def _ewald_exxdiv_1d2d(cell, kpts, dms, vk, kpts_band=None):
s = cell.pbc_intor('int1e_ovlp', hermi=1, kpts=kpts)
madelung = tools.pbc.madelung(cell, kpts)
Gv, Gvbase, kws = cell.get_Gv_weights(cell.mesh)
G0idx, SI_on_z = gto.cell._SI_for_uniform_model_charge(cell, Gv)
coulG = 4 * numpy.pi / numpy.linalg.norm(Gv[G0idx], axis=1)**2
wcoulG = coulG * kws[G0idx]
aoao_ij = ft_ao._ft_aopair_kpts(cell, Gv[G0idx], kptjs=kpts)
aoao_kl = ft_ao._ft_aopair_kpts(cell, -Gv[G0idx], kptjs=kpts)
def _contract_(vk, dms, s, aoao_ij, aoao_kl, kweight):
# Without removing aoao(Gx=0,Gy=0), the summation of vk and ewald probe
# charge correction (as _ewald_exxdiv_3d did) gives the reasonable
# finite value for vk. Here madelung constant and vk were calculated
# without (Gx=0,Gy=0). The code below restores the (Gx=0,Gy=0) part.
madelung_mod = numpy.einsum('g,g,g', SI_on_z.conj(), wcoulG, SI_on_z)
tmp_ij = numpy.einsum('gij,g,g->ij', aoao_ij, wcoulG, SI_on_z.conj())
tmp_kl = numpy.einsum('gij,g,g->ij', aoao_kl, wcoulG, SI_on_z)
for i, dm in enumerate(dms):
#:aoaomod_ij = aoao_ij - numpy.einsum('g,ij->gij', SI_on_z , s)
#:aoaomod_kl = aoao_kl - numpy.einsum('g,ij->gij', SI_on_z.conj(), s)
#:ktmp = kweight * lib.einsum('gij,jk,g,gkl->il', aoao_ij , dm, wcoulG, aoao_kl )
#:ktmp -= kweight * lib.einsum('gij,jk,g,gkl->il', aoaomod_ij, dm, wcoulG, aoaomod_kl)
#:ktmp += (madelung - kweight*wcoulG.sum()) * reduce(numpy.dot, (s, dm, s))
ktmp = kweight * lib.einsum('ij,jk,kl->il', tmp_ij, dm, s)
ktmp += kweight * lib.einsum('ij,jk,kl->il', s, dm, tmp_kl)
ktmp += (
(madelung - kweight * wcoulG.sum() - kweight * madelung_mod) *
reduce(numpy.dot, (s, dm, s)))
if vk.dtype == numpy.double:
vk[i] += ktmp.real
else:
vk[i] += ktmp
if kpts is None:
_contract_(vk, dms, s, aoao_ij[0], aoao_kl[0], 1)
elif numpy.shape(kpts) == (3, ):
if kpts_band is None or is_zero(kpts_band - kpts):
_contract_(vk, dms, s, aoao_ij[0], aoao_kl[0], 1)
elif kpts_band is None or numpy.array_equal(kpts, kpts_band):
nkpts = len(kpts)
for k in range(nkpts):
_contract_(vk[:, k], dms[:, k], s[k], aoao_ij[k], aoao_kl[k],
1. / nkpts)
else:
nkpts = len(kpts)
for k, kpt in enumerate(kpts):
for kp in member(kpt, kpts_band.reshape(-1, 3)):
_contract_(vk[:, kp], dms[:, k], s[k], aoao_ij[k], aoao_kl[k],
1. / nkpts)
def pw_contract(istep, sh_range, j3cR, j3cI):
bstart, bend, ncol = sh_range
if aosym == 's2':
shls_slice = (bstart, bend, 0, bend)
else:
shls_slice = (bstart, bend, 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, ji 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)
else:
v = lib.dot(j2c, v)
feri['j3c/%d/%d'%(ji,istep)] = v
def ft_loop(self, cell, gs=None, kpt=numpy.zeros(3),
kpts=None, shls_slice=None, max_memory=4000):
'''
Fourier transform iterator for all kpti which satisfy kpt = kpts - kpti
'''
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)
nao = cell.nao_nr()
gxyz = lib.cartesian_prod((numpy.append(range(gs[0]+1), range(-gs[0],0)),
numpy.append(range(gs[1]+1), range(-gs[1],0)),
numpy.append(range(gs[2]+1), range(-gs[2],0))))
invh = numpy.linalg.inv(cell._h)
Gv = 2*numpy.pi * numpy.dot(gxyz, invh)
ngs = gxyz.shape[0]
# Theoretically, hermitian symmetry can be also found for kpti == kptj:
# f_ji(G) = \int f_ji exp(-iGr) = \int f_ij^* exp(-iGr) = [f_ij(-G)]^*
# The hermi operation needs reordering the axis-0. It is inefficient
if gamma_point(kpt) and gamma_point(kpts):
aosym = 's1hermi'
else:
aosym = 's1'
blksize = min(max(16, int(max_memory*.9e6/(nao**2*(nkpts+1)*16))), 16384)
buf = [numpy.zeros(nao*nao*blksize, dtype=numpy.complex128)
for k in range(nkpts)]
pqkRbuf = numpy.empty(nao*nao*blksize)
pqkIbuf = numpy.empty(nao*nao*blksize)
for p0, p1 in self.prange(0, ngs, blksize):
ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym, invh,
gxyz[p0:p1], gs, kpt, kpts, out=buf)
nG = p1 - p0
for k in range(nkpts):
aoao = numpy.ndarray((nG,nao,nao), dtype=numpy.complex128,
order='F', buffer=buf[k])
pqkR = numpy.ndarray((nao,nao,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nao,nao,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 ft_loop(self,
mesh=None,
q=numpy.zeros(3),
kpts=None,
shls_slice=None,
max_memory=4000,
aosym='s1',
intor='GTO_ft_ovlp',
comp=1):
'''
Fourier transform iterator for all kpti which satisfy
2pi*N = (kpts - kpti - q)*a, N = -1, 0, 1
'''
cell = self.cell
if mesh is None:
mesh = self.mesh
if kpts is None:
assert (is_zero(q))
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(mesh)
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
ngrids = 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 * 16 * comp)))
blksize = min(blksize, ngrids, 16384)
buf = numpy.empty(nkpts * nij * blksize * comp, dtype=numpy.complex128)
for p0, p1 in self.prange(0, ngrids, blksize):
dat = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
q,
kpts,
intor,
comp,
out=buf)
yield dat, p0, p1
def test_ft_aoao_with_kpts(self):
numpy.random.seed(1)
kpti, kptj = kpts = numpy.random.random((2,3))
Gv = cell.get_Gv([5]*3)
kpt = numpy.random.random(3)
dat = ft_ao._ft_aopair_kpts(cell, Gv, kpt=kpt, kptjs=kpts)
self.assertAlmostEqual(finger(dat[0]), (2.3753953914129382-2.5365192689115088j), 9)
self.assertAlmostEqual(finger(dat[1]), (2.4951510097641840-3.1990956672116355j), 9)
dat = ft_ao.ft_aopair(cell, Gv)
self.assertAlmostEqual(finger(dat), (1.2534723618134684+1.830086071817564j), 9)
def pw_contract(istep, sh_range, j3cR, j3cI):
bstart, bend, ncol = sh_range
if aosym == 's2':
shls_slice = (bstart, bend, 0, bend)
else:
shls_slice = (bstart, bend, 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)
if (cell.dimension == 1 or cell.dimension == 2) and is_zero(kpt):
G0idx, SI_on_z = pbcgto.cell._SI_for_uniform_model_charge(cell, Gv[p0:p1])
if SI_on_z.size > 0:
for k, aoao in enumerate(dat):
aoao[G0idx] -= numpy.einsum('g,i->gi', SI_on_z, ovlp[k])
aux = fuse(ft_ao.ft_ao(fused_cell, Gv[p0:p1][G0idx]).T)
vG_mod = numpy.einsum('ig,g,g->i', aux.conj(),
wcoulG[p0:p1][G0idx], SI_on_z)
if gamma_point(adapted_kptjs[k]):
j3cR[k][:naux] -= vG_mod[:,None].real * ovlp[k]
else:
tmp = vG_mod[:,None] * ovlp[k]
j3cR[k][:naux] -= tmp.real
j3cI[k][:naux] -= tmp.imag
tmp = aux = vG_mod
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, 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 j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c, v, lower=True, overwrite_b=True)
else:
v = lib.dot(j2c, v)
feri['j3c/%d/%d'%(ji,istep)] = v
def pw_loop(self, cell, gs=None, kpti_kptj=None, shls_slice=None,
max_memory=2000):
'''Plane wave part'''
if gs is None:
gs = self.gs
if kpti_kptj is None:
kpti = kptj = numpy.zeros(3)
else:
kpti, kptj = kpti_kptj
nao = cell.nao_nr()
gxyz = lib.cartesian_prod((numpy.append(range(gs[0]+1), range(-gs[0],0)),
numpy.append(range(gs[1]+1), range(-gs[1],0)),
numpy.append(range(gs[2]+1), range(-gs[2],0))))
invh = numpy.linalg.inv(cell._h)
Gv = 2*numpy.pi * numpy.dot(gxyz, invh)
ngs = gxyz.shape[0]
# Theoretically, hermitian symmetry can be also found for kpti == kptj:
# f_ji(G) = \int f_ji exp(-iGr) = \int f_ij^* exp(-iGr) = [f_ij(-G)]^*
# The hermi operation needs reordering the axis-0. It is inefficient
if gamma_point(kpti) and gamma_point(kptj):
aosym = 's1hermi'
else:
aosym = 's1'
blksize = min(max(16, int(max_memory*1e6*.75/16/nao**2)), 16384)
sublk = max(16, int(blksize//4))
buf = [numpy.zeros(nao*nao*blksize, dtype=numpy.complex128)]
pqkRbuf = numpy.empty(nao*nao*sublk)
pqkIbuf = numpy.empty(nao*nao*sublk)
for p0, p1 in self.prange(0, ngs, blksize):
#aoao = ft_ao.ft_aopair(cell, Gv[p0:p1], shls_slice, aosym, invh,
# gxyz[p0:p1], gs, (kpti, kptj))
aoao = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
invh, gxyz[p0:p1], gs,
kptj-kpti, kptj.reshape(1,3), out=buf)[0]
for i0, i1 in lib.prange(0, p1-p0, sublk):
nG = i1 - i0
pqkR = numpy.ndarray((nao,nao,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nao,nao,nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.transpose(1,2,0)
pqkI[:] = aoao[i0:i1].imag.transpose(1,2,0)
yield (pqkR.reshape(-1,nG),
pqkI.reshape(-1,nG), p0+i0, p0+i1)
aoao[:] = 0
def ft_loop(self, mesh=None, q=numpy.zeros(3), kpts=None, shls_slice=None,
max_memory=4000, aosym='s1', intor='GTO_ft_ovlp', comp=1):
'''
Fourier transform iterator for all kpti which satisfy
2pi*N = (kpts - kpti - q)*a, N = -1, 0, 1
'''
cell = self.cell
if mesh is None:
mesh = self.mesh
if kpts is None:
assert(is_zero(q))
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(mesh)
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
ngrids = 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*16*comp)))
blksize = min(blksize, ngrids, 16384)
buf = numpy.empty(nkpts*nij*blksize*comp, dtype=numpy.complex128)
for p0, p1 in self.prange(0, ngrids, blksize):
dat = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
b, gxyz[p0:p1], Gvbase, q, kpts,
intor, comp, out=buf)
yield dat, p0, p1
def pw_contract(istep, sh_range, j3cR, j3cI):
bstart, bend, ncol = sh_range
if aosym == 's2':
shls_slice = (bstart, bend, 0, bend)
else:
shls_slice = (bstart, bend, 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][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, 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 j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c, v, lower=True, overwrite_b=True)
feri['j3c/%d/%d'%(ji,istep)] = v
else:
feri['j3c/%d/%d'%(ji,istep)] = lib.dot(j2c, v)
# low-dimension systems
if j2c_negative is not None:
feri['j3c-/%d/%d'%(ji,istep)] = lib.dot(j2c_negative, v)
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 * 0.6 * 1e6 / 16 / naux / (nkptj + 1)), 1), nao_pair)
shranges = pyscf.df.outcore._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 * 0.2 * 1e6 / 16 / buflen / (nkptj + 1)))
else:
Gblksize = max(16, int(max_memory * 0.4 * 1e6 / 16 / buflen / (nkptj + 1)))
Gblksize = min(Gblksize, ngs)
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 = fuse(numpy.asarray(feri["j3c/%d" % idx][:, col0:col1]))
if mydf.approx_sr_level == 0:
Lpq = numpy.asarray(feri["Lpq/%d" % idx][:, col0:col1])
elif aosym == "s2":
Lpq = numpy.asarray(feri["Lpq/0"][:, col0:col1])
else:
Lpq = numpy.asarray(Lpq_fake[:, col0:col1])
lib.dot(j2c[uniq_kptji_id], Lpq, -0.5, v, 1)
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 = Lpq = 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, invh, gxyz[p0:p1], gs, 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], 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)
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, invh, gxyz[p0:p1], gs, 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], j3cI[k], 1)
for k, ji in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
save("j3c/%d" % ji, j3cR[k], col0, col1)
else:
save("j3c/%d" % ji, j3cR[k] + j3cI[k] * 1j, col0, col1)
def pw_loop(self,
mesh=None,
kpti_kptj=None,
q=None,
shls_slice=None,
max_memory=2000,
aosym='s1',
blksize=None,
intor='GTO_ft_ovlp',
comp=1):
'''
Fourier transform iterator for AO pair
'''
cell = self.cell
if mesh is None:
mesh = self.mesh
if kpti_kptj is None:
kpti = kptj = numpy.zeros(3)
else:
kpti, kptj = kpti_kptj
if q is None:
q = kptj - kpti
ao_loc = cell.ao_loc_nr()
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]
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
if blksize is None:
blksize = min(
max(64, int(max_memory * 1e6 * .75 / (nij * 16 * comp))),
16384)
sublk = int(blksize // 4)
else:
sublk = blksize
buf = numpy.empty(nij * blksize * comp, dtype=numpy.complex128)
pqkRbuf = numpy.empty(nij * sublk * comp)
pqkIbuf = numpy.empty(nij * sublk * comp)
for p0, p1 in self.prange(0, ngrids, blksize):
#aoao = ft_ao.ft_aopair(cell, Gv[p0:p1], shls_slice, aosym,
# b, Gvbase, gxyz[p0:p1], mesh, (kpti, kptj), q)
aoao = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
q,
kptj.reshape(1, 3),
intor,
comp,
out=buf)[0]
aoao = aoao.reshape(p1 - p0, nij)
for i0, i1 in lib.prange(0, p1 - p0, sublk):
nG = i1 - i0
if comp == 1:
pqkR = numpy.ndarray((nij, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nij, nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.T
pqkI[:] = aoao[i0:i1].imag.T
else:
pqkR = numpy.ndarray((comp, nij, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((comp, nij, nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.transpose(0, 2, 1)
pqkI[:] = aoao[i0:i1].imag.transpose(0, 2, 1)
yield (pqkR, pqkI, p0 + i0, p0 + i1)
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 pw_loop(self,
gs=None,
kpti_kptj=None,
q=None,
shls_slice=None,
max_memory=2000,
aosym='s1',
blksize=None):
'''Plane wave part'''
cell = self.cell
if gs is None:
gs = self.gs
if kpti_kptj is None:
kpti = kptj = numpy.zeros(3)
else:
kpti, kptj = kpti_kptj
if q is None:
q = kptj - kpti
ao_loc = cell.ao_loc_nr()
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]
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
if blksize is None:
blksize = min(max(16, int(max_memory * 1e6 * .75 / 16 / nij)),
16384)
sublk = max(16, int(blksize // 4))
else:
sublk = blksize
buf = numpy.empty(nij * blksize, dtype=numpy.complex128)
pqkRbuf = numpy.empty(nij * sublk)
pqkIbuf = numpy.empty(nij * sublk)
for p0, p1 in self.prange(0, ngs, blksize):
#aoao = ft_ao.ft_aopair(cell, Gv[p0:p1], shls_slice, aosym,
# b, Gvbase, gxyz[p0:p1], gs, (kpti, kptj), q)
aoao = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
q,
kptj.reshape(1, 3),
out=buf)[0]
aoao = aoao.reshape(p1 - p0, nij)
for i0, i1 in lib.prange(0, p1 - p0, sublk):
nG = i1 - i0
pqkR = numpy.ndarray((nij, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nij, nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.T
pqkI[:] = aoao[i0:i1].imag.T
yield (pqkR, pqkI, p0 + i0, p0 + i1)
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_loop(self,
mesh=None,
q=numpy.zeros(3),
kpts=None,
shls_slice=None,
max_memory=4000,
aosym='s1',
intor='GTO_ft_ovlp',
comp=1):
'''
Fourier transform iterator for all kpti which satisfy
2pi*N = (kpts - kpti - q)*a, N = -1, 0, 1
'''
cell = self.cell
if mesh is None:
mesh = self.mesh
if kpts is None:
assert (is_zero(q))
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(mesh)
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
ngrids = 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
if (abs(q).sum() < 1e-6 and intor[:11] == 'GTO_ft_ovlp'
and (cell.dimension == 1 or cell.dimension == 2)):
s = cell.pbc_intor('int1e_ovlp', kpts=kpts)
if aosym == 's2':
s = [lib.pack_tril(x) for x in s]
else:
s = None
blksize = max(16, int(max_memory * .9e6 / (nij * nkpts * 16 * comp)))
blksize = min(blksize, ngrids, 16384)
buf = numpy.empty(nkpts * nij * blksize * comp, dtype=numpy.complex128)
for p0, p1 in self.prange(0, ngrids, blksize):
dat = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
b,
gxyz[p0:p1],
Gvbase,
q,
kpts,
intor,
comp,
out=buf)
if s is not None: # to remove the divergent part in 1D/2D systems
G0idx, SI_on_z = pbcgto.cell._SI_for_uniform_model_charge(
cell, Gv[p0:p1])
if SI_on_z.size > 0:
for k, kpt in enumerate(kpts):
dat[k][G0idx] -= numpy.einsum('g,...->g...', SI_on_z,
s[k])
yield dat, p0, p1
def ft_loop(self,
cell,
gs=None,
kpt=numpy.zeros(3),
kpts=None,
shls_slice=None,
max_memory=4000):
'''
Fourier transform iterator for all kpti which satisfy kpt = kpts - kpti
'''
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)
nao = cell.nao_nr()
gxyz = lib.cartesian_prod((numpy.append(range(gs[0] + 1),
range(-gs[0], 0)),
numpy.append(range(gs[1] + 1),
range(-gs[1], 0)),
numpy.append(range(gs[2] + 1),
range(-gs[2], 0))))
invh = numpy.linalg.inv(cell._h)
Gv = 2 * numpy.pi * numpy.dot(gxyz, invh)
ngs = gxyz.shape[0]
# Theoretically, hermitian symmetry can be also found for kpti == kptj:
# f_ji(G) = \int f_ji exp(-iGr) = \int f_ij^* exp(-iGr) = [f_ij(-G)]^*
# The hermi operation needs reordering the axis-0. It is inefficient
if gamma_point(kpt) and gamma_point(kpts):
aosym = 's1hermi'
else:
aosym = 's1'
blksize = min(
max(16, int(max_memory * .9e6 / (nao**2 * (nkpts + 1) * 16))),
16384)
buf = [
numpy.zeros(nao * nao * blksize, dtype=numpy.complex128)
for k in range(nkpts)
]
pqkRbuf = numpy.empty(nao * nao * blksize)
pqkIbuf = numpy.empty(nao * nao * blksize)
for p0, p1 in self.prange(0, ngs, blksize):
ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
invh,
gxyz[p0:p1],
gs,
kpt,
kpts,
out=buf)
nG = p1 - p0
for k in range(nkpts):
aoao = numpy.ndarray((nG, nao, nao),
dtype=numpy.complex128,
order='F',
buffer=buf[k])
pqkR = numpy.ndarray((nao, nao, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nao, nao, 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 make_kpt(uniq_kptji_id, cholesky_j2c):
kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti
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)
j2c, j2c_negative, j2ctag = cholesky_j2c
shls_slice = (auxcell.nbas, fused_cell.nbas)
Gaux = ft_ao.ft_ao(fused_cell, Gv, shls_slice, b, gxyz, Gvbase, kpt)
wcoulG = mydf.weighted_coulG(kpt, False, mesh)
Gaux *= wcoulG.reshape(-1, 1)
kLR = Gaux.real.copy('C')
kLI = Gaux.imag.copy('C')
Gaux = None
if is_zero(kpt): # kpti == kptj
aosym = 's2'
nao_pair = nao * (nao + 1) // 2
if 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]
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 * .38e6 / 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 * .1e6 / 16 / buflen / (nkptj + 1)))
else:
Gblksize = max(16,
int(max_memory * .2e6 / 16 / buflen / (nkptj + 1)))
Gblksize = min(Gblksize, ngrids, 16384)
def load(aux_slice):
col0, col1 = aux_slice
j3cR = []
j3cI = []
for k, idx in enumerate(adapted_ji_idx):
v = numpy.vstack([
fswap['j3c-junk/%d/%d' % (idx, i)][0, col0:col1].T
for i in range(nsegs)
])
# vbar is the interaction between the background charge
# and the auxiliary basis. 0D, 1D, 2D do not have vbar.
if is_zero(kpt) and cell.dimension == 3:
for i in numpy.where(vbar != 0)[0]:
v[i] -= vbar[i] * 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
return j3cR, j3cI
pqkRbuf = numpy.empty(buflen * Gblksize)
pqkIbuf = numpy.empty(buflen * Gblksize)
# buf for ft_aopair
buf = numpy.empty(nkptj * buflen * Gblksize, dtype=numpy.complex128)
cols = [sh_range[2] for sh_range in shranges]
locs = numpy.append(0, numpy.cumsum(cols))
tasks = zip(locs[:-1], locs[1:])
for istep, (j3cR,
j3cI) in enumerate(lib.map_with_prefetch(load, tasks)):
bstart, bend, ncol = shranges[istep]
log.debug1('int3c2e [%d/%d], AO [%d:%d], ncol = %d', istep + 1,
len(shranges), bstart, bend, ncol)
if aosym == 's2':
shls_slice = (bstart, bend, 0, bend)
else:
shls_slice = (bstart, bend, 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][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, 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 j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c,
v,
lower=True,
overwrite_b=True)
feri['j3c/%d/%d' % (ji, istep)] = v
else:
feri['j3c/%d/%d' % (ji, istep)] = lib.dot(j2c, v)
# low-dimension systems
if j2c_negative is not None:
feri['j3c-/%d/%d' % (ji, istep)] = lib.dot(j2c_negative, v)
j3cR = j3cI = None
for ji in adapted_ji_idx:
del (fswap['j3c-junk/%d' % ji])
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 pw_loop(self, gs=None, kpti_kptj=None, shls_slice=None,
max_memory=2000, aosym='s1', blksize=None):
'''Plane wave part'''
cell = self.cell
if gs is None:
gs = self.gs
if kpti_kptj is None:
kpti = kptj = numpy.zeros(3)
else:
kpti, kptj = kpti_kptj
ao_loc = cell.ao_loc_nr()
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]
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
if blksize is None:
blksize = min(max(16, int(max_memory*1e6*.75/16/nij)), 16384)
sublk = max(16, int(blksize//4))
else:
subblk = blksize
buf = [numpy.zeros(nij*blksize, dtype=numpy.complex128)]
pqkRbuf = numpy.empty(nij*sublk)
pqkIbuf = numpy.empty(nij*sublk)
if aosym == 's2':
for p0, p1 in self.prange(0, ngs, blksize):
aoao = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
b, gxyz[p0:p1], Gvbase, kptj-kpti,
kptj.reshape(1,3), out=buf)[0]
for i0, i1 in lib.prange(0, p1-p0, sublk):
nG = i1 - i0
pqkR = numpy.ndarray((nij,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nij,nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.T
pqkI[:] = aoao[i0:i1].imag.T
yield (pqkR, pqkI, p0+i0, p0+i1)
aoao[:] = 0
else:
for p0, p1 in self.prange(0, ngs, blksize):
#aoao = ft_ao.ft_aopair(cell, Gv[p0:p1], shls_slice, aosym,
# b, Gvbase, gxyz[p0:p1], gs, (kpti, kptj))
aoao = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
b, gxyz[p0:p1], Gvbase, kptj-kpti,
kptj.reshape(1,3), out=buf)[0]
for i0, i1 in lib.prange(0, p1-p0, sublk):
nG = i1 - i0
pqkR = numpy.ndarray((ni,nj,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ni,nj,nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.transpose(1,2,0)
pqkI[:] = aoao[i0:i1].imag.transpose(1,2,0)
yield (pqkR.reshape(-1,nG), pqkI.reshape(-1,nG), p0+i0, p0+i1)
aoao[:] = 0
def ft_loop(self,
gs=None,
q=numpy.zeros(3),
kpts=None,
shls_slice=None,
max_memory=4000,
aosym='s1'):
'''
Fourier transform iterator for all kpti which satisfy 2pi*N = (kpts - kpti - q)*a
N = -1, 0, 1
'''
cell = self.cell
if gs is None:
gs = self.gs
if kpts is None:
assert (is_zero(q))
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,
q,
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,
q,
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 pw_loop(self, mesh=None, kpti_kptj=None, q=None, shls_slice=None,
max_memory=2000, aosym='s1', blksize=None,
intor='GTO_ft_ovlp', comp=1):
'''
Fourier transform iterator for AO pair
'''
cell = self.cell
if mesh is None:
mesh = self.mesh
if kpti_kptj is None:
kpti = kptj = numpy.zeros(3)
else:
kpti, kptj = kpti_kptj
if q is None:
q = kptj - kpti
ao_loc = cell.ao_loc_nr()
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]
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
if blksize is None:
blksize = min(max(64, int(max_memory*1e6*.75/(nij*16*comp))), 16384)
sublk = int(blksize//4)
else:
sublk = blksize
buf = numpy.empty(nij*blksize*comp, dtype=numpy.complex128)
pqkRbuf = numpy.empty(nij*sublk*comp)
pqkIbuf = numpy.empty(nij*sublk*comp)
for p0, p1 in self.prange(0, ngrids, blksize):
#aoao = ft_ao.ft_aopair(cell, Gv[p0:p1], shls_slice, aosym,
# b, Gvbase, gxyz[p0:p1], mesh, (kpti, kptj), q)
aoao = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym,
b, gxyz[p0:p1], Gvbase, q,
kptj.reshape(1,3), intor, comp, out=buf)[0]
aoao = aoao.reshape(p1-p0,nij)
for i0, i1 in lib.prange(0, p1-p0, sublk):
nG = i1 - i0
if comp == 1:
pqkR = numpy.ndarray((nij,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nij,nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.T
pqkI[:] = aoao[i0:i1].imag.T
else:
pqkR = numpy.ndarray((comp,nij,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((comp,nij,nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.transpose(0,2,1)
pqkI[:] = aoao[i0:i1].imag.transpose(0,2,1)
yield (pqkR, pqkI, p0+i0, p0+i1)
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 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)
Gaux = ft_ao.ft_ao(fused_cell, Gv, None, b, gxyz, Gvbase, kpt).T
Gaux = fuse(Gaux)
Gaux *= mydf.weighted_coulG(kpt, False, gs)
kLR = Gaux.T.real.copy('C')
kLI = Gaux.T.imag.copy('C')
j2c = numpy.asarray(feri['j2c/%d' % uniq_kptji_id])
# Note large difference may be found in results between the CD/eig treatments.
# In some systems, small integral errors can lead to different treatments of
# linear dependency which can be observed in the total energy/orbital energy
# around 4th decimal place.
# try:
# j2c = scipy.linalg.cholesky(j2c, lower=True)
# j2ctag = 'CD'
# except scipy.linalg.LinAlgError as e:
#
# Abandon CD treatment for better numerical stablity
w, v = scipy.linalg.eigh(j2c)
log.debug('MDF metric for kpt %s cond = %.4g, drop %d bfns',
uniq_kptji_id, w[-1] / w[0],
numpy.count_nonzero(w < mydf.linear_dep_threshold))
v = v[:, w > mydf.linear_dep_threshold].T.conj()
v /= numpy.sqrt(w[w > mydf.linear_dep_threshold]).reshape(-1, 1)
j2c = v
j2ctag = 'eig'
naux0 = j2c.shape[0]
if is_zero(kpt): # kpti == kptj
aosym = 's2'
nao_pair = nao * (nao + 1) // 2
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('int1e_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.empty((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 = fuse(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)
else:
shls_slice = (bstart, bend, 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], 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, ji 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)
else:
v = lib.dot(j2c, v)
feri['j3c/%d' % ji][:naux0, col0:col1] = v
del (feri['j2c/%d' % 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 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_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)
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])
try:
j2c = scipy.linalg.cholesky(j2c, lower=True)
j2ctag = 'CD'
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.debug('DF metric linear dependency for kpt %s', uniq_kptji_id)
log.debug('cond = %.4g, drop %d bfns', w[-1] / w[0],
numpy.count_nonzero(w < mydf.linear_dep_threshold))
v = v[:, w > mydf.linear_dep_threshold].T.conj()
v /= numpy.sqrt(w[w > mydf.linear_dep_threshold]).reshape(-1, 1)
j2c = v
j2ctag = 'eig'
naux0 = j2c.shape[0]
if is_zero(kpt): # kpti == kptj
aosym = 's2'
nao_pair = nao * (nao + 1) // 2
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('int1e_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.empty(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)
else:
shls_slice = (bstart, bend, 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, 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 j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c,
v,
lower=True,
overwrite_b=True)
else:
v = lib.dot(j2c, v)
feri['j3c/%d' % ji][:naux0, col0:col1] = v
del (feri['j2c/%d' % 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):
max_memory = max(2000, mydf.max_memory-pyscflib.current_memory()[0])
fused_cell, fuse = df.df.fuse_auxcell(mydf, auxcell)
log = Logger(mydf.stdout, mydf.verbose)
nao, nfao = cell.nao_nr(), fused_cell.nao_nr()
jobs = np.arange(fused_cell.nbas)
tasks = list(static_partition(jobs))
ntasks = max(comm.allgather(len(tasks)))
j3c_junk = ctf.zeros([len(kptij_lst), nao**2, nfao], dtype=np.complex128)
t1 = t0 = (time.clock(), time.time())
idx_full = np.arange(j3c_junk.size).reshape(j3c_junk.shape)
if len(tasks) > 0:
q0, q1 = tasks[0], tasks[-1] + 1
shls_slice = (0, cell.nbas, 0, cell.nbas, q0, q1)
bstart, bend = fused_cell.ao_loc_nr()[q0], fused_cell.ao_loc_nr()[q1]
idx = idx_full[:,:,bstart:bend].ravel()
tmp = df.incore.aux_e2(cell, fused_cell, intor='int3c2e', aosym='s2', kptij_lst=kptij_lst, shls_slice=shls_slice)
nao_pair = nao**2
if tmp.shape[-2] != nao_pair and tmp.ndim == 2:
tmp = pyscflib.unpack_tril(tmp, axis=0).reshape(nao_pair,-1)
j3c_junk.write(idx, tmp.ravel())
else:
j3c_junk.write([],[])
t1 = log.timer('j3c_junk', *t1)
naux = auxcell.nao_nr()
mesh = mydf.mesh
Gv, Gvbase, kws = cell.get_Gv_weights(mesh)
b = cell.reciprocal_vectors()
gxyz = pyscflib.cartesian_prod([np.arange(len(x)) for x in Gvbase])
ngrids = gxyz.shape[0]
kptis = kptij_lst[:,0]
kptjs = kptij_lst[:,1]
kpt_ji = kptjs - kptis
mydf.kptij_lst = kptij_lst
uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji)
jobs = np.arange(len(uniq_kpts))
tasks = list(static_partition(jobs))
ntasks = max(comm.allgather(len(tasks)))
blksize = max(2048, int(max_memory*.5e6/16/fused_cell.nao_nr()))
log.debug2('max_memory %s (MB) blocksize %s', max_memory, blksize)
j2c = ctf.zeros([len(uniq_kpts),naux,naux], dtype=np.complex128)
a = cell.lattice_vectors() / (2*np.pi)
def kconserve_indices(kpt):
'''search which (kpts+kpt) satisfies momentum conservation'''
kdif = np.einsum('wx,ix->wi', a, uniq_kpts + kpt)
kdif_int = np.rint(kdif)
mask = np.einsum('wi->i', abs(kdif - kdif_int)) < KPT_DIFF_TOL
uniq_kptji_ids = np.where(mask)[0]
return uniq_kptji_ids
def cholesky_decomposed_metric(j2c_kptij):
j2c_negative = None
try:
j2c_kptij = scipy.linalg.cholesky(j2c_kptij, lower=True)
j2ctag = 'CD'
except scipy.linalg.LinAlgError as e:
w, v = scipy.linalg.eigh(j2c_kptij)
log.debug('cond = %.4g, drop %d bfns',
w[-1]/w[0], np.count_nonzero(w<mydf.linear_dep_threshold))
v1 = np.zeros(v.T.shape, dtype=v.dtype)
v1[w>mydf.linear_dep_threshold,:] = v[:,w>mydf.linear_dep_threshold].conj().T
v1[w>mydf.linear_dep_threshold,:] /= np.sqrt(w[w>mydf.linear_dep_threshold]).reshape(-1,1)
j2c_kptij = v1
if cell.dimension == 2 and cell.low_dim_ft_type != 'inf_vacuum':
idx = np.where(w < -mydf.linear_dep_threshold)[0]
if len(idx) > 0:
j2c_negative = np.zeros(v1.shape, dtype=v1.dtype)
j2c_negative[idx,:] = (v[:,idx]/np.sqrt(-w[idx])).conj().T
w = v = None
j2ctag = 'eig'
return j2c_kptij, j2c_negative, j2ctag
for itask in range(ntasks):
if itask >= len(tasks):
j2c.write([],[])
continue
k = tasks[itask]
kpt = uniq_kpts[k]
j2ctmp = np.asarray(fused_cell.pbc_intor('int2c2e', hermi=1, kpts=kpt))
coulG = mydf.weighted_coulG(kpt, False, mesh)
for p0, p1 in pyscflib.prange(0, ngrids, blksize):
aoaux = ft_ao.ft_ao(fused_cell, Gv[p0:p1], None, b, gxyz[p0:p1], Gvbase, kpt).T
if is_zero(kpt):
j2ctmp[naux:] -= np.dot(aoaux[naux:].conj()*coulG[p0:p1].conj(), aoaux.T).real
j2ctmp[:naux,naux:] = j2ctmp[naux:,:naux].T
else:
j2ctmp[naux:] -= np.dot(aoaux[naux:].conj()*coulG[p0:p1].conj(), aoaux.T)
j2ctmp[:naux,naux:] = j2ctmp[naux:,:naux].T.conj()
tmp = fuse(fuse(j2ctmp).T).T
idx = k * naux**2 + np.arange(naux**2)
j2c.write(idx, tmp.ravel())
j2ctmp = tmp = None
coulG = None
t1 = log.timer('j2c', *t1)
j3c = ctf.zeros([len(kpt_ji),nao,nao,naux], dtype=np.complex128)
jobs = np.arange(len(kpt_ji))
tasks = list(static_partition(jobs))
ntasks = max(comm.allgather(len(tasks)))
for itask in range(ntasks):
if itask >= len(tasks):
j2c_ji = j2c.read([])
j3ctmp = j3c_junk.read([])
j3c.write([],[])
continue
idx_ji = tasks[itask]
kpti, kptj = kptij_lst[idx_ji]
idxi, idxj = member(kpti, mydf.kpts), member(kptj, mydf.kpts)
uniq_idx = uniq_inverse[idx_ji]
kpt = uniq_kpts[uniq_idx]
id_eq = kconserve_indices(-kpt)
id_conj = kconserve_indices(kpt)
id_conj = np.asarray([i for i in id_conj if i not in id_eq], dtype=int)
id_full = np.hstack((id_eq, id_conj))
map_id, conj = min(id_full), np.argmin(id_full) >=len(id_eq)
j2cidx = map_id * naux**2 + np.arange(naux**2)
j2c_ji = j2c.read(j2cidx).reshape(naux, naux) # read to be added
j2c_ji, j2c_negative, j2ctag = cholesky_decomposed_metric(j2c_ji)
if conj: j2c_ji = j2c_ji.conj()
shls_slice= (auxcell.nbas, fused_cell.nbas)
Gaux = ft_ao.ft_ao(fused_cell, Gv, shls_slice, b, gxyz, Gvbase, kpt)
wcoulG = mydf.weighted_coulG(kpt, False, mesh)
Gaux *= wcoulG.reshape(-1,1)
j3c_id = idx_ji * nao**2*nfao + np.arange(nao**2*nfao)
j3ctmp = j3c_junk.read(j3c_id).reshape(nao**2, fused_cell.nao_nr()).T
if is_zero(kpt): # kpti == kptj
if cell.dimension == 3:
vbar = fuse(mydf.auxbar(fused_cell))
ovlp = cell.pbc_intor('int1e_ovlp', hermi=1, kpts=kptj)
for i in np.where(vbar != 0)[0]:
j3ctmp[i] -= vbar[i] * ovlp.reshape(-1)
aoao = ft_ao._ft_aopair_kpts(cell, Gv, None, 's1', b, gxyz, Gvbase, kpt, kptj)[0].reshape(len(Gv),-1)
j3ctmp[naux:] -= np.dot(Gaux.T.conj(), aoao)
j3ctmp = fuse(j3ctmp)
if j2ctag == 'CD':
v = scipy.linalg.solve_triangular(j2c_ji, j3ctmp, lower=True, overwrite_b=True)
else:
v = np.dot(j2c_ji, j3ctmp)
v = v.T.reshape(nao,nao,naux)
j3c_id = idx_ji * nao**2*naux + np.arange(nao**2*naux)
j3c.write(j3c_id, v.ravel())
mydf.j3c = j3c
return None
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 pw_loop(self,
cell,
gs=None,
kpti_kptj=None,
shls_slice=None,
max_memory=2000):
'''Plane wave part'''
if gs is None:
gs = self.gs
if kpti_kptj is None:
kpti = kptj = numpy.zeros(3)
else:
kpti, kptj = kpti_kptj
nao = cell.nao_nr()
gxyz = lib.cartesian_prod((numpy.append(range(gs[0] + 1),
range(-gs[0], 0)),
numpy.append(range(gs[1] + 1),
range(-gs[1], 0)),
numpy.append(range(gs[2] + 1),
range(-gs[2], 0))))
invh = numpy.linalg.inv(cell._h)
Gv = 2 * numpy.pi * numpy.dot(gxyz, invh)
ngs = gxyz.shape[0]
# Theoretically, hermitian symmetry can be also found for kpti == kptj:
# f_ji(G) = \int f_ji exp(-iGr) = \int f_ij^* exp(-iGr) = [f_ij(-G)]^*
# The hermi operation needs reordering the axis-0. It is inefficient
if gamma_point(kpti) and gamma_point(kptj):
aosym = 's1hermi'
else:
aosym = 's1'
blksize = min(max(16, int(max_memory * 1e6 * .75 / 16 / nao**2)),
16384)
sublk = max(16, int(blksize // 4))
buf = [numpy.zeros(nao * nao * blksize, dtype=numpy.complex128)]
pqkRbuf = numpy.empty(nao * nao * sublk)
pqkIbuf = numpy.empty(nao * nao * sublk)
for p0, p1 in self.prange(0, ngs, blksize):
#aoao = ft_ao.ft_aopair(cell, Gv[p0:p1], shls_slice, aosym, invh,
# gxyz[p0:p1], gs, (kpti, kptj))
aoao = ft_ao._ft_aopair_kpts(cell,
Gv[p0:p1],
shls_slice,
aosym,
invh,
gxyz[p0:p1],
gs,
kptj - kpti,
kptj.reshape(1, 3),
out=buf)[0]
for i0, i1 in lib.prange(0, p1 - p0, sublk):
nG = i1 - i0
pqkR = numpy.ndarray((nao, nao, nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((nao, nao, nG), buffer=pqkIbuf)
pqkR[:] = aoao[i0:i1].real.transpose(1, 2, 0)
pqkI[:] = aoao[i0:i1].imag.transpose(1, 2, 0)
yield (pqkR.reshape(-1,
nG), pqkI.reshape(-1,
nG), p0 + i0, p0 + i1)
aoao[:] = 0
