_real:
vk = vkR
else:
vk = vkR + vkI * 1j
if cell.dimension != 3 and exxdiv is not None:
assert(exxdiv.lower() == 'ewald')
_ewald_exxdiv_for_G0(cell, kpt, dms, vk)
vk = vk.reshape(dm.shape)
return vj, vk
def get_k_kpts(mydf, dm_kpts, hermi=1, kpts=numpy.zeros((1,3)),
kpts_band=None, exxdiv=None):
mydf = _sync_mydf(mydf)
cell = mydf.cell
mesh = mydf.mesh
coords = cell.gen_uniform_grids(mesh)
ngrids = coords.shape[0]
if hasattr(dm_kpts, 'mo_coeff'):
if dm_kpts.ndim == 3: # KRHF
mo_coeff = [dm_kpts.mo_coeff]
mo_occ = [dm_kpts.mo_occ ]
else: # KUHF
mo_coeff = dm_kpts.mo_coeff
mo_occ = dm_kpts.mo_occ
elif hasattr(dm_kpts[0], 'mo_coeff'):
mo_coeff = [dm.mo_coeff for dm in dm_kpts]
mo_occ = [dm.mo_occ for dm in dm_kpts]
else:
mo_coeff = None
kpts = numpy.asarray(kpts)
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
weight = 1./nkpts * (cell.vol/ngrids)
kpts_band, input_band = _format_kpts_band(kpts_band, kpts), kpts_band
nband = len(kpts_band)
if gamma_point(kpts_band) and gamma_point(kpts):
vk_kpts = numpy.zeros((nset,nband,nao,nao), dtype=dms.dtype)
else:
vk_kpts = numpy.zeros((nset,nband,nao,nao), dtype=numpy.complex128)
coords = mydf.grids.coords
ao2_kpts = [numpy.asarray(ao.T, order='C')
for ao in mydf._numint.eval_ao(cell, coords, kpts=kpts)]
if input_band is None:
ao1_kpts = ao2_kpts
else:
ao1_kpts = [numpy.asarray(ao.T, order='C')
for ao in mydf._numint.eval_ao(cell, coords, kpts=kpts_band)]
mem_now = lib.current_memory()[0]
max_memory = mydf.max_memory - mem_now
blksize = int(min(nao, max(1, (max_memory-mem_now)*1e6/16/4/ngrids/nao)))
lib.logger.debug1(mydf, 'max_memory %s blksize %d', max_memory, blksize)
ao1_dtype = numpy.result_type(*ao1_kpts)
ao2_dtype = numpy.result_type(*ao2_kpts)
vR_dm = numpy.empty((nset,nao,ngrids), dtype=vk_kpts.dtype)
ao_dms_buf = [None] * nkpts
tasks = [(k1,k2) for k2 in range(nkpts) for k1 in range(nband)]
for k1, k2 in mpi.static_partition(tasks):
ao1T = ao1_kpts[k1]
ao2T = ao2_kpts[k2]
kpt1 = kpts_band[k1]
kpt2 = kpts[k2]
if ao2T.size == 0 or ao1T.size == 0:
continue
# If we have an ewald exxdiv, we add the G=0 correction near the
# end of the function to bypass any discretization errors
# that arise from the FFT.
mydf.exxdiv = exxdiv
if exxdiv == 'ewald' or exxdiv is None:
coulG = tools.get_coulG(cell, kpt2-kpt1, False, mydf, mesh)
else:
coulG = tools.get_coulG(cell, kpt2-kpt1, True, mydf, mesh)
if is_zero(kpt1-kpt2):
expmikr = numpy.array(1.)
else:
expmikr = numpy.exp(-1j * numpy.dot(coords, kpt2-kpt1))
if ao_dms_buf[k2] is None:
if mo_coeff is None:
ao_dms = [lib.dot(dm[k2], ao2T.conj()) for dm in dms]
else:
ao_dms = []
for i, dm in enumerate(dms):
occ = mo_occ[i][k2]
mo_scaled = mo_coeff[i][k2][:,occ>0] * numpy.sqrt(occ[occ>0])
ao_dms.append(lib.dot(mo_scaled.T, ao2T).conj())
ao_dms_buf[k2] = ao_dms
else:
ao_dms = ao_dms_buf[k2]
if mo_coeff is None:
for p0, p1 in lib.prange(0, nao, blksize):
rho1 = numpy.einsum('ig,jg->ijg', ao1T[p0:p1].conj()*expmikr, ao2T)
vG = tools.fft(rho1.reshape(-1,ngrids), mesh)
rho1 = None
vG *= coulG
vR = tools.ifft(vG, mesh).reshape(p1-p0,nao,ngrids)
vG = None
if vR_dm.dtype == numpy.double:
vR = vR.real
for i in range(nset):
numpy.einsum('ijg,jg->ig', vR, ao_dms[i], out=vR_dm[i,p0:p1])
vR = None
else:
for p0, p1 in lib.prange(0, nao, blksize):
for i in range(nset):
rho1 = numpy.einsum('ig,jg->ijg',
ao1T[p0:p1].conj()*expmikr,
ao_dms[i].conj())
vG = tools.fft(rho1.reshape(-1,ngrids), mesh)
rho1 = None
vG *= coulG
vR = tools.ifft(vG, mesh).reshape(p1-p0,-1,ngrids)
vG = None
if vR_dm.dtype == numpy.double:
vR = vR.real
numpy.einsum('ijg,jg->ig', vR, ao_dms[i], out=vR_dm[i,p0:p1])
vR = None
vR_dm *= expmikr.conj()
for i in range(nset):
vk_kpts[i,k1] += weight * lib.dot(vR_dm[i], ao1T.T)
vk_kpts = mpi.reduce(lib.asarray(vk_kpts))
if gamma_point(kpts_band) and gamma_point(kpts):
vk_kpts = vk_kpts.real
if rank == 0:
if exxdiv == 'ewald':
_ewald_exxdiv_for_G0(cell, kpts, dms, vk_kpts, kpts_band=kpts_band)
return _format_jks(vk_kpts, dm_kpts, input_band, kpts)
def get_k_kpts(mydf, dm_kpts, hermi=1, kpts=numpy.zeros((1,3)), kpt_band=None,
exxdiv=None):
cell = mydf.cell
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = (time.clock(), time.time())
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
if kpt_band is None:
kpts_band = kpts
swap_2e = True
else:
kpts_band = numpy.reshape(kpt_band, (-1,3))
nband = len(kpts_band)
kk_table = kpts_band.reshape(-1,1,3) - kpts.reshape(1,-1,3)
kk_todo = numpy.ones(kk_table.shape[:2], dtype=bool)
vkR = numpy.zeros((nset,nband,nao,nao))
vkI = numpy.zeros((nset,nband,nao,nao))
dmsR = numpy.asarray(dms.real, order='C')
dmsI = numpy.asarray(dms.imag, order='C')
mem_now = lib.current_memory()[0]
max_memory = max(2000, (mydf.max_memory - mem_now)) * .8
log.debug1('max_memory = %d MB (%d in use)', max_memory, mem_now)
# K_pq = ( p{k1} i{k2} | i{k2} q{k1} )
def make_kpt(kpt): # kpt = kptj - kpti
# search for all possible ki and kj that has ki-kj+kpt=0
kk_match = numpy.einsum('ijx->ij', abs(kk_table + kpt)) < 1e-9
kpti_idx, kptj_idx = numpy.where(kk_todo & kk_match)
nkptj = len(kptj_idx)
log.debug1('kpt = %s', kpt)
log.debug2('kpti_idx = %s', kpti_idx)
log.debug2('kptj_idx = %s', kptj_idx)
kk_todo[kpti_idx,kptj_idx] = False
if swap_2e and not is_zero(kpt):
kk_todo[kptj_idx,kpti_idx] = False
max_memory1 = max_memory * (nkptj+1)/(nkptj+5)
blksize = max(int(max_memory1*4e6/(nkptj+5)/16/nao**2), 16)
bufR = numpy.empty((blksize*nao**2))
bufI = numpy.empty((blksize*nao**2))
# Use DF object to mimic KRHF/KUHF object in function get_coulG
mydf.exxdiv = exxdiv
vkcoulG = mydf.weighted_coulG(kpt, True, mydf.gs)
kptjs = kpts[kptj_idx]
# <r|-G+k_rs|s> = conj(<s|G-k_rs|r>) = conj(<s|G+k_sr|r>)
for k, pqkR, pqkI, p0, p1 \
in mydf.ft_loop(mydf.gs, kpt, kptjs, max_memory=max_memory1):
ki = kpti_idx[k]
kj = kptj_idx[k]
coulG = numpy.sqrt(vkcoulG[p0:p1])
# case 1: k_pq = (pi|iq)
#:v4 = numpy.einsum('ijL,lkL->ijkl', pqk, pqk.conj())
#:vk += numpy.einsum('ijkl,jk->il', v4, dm)
pqkR *= coulG
pqkI *= coulG
pLqR = lib.transpose(pqkR.reshape(nao,nao,-1), axes=(0,2,1), out=bufR)
pLqI = lib.transpose(pqkI.reshape(nao,nao,-1), axes=(0,2,1), out=bufI)
iLkR = numpy.empty((nao*(p1-p0),nao))
iLkI = numpy.empty((nao*(p1-p0),nao))
for i in range(nset):
iLkR, iLkI = zdotNN(pLqR.reshape(-1,nao), pLqI.reshape(-1,nao),
dmsR[i,kj], dmsI[i,kj], 1, iLkR, iLkI)
zdotNC(iLkR.reshape(nao,-1), iLkI.reshape(nao,-1),
pLqR.reshape(nao,-1).T, pLqI.reshape(nao,-1).T,
1, vkR[i,ki], vkI[i,ki], 1)
# case 2: k_pq = (iq|pi)
#:v4 = numpy.einsum('iLj,lLk->ijkl', pqk, pqk.conj())
#:vk += numpy.einsum('ijkl,li->kj', v4, dm)
if swap_2e and not is_zero(kpt):
iLkR = iLkR.reshape(nao,-1)
iLkI = iLkI.reshape(nao,-1)
for i in range(nset):
iLkR, iLkI = zdotNN(dmsR[i,ki], dmsI[i,ki], pLqR.reshape(nao,-1),
pLqI.reshape(nao,-1), 1, iLkR, iLkI)
zdotCN(pLqR.reshape(-1,nao).T, pLqI.reshape(-1,nao).T,
iLkR.reshape(-1,nao), iLkI.reshape(-1,nao),
1, vkR[i,kj], vkI[i,kj], 1)
pqkR = pqkI = coulG = pLqR = pLqI = iLkR = iLkI = None
for ki, kpti in enumerate(kpts_band):
for kj, kptj in enumerate(kpts):
if kk_todo[ki,kj]:
make_kpt(kptj-kpti)
if (gamma_point(kpts) and gamma_point(kpts_band) and
not numpy.iscomplexobj(dm_kpts)):
vk_kpts = vkR
else:
vk_kpts = vkR + vkI * 1j
vk_kpts *= 1./nkpts
# G=0 was not included in the non-uniform grids
if cell.dimension != 3 and exxdiv is not None:
assert(exxdiv.lower() == 'ewald')
_ewald_exxdiv_for_G0(cell, kpts_band, dms, vk_kpts)
if kpt_band is not None and numpy.shape(kpt_band) == (3,):
if dm_kpts.ndim == 3: # One set of dm_kpts for KRHF
return vk_kpts[0,0]
else:
return vk_kpts[:,0]
else:
return vk_kpts.reshape(dm_kpts.shape)
def make_kpt(uniq_kptji_id): # kpt = kptj - kpti
kpt = uniq_kpts[uniq_kptji_id]
log.debug1('kpt = %s', kpt)
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
log.debug1('adapted_ji_idx = %s', adapted_ji_idx)
kLR = kLRs[uniq_kptji_id]
kLI = kLIs[uniq_kptji_id]
if is_zero(kpt): # kpti == kptj
aosym = 's2'
nao_pair = nao * (nao + 1) // 2
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('cint1e_ovlp_sph',
hermi=1,
kpts=adapted_kptjs)
for k, ji in enumerate(adapted_ji_idx):
ovlp[k] = lib.pack_tril(ovlp[k])
else:
aosym = 's1'
nao_pair = nao**2
mem_now = lib.current_memory()[0]
log.debug2('memory = %s', mem_now)
max_memory = max(2000, mydf.max_memory - mem_now)
# nkptj for 3c-coulomb arrays plus 1 Lpq array
buflen = min(
max(int(max_memory * .6 * 1e6 / 16 / naux / (nkptj + 1)), 1),
nao_pair)
shranges = _guess_shell_ranges(cell, buflen, aosym)
buflen = max([x[2] for x in shranges])
# +1 for a pqkbuf
if aosym == 's2':
Gblksize = max(
16, int(max_memory * .2 * 1e6 / 16 / buflen / (nkptj + 1)))
else:
Gblksize = max(
16, int(max_memory * .4 * 1e6 / 16 / buflen / (nkptj + 1)))
Gblksize = min(Gblksize, ngs, 16384)
pqkRbuf = numpy.empty(buflen * Gblksize)
pqkIbuf = numpy.empty(buflen * Gblksize)
# buf for ft_aopair
buf = numpy.zeros((nkptj, buflen * Gblksize), dtype=numpy.complex128)
col1 = 0
for istep, sh_range in enumerate(shranges):
log.debug1('int3c2e [%d/%d], AO [%d:%d], ncol = %d', \
istep+1, len(shranges), *sh_range)
bstart, bend, ncol = sh_range
col0, col1 = col1, col1 + ncol
j3cR = []
j3cI = []
for k, idx in enumerate(adapted_ji_idx):
v = numpy.asarray(feri['j3c/%d' % idx][:, col0:col1])
if is_zero(kpt):
for i, c in enumerate(vbar):
if c != 0:
v[i] -= c * ovlp[k][col0:col1]
j3cR.append(numpy.asarray(v.real, order='C'))
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
j3cI.append(None)
else:
j3cI.append(numpy.asarray(v.imag, order='C'))
v = None
if aosym == 's2':
shls_slice = (bstart, bend, 0, bend)
for p0, p1 in lib.prange(0, ngs, Gblksize):
ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
kpt,
adapted_kptjs,
out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = numpy.ndarray((nG, ncol),
dtype=numpy.complex128,
order='F',
buffer=buf[k])
pqkR = numpy.ndarray((ncol, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol, nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
aoao[:] = 0
lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k][naux:], 1)
lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k][naux:], 1)
if not (is_zero(kpt)
and gamma_point(adapted_kptjs[k])):
lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k][naux:],
1)
lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k][naux:], 1)
else:
shls_slice = (bstart, bend, 0, cell.nbas)
ni = ncol // nao
for p0, p1 in lib.prange(0, ngs, Gblksize):
ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
kpt,
adapted_kptjs,
out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = numpy.ndarray((nG, ni, nao),
dtype=numpy.complex128,
order='F',
buffer=buf[k])
pqkR = numpy.ndarray((ni, nao, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ni, nao, nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.transpose(1, 2, 0)
pqkI[:] = aoao.imag.transpose(1, 2, 0)
aoao[:] = 0
pqkR = pqkR.reshape(-1, nG)
pqkI = pqkI.reshape(-1, nG)
zdotCN(kLR[p0:p1].T, kLI[p0:p1].T, pqkR.T, pqkI.T, -1,
j3cR[k][naux:], j3cI[k][naux:], 1)
naux0 = nauxs[uniq_kptji_id]
for k, ji in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
v = fuse(j3cR[k])
else:
v = fuse(j3cR[k] + j3cI[k] * 1j)
if j2c[uniq_kptji_id][0] == 'CD':
v = scipy.linalg.solve_triangular(j2c[uniq_kptji_id][1],
v,
lower=True,
overwrite_b=True)
else:
v = lib.dot(j2c[uniq_kptji_id][1], v)
feri['j3c/%d' % ji][:naux0, col0:col1] = v
naux0 = nauxs[uniq_kptji_id]
for k, ji in enumerate(adapted_ji_idx):
v = feri['j3c/%d' % ji][:naux0]
del (feri['j3c/%d' % ji])
feri['j3c/%d' % ji] = v
def _make_j3c(mydf, cell, auxcell, kptij_lst, cderi_file):
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = t0 = (time.clock(), time.time())
fused_cell, fuse = fuse_auxcell(mydf, mydf.auxcell)
ao_loc = cell.ao_loc_nr()
nao = ao_loc[-1]
naux = auxcell.nao_nr()
nkptij = len(kptij_lst)
gs = mydf.gs
Gv, Gvbase, kws = cell.get_Gv_weights(gs)
b = cell.reciprocal_vectors()
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
ngs = gxyz.shape[0]
kptis = kptij_lst[:, 0]
kptjs = kptij_lst[:, 1]
kpt_ji = kptjs - kptis
uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji)
log.debug('Num uniq kpts %d', len(uniq_kpts))
log.debug2('uniq_kpts %s', uniq_kpts)
# j2c ~ (-kpt_ji | kpt_ji)
j2c = fused_cell.pbc_intor('int2c2e_sph', hermi=1, kpts=uniq_kpts)
j2ctags = []
nauxs = []
t1 = log.timer_debug1('2c2e', *t1)
if h5py.is_hdf5(cderi_file):
feri = h5py.File(cderi_file)
else:
feri = h5py.File(cderi_file, 'w')
for k, kpt in enumerate(uniq_kpts):
aoaux = ft_ao.ft_ao(fused_cell, Gv, None, b, gxyz, Gvbase, kpt).T
coulG = numpy.sqrt(mydf.weighted_coulG(kpt, False, gs))
kLR = (aoaux.real * coulG).T
kLI = (aoaux.imag * coulG).T
if not kLR.flags.c_contiguous: kLR = lib.transpose(kLR.T)
if not kLI.flags.c_contiguous: kLI = lib.transpose(kLI.T)
aoaux = None
kLR1 = numpy.asarray(kLR[:, naux:], order='C')
kLI1 = numpy.asarray(kLI[:, naux:], order='C')
if is_zero(kpt): # kpti == kptj
for p0, p1 in mydf.mpi_prange(0, ngs):
j2cR = lib.ddot(kLR1[p0:p1].T, kLR[p0:p1])
j2cR = lib.ddot(kLI1[p0:p1].T, kLI[p0:p1], 1, j2cR, 1)
j2c[k][naux:] -= mpi.allreduce(j2cR)
j2c[k][:naux, naux:] = j2c[k][naux:, :naux].T
else:
for p0, p1 in mydf.mpi_prange(0, ngs):
j2cR, j2cI = zdotCN(kLR1[p0:p1].T, kLI1[p0:p1].T, kLR[p0:p1],
kLI[p0:p1])
j2cR = mpi.allreduce(j2cR)
j2cI = mpi.allreduce(j2cI)
j2c[k][naux:] -= j2cR + j2cI * 1j
j2c[k][:naux, naux:] = j2c[k][naux:, :naux].T.conj()
j2c[k] = fuse(fuse(j2c[k]).T).T
try:
feri['j2c/%d' % k] = scipy.linalg.cholesky(j2c[k], lower=True)
j2ctags.append('CD')
nauxs.append(naux)
except scipy.linalg.LinAlgError as e:
#msg =('===================================\n'
# 'J-metric not positive definite.\n'
# 'It is likely that gs is not enough.\n'
# '===================================')
#log.error(msg)
#raise scipy.linalg.LinAlgError('\n'.join([e.message, msg]))
w, v = scipy.linalg.eigh(j2c)
log.debug2('metric linear dependency for kpt %s', uniq_kptji_id)
log.debug2('cond = %.4g, drop %d bfns', w[0] / w[-1],
numpy.count_nonzero(w < LINEAR_DEP_THR))
v = v[:, w > LINEAR_DEP_THR].T.conj()
v /= numpy.sqrt(w[w > LINEAR_DEP_THR]).reshape(-1, 1)
feri['j2c/%d' % k] = v
j2ctags.append('eig')
nauxs.append(v.shape[0])
kLR = kLI = kLR1 = kLI1 = coulG = None
j2c = None
aosym_s2 = numpy.einsum('ix->i', abs(kptis - kptjs)) < 1e-9
j_only = numpy.all(aosym_s2)
if gamma_point(kptij_lst):
dtype = 'f8'
else:
dtype = 'c16'
vbar = mydf.auxbar(fused_cell)
vbar = fuse(vbar)
ovlp = cell.pbc_intor('int1e_ovlp_sph', hermi=1, kpts=kptjs[aosym_s2])
ovlp = [lib.pack_tril(s) for s in ovlp]
t1 = log.timer_debug1('aoaux and int2c', *t1)
# Estimates the buffer size based on the last contraction in G-space.
# This contraction requires to hold nkptj copies of (naux,?) array
# simultaneously in memory.
mem_now = max(comm.allgather(lib.current_memory()[0]))
max_memory = max(2000, mydf.max_memory - mem_now)
nkptj_max = max((uniq_inverse == x).sum() for x in set(uniq_inverse))
buflen = max(
int(
min(max_memory * .5e6 / 16 / naux / (nkptj_max + 2) / nao,
nao / 3 / mpi.pool.size)), 1)
chunks = (buflen, nao)
j3c_jobs = grids2d_int3c_jobs(cell, auxcell, kptij_lst, chunks, j_only)
log.debug1('max_memory = %d MB (%d in use) chunks %s', max_memory,
mem_now, chunks)
log.debug2('j3c_jobs %s', j3c_jobs)
if j_only:
int3c = wrap_int3c(cell, fused_cell, 'int3c2e_sph', 's2', 1, kptij_lst)
else:
int3c = wrap_int3c(cell, fused_cell, 'int3c2e_sph', 's1', 1, kptij_lst)
idxb = numpy.tril_indices(nao)
idxb = (idxb[0] * nao + idxb[1]).astype('i')
aux_loc = fused_cell.ao_loc_nr('ssc' in 'int3c2e_sph')
def gen_int3c(auxcell, job_id, ish0, ish1):
dataname = 'j3c-chunks/%d' % job_id
if dataname in feri:
del (feri[dataname])
i0 = ao_loc[ish0]
i1 = ao_loc[ish1]
dii = i1 * (i1 + 1) // 2 - i0 * (i0 + 1) // 2
dij = (i1 - i0) * nao
if j_only:
buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dii + dii)))
else:
buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dij + dij)))
auxranges = balance_segs(aux_loc[1:] - aux_loc[:-1], buflen)
buflen = max([x[2] for x in auxranges])
buf = numpy.empty(nkptij * dij * buflen, dtype=dtype)
buf1 = numpy.empty(dij * buflen, dtype=dtype)
naux = aux_loc[-1]
for kpt_id, kptij in enumerate(kptij_lst):
key = '%s/%d' % (dataname, kpt_id)
if aosym_s2[kpt_id]:
shape = (naux, dii)
else:
shape = (naux, dij)
if gamma_point(kptij):
feri.create_dataset(key, shape, 'f8')
else:
feri.create_dataset(key, shape, 'c16')
naux0 = 0
for istep, auxrange in enumerate(auxranges):
log.alldebug2("aux_e2 job_id %d step %d", job_id, istep)
sh0, sh1, nrow = auxrange
sub_slice = (ish0, ish1, 0, cell.nbas, sh0, sh1)
if j_only:
mat = numpy.ndarray((nkptij, dii, nrow),
dtype=dtype,
buffer=buf)
else:
mat = numpy.ndarray((nkptij, dij, nrow),
dtype=dtype,
buffer=buf)
mat = int3c(sub_slice, mat)
for k, kptij in enumerate(kptij_lst):
h5dat = feri['%s/%d' % (dataname, k)]
v = lib.transpose(mat[k], out=buf1)
if not j_only and aosym_s2[k]:
idy = idxb[i0 * (i0 + 1) // 2:i1 *
(i1 + 1) // 2] - i0 * nao
out = numpy.ndarray((nrow, dii),
dtype=v.dtype,
buffer=mat[k])
v = numpy.take(v, idy, axis=1, out=out)
if gamma_point(kptij):
h5dat[naux0:naux0 + nrow] = v.real
else:
h5dat[naux0:naux0 + nrow] = v
naux0 += nrow
def ft_fuse(job_id, uniq_kptji_id, sh0, sh1):
kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
shls_slice = (auxcell.nbas, fused_cell.nbas)
Gaux = ft_ao.ft_ao(fused_cell, Gv, shls_slice, b, gxyz, Gvbase, kpt)
Gaux *= mydf.weighted_coulG(kpt, False, gs).reshape(-1, 1)
kLR = Gaux.real.copy('C')
kLI = Gaux.imag.copy('C')
j2c = numpy.asarray(feri['j2c/%d' % uniq_kptji_id])
j2ctag = j2ctags[uniq_kptji_id]
naux0 = j2c.shape[0]
if is_zero(kpt):
aosym = 's2'
else:
aosym = 's1'
j3cR = [None] * nkptj
j3cI = [None] * nkptj
i0 = ao_loc[sh0]
i1 = ao_loc[sh1]
for k, idx in enumerate(adapted_ji_idx):
key = 'j3c-chunks/%d/%d' % (job_id, idx)
v = numpy.asarray(feri[key])
if is_zero(kpt):
for i, c in enumerate(vbar):
if c != 0:
v[i] -= c * ovlp[k][i0 * (i0 + 1) // 2:i1 *
(i1 + 1) // 2].ravel()
j3cR[k] = numpy.asarray(v.real, order='C')
if v.dtype == numpy.complex128:
j3cI[k] = numpy.asarray(v.imag, order='C')
v = None
ncol = j3cR[0].shape[1]
Gblksize = max(16, int(max_memory * 1e6 / 16 / ncol /
(nkptj + 1))) # +1 for pqkRbuf/pqkIbuf
Gblksize = min(Gblksize, ngs, 16384)
pqkRbuf = numpy.empty(ncol * Gblksize)
pqkIbuf = numpy.empty(ncol * Gblksize)
buf = numpy.empty(nkptj * ncol * Gblksize, dtype=numpy.complex128)
log.alldebug2(' blksize (%d,%d)', Gblksize, ncol)
shls_slice = (sh0, sh1, 0, cell.nbas)
for p0, p1 in lib.prange(0, ngs, Gblksize):
dat = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
kpt,
adapted_kptjs,
out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = dat[k].reshape(nG, ncol)
pqkR = numpy.ndarray((ncol, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol, nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k][naux:], 1)
lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k][naux:], 1)
if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])):
lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k][naux:], 1)
lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k][naux:], 1)
for k, idx in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
v = fuse(j3cR[k])
else:
v = fuse(j3cR[k] + j3cI[k] * 1j)
if j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c,
v,
lower=True,
overwrite_b=True)
else:
v = lib.dot(j2c, v)
feri['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = v
t2 = t1
j3c_workers = numpy.zeros(len(j3c_jobs), dtype=int)
#for job_id, ish0, ish1 in mpi.work_share_partition(j3c_jobs):
for job_id, ish0, ish1 in mpi.work_stealing_partition(j3c_jobs):
gen_int3c(fused_cell, job_id, ish0, ish1)
t2 = log.alltimer_debug2('int j3c %d' % job_id, *t2)
for k, kpt in enumerate(uniq_kpts):
ft_fuse(job_id, k, ish0, ish1)
t2 = log.alltimer_debug2('ft-fuse %d k %d' % (job_id, k), *t2)
j3c_workers[job_id] = rank
j3c_workers = mpi.allreduce(j3c_workers)
log.debug2('j3c_workers %s', j3c_workers)
j2c = kLRs = kLIs = ovlp = vbar = fuse = gen_int3c = ft_fuse = None
t1 = log.timer_debug1('int3c and fuse', *t1)
def get_segs_loc(aosym):
off0 = numpy.asarray([ao_loc[i0] for x, i0, i1 in j3c_jobs])
off1 = numpy.asarray([ao_loc[i1] for x, i0, i1 in j3c_jobs])
if aosym: # s2
dims = off1 * (off1 + 1) // 2 - off0 * (off0 + 1) // 2
else:
dims = (off1 - off0) * nao
#dims = numpy.asarray([ao_loc[i1]-ao_loc[i0] for x,i0,i1 in j3c_jobs])
dims = numpy.hstack(
[dims[j3c_workers == w] for w in range(mpi.pool.size)])
job_idx = numpy.hstack(
[numpy.where(j3c_workers == w)[0] for w in range(mpi.pool.size)])
segs_loc = numpy.append(0, numpy.cumsum(dims))
segs_loc = [(segs_loc[j], segs_loc[j + 1])
for j in numpy.argsort(job_idx)]
return segs_loc
segs_loc_s1 = get_segs_loc(False)
segs_loc_s2 = get_segs_loc(True)
if 'j3c' in feri: del (feri['j3c'])
segsize = (max(nauxs) + mpi.pool.size - 1) // mpi.pool.size
naux0 = rank * segsize
for k, kptij in enumerate(kptij_lst):
naux1 = min(nauxs[uniq_inverse[k]], naux0 + segsize)
nrow = max(0, naux1 - naux0)
if gamma_point(kptij):
dtype = 'f8'
else:
dtype = 'c16'
if aosym_s2[k]:
nao_pair = nao * (nao + 1) // 2
else:
nao_pair = nao * nao
feri.create_dataset('j3c/%d' % k, (nrow, nao_pair),
dtype,
maxshape=(None, nao_pair))
def load(k, p0, p1):
naux1 = nauxs[uniq_inverse[k]]
slices = [(min(i * segsize + p0, naux1), min(i * segsize + p1, naux1))
for i in range(mpi.pool.size)]
segs = []
for p0, p1 in slices:
val = []
for job_id, worker in enumerate(j3c_workers):
if rank == worker:
key = 'j3c-chunks/%d/%d' % (job_id, k)
val.append(feri[key][p0:p1].ravel())
if val:
segs.append(numpy.hstack(val))
else:
segs.append(numpy.zeros(0))
return segs
def save(k, p0, p1, segs):
segs = mpi.alltoall(segs)
naux1 = nauxs[uniq_inverse[k]]
loc0, loc1 = min(p0, naux1 - naux0), min(p1, naux1 - naux0)
nL = loc1 - loc0
if nL > 0:
if aosym_s2[k]:
segs = numpy.hstack([
segs[i0 * nL:i1 * nL].reshape(nL, -1)
for i0, i1 in segs_loc_s2
])
else:
segs = numpy.hstack([
segs[i0 * nL:i1 * nL].reshape(nL, -1)
for i0, i1 in segs_loc_s1
])
feri['j3c/%d' % k][loc0:loc1] = segs
mem_now = max(comm.allgather(lib.current_memory()[0]))
max_memory = max(2000, min(8000, mydf.max_memory - mem_now))
if numpy.all(aosym_s2):
if gamma_point(kptij_lst):
blksize = max(16, int(max_memory * .5e6 / 8 / nao**2))
else:
blksize = max(16, int(max_memory * .5e6 / 16 / nao**2))
else:
blksize = max(16, int(max_memory * .5e6 / 16 / nao**2 / 2))
log.debug1('max_momory %d MB (%d in use), blksize %d', max_memory, mem_now,
blksize)
t2 = t1
with lib.call_in_background(save) as async_write:
for k, kptji in enumerate(kptij_lst):
for p0, p1 in lib.prange(0, segsize, blksize):
segs = load(k, p0, p1)
async_write(k, p0, p1, segs)
t2 = log.timer_debug1(
'assemble k=%d %d:%d (in %d)' % (k, p0, p1, segsize), *t2)
if 'j3c-chunks' in feri: del (feri['j3c-chunks'])
if 'j3c-kptij' in feri: del (feri['j3c-kptij'])
feri['j3c-kptij'] = kptij_lst
t1 = log.alltimer_debug1('assembling j3c', *t1)
feri.close()
def _assemble(mydf, kptij_lst, j3c_jobs, gen_int3c, ft_fuse, cderi_file, fswap,
log):
t1 = (time.clock(), time.time())
cell = mydf.cell
ao_loc = cell.ao_loc_nr()
nao = ao_loc[-1]
kptis = kptij_lst[:, 0]
kptjs = kptij_lst[:, 1]
kpt_ji = kptjs - kptis
uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji)
aosym_s2 = numpy.einsum('ix->i', abs(kptis - kptjs)) < 1e-9
t2 = t1
j3c_workers = numpy.zeros(len(j3c_jobs), dtype=int)
#for job_id, ish0, ish1 in mpi.work_share_partition(j3c_jobs):
for job_id, ish0, ish1 in mpi.work_stealing_partition(j3c_jobs):
gen_int3c(job_id, ish0, ish1)
t2 = log.alltimer_debug2('int j3c %d' % job_id, *t2)
for k, kpt in enumerate(uniq_kpts):
ft_fuse(job_id, k, ish0, ish1)
t2 = log.alltimer_debug2('ft-fuse %d k %d' % (job_id, k), *t2)
j3c_workers[job_id] = rank
j3c_workers = mpi.allreduce(j3c_workers)
log.debug2('j3c_workers %s', j3c_workers)
t1 = log.timer_debug1('int3c and fuse', *t1)
# Pass 2
# Transpose 3-index tensor and save data in cderi_file
feri = h5py.File(cderi_file, 'w')
nauxs = [fswap['j2c/%d' % k].shape[0] for k, kpt in enumerate(uniq_kpts)]
segsize = (max(nauxs) + mpi.pool.size - 1) // mpi.pool.size
naux0 = rank * segsize
for k, kptij in enumerate(kptij_lst):
naux1 = min(nauxs[uniq_inverse[k]], naux0 + segsize)
nrow = max(0, naux1 - naux0)
if gamma_point(kptij):
dtype = 'f8'
else:
dtype = 'c16'
if aosym_s2[k]:
nao_pair = nao * (nao + 1) // 2
else:
nao_pair = nao * nao
feri.create_dataset('j3c/%d' % k, (nrow, nao_pair),
dtype,
maxshape=(None, nao_pair))
def get_segs_loc(aosym):
off0 = numpy.asarray([ao_loc[i0] for x, i0, i1 in j3c_jobs])
off1 = numpy.asarray([ao_loc[i1] for x, i0, i1 in j3c_jobs])
if aosym: # s2
dims = off1 * (off1 + 1) // 2 - off0 * (off0 + 1) // 2
else:
dims = (off1 - off0) * nao
#dims = numpy.asarray([ao_loc[i1]-ao_loc[i0] for x,i0,i1 in j3c_jobs])
dims = numpy.hstack(
[dims[j3c_workers == w] for w in range(mpi.pool.size)])
job_idx = numpy.hstack(
[numpy.where(j3c_workers == w)[0] for w in range(mpi.pool.size)])
segs_loc = numpy.append(0, numpy.cumsum(dims))
segs_loc = [(segs_loc[j], segs_loc[j + 1])
for j in numpy.argsort(job_idx)]
return segs_loc
segs_loc_s1 = get_segs_loc(False)
segs_loc_s2 = get_segs_loc(True)
job_ids = numpy.where(rank == j3c_workers)[0]
def load(k, p0, p1):
naux1 = nauxs[uniq_inverse[k]]
slices = [(min(i * segsize + p0, naux1), min(i * segsize + p1, naux1))
for i in range(mpi.pool.size)]
segs = []
for p0, p1 in slices:
val = [
fswap['j3c-chunks/%d/%d' % (job, k)][p0:p1].ravel()
for job in job_ids
]
if val:
segs.append(numpy.hstack(val))
else:
segs.append(numpy.zeros(0))
return segs
def save(k, p0, p1, segs):
segs = mpi.alltoall(segs)
naux1 = nauxs[uniq_inverse[k]]
loc0, loc1 = min(p0, naux1 - naux0), min(p1, naux1 - naux0)
nL = loc1 - loc0
if nL > 0:
if aosym_s2[k]:
segs = numpy.hstack([
segs[i0 * nL:i1 * nL].reshape(nL, -1)
for i0, i1 in segs_loc_s2
])
else:
segs = numpy.hstack([
segs[i0 * nL:i1 * nL].reshape(nL, -1)
for i0, i1 in segs_loc_s1
])
feri['j3c/%d' % k][loc0:loc1] = segs
mem_now = max(comm.allgather(lib.current_memory()[0]))
max_memory = max(2000, min(8000, mydf.max_memory - mem_now))
if numpy.all(aosym_s2):
if gamma_point(kptij_lst):
blksize = max(16, int(max_memory * .5e6 / 8 / nao**2))
else:
blksize = max(16, int(max_memory * .5e6 / 16 / nao**2))
else:
blksize = max(16, int(max_memory * .5e6 / 16 / nao**2 / 2))
log.debug1('max_momory %d MB (%d in use), blksize %d', max_memory, mem_now,
blksize)
t2 = t1
with lib.call_in_background(save) as async_write:
for k, kptji in enumerate(kptij_lst):
for p0, p1 in lib.prange(0, segsize, blksize):
segs = load(k, p0, p1)
async_write(k, p0, p1, segs)
t2 = log.timer_debug1(
'assemble k=%d %d:%d (in %d)' % (k, p0, p1, segsize), *t2)
if 'j2c-' in fswap:
j2c_kpts_lists = []
for k, kpt in enumerate(uniq_kpts):
if ('j2c-/%d' % k) in fswap:
adapted_ji_idx = numpy.where(uniq_inverse == k)[0]
j2c_kpts_lists.append(adapted_ji_idx)
for k in numpy.hstack(j2c_kpts_lists):
val = [
numpy.asarray(fswap['j3c-/%d/%d' % (job, k)]).ravel()
for job in job_ids
]
val = mpi.gather(numpy.hstack(val))
if rank == 0:
naux1 = fswap['j3c-/0/%d' % k].shape[0]
if aosym_s2[k]:
v = [
val[i0 * naux1:i1 * naux1].reshape(naux1, -1)
for i0, i1 in segs_loc_s2
]
else:
v = [
val[i0 * naux1:i1 * naux1].reshape(naux1, -1)
for i0, i1 in segs_loc_s1
]
feri['j3c-/%d' % k] = numpy.hstack(v)
if 'j3c-kptij' in feri: del (feri['j3c-kptij'])
feri['j3c-kptij'] = kptij_lst
t1 = log.alltimer_debug1('assembling j3c', *t1)
feri.close()
def get_nuc(mydf, kpts=None):
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = t0 = (time.clock(), time.time())
nkpts = len(kpts_lst)
nao = cell.nao_nr()
nao_pair = nao * (nao+1) // 2
Gv, Gvbase, kws = cell.get_Gv_weights(mydf.gs)
kpt_allow = numpy.zeros(3)
if mydf.eta == 0:
vpplocG = pseudo.pp_int.get_gth_vlocG_part1(cell, Gv)
vpplocG = -numpy.einsum('ij,ij->j', cell.get_SI(Gv), vpplocG)
vpplocG *= kws
vGR = vpplocG.real
vGI = vpplocG.imag
vjR = numpy.zeros((nkpts,nao_pair))
vjI = numpy.zeros((nkpts,nao_pair))
else:
nuccell = copy.copy(cell)
half_sph_norm = .5/numpy.sqrt(numpy.pi)
norm = half_sph_norm/gto.mole._gaussian_int(2, mydf.eta)
chg_env = [mydf.eta, norm]
ptr_eta = cell._env.size
ptr_norm = ptr_eta + 1
chg_bas = [[ia, 0, 1, 1, 0, ptr_eta, ptr_norm, 0] for ia in range(cell.natm)]
nuccell._atm = cell._atm
nuccell._bas = numpy.asarray(chg_bas, dtype=numpy.int32)
nuccell._env = numpy.hstack((cell._env, chg_env))
# PP-loc part1 is handled by fakenuc in _int_nuc_vloc
vj = lib.asarray(mydf._int_nuc_vloc(nuccell, kpts_lst))
vjR = vj.real
vjI = vj.imag
t1 = log.timer_debug1('vnuc pass1: analytic int', *t1)
charge = -cell.atom_charges()
coulG = tools.get_coulG(cell, kpt_allow, gs=mydf.gs, Gv=Gv)
coulG *= kws
aoaux = ft_ao.ft_ao(nuccell, Gv)
vGR = numpy.einsum('i,xi->x', charge, aoaux.real) * coulG
vGI = numpy.einsum('i,xi->x', charge, aoaux.imag) * coulG
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
for k, pqkR, pqkI, p0, p1 \
in mydf.ft_loop(mydf.gs, kpt_allow, kpts_lst,
max_memory=max_memory, aosym='s2'):
# rho_ij(G) nuc(-G) / G^2
# = [Re(rho_ij(G)) + Im(rho_ij(G))*1j] [Re(nuc(G)) - Im(nuc(G))*1j] / G^2
if not gamma_point(kpts_lst[k]):
vjI[k] += numpy.einsum('k,xk->x', vGR[p0:p1], pqkI)
vjI[k] -= numpy.einsum('k,xk->x', vGI[p0:p1], pqkR)
vjR[k] += numpy.einsum('k,xk->x', vGR[p0:p1], pqkR)
vjR[k] += numpy.einsum('k,xk->x', vGI[p0:p1], pqkI)
t1 = log.timer_debug1('contracting Vnuc', *t1)
if mydf.eta != 0 and cell.dimension == 3:
nucbar = sum([z/nuccell.bas_exp(i)[0] for i,z in enumerate(charge)])
nucbar *= numpy.pi/cell.vol
ovlp = cell.pbc_intor('cint1e_ovlp_sph', 1, lib.HERMITIAN, kpts_lst)
for k in range(nkpts):
s = lib.pack_tril(ovlp[k])
vjR[k] -= nucbar * s.real
vjI[k] -= nucbar * s.imag
vj = []
for k, kpt in enumerate(kpts_lst):
if gamma_point(kpt):
vj.append(lib.unpack_tril(vjR[k]))
else:
vj.append(lib.unpack_tril(vjR[k]+vjI[k]*1j))
if kpts is None or numpy.shape(kpts) == (3,):
vj = vj[0]
return vj
def ft_loop(self, gs=None, kpt=numpy.zeros(3), kpts=None, shls_slice=None,
max_memory=4000, aosym='s1'):
'''
Fourier transform iterator for all kpti which satisfy kpt = kpts - kpti
'''
cell = self.cell
if gs is None:
gs = self.gs
if kpts is None:
assert(gamma_point(kpt))
kpts = self.kpts
kpts = numpy.asarray(kpts)
nkpts = len(kpts)
ao_loc = cell.ao_loc_nr()
b = cell.reciprocal_vectors()
Gv, Gvbase, kws = cell.get_Gv_weights(gs)
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
ngs = gxyz.shape[0]
if shls_slice is None:
shls_slice = (0, cell.nbas, 0, cell.nbas)
if aosym == 's2':
assert(shls_slice[2] == 0)
i0 = ao_loc[shls_slice[0]]
i1 = ao_loc[shls_slice[1]]
nij = i1*(i1+1)//2 - i0*(i0+1)//2
else:
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
nij = ni*nj
blksize = max(16, int(max_memory*.9e6/(nij*(nkpts+1)*16)))
blksize = min(blksize, ngs, 16384)
buf = [numpy.zeros(nij*blksize, dtype='D') for k in range(nkpts)]
pqkRbuf = numpy.empty(nij*blksize)
pqkIbuf = numpy.empty(nij*blksize)
if aosym == 's2':
for p0, p1 in self.prange(0, ngs, blksize):
ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
b, gxyz[p0:p1], Gvbase, kpt, kpts, out=buf)
nG = p1 - p0
for k in range(nkpts):
aoao = numpy.ndarray((nG,nij), dtype=numpy.complex128,
order='F', buffer=buf[k])
pqkR = numpy.ndarray((nij,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nij,nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
yield (k, pqkR, pqkI, p0, p1)
aoao[:] = 0 # == buf[k][:] = 0
else:
for p0, p1 in self.prange(0, ngs, blksize):
ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
b, gxyz[p0:p1], Gvbase, kpt, kpts, out=buf)
nG = p1 - p0
for k in range(nkpts):
aoao = numpy.ndarray((nG,ni,nj), dtype=numpy.complex128,
order='F', buffer=buf[k])
pqkR = numpy.ndarray((ni,nj,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ni,nj,nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.transpose(1,2,0)
pqkI[:] = aoao.imag.transpose(1,2,0)
yield (k, pqkR.reshape(-1,nG), pqkI.reshape(-1,nG), p0, p1)
aoao[:] = 0 # == buf[k][:] = 0
def get_nuc(mydf, kpts=None):
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = t0 = (time.clock(), time.time())
nkpts = len(kpts_lst)
nao = cell.nao_nr()
nao_pair = nao * (nao + 1) // 2
Gv, Gvbase, kws = cell.get_Gv_weights(mydf.gs)
kpt_allow = numpy.zeros(3)
if mydf.eta == 0:
vpplocG = pseudo.pp_int.get_gth_vlocG_part1(cell, Gv)
vpplocG = -numpy.einsum('ij,ij->j', cell.get_SI(Gv), vpplocG)
vpplocG *= kws
vGR = vpplocG.real
vGI = vpplocG.imag
vjR = numpy.zeros((nkpts, nao_pair))
vjI = numpy.zeros((nkpts, nao_pair))
else:
nuccell = copy.copy(cell)
half_sph_norm = .5 / numpy.sqrt(numpy.pi)
norm = half_sph_norm / gto.mole._gaussian_int(2, mydf.eta)
chg_env = [mydf.eta, norm]
ptr_eta = cell._env.size
ptr_norm = ptr_eta + 1
chg_bas = [[ia, 0, 1, 1, 0, ptr_eta, ptr_norm, 0]
for ia in range(cell.natm)]
nuccell._atm = cell._atm
nuccell._bas = numpy.asarray(chg_bas, dtype=numpy.int32)
nuccell._env = numpy.hstack((cell._env, chg_env))
# PP-loc part1 is handled by fakenuc in _int_nuc_vloc
vj = lib.asarray(mydf._int_nuc_vloc(nuccell, kpts_lst))
vjR = vj.real
vjI = vj.imag
t1 = log.timer_debug1('vnuc pass1: analytic int', *t1)
charge = -cell.atom_charges()
coulG = tools.get_coulG(cell, kpt_allow, gs=mydf.gs, Gv=Gv)
coulG *= kws
aoaux = ft_ao.ft_ao(nuccell, Gv)
vGR = numpy.einsum('i,xi->x', charge, aoaux.real) * coulG
vGI = numpy.einsum('i,xi->x', charge, aoaux.imag) * coulG
max_memory = max(2000, mydf.max_memory - lib.current_memory()[0])
for k, pqkR, pqkI, p0, p1 \
in mydf.ft_loop(mydf.gs, kpt_allow, kpts_lst,
max_memory=max_memory, aosym='s2'):
# rho_ij(G) nuc(-G) / G^2
# = [Re(rho_ij(G)) + Im(rho_ij(G))*1j] [Re(nuc(G)) - Im(nuc(G))*1j] / G^2
if not gamma_point(kpts_lst[k]):
vjI[k] += numpy.einsum('k,xk->x', vGR[p0:p1], pqkI)
vjI[k] -= numpy.einsum('k,xk->x', vGI[p0:p1], pqkR)
vjR[k] += numpy.einsum('k,xk->x', vGR[p0:p1], pqkR)
vjR[k] += numpy.einsum('k,xk->x', vGI[p0:p1], pqkI)
t1 = log.timer_debug1('contracting Vnuc', *t1)
vj = []
for k, kpt in enumerate(kpts_lst):
if gamma_point(kpt):
vj.append(lib.unpack_tril(vjR[k]))
else:
vj.append(lib.unpack_tril(vjR[k] + vjI[k] * 1j))
if kpts is None or numpy.shape(kpts) == (3, ):
vj = vj[0]
return vj
def _assemble(mydf, kptij_lst, j3c_jobs, gen_int3c, ft_fuse, cderi_file, fswap, log):
t1 = (time.clock(), time.time())
cell = mydf.cell
ao_loc = cell.ao_loc_nr()
nao = ao_loc[-1]
kptis = kptij_lst[:,0]
kptjs = kptij_lst[:,1]
kpt_ji = kptjs - kptis
uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji)
aosym_s2 = numpy.einsum('ix->i', abs(kptis-kptjs)) < 1e-9
t2 = t1
j3c_workers = numpy.zeros(len(j3c_jobs), dtype=int)
#for job_id, ish0, ish1 in mpi.work_share_partition(j3c_jobs):
for job_id, ish0, ish1 in mpi.work_stealing_partition(j3c_jobs):
gen_int3c(job_id, ish0, ish1)
t2 = log.alltimer_debug2('int j3c %d' % job_id, *t2)
for k, kpt in enumerate(uniq_kpts):
ft_fuse(job_id, k, ish0, ish1)
t2 = log.alltimer_debug2('ft-fuse %d k %d' % (job_id, k), *t2)
j3c_workers[job_id] = rank
j3c_workers = mpi.allreduce(j3c_workers)
log.debug2('j3c_workers %s', j3c_workers)
t1 = log.timer_debug1('int3c and fuse', *t1)
# Pass 2
# Transpose 3-index tensor and save data in cderi_file
feri = h5py.File(cderi_file, 'w')
nauxs = [fswap['j2c/%d'%k].shape[0] for k, kpt in enumerate(uniq_kpts)]
segsize = (max(nauxs)+mpi.pool.size-1) // mpi.pool.size
naux0 = rank * segsize
for k, kptij in enumerate(kptij_lst):
naux1 = min(nauxs[uniq_inverse[k]], naux0+segsize)
nrow = max(0, naux1-naux0)
if gamma_point(kptij):
dtype = 'f8'
else:
dtype = 'c16'
if aosym_s2[k]:
nao_pair = nao * (nao+1) // 2
else:
nao_pair = nao * nao
feri.create_dataset('j3c/%d'%k, (nrow,nao_pair), dtype, maxshape=(None,nao_pair))
def get_segs_loc(aosym):
off0 = numpy.asarray([ao_loc[i0] for x,i0,i1 in j3c_jobs])
off1 = numpy.asarray([ao_loc[i1] for x,i0,i1 in j3c_jobs])
if aosym: # s2
dims = off1*(off1+1)//2 - off0*(off0+1)//2
else:
dims = (off1-off0) * nao
#dims = numpy.asarray([ao_loc[i1]-ao_loc[i0] for x,i0,i1 in j3c_jobs])
dims = numpy.hstack([dims[j3c_workers==w] for w in range(mpi.pool.size)])
job_idx = numpy.hstack([numpy.where(j3c_workers==w)[0]
for w in range(mpi.pool.size)])
segs_loc = numpy.append(0, numpy.cumsum(dims))
segs_loc = [(segs_loc[j], segs_loc[j+1]) for j in numpy.argsort(job_idx)]
return segs_loc
segs_loc_s1 = get_segs_loc(False)
segs_loc_s2 = get_segs_loc(True)
job_ids = numpy.where(rank == j3c_workers)[0]
def load(k, p0, p1):
naux1 = nauxs[uniq_inverse[k]]
slices = [(min(i*segsize+p0,naux1), min(i*segsize+p1,naux1))
for i in range(mpi.pool.size)]
segs = []
for p0, p1 in slices:
val = [fswap['j3c-chunks/%d/%d' % (job, k)][p0:p1].ravel()
for job in job_ids]
if val:
segs.append(numpy.hstack(val))
else:
segs.append(numpy.zeros(0))
return segs
def save(k, p0, p1, segs):
segs = mpi.alltoall(segs)
naux1 = nauxs[uniq_inverse[k]]
loc0, loc1 = min(p0, naux1-naux0), min(p1, naux1-naux0)
nL = loc1 - loc0
if nL > 0:
if aosym_s2[k]:
segs = numpy.hstack([segs[i0*nL:i1*nL].reshape(nL,-1)
for i0,i1 in segs_loc_s2])
else:
segs = numpy.hstack([segs[i0*nL:i1*nL].reshape(nL,-1)
for i0,i1 in segs_loc_s1])
feri['j3c/%d'%k][loc0:loc1] = segs
mem_now = max(comm.allgather(lib.current_memory()[0]))
max_memory = max(2000, min(8000, mydf.max_memory - mem_now))
if numpy.all(aosym_s2):
if gamma_point(kptij_lst):
blksize = max(16, int(max_memory*.5e6/8/nao**2))
else:
blksize = max(16, int(max_memory*.5e6/16/nao**2))
else:
blksize = max(16, int(max_memory*.5e6/16/nao**2/2))
log.debug1('max_momory %d MB (%d in use), blksize %d',
max_memory, mem_now, blksize)
t2 = t1
with lib.call_in_background(save) as async_write:
for k, kptji in enumerate(kptij_lst):
for p0, p1 in lib.prange(0, segsize, blksize):
segs = load(k, p0, p1)
async_write(k, p0, p1, segs)
t2 = log.timer_debug1('assemble k=%d %d:%d (in %d)' %
(k, p0, p1, segsize), *t2)
if 'j2c-' in fswap:
j2c_kpts_lists = []
for k, kpt in enumerate(uniq_kpts):
if ('j2c-/%d' % k) in fswap:
adapted_ji_idx = numpy.where(uniq_inverse == k)[0]
j2c_kpts_lists.append(adapted_ji_idx)
for k in numpy.hstack(j2c_kpts_lists):
val = [numpy.asarray(fswap['j3c-/%d/%d' % (job, k)]).ravel()
for job in job_ids]
val = mpi.gather(numpy.hstack(val))
if rank == 0:
naux1 = fswap['j3c-/0/%d'%k].shape[0]
if aosym_s2[k]:
v = [val[i0*naux1:i1*naux1].reshape(naux1,-1)
for i0,i1 in segs_loc_s2]
else:
v = [val[i0*naux1:i1*naux1].reshape(naux1,-1)
for i0,i1 in segs_loc_s1]
feri['j3c-/%d'%k] = numpy.hstack(v)
if 'j3c-kptij' in feri: del(feri['j3c-kptij'])
feri['j3c-kptij'] = kptij_lst
t1 = log.alltimer_debug1('assembling j3c', *t1)
feri.close()
def make_kpt(uniq_kptji_id): # kpt = kptj - kpti
kpt = uniq_kpts[uniq_kptji_id]
log.debug1('kpt = %s', kpt)
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
log.debug1('adapted_ji_idx = %s', adapted_ji_idx)
kLR = kLRs[uniq_kptji_id]
kLI = kLIs[uniq_kptji_id]
if is_zero(kpt): # kpti == kptj
aosym = 's2'
nao_pair = nao*(nao+1)//2
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('cint1e_ovlp_sph', hermi=1, kpts=adapted_kptjs)
for k, ji in enumerate(adapted_ji_idx):
ovlp[k] = lib.pack_tril(ovlp[k])
else:
aosym = 's1'
nao_pair = nao**2
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
# nkptj for 3c-coulomb arrays plus 1 Lpq array
buflen = min(max(int(max_memory*.6*1e6/16/naux/(nkptj+1)), 1), nao_pair)
shranges = _guess_shell_ranges(cell, buflen, aosym)
buflen = max([x[2] for x in shranges])
# +1 for a pqkbuf
if aosym == 's2':
Gblksize = max(16, int(max_memory*.2*1e6/16/buflen/(nkptj+1)))
else:
Gblksize = max(16, int(max_memory*.4*1e6/16/buflen/(nkptj+1)))
Gblksize = min(Gblksize, ngs, 16384)
pqkRbuf = numpy.empty(buflen*Gblksize)
pqkIbuf = numpy.empty(buflen*Gblksize)
# buf for ft_aopair
buf = numpy.zeros((nkptj,buflen*Gblksize), dtype=numpy.complex128)
col1 = 0
for istep, sh_range in enumerate(shranges):
log.debug1('int3c2e [%d/%d], AO [%d:%d], ncol = %d', \
istep+1, len(shranges), *sh_range)
bstart, bend, ncol = sh_range
col0, col1 = col1, col1+ncol
j3cR = []
j3cI = []
for k, idx in enumerate(adapted_ji_idx):
v = numpy.asarray(feri['j3c/%d'%idx][:,col0:col1])
if is_zero(kpt):
for i, c in enumerate(vbar):
if c != 0:
v[i] -= c * ovlp[k][col0:col1]
j3cR.append(numpy.asarray(v.real, order='C'))
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
j3cI.append(None)
else:
j3cI.append(numpy.asarray(v.imag, order='C'))
if aosym == 's2':
shls_slice = (bstart, bend, 0, bend)
for p0, p1 in lib.prange(0, ngs, Gblksize):
ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
b, gxyz[p0:p1], Gvbase, kpt,
adapted_kptjs, out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = numpy.ndarray((nG,ncol), dtype=numpy.complex128,
order='F', buffer=buf[k])
pqkR = numpy.ndarray((ncol,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol,nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
aoao[:] = 0
lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k][naux:], 1)
lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k][naux:], 1)
if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])):
lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k][naux:], 1)
lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k][naux:], 1)
else:
shls_slice = (bstart, bend, 0, cell.nbas)
ni = ncol // nao
for p0, p1 in lib.prange(0, ngs, Gblksize):
ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
b, gxyz[p0:p1], Gvbase, kpt,
adapted_kptjs, out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = numpy.ndarray((nG,ni,nao), dtype=numpy.complex128,
order='F', buffer=buf[k])
pqkR = numpy.ndarray((ni,nao,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ni,nao,nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.transpose(1,2,0)
pqkI[:] = aoao.imag.transpose(1,2,0)
aoao[:] = 0
pqkR = pqkR.reshape(-1,nG)
pqkI = pqkI.reshape(-1,nG)
zdotCN(kLR[p0:p1].T, kLI[p0:p1].T, pqkR.T, pqkI.T,
-1, j3cR[k][naux:], j3cI[k][naux:], 1)
for k, ji in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
v = fuse(j3cR[k])
else:
v = fuse(j3cR[k] + j3cI[k] * 1j)
v = scipy.linalg.solve_triangular(j2c[uniq_kptji_id], v,
lower=True, overwrite_b=True)
feri['j3c/%d'%ji][:naux,col0:col1] = v
def ft_fuse(job_id, uniq_kptji_id, sh0, sh1):
kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
j2c = numpy.asarray(fswap['j2c/%d' % uniq_kptji_id])
j2ctag = j2ctags[uniq_kptji_id]
naux0 = j2c.shape[0]
if ('j2c-/%d' % uniq_kptji_id) in fswap:
j2c_negative = numpy.asarray(fswap['j2c-/%d' % uniq_kptji_id])
else:
j2c_negative = None
if is_zero(kpt):
aosym = 's2'
else:
aosym = 's1'
if aosym == 's2' and cell.dimension == 3:
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('int1e_ovlp', hermi=1, kpts=adapted_kptjs)
ovlp = [lib.pack_tril(s) for s in ovlp]
j3cR = [None] * nkptj
j3cI = [None] * nkptj
i0 = ao_loc[sh0]
i1 = ao_loc[sh1]
for k, idx in enumerate(adapted_ji_idx):
key = 'j3c-chunks/%d/%d' % (job_id, idx)
v = numpy.asarray(fswap[key])
if aosym == 's2' and cell.dimension == 3:
for i in numpy.where(vbar != 0)[0]:
v[i] -= vbar[i] * ovlp[k][i0 * (i0 + 1) // 2:i1 *
(i1 + 1) // 2].ravel()
j3cR[k] = numpy.asarray(v.real, order='C')
if v.dtype == numpy.complex128:
j3cI[k] = numpy.asarray(v.imag, order='C')
v = None
ncol = j3cR[0].shape[1]
Gblksize = max(16, int(max_memory * 1e6 / 16 / ncol /
(nkptj + 1))) # +1 for pqkRbuf/pqkIbuf
Gblksize = min(Gblksize, ngrids, 16384)
pqkRbuf = numpy.empty(ncol * Gblksize)
pqkIbuf = numpy.empty(ncol * Gblksize)
buf = numpy.empty(nkptj * ncol * Gblksize, dtype=numpy.complex128)
log.alldebug2('job_id %d blksize (%d,%d)', job_id, Gblksize, ncol)
wcoulG = mydf.weighted_coulG(kpt, False, mesh)
fused_cell_slice = (auxcell.nbas, fused_cell.nbas)
if aosym == 's2':
shls_slice = (sh0, sh1, 0, sh1)
else:
shls_slice = (sh0, sh1, 0, cell.nbas)
for p0, p1 in lib.prange(0, ngrids, Gblksize):
Gaux = ft_ao.ft_ao(fused_cell, Gv[p0:p1], fused_cell_slice, b,
gxyz[p0:p1], Gvbase, kpt)
Gaux *= wcoulG[p0:p1, None]
kLR = Gaux.real.copy('C')
kLI = Gaux.imag.copy('C')
Gaux = None
dat = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
kpt,
adapted_kptjs,
out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = dat[k].reshape(nG, ncol)
pqkR = numpy.ndarray((ncol, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol, nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
lib.dot(kLR.T, pqkR.T, -1, j3cR[k][naux:], 1)
lib.dot(kLI.T, pqkI.T, -1, j3cR[k][naux:], 1)
if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])):
lib.dot(kLR.T, pqkI.T, -1, j3cI[k][naux:], 1)
lib.dot(kLI.T, pqkR.T, 1, j3cI[k][naux:], 1)
kLR = kLI = None
for k, idx in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
v = fuse(j3cR[k])
else:
v = fuse(j3cR[k] + j3cI[k] * 1j)
if j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c,
v,
lower=True,
overwrite_b=True)
fswap['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = v
else:
fswap['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = lib.dot(
j2c, v)
# low-dimension systems
if j2c_negative is not None:
fswap['j3c-/%d/%d' % (job_id, idx)] = lib.dot(j2c_negative, v)
def ft_fuse(job_id, uniq_kptji_id, sh0, sh1):
kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
Gaux = ft_ao.ft_ao(fused_cell, Gv, None, b, gxyz, Gvbase, kpt).T
Gaux = fuse(Gaux)
Gaux *= mydf.weighted_coulG(kpt, False, mesh)
kLR = lib.transpose(numpy.asarray(Gaux.real, order='C'))
kLI = lib.transpose(numpy.asarray(Gaux.imag, order='C'))
j2c = numpy.asarray(fswap['j2c/%d'%uniq_kptji_id])
j2ctag = j2ctags[uniq_kptji_id]
naux0 = j2c.shape[0]
if ('j2c-/%d' % uniq_kptji_id) in fswap:
j2c_negative = numpy.asarray(fswap['j2c-/%d'%uniq_kptji_id])
else:
j2c_negative = None
if is_zero(kpt):
aosym = 's2'
else:
aosym = 's1'
if aosym == 's2' and cell.dimension == 3:
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('int1e_ovlp', hermi=1, kpts=adapted_kptjs)
ovlp = [lib.pack_tril(s) for s in ovlp]
j3cR = [None] * nkptj
j3cI = [None] * nkptj
i0 = ao_loc[sh0]
i1 = ao_loc[sh1]
for k, idx in enumerate(adapted_ji_idx):
key = 'j3c-chunks/%d/%d' % (job_id, idx)
v = fuse(numpy.asarray(fswap[key]))
if aosym == 's2' and cell.dimension == 3:
for i in numpy.where(vbar != 0)[0]:
v[i] -= vbar[i] * ovlp[k][i0*(i0+1)//2:i1*(i1+1)//2].ravel()
j3cR[k] = numpy.asarray(v.real, order='C')
if v.dtype == numpy.complex128:
j3cI[k] = numpy.asarray(v.imag, order='C')
v = None
ncol = j3cR[0].shape[1]
Gblksize = max(16, int(max_memory*1e6/16/ncol/(nkptj+1))) # +1 for pqkRbuf/pqkIbuf
Gblksize = min(Gblksize, ngrids, 16384)
pqkRbuf = numpy.empty(ncol*Gblksize)
pqkIbuf = numpy.empty(ncol*Gblksize)
buf = numpy.empty(nkptj*ncol*Gblksize, dtype=numpy.complex128)
log.alldebug2(' blksize (%d,%d)', Gblksize, ncol)
if aosym == 's2':
shls_slice = (sh0, sh1, 0, sh1)
else:
shls_slice = (sh0, sh1, 0, cell.nbas)
for p0, p1 in lib.prange(0, ngrids, Gblksize):
dat = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym, b,
gxyz[p0:p1], Gvbase, kpt,
adapted_kptjs, out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = dat[k].reshape(nG,ncol)
pqkR = numpy.ndarray((ncol,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol,nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k], 1)
lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k], 1)
if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])):
lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k], 1)
lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k], 1)
for k, idx in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
v = j3cR[k]
else:
v = j3cR[k] + j3cI[k] * 1j
if j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c, v, lower=True, overwrite_b=True)
fswap['j3c-chunks/%d/%d'%(job_id,idx)][:naux0] = v
else:
fswap['j3c-chunks/%d/%d'%(job_id,idx)][:naux0] = lib.dot(j2c, v)
# low-dimension systems
if j2c_negative is not None:
fswap['j3c-/%d/%d'%(job_id,idx)] = lib.dot(j2c_negative, v)
def _make_j3c(mydf, cell, auxcell, kptij_lst, cderi_file):
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = t0 = (time.clock(), time.time())
fused_cell, fuse = fuse_auxcell(mydf, mydf.auxcell)
ao_loc = cell.ao_loc_nr()
nao = ao_loc[-1]
naux = auxcell.nao_nr()
nkptij = len(kptij_lst)
mesh = mydf.mesh
Gv, Gvbase, kws = cell.get_Gv_weights(mesh)
b = cell.reciprocal_vectors()
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
ngrids = gxyz.shape[0]
kptis = kptij_lst[:, 0]
kptjs = kptij_lst[:, 1]
kpt_ji = kptjs - kptis
uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji)
log.debug('Num uniq kpts %d', len(uniq_kpts))
log.debug2('uniq_kpts %s', uniq_kpts)
# j2c ~ (-kpt_ji | kpt_ji)
j2c = fused_cell.pbc_intor('int2c2e', hermi=1, kpts=uniq_kpts)
j2ctags = []
t1 = log.timer_debug1('2c2e', *t1)
swapfile = tempfile.NamedTemporaryFile(dir=os.path.dirname(cderi_file))
fswap = lib.H5TmpFile(swapfile.name)
# Unlink swapfile to avoid trash
swapfile = None
mem_now = max(comm.allgather(lib.current_memory()[0]))
max_memory = max(2000, mydf.max_memory - mem_now)
blksize = max(2048, int(max_memory * .5e6 / 16 / fused_cell.nao_nr()))
log.debug2('max_memory %s (MB) blocksize %s', max_memory, blksize)
for k, kpt in enumerate(uniq_kpts):
coulG = mydf.weighted_coulG(kpt, False, mesh)
j2c_k = numpy.zeros_like(j2c[k])
for p0, p1 in mydf.prange(0, ngrids, blksize):
aoaux = ft_ao.ft_ao(fused_cell, Gv[p0:p1], None, b, gxyz[p0:p1],
Gvbase, kpt).T
LkR = numpy.asarray(aoaux.real, order='C')
LkI = numpy.asarray(aoaux.imag, order='C')
aoaux = None
if is_zero(kpt): # kpti == kptj
j2c_k[naux:] += lib.ddot(LkR[naux:] * coulG[p0:p1], LkR.T)
j2c_k[naux:] += lib.ddot(LkI[naux:] * coulG[p0:p1], LkI.T)
else:
j2cR, j2cI = zdotCN(LkR[naux:] * coulG[p0:p1],
LkI[naux:] * coulG[p0:p1], LkR.T, LkI.T)
j2c_k[naux:] += j2cR + j2cI * 1j
kLR = kLI = None
j2c_k[:naux, naux:] = j2c_k[naux:, :naux].conj().T
j2c[k] -= mpi.allreduce(j2c_k)
j2c[k] = fuse(fuse(j2c[k]).T).T
try:
fswap['j2c/%d' % k] = scipy.linalg.cholesky(j2c[k], lower=True)
j2ctags.append('CD')
except scipy.linalg.LinAlgError as e:
#msg =('===================================\n'
# 'J-metric not positive definite.\n'
# 'It is likely that mesh is not enough.\n'
# '===================================')
#log.error(msg)
#raise scipy.linalg.LinAlgError('\n'.join([str(e), msg]))
w, v = scipy.linalg.eigh(j2c[k])
log.debug2('metric linear dependency for kpt %s', k)
log.debug2('cond = %.4g, drop %d bfns', w[0] / w[-1],
numpy.count_nonzero(w < mydf.linear_dep_threshold))
v1 = v[:, w > mydf.linear_dep_threshold].T.conj()
v1 /= numpy.sqrt(w[w > mydf.linear_dep_threshold]).reshape(-1, 1)
fswap['j2c/%d' % k] = v1
if cell.dimension == 2 and cell.low_dim_ft_type != 'inf_vacuum':
idx = numpy.where(w < -mydf.linear_dep_threshold)[0]
if len(idx) > 0:
fswap['j2c-/%d' % k] = (v[:, idx] /
numpy.sqrt(-w[idx])).conj().T
w = v = v1 = None
j2ctags.append('eig')
j2c = coulG = None
aosym_s2 = numpy.einsum('ix->i', abs(kptis - kptjs)) < 1e-9
j_only = numpy.all(aosym_s2)
if gamma_point(kptij_lst):
dtype = 'f8'
else:
dtype = 'c16'
t1 = log.timer_debug1('aoaux and int2c', *t1)
# Estimates the buffer size based on the last contraction in G-space.
# This contraction requires to hold nkptj copies of (naux,?) array
# simultaneously in memory.
mem_now = max(comm.allgather(lib.current_memory()[0]))
max_memory = max(2000, mydf.max_memory - mem_now)
nkptj_max = max((uniq_inverse == x).sum() for x in set(uniq_inverse))
buflen = max(
int(
min(max_memory * .5e6 / 16 / naux / (nkptj_max + 2) / nao,
nao / 3 / mpi.pool.size)), 1)
chunks = (buflen, nao)
j3c_jobs = grids2d_int3c_jobs(cell, auxcell, kptij_lst, chunks, j_only)
log.debug1('max_memory = %d MB (%d in use) chunks %s', max_memory,
mem_now, chunks)
log.debug2('j3c_jobs %s', j3c_jobs)
if j_only:
int3c = wrap_int3c(cell, fused_cell, 'int3c2e', 's2', 1, kptij_lst)
else:
int3c = wrap_int3c(cell, fused_cell, 'int3c2e', 's1', 1, kptij_lst)
idxb = numpy.tril_indices(nao)
idxb = (idxb[0] * nao + idxb[1]).astype('i')
aux_loc = fused_cell.ao_loc_nr('ssc' in 'int3c2e')
def gen_int3c(job_id, ish0, ish1):
dataname = 'j3c-chunks/%d' % job_id
i0 = ao_loc[ish0]
i1 = ao_loc[ish1]
dii = i1 * (i1 + 1) // 2 - i0 * (i0 + 1) // 2
if j_only:
dij = dii
buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dii + dii)))
else:
dij = (i1 - i0) * nao
buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dij + dij)))
auxranges = balance_segs(aux_loc[1:] - aux_loc[:-1], buflen)
buflen = max([x[2] for x in auxranges])
buf = numpy.empty(nkptij * dij * buflen, dtype=dtype)
buf1 = numpy.empty(dij * buflen, dtype=dtype)
naux = aux_loc[-1]
for kpt_id, kptij in enumerate(kptij_lst):
key = '%s/%d' % (dataname, kpt_id)
if aosym_s2[kpt_id]:
shape = (naux, dii)
else:
shape = (naux, dij)
if gamma_point(kptij):
fswap.create_dataset(key, shape, 'f8')
else:
fswap.create_dataset(key, shape, 'c16')
naux0 = 0
for istep, auxrange in enumerate(auxranges):
log.alldebug2("aux_e1 job_id %d step %d", job_id, istep)
sh0, sh1, nrow = auxrange
sub_slice = (ish0, ish1, 0, cell.nbas, sh0, sh1)
mat = numpy.ndarray((nkptij, dij, nrow), dtype=dtype, buffer=buf)
mat = int3c(sub_slice, mat)
for k, kptij in enumerate(kptij_lst):
h5dat = fswap['%s/%d' % (dataname, k)]
v = lib.transpose(mat[k], out=buf1)
if not j_only and aosym_s2[k]:
idy = idxb[i0 * (i0 + 1) // 2:i1 *
(i1 + 1) // 2] - i0 * nao
out = numpy.ndarray((nrow, dii),
dtype=v.dtype,
buffer=mat[k])
v = numpy.take(v, idy, axis=1, out=out)
if gamma_point(kptij):
h5dat[naux0:naux0 + nrow] = v.real
else:
h5dat[naux0:naux0 + nrow] = v
naux0 += nrow
def ft_fuse(job_id, uniq_kptji_id, sh0, sh1):
kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
j2c = numpy.asarray(fswap['j2c/%d' % uniq_kptji_id])
j2ctag = j2ctags[uniq_kptji_id]
naux0 = j2c.shape[0]
if ('j2c-/%d' % uniq_kptji_id) in fswap:
j2c_negative = numpy.asarray(fswap['j2c-/%d' % uniq_kptji_id])
else:
j2c_negative = None
if is_zero(kpt):
aosym = 's2'
else:
aosym = 's1'
if aosym == 's2' and cell.dimension == 3:
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('int1e_ovlp', hermi=1, kpts=adapted_kptjs)
ovlp = [lib.pack_tril(s) for s in ovlp]
j3cR = [None] * nkptj
j3cI = [None] * nkptj
i0 = ao_loc[sh0]
i1 = ao_loc[sh1]
for k, idx in enumerate(adapted_ji_idx):
key = 'j3c-chunks/%d/%d' % (job_id, idx)
v = numpy.asarray(fswap[key])
if aosym == 's2' and cell.dimension == 3:
for i in numpy.where(vbar != 0)[0]:
v[i] -= vbar[i] * ovlp[k][i0 * (i0 + 1) // 2:i1 *
(i1 + 1) // 2].ravel()
j3cR[k] = numpy.asarray(v.real, order='C')
if v.dtype == numpy.complex128:
j3cI[k] = numpy.asarray(v.imag, order='C')
v = None
ncol = j3cR[0].shape[1]
Gblksize = max(16, int(max_memory * 1e6 / 16 / ncol /
(nkptj + 1))) # +1 for pqkRbuf/pqkIbuf
Gblksize = min(Gblksize, ngrids, 16384)
pqkRbuf = numpy.empty(ncol * Gblksize)
pqkIbuf = numpy.empty(ncol * Gblksize)
buf = numpy.empty(nkptj * ncol * Gblksize, dtype=numpy.complex128)
log.alldebug2('job_id %d blksize (%d,%d)', job_id, Gblksize, ncol)
wcoulG = mydf.weighted_coulG(kpt, False, mesh)
fused_cell_slice = (auxcell.nbas, fused_cell.nbas)
if aosym == 's2':
shls_slice = (sh0, sh1, 0, sh1)
else:
shls_slice = (sh0, sh1, 0, cell.nbas)
for p0, p1 in lib.prange(0, ngrids, Gblksize):
Gaux = ft_ao.ft_ao(fused_cell, Gv[p0:p1], fused_cell_slice, b,
gxyz[p0:p1], Gvbase, kpt)
Gaux *= wcoulG[p0:p1, None]
kLR = Gaux.real.copy('C')
kLI = Gaux.imag.copy('C')
Gaux = None
dat = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
kpt,
adapted_kptjs,
out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = dat[k].reshape(nG, ncol)
pqkR = numpy.ndarray((ncol, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol, nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
lib.dot(kLR.T, pqkR.T, -1, j3cR[k][naux:], 1)
lib.dot(kLI.T, pqkI.T, -1, j3cR[k][naux:], 1)
if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])):
lib.dot(kLR.T, pqkI.T, -1, j3cI[k][naux:], 1)
lib.dot(kLI.T, pqkR.T, 1, j3cI[k][naux:], 1)
kLR = kLI = None
for k, idx in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
v = fuse(j3cR[k])
else:
v = fuse(j3cR[k] + j3cI[k] * 1j)
if j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c,
v,
lower=True,
overwrite_b=True)
fswap['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = v
else:
fswap['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = lib.dot(
j2c, v)
# low-dimension systems
if j2c_negative is not None:
fswap['j3c-/%d/%d' % (job_id, idx)] = lib.dot(j2c_negative, v)
_assemble(mydf, kptij_lst, j3c_jobs, gen_int3c, ft_fuse, cderi_file, fswap,
log)
def _make_j3c(mydf, cell, auxcell, kptij_lst, cderi_file):
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = t0 = (time.clock(), time.time())
fused_cell, fuse = fuse_auxcell(mydf, mydf.auxcell)
ao_loc = cell.ao_loc_nr()
nao = ao_loc[-1]
naux = auxcell.nao_nr()
nkptij = len(kptij_lst)
mesh = mydf.mesh
Gv, Gvbase, kws = cell.get_Gv_weights(mesh)
b = cell.reciprocal_vectors()
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
ngrids = gxyz.shape[0]
kptis = kptij_lst[:,0]
kptjs = kptij_lst[:,1]
kpt_ji = kptjs - kptis
uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji)
log.debug('Num uniq kpts %d', len(uniq_kpts))
log.debug2('uniq_kpts %s', uniq_kpts)
# j2c ~ (-kpt_ji | kpt_ji)
j2c = fused_cell.pbc_intor('int2c2e', hermi=1, kpts=uniq_kpts)
j2ctags = []
t1 = log.timer_debug1('2c2e', *t1)
swapfile = tempfile.NamedTemporaryFile(dir=os.path.dirname(cderi_file))
fswap = lib.H5TmpFile(swapfile.name)
# Unlink swapfile to avoid trash
swapfile = None
for k, kpt in enumerate(uniq_kpts):
coulG = mydf.weighted_coulG(kpt, False, mesh)
j2c[k] = fuse(fuse(j2c[k]).T).T.copy()
j2c_k = numpy.zeros_like(j2c[k])
for p0, p1 in mydf.mpi_prange(0, ngrids):
aoaux = ft_ao.ft_ao(fused_cell, Gv[p0:p1], None, b, gxyz[p0:p1], Gvbase, kpt).T
aoaux = fuse(aoaux)
LkR = numpy.asarray(aoaux.real, order='C')
LkI = numpy.asarray(aoaux.imag, order='C')
aoaux = None
if is_zero(kpt): # kpti == kptj
j2cR = lib.dot(LkR*coulG[p0:p1], LkR.T)
j2c_k += lib.dot(LkI*coulG[p0:p1], LkI.T, 1, j2cR, 1)
else:
# aoaux ~ kpt_ij, aoaux.conj() ~ kpt_kl
j2cR, j2cI = zdotCN(LkR*coulG[p0:p1], LkI*coulG[p0:p1], LkR.T, LkI.T)
j2c_k += j2cR + j2cI * 1j
LkR = LkI = None
j2c[k] -= mpi.allreduce(j2c_k)
try:
fswap['j2c/%d'%k] = scipy.linalg.cholesky(j2c[k], lower=True)
j2ctags.append('CD')
except scipy.linalg.LinAlgError:
w, v = scipy.linalg.eigh(j2c[k])
log.debug2('metric linear dependency for kpt %s', k)
log.debug2('cond = %.4g, drop %d bfns',
w[0]/w[-1], numpy.count_nonzero(w<mydf.linear_dep_threshold))
v1 = v[:,w>mydf.linear_dep_threshold].T.conj()
v1 /= numpy.sqrt(w[w>mydf.linear_dep_threshold]).reshape(-1,1)
fswap['j2c/%d'%k] = v1
if cell.dimension == 2 and cell.low_dim_ft_type != 'inf_vacuum':
idx = numpy.where(w < -mydf.linear_dep_threshold)[0]
if len(idx) > 0:
fswap['j2c-/%d'%k] = (v[:,idx]/numpy.sqrt(-w[idx])).conj().T
w = v = v1 = v2 = None
j2ctags.append('eig')
aoaux = kLR = kLI = j2cR = j2cI = coulG = None
j2c = None
aosym_s2 = numpy.einsum('ix->i', abs(kptis-kptjs)) < 1e-9
j_only = numpy.all(aosym_s2)
if gamma_point(kptij_lst):
dtype = 'f8'
else:
dtype = 'c16'
t1 = log.timer_debug1('aoaux and int2c', *t1)
# Estimates the buffer size based on the last contraction in G-space.
# This contraction requires to hold nkptj copies of (naux,?) array
# simultaneously in memory.
mem_now = max(comm.allgather(lib.current_memory()[0]))
max_memory = max(2000, mydf.max_memory - mem_now)
nkptj_max = max((uniq_inverse==x).sum() for x in set(uniq_inverse))
buflen = max(int(min(max_memory*.5e6/16/naux/(nkptj_max+2)/nao,
nao/3/mpi.pool.size)), 1)
chunks = (buflen, nao)
j3c_jobs = mpi_df.grids2d_int3c_jobs(cell, auxcell, kptij_lst, chunks, j_only)
log.debug1('max_memory = %d MB (%d in use) chunks %s',
max_memory, mem_now, chunks)
log.debug2('j3c_jobs %s', j3c_jobs)
if j_only:
int3c = wrap_int3c(cell, fused_cell, 'int3c2e', 's2', 1, kptij_lst)
else:
int3c = wrap_int3c(cell, fused_cell, 'int3c2e', 's1', 1, kptij_lst)
idxb = numpy.tril_indices(nao)
idxb = (idxb[0] * nao + idxb[1]).astype('i')
aux_loc = fused_cell.ao_loc_nr(fused_cell.cart)
def gen_int3c(job_id, ish0, ish1):
dataname = 'j3c-chunks/%d' % job_id
i0 = ao_loc[ish0]
i1 = ao_loc[ish1]
dii = i1*(i1+1)//2 - i0*(i0+1)//2
dij = (i1 - i0) * nao
if j_only:
buflen = max(8, int(max_memory*1e6/16/(nkptij*dii+dii)))
else:
buflen = max(8, int(max_memory*1e6/16/(nkptij*dij+dij)))
auxranges = balance_segs(aux_loc[1:]-aux_loc[:-1], buflen)
buflen = max([x[2] for x in auxranges])
buf = numpy.empty(nkptij*dij*buflen, dtype=dtype)
buf1 = numpy.empty(dij*buflen, dtype=dtype)
naux = aux_loc[-1]
for kpt_id, kptij in enumerate(kptij_lst):
key = '%s/%d' % (dataname, kpt_id)
if aosym_s2[kpt_id]:
shape = (naux, dii)
else:
shape = (naux, dij)
if gamma_point(kptij):
fswap.create_dataset(key, shape, 'f8')
else:
fswap.create_dataset(key, shape, 'c16')
naux0 = 0
for istep, auxrange in enumerate(auxranges):
log.alldebug2("aux_e1 job_id %d step %d", job_id, istep)
sh0, sh1, nrow = auxrange
sub_slice = (ish0, ish1, 0, cell.nbas, sh0, sh1)
if j_only:
mat = numpy.ndarray((nkptij,dii,nrow), dtype=dtype, buffer=buf)
else:
mat = numpy.ndarray((nkptij,dij,nrow), dtype=dtype, buffer=buf)
mat = int3c(sub_slice, mat)
for k, kptij in enumerate(kptij_lst):
h5dat = fswap['%s/%d'%(dataname,k)]
v = lib.transpose(mat[k], out=buf1)
if not j_only and aosym_s2[k]:
idy = idxb[i0*(i0+1)//2:i1*(i1+1)//2] - i0 * nao
out = numpy.ndarray((nrow,dii), dtype=v.dtype, buffer=mat[k])
v = numpy.take(v, idy, axis=1, out=out)
if gamma_point(kptij):
h5dat[naux0:naux0+nrow] = v.real
else:
h5dat[naux0:naux0+nrow] = v
naux0 += nrow
def ft_fuse(job_id, uniq_kptji_id, sh0, sh1):
kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
Gaux = ft_ao.ft_ao(fused_cell, Gv, None, b, gxyz, Gvbase, kpt).T
Gaux = fuse(Gaux)
Gaux *= mydf.weighted_coulG(kpt, False, mesh)
kLR = lib.transpose(numpy.asarray(Gaux.real, order='C'))
kLI = lib.transpose(numpy.asarray(Gaux.imag, order='C'))
j2c = numpy.asarray(fswap['j2c/%d'%uniq_kptji_id])
j2ctag = j2ctags[uniq_kptji_id]
naux0 = j2c.shape[0]
if ('j2c-/%d' % uniq_kptji_id) in fswap:
j2c_negative = numpy.asarray(fswap['j2c-/%d'%uniq_kptji_id])
else:
j2c_negative = None
if is_zero(kpt):
aosym = 's2'
else:
aosym = 's1'
if aosym == 's2' and cell.dimension == 3:
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('int1e_ovlp', hermi=1, kpts=adapted_kptjs)
ovlp = [lib.pack_tril(s) for s in ovlp]
j3cR = [None] * nkptj
j3cI = [None] * nkptj
i0 = ao_loc[sh0]
i1 = ao_loc[sh1]
for k, idx in enumerate(adapted_ji_idx):
key = 'j3c-chunks/%d/%d' % (job_id, idx)
v = fuse(numpy.asarray(fswap[key]))
if aosym == 's2' and cell.dimension == 3:
for i in numpy.where(vbar != 0)[0]:
v[i] -= vbar[i] * ovlp[k][i0*(i0+1)//2:i1*(i1+1)//2].ravel()
j3cR[k] = numpy.asarray(v.real, order='C')
if v.dtype == numpy.complex128:
j3cI[k] = numpy.asarray(v.imag, order='C')
v = None
ncol = j3cR[0].shape[1]
Gblksize = max(16, int(max_memory*1e6/16/ncol/(nkptj+1))) # +1 for pqkRbuf/pqkIbuf
Gblksize = min(Gblksize, ngrids, 16384)
pqkRbuf = numpy.empty(ncol*Gblksize)
pqkIbuf = numpy.empty(ncol*Gblksize)
buf = numpy.empty(nkptj*ncol*Gblksize, dtype=numpy.complex128)
log.alldebug2(' blksize (%d,%d)', Gblksize, ncol)
if aosym == 's2':
shls_slice = (sh0, sh1, 0, sh1)
else:
shls_slice = (sh0, sh1, 0, cell.nbas)
for p0, p1 in lib.prange(0, ngrids, Gblksize):
dat = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym, b,
gxyz[p0:p1], Gvbase, kpt,
adapted_kptjs, out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = dat[k].reshape(nG,ncol)
pqkR = numpy.ndarray((ncol,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol,nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k], 1)
lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k], 1)
if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])):
lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k], 1)
lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k], 1)
for k, idx in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
v = j3cR[k]
else:
v = j3cR[k] + j3cI[k] * 1j
if j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c, v, lower=True, overwrite_b=True)
fswap['j3c-chunks/%d/%d'%(job_id,idx)][:naux0] = v
else:
fswap['j3c-chunks/%d/%d'%(job_id,idx)][:naux0] = lib.dot(j2c, v)
# low-dimension systems
if j2c_negative is not None:
fswap['j3c-/%d/%d'%(job_id,idx)] = lib.dot(j2c_negative, v)
mpi_df._assemble(mydf, kptij_lst, j3c_jobs, gen_int3c, ft_fuse, cderi_file, fswap, log)