def get_mo_pairs_G(mydf, mo_coeffs, kpts=numpy.zeros((2,3)), q=None, compact=False):
'''Calculate forward (G|ij) FFT of all MO pairs.
Args:
mo_coeff: length-2 list of (nao,nmo) ndarrays
The two sets of MO coefficients to use in calculating the
product |ij).
Returns:
mo_pairs_G : (ngs, nmoi*nmoj) ndarray
The FFT of the real-space MO pairs.
'''
if kpts is None: kpts = numpy.zeros((2,3))
cell = mydf.cell
kpts = numpy.asarray(kpts)
coords = cell.gen_uniform_grids(mydf.gs)
nmoi = mo_coeffs[0].shape[1]
nmoj = mo_coeffs[1].shape[1]
ngs = len(coords)
def trans(aoiR, aojR, fac=1):
if id(aoiR) == id(aojR) and iden_coeffs(mo_coeffs[0], mo_coeffs[1]):
moiR = mojR = numpy.asarray(lib.dot(mo_coeffs[0].T,aoiR.T), order='C')
else:
moiR = numpy.asarray(lib.dot(mo_coeffs[0].T, aoiR.T), order='C')
mojR = numpy.asarray(lib.dot(mo_coeffs[1].T, aojR.T), order='C')
mo_pairs_G = numpy.empty((nmoi,nmoj,ngs), dtype=numpy.complex128)
for i in range(nmoi):
mo_pairs_G[i] = tools.fft(fac * moiR[i].conj() * mojR, mydf.gs)
mo_pairs_G = mo_pairs_G.reshape(-1,ngs).T
return mo_pairs_G
if gamma_point(kpts): # gamma point, real
aoR = mydf._numint.eval_ao(cell, coords, kpts[:1])[0]
if compact and iden_coeffs(mo_coeffs[0], mo_coeffs[1]):
moR = numpy.asarray(lib.dot(mo_coeffs[0].T, aoR.T), order='C')
npair = nmoi*(nmoi+1)//2
mo_pairs_G = numpy.empty((npair,ngs), dtype=numpy.complex128)
ij = 0
for i in range(nmoi):
mo_pairs_G[ij:ij+i+1] = tools.fft(moR[i].conj() * moR[:i+1], mydf.gs)
ij += i + 1
mo_pairs_G = mo_pairs_G.T
else:
mo_pairs_G = trans(aoR, aoR)
elif is_zero(kpts[0]-kpts[1]):
aoR = mydf._numint.eval_ao(cell, coords, kpts[:1])[0]
mo_pairs_G = trans(aoR, aoR)
else:
if q is None:
q = kpts[1] - kpts[0]
aoiR, aojR = mydf._numint.eval_ao(cell, coords, kpts)
fac = numpy.exp(-1j * numpy.dot(coords, q))
mo_pairs_G = trans(aoiR, aojR, fac)
return mo_pairs_G
def get_j_for_bands(mydf,
dm_kpts,
hermi=1,
kpts=numpy.zeros((1, 3)),
kpts_band=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]
dmsR = dms.real.reshape(nset, nkpts, nao**2)
dmsI = dms.imag.reshape(nset, nkpts, nao**2)
kpt_allow = numpy.zeros(3)
coulG = mydf.weighted_coulG(kpt_allow, False, mydf.gs)
ngs = len(coulG)
vG = numpy.zeros((nset, ngs), dtype=numpy.complex128)
max_memory = (mydf.max_memory - lib.current_memory()[0]) * .8
dmsC = dms.conj()
for aoaoks, p0, p1 in mydf.ft_loop(mydf.gs,
kpt_allow,
kpts,
max_memory=max_memory):
#:rho = numpy.einsum('lkL,lk->L', pqk.conj(), dm)
for k, aoao in enumerate(aoaoks):
for i in range(nset):
rho = numpy.einsum('ij,Lij->L', dmsC[i, k], aoao).conj()
vG[i, p0:p1] += rho * coulG[p0:p1]
aoao = aoaoks = p0 = p1 = None
weight = 1. / len(kpts)
vG *= weight
t1 = log.timer_debug1('get_j pass 1 to compute J(G)', *t1)
kpts_band, single_kpt_band = _format_kpts_band(kpts_band, kpts)
nband = len(kpts_band)
vj_kpts = numpy.zeros((nset, nband, nao, nao), dtype=numpy.complex128)
for aoaoks, p0, p1 in mydf.ft_loop(mydf.gs,
kpt_allow,
kpts_band,
max_memory=max_memory):
for k, aoao in enumerate(aoaoks):
for i in range(nset):
vj_kpts[i, k] += numpy.einsum('L,Lij->ij', vG[i, p0:p1], aoao)
aoao = aoaoks = p0 = p1 = None
if gamma_point(kpts_band):
vj_kpts = vj_kpts.real.copy()
t1 = log.timer_debug1('get_j pass 2', *t1)
return _format_jks(vj_kpts, dm_kpts, kpts_band, kpts, single_kpt_band)
def ft_ao(mol,
Gv,
shls_slice=None,
b=None,
gxyz=None,
Gvbase=None,
kpt=numpy.zeros(3),
verbose=None):
if gamma_point(kpt):
return mol_ft_ao(mol, Gv, shls_slice, b, gxyz, Gvbase, verbose)
else:
kG = Gv + kpt
return mol_ft_ao(mol, kG, shls_slice, None, None, None, verbose)
def general(mydf, mo_coeffs, kpts=None, compact=False):
'''General MO integral transformation'''
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2:
mo_coeffs = (mo_coeffs, ) * 4
mo_coeffs = [numpy.asarray(mo, order='F') for mo in mo_coeffs]
allreal = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs)
q = kptj - kpti
coulG = tools.get_coulG(cell, q, gs=mydf.gs)
coords = cell.gen_uniform_grids(mydf.gs)
max_memory = mydf.max_memory - lib.current_memory()[0]
if gamma_point(kptijkl) and allreal:
ao = mydf._numint.eval_ao(cell, coords, kpti)[0]
if ((iden_coeffs(mo_coeffs[0], mo_coeffs[2])
and iden_coeffs(mo_coeffs[1], mo_coeffs[3]))):
moiT = mojT = numpy.asarray(lib.dot(mo_coeffs[0].T, ao.T),
order='C')
ao = None
max_memory = max_memory - moiT.nbytes * 1e-6
eri = _contract_compact(mydf, (moiT, mojT),
coulG,
max_memory=max_memory)
if not compact:
nmo = moiT.shape[0]
eri = ao2mo.restore(1, eri, nmo).reshape(nmo**2, nmo**2)
else:
mos = [
numpy.asarray(lib.dot(c.T, ao.T), order='C') for c in mo_coeffs
]
ao = None
fac = numpy.array(1.)
max_memory = max_memory - sum([x.nbytes for x in mos]) * 1e-6
eri = _contract_plain(mydf, mos, coulG, fac,
max_memory=max_memory).real
return eri
else:
aos = mydf._numint.eval_ao(cell, coords, kptijkl)
mos = [
numpy.asarray(lib.dot(c.T, aos[i].T), order='C')
for i, c in enumerate(mo_coeffs)
]
aos = None
fac = numpy.exp(-1j * numpy.dot(coords, q))
max_memory = max_memory - sum([x.nbytes for x in mos]) * 1e-6
eri = _contract_plain(mydf, mos, coulG, fac, max_memory=max_memory)
return eri
def 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, input_band = _format_kpts_band(kpts_band, kpts), kpts_band
nband = len(kpts_band)
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, input_band, kpts)
def get_eri(mydf, kpts=None, compact=False):
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
q = kptj - kpti
coulG = tools.get_coulG(cell, q, gs=mydf.gs)
coords = cell.gen_uniform_grids(mydf.gs)
max_memory = mydf.max_memory - lib.current_memory()[0]
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl):
#:ao_pairs_G = get_ao_pairs_G(mydf, kptijkl[:2], q, compact=compact)
#:ao_pairs_G *= numpy.sqrt(coulG).reshape(-1,1)
#:eri = lib.dot(ao_pairs_G.T, ao_pairs_G, cell.vol/ngs**2)
ao = mydf._numint.eval_ao(cell, coords, kpti)[0]
ao = numpy.asarray(ao.T, order='C')
eri = _contract_compact(mydf, (ao, ao), coulG, max_memory=max_memory)
if not compact:
nao = cell.nao_nr()
eri = ao2mo.restore(1, eri, nao).reshape(nao**2, nao**2)
return eri
####################
# aosym = s1, complex integrals
else:
#:ao_pairs_G = get_ao_pairs_G(mydf, kptijkl[:2], q, compact=False)
#:# ao_pairs_invG = rho_kl(-(G+k_ij)) = conj(rho_lk(G+k_ij)).swap(r,s)
#:#=get_ao_pairs_G(mydf, [kptl,kptk], q, compact=False).transpose(0,2,1).conj()
#:ao_pairs_invG = get_ao_pairs_G(mydf, -kptijkl[2:], q, compact=False).conj()
#:ao_pairs_G *= coulG.reshape(-1,1)
#:eri = lib.dot(ao_pairs_G.T, ao_pairs_invG, cell.vol/ngs**2)
if is_zero(kpti - kptl) and is_zero(kptj - kptk):
if is_zero(kpti - kptj):
aoi = mydf._numint.eval_ao(cell, coords, kpti)[0]
aoi = aoj = numpy.asarray(aoi.T, order='C')
else:
aoi, aoj = mydf._numint.eval_ao(cell, coords, kptijkl[:2])
aoi = numpy.asarray(aoi.T, order='C')
aoj = numpy.asarray(aoj.T, order='C')
aos = (aoi, aoj, aoj, aoi)
else:
aos = mydf._numint.eval_ao(cell, coords, kptijkl)
aos = [numpy.asarray(x.T, order='C') for x in aos]
fac = numpy.exp(-1j * numpy.dot(coords, q))
max_memory = max_memory - aos[0].nbytes * 4 * 1e-6
eri = _contract_plain(mydf, aos, coulG, fac, max_memory=max_memory)
return eri
def aux_e2(cell,
auxcell,
intor='int3c2e_sph',
aosym='s1',
comp=1,
kptij_lst=numpy.zeros((1, 2, 3)),
shls_slice=None):
'''3-center AO integrals (ij|L) with double lattice sum:
\sum_{lm} (i[l]j[m]|L[0]), where L is the auxiliary basis.
Returns:
(nao_pair, naux) array
'''
intor = gto.moleintor.ascint3(intor)
if shls_slice is None:
shls_slice = (0, cell.nbas, 0, cell.nbas, 0, auxcell.nbas)
ao_loc = cell.ao_loc_nr()
aux_loc = auxcell.ao_loc_nr('ssc' in intor)[:shls_slice[5] + 1]
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
naux = aux_loc[shls_slice[5]] - aux_loc[shls_slice[4]]
nkptij = len(kptij_lst)
kpti = kptij_lst[:, 0]
kptj = kptij_lst[:, 1]
j_only = is_zero(kpti - kptj)
if j_only and aosym[:2] == 's2':
assert (shls_slice[2] == 0)
nao_pair = (ao_loc[shls_slice[1]] * (ao_loc[shls_slice[1]] + 1) // 2 -
ao_loc[shls_slice[0]] * (ao_loc[shls_slice[0]] + 1) // 2)
else:
nao_pair = ni * nj
if gamma_point(kptij_lst):
dtype = numpy.double
else:
dtype = numpy.complex128
int3c = wrap_int3c(cell, auxcell, intor, aosym, comp, kptij_lst)
out = numpy.empty((nkptij, comp, nao_pair, naux), dtype=dtype)
out = int3c(shls_slice, out)
if comp == 1:
out = out[:, 0]
if nkptij == 1:
out = out[0]
return out
def get_eri(mydf, kpts=None, compact=False):
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
nao = cell.nao_nr()
nao_pair = nao * (nao+1) // 2
q = kptj - kpti
coulG = tools.get_coulG(cell, q, gs=mydf.gs)
ngs = len(coulG)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl):
ao_pairs_G = get_ao_pairs_G(mydf, kptijkl[:2], q, compact=compact)
ao_pairs_G *= numpy.sqrt(coulG).reshape(-1,1)
aoijR = ao_pairs_G.real.copy()
aoijI = ao_pairs_G.imag.copy()
ao_pairs_G = None
eri = lib.dot(aoijR.T, aoijR, cell.vol/ngs**2)
eri = lib.dot(aoijI.T, aoijI, cell.vol/ngs**2, eri, 1)
return eri
####################
# (kpt) i == j == k == l != 0
# (kpt) i == l && j == k && i != j && j != k =>
#
# complex integrals, N^4 elements
elif is_zero(kpti-kptl) and is_zero(kptj-kptk):
ao_pairs_G = get_ao_pairs_G(mydf, kptijkl[:2], q, compact=False)
ao_pairs_G *= numpy.sqrt(coulG).reshape(-1,1)
ao_pairs_invG = ao_pairs_G.T.reshape(nao,nao,-1).transpose(1,0,2).conj()
ao_pairs_invG = ao_pairs_invG.reshape(-1,ngs)
return lib.dot(ao_pairs_G.T, ao_pairs_invG.T, cell.vol/ngs**2)
####################
# aosym = s1, complex integrals
#
else:
ao_pairs_G = get_ao_pairs_G(mydf, kptijkl[:2], q, compact=False)
# ao_pairs_invG = rho_rs(-G+k_rs) = conj(rho_sr(G+k_sr)).swap(r,s)
ao_pairs_invG = get_ao_pairs_G(mydf, -kptijkl[2:], q, compact=False).conj()
ao_pairs_G *= coulG.reshape(-1,1)
return lib.dot(ao_pairs_G.T, ao_pairs_invG, cell.vol/ngs**2)
def get_j_kpts(mydf,
dm_kpts,
hermi=1,
kpts=numpy.zeros((1, 3)),
kpts_band=None):
if kpts_band is not None:
return get_j_for_bands(mydf, dm_kpts, hermi, kpts, kpts_band)
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]
vj_kpts = numpy.zeros((nset, nkpts, nao, nao), dtype=numpy.complex128)
kpt_allow = numpy.zeros(3)
coulG = mydf.weighted_coulG(kpt_allow, False, mydf.gs)
max_memory = (mydf.max_memory - lib.current_memory()[0]) * .8
weight = 1. / len(kpts)
dmsC = dms.conj()
for aoaoks, p0, p1 in mydf.ft_loop(mydf.gs,
kpt_allow,
kpts,
max_memory=max_memory):
vG = [0] * nset
#:rho = numpy.einsum('lkL,lk->L', pqk.conj(), dm)
for k, aoao in enumerate(aoaoks):
for i in range(nset):
rho = numpy.einsum('ij,Lij->L', dmsC[i, k], aoao).conj()
vG[i] += rho * coulG[p0:p1]
for i in range(nset):
vG[i] *= weight
for k, aoao in enumerate(aoaoks):
for i in range(nset):
vj_kpts[i, k] += numpy.einsum('L,Lij->ij', vG[i], aoao)
aoao = aoaoks = p0 = p1 = None
if gamma_point(kpts):
vj_kpts = vj_kpts.real.copy()
return _format_jks(vj_kpts, dm_kpts, kpts_band, kpts)
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 = (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
vG = vpplocG
vj = numpy.zeros((nkpts, nao_pair), dtype=numpy.complex128)
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))
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)
vG = numpy.einsum('i,xi->x', charge, aoaux) * coulG
max_memory = max(2000, mydf.max_memory - lib.current_memory()[0])
for aoaoks, p0, p1 in mydf.ft_loop(mydf.gs,
kpt_allow,
kpts_lst,
max_memory=max_memory,
aosym='s2'):
for k, aoao in enumerate(aoaoks):
# 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 gamma_point(kpts_lst[k]):
vj[k] += numpy.einsum('k,kx->x', vG[p0:p1].real, aoao.real)
vj[k] += numpy.einsum('k,kx->x', vG[p0:p1].imag, aoao.imag)
else:
vj[k] += numpy.einsum('k,kx->x', vG[p0:p1].conj(), aoao)
t1 = log.timer_debug1('contracting Vnuc', *t1)
vj_kpts = []
for k, kpt in enumerate(kpts_lst):
if gamma_point(kpt):
vj_kpts.append(lib.unpack_tril(vj[k].real.copy()))
else:
vj_kpts.append(lib.unpack_tril(vj[k]))
if kpts is None or numpy.shape(kpts) == (3, ):
vj_kpts = vj_kpts[0]
return numpy.asarray(vj_kpts)
def get_jk(mydf,
dm,
hermi=1,
kpt=numpy.zeros(3),
kpts_band=None,
with_j=True,
with_k=True,
exxdiv=None):
'''JK for given k-point'''
vj = vk = None
if kpts_band is not None and abs(kpt - kpts_band).sum() > 1e-9:
kpt = numpy.reshape(kpt, (1, 3))
if with_k:
vk = get_k_kpts(mydf, dm, hermi, kpt, kpts_band, exxdiv)
if with_j:
vj = get_j_kpts(mydf, dm, hermi, kpt, kpts_band)
return vj, vk
cell = mydf.cell
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = (time.clock(), time.time())
if mydf._cderi is None or not mydf.has_kpts(kpts_band):
if mydf._cderi is not None:
log.warn(
'DF integrals for band k-points were not found %s. '
'DF integrals will be rebuilt to include band k-points.',
mydf._cderi)
mydf.build(kpts_band=kpts_band)
t1 = log.timer_debug1('Init get_jk', *t1)
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))
dmsR = dms.real.reshape(nset, nao, nao)
dmsI = dms.imag.reshape(nset, nao, nao)
mem_now = lib.current_memory()[0]
max_memory = max(2000, (mydf.max_memory - mem_now))
if with_j:
vjR = numpy.zeros((nset, nao, nao))
vjI = numpy.zeros((nset, nao, nao))
if with_k:
vkR = numpy.zeros((nset, nao, nao))
vkI = numpy.zeros((nset, nao, nao))
buf1R = numpy.empty((mydf.blockdim * nao**2))
buf2R = numpy.empty((mydf.blockdim * nao**2))
buf1I = numpy.zeros((mydf.blockdim * nao**2))
buf2I = numpy.empty((mydf.blockdim * nao**2))
max_memory *= .5
log.debug1('max_memory = %d MB (%d in use)', max_memory, mem_now)
def contract_k(pLqR, pLqI):
# K ~ 'iLj,lLk*,li->kj' + 'lLk*,iLj,li->kj'
#:pLq = (LpqR + LpqI.reshape(-1,nao,nao)*1j).transpose(1,0,2)
#:tmp = numpy.dot(dm, pLq.reshape(nao,-1))
#:vk += numpy.dot(pLq.reshape(-1,nao).conj().T, tmp.reshape(-1,nao))
nrow = pLqR.shape[1]
tmpR = numpy.ndarray((nao, nrow * nao), buffer=buf2R)
if k_real:
for i in range(nset):
lib.ddot(dmsR[i], pLqR.reshape(nao, -1), 1, tmpR)
lib.ddot(
pLqR.reshape(-1, nao).T, tmpR.reshape(-1, nao), 1, vkR[i],
1)
else:
tmpI = numpy.ndarray((nao, nrow * nao), buffer=buf2I)
for i in range(nset):
zdotNN(dmsR[i], dmsI[i], pLqR.reshape(nao, -1),
pLqI.reshape(nao, -1), 1, tmpR, tmpI, 0)
zdotCN(
pLqR.reshape(-1, nao).T,
pLqI.reshape(-1, nao).T, tmpR.reshape(-1, nao),
tmpI.reshape(-1, nao), 1, vkR[i], vkI[i], 1)
pLqI = None
thread_k = None
for LpqR, LpqI in mydf.sr_loop(kptii, max_memory, False):
LpqR = LpqR.reshape(-1, nao, nao)
t1 = log.timer_debug1(' load', *t1)
if thread_k is not None:
thread_k.join()
if with_j:
#:rho_coeff = numpy.einsum('Lpq,xqp->xL', Lpq, dms)
#:vj += numpy.dot(rho_coeff, Lpq.reshape(-1,nao**2))
rhoR = numpy.einsum('Lpq,xpq->xL', LpqR, dmsR)
if not j_real:
LpqI = LpqI.reshape(-1, nao, nao)
rhoR -= numpy.einsum('Lpq,xpq->xL', LpqI, dmsI)
rhoI = numpy.einsum('Lpq,xpq->xL', LpqR, dmsI)
rhoI += numpy.einsum('Lpq,xpq->xL', LpqI, dmsR)
vjR += numpy.einsum('xL,Lpq->xpq', rhoR, LpqR)
if not j_real:
vjR -= numpy.einsum('xL,Lpq->xpq', rhoI, LpqI)
vjI += numpy.einsum('xL,Lpq->xpq', rhoR, LpqI)
vjI += numpy.einsum('xL,Lpq->xpq', rhoI, LpqR)
t1 = log.timer_debug1(' with_j', *t1)
if with_k:
nrow = LpqR.shape[0]
pLqR = numpy.ndarray((nao, nrow, nao), buffer=buf1R)
pLqR[:] = LpqR.transpose(1, 0, 2)
if not k_real:
pLqI = numpy.ndarray((nao, nrow, nao), buffer=buf1I)
if LpqI is not None:
pLqI[:] = LpqI.reshape(-1, nao, nao).transpose(1, 0, 2)
thread_k = lib.background_thread(contract_k, pLqR, pLqI)
t1 = log.timer_debug1(' with_k', *t1)
LpqR = LpqI = pLqR = pLqI = None
if thread_k is not None:
thread_k.join()
thread_k = None
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 exxdiv:
assert (exxdiv.lower() == 'ewald')
_ewald_exxdiv_for_G0(cell, kpt, dms, vk)
vk = vk.reshape(dm.shape)
t1 = log.timer('sr jk', *t1)
return vj, vk
def get_eri(mydf, kpts=None, compact=True):
if mydf._cderi is None or mydf.auxcell is None:
mydf.build()
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
nao = cell.nao_nr()
nao_pair = nao * (nao + 1) // 2
max_memory = max(
2000, mydf.max_memory - lib.current_memory()[0] - nao**4 * 8 / 1e6)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl):
eriR = numpy.zeros((nao_pair, nao_pair))
for LpqR, LpqI in mydf.sr_loop(kptijkl[:2], max_memory, True):
lib.ddot(LpqR.T, LpqR, 1, eriR, 1)
LpqR = LpqI = None
if not compact:
eriR = ao2mo.restore(1, eriR, nao).reshape(nao**2, -1)
return eriR
elif is_zero(kpti - kptk) and is_zero(kptj - kptl):
eriR = numpy.zeros((nao * nao, nao * nao))
eriI = numpy.zeros((nao * nao, nao * nao))
for LpqR, LpqI in mydf.sr_loop(kptijkl[:2], max_memory, False):
zdotNN(LpqR.T, LpqI.T, LpqR, LpqI, 1, eriR, eriI, 1)
LpqR = LpqI = None
return eriR + eriI * 1j
####################
# (kpt) i == j == k == l != 0
#
# (kpt) i == l && j == k && i != j && j != k =>
# both vbar and ovlp are zero. It corresponds to the exchange integral.
#
# complex integrals, N^4 elements
elif is_zero(kpti - kptl) and is_zero(kptj - kptk):
eriR = numpy.zeros((nao * nao, nao * nao))
eriI = numpy.zeros((nao * nao, nao * nao))
for LpqR, LpqI in mydf.sr_loop(kptijkl[:2], max_memory, False):
zdotNC(LpqR.T, LpqI.T, LpqR, LpqI, 1, eriR, eriI, 1)
LpqR = LpqI = None
# transpose(0,1,3,2) because
# j == k && i == l =>
# (L|ij).transpose(0,2,1).conj() = (L^*|ji) = (L^*|kl) => (M|kl)
eri = lib.transpose((eriR + eriI * 1j).reshape(-1, nao, nao),
axes=(0, 2, 1))
return eri.reshape(nao**2, -1)
####################
# aosym = s1, complex integrals
#
# kpti == kptj => kptl == kptk
# If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave
# vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition.
# So kptl/b - kptk/b must be -1 < k/b < 1.
#
else:
eriR = numpy.zeros((nao * nao, nao * nao))
eriI = numpy.zeros((nao * nao, nao * nao))
for (LpqR, LpqI), (LrsR, LrsI) in \
lib.izip(mydf.sr_loop(kptijkl[:2], max_memory, False),
mydf.sr_loop(kptijkl[2:], max_memory, False)):
zdotNN(LpqR.T, LpqI.T, LrsR, LrsI, 1, eriR, eriI, 1)
LpqR = LpqI = LrsR = LrsI = None
return eriR + eriI * 1j
def general(mydf, mo_coeffs, kpts=None, compact=True):
if mydf._cderi is None or mydf.auxcell is None:
mydf.build()
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2:
mo_coeffs = (mo_coeffs, ) * 4
all_real = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs)
max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .5)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl) and all_real:
ijmosym, nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0],
mo_coeffs[1], compact)
klmosym, nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2],
mo_coeffs[3], compact)
eri_mo = numpy.zeros((nij_pair, nkl_pair))
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2])
and iden_coeffs(mo_coeffs[1], mo_coeffs[3]))
ijR = klR = None
for LpqR, LpqI in mydf.sr_loop(kptijkl[:2], max_memory, True):
ijR, klR = _dtrans(LpqR, ijR, ijmosym, moij, ijslice, LpqR, klR,
klmosym, mokl, klslice, sym)
lib.ddot(ijR.T, klR, 1, eri_mo, 1)
LpqR = LpqI = None
return eri_mo
elif is_zero(kpti - kptk) and is_zero(kptj - kptl):
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:]
eri_mo = numpy.zeros((nij_pair, nkl_pair), dtype=numpy.complex)
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2])
and iden_coeffs(mo_coeffs[1], mo_coeffs[3]))
zij = zkl = None
for LpqR, LpqI in mydf.sr_loop(kptijkl[:2], max_memory, False):
buf = LpqR + LpqI * 1j
zij, zkl = _ztrans(buf, zij, moij, ijslice, buf, zkl, mokl,
klslice, sym)
lib.dot(zij.T, zkl, 1, eri_mo, 1)
LpqR = LpqI = buf = None
return eri_mo
####################
# (kpt) i == j == k == l != 0
# (kpt) i == l && j == k && i != j && j != k =>
#
elif is_zero(kpti - kptl) and is_zero(kptj - kptk):
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nlk_pair, molk, lkslice = _conc_mos(mo_coeffs[3], mo_coeffs[2])[1:]
eri_mo = numpy.zeros((nij_pair, nlk_pair), dtype=numpy.complex)
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[3])
and iden_coeffs(mo_coeffs[1], mo_coeffs[2]))
zij = zlk = None
for LpqR, LpqI in mydf.sr_loop(kptijkl[:2], max_memory, False):
buf = LpqR + LpqI * 1j
zij, zlk = _ztrans(buf, zij, moij, ijslice, buf, zlk, molk,
lkslice, sym)
lib.dot(zij.T, zlk.conj(), 1, eri_mo, 1)
LpqR = LpqI = buf = None
nmok = mo_coeffs[2].shape[1]
nmol = mo_coeffs[3].shape[1]
eri_mo = lib.transpose(eri_mo.reshape(-1, nmol, nmok), axes=(0, 2, 1))
return eri_mo.reshape(nij_pair, nlk_pair)
####################
# aosym = s1, complex integrals
#
# If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave
# vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition.
# So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk
#
else:
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:]
eri_mo = numpy.zeros((nij_pair, nkl_pair), dtype=numpy.complex)
zij = zkl = None
for (LpqR, LpqI), (LrsR, LrsI) in \
lib.izip(mydf.sr_loop(kptijkl[:2], max_memory, False),
mydf.sr_loop(kptijkl[2:], max_memory, False)):
zij, zkl = _ztrans(LpqR + LpqI * 1j, zij, moij, ijslice,
LrsR + LrsI * 1j, zkl, mokl, klslice, False)
lib.dot(zij.T, zkl, 1, eri_mo, 1)
LpqR = LpqI = LrsR = LrsI = None
return eri_mo
def get_eri(mydf, kpts=None, compact=True):
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
q = kptj - kpti
coulG = mydf.weighted_coulG(q, False, mydf.gs)
nao = cell.nao_nr()
nao_pair = nao * (nao + 1) // 2
max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .8)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl):
eriR = numpy.zeros((nao_pair, nao_pair))
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mydf.gs, kptijkl[:2], q, max_memory=max_memory,
aosym='s2'):
vG = numpy.sqrt(coulG[p0:p1])
pqkR *= vG
pqkI *= vG
lib.ddot(pqkR, pqkR.T, 1, eriR, 1)
lib.ddot(pqkI, pqkI.T, 1, eriR, 1)
pqkR = pqkI = None
if not compact:
eriR = ao2mo.restore(1, eriR, nao).reshape(nao**2, -1)
return eriR
####################
# (kpt) i == j == k == l != 0
# (kpt) i == l && j == k && i != j && j != k =>
#
# complex integrals, N^4 elements
elif is_zero(kpti - kptl) and is_zero(kptj - kptk):
eriR = numpy.zeros((nao**2, nao**2))
eriI = numpy.zeros((nao**2, nao**2))
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mydf.gs, kptijkl[:2], q, max_memory=max_memory):
vG = numpy.sqrt(coulG[p0:p1])
pqkR *= vG
pqkI *= vG
# rho_pq(G+k_pq) * conj(rho_rs(G-k_rs))
zdotNC(pqkR, pqkI, pqkR.T, pqkI.T, 1, eriR, eriI, 1)
pqkR = pqkI = None
pqkR = pqkI = coulG = None
# transpose(0,1,3,2) because
# j == k && i == l =>
# (L|ij).transpose(0,2,1).conj() = (L^*|ji) = (L^*|kl) => (M|kl)
# rho_rs(-G+k_rs) = conj(transpose(rho_sr(G+k_sr), (0,2,1)))
eri = lib.transpose((eriR + eriI * 1j).reshape(-1, nao, nao),
axes=(0, 2, 1))
return eri.reshape(nao**2, -1)
####################
# aosym = s1, complex integrals
#
# If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave
# vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition.
# So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk
#
else:
eriR = numpy.zeros((nao**2, nao**2))
eriI = numpy.zeros((nao**2, nao**2))
# rho_rs(-G-k) = rho_rs(conj(G+k)) = conj(rho_sr(G+k))
for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \
lib.izip(mydf.pw_loop(mydf.gs, kptijkl[:2], q, max_memory=max_memory*.5),
mydf.pw_loop(mydf.gs,-kptijkl[2:], q, max_memory=max_memory*.5)):
pqkR *= coulG[p0:p1]
pqkI *= coulG[p0:p1]
# rho_pq(G+k_pq) * conj(rho_sr(G+k_pq))
zdotNC(pqkR, pqkI, rskR.T, rskI.T, 1, eriR, eriI, 1)
pqkR = pqkI = rskR = rskI = None
return (eriR + eriI * 1j)
def general(mydf, mo_coeffs, kpts=None, compact=True):
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2:
mo_coeffs = (mo_coeffs, ) * 4
q = kptj - kpti
coulG = mydf.weighted_coulG(q, False, mydf.gs)
all_real = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs)
max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .5)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl) and all_real:
ijmosym, nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0],
mo_coeffs[1], compact)
klmosym, nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2],
mo_coeffs[3], compact)
eri_mo = numpy.zeros((nij_pair, nkl_pair))
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2])
and iden_coeffs(mo_coeffs[1], mo_coeffs[3]))
ijR = ijI = klR = klI = buf = None
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mydf.gs, kptijkl[:2], q, max_memory=max_memory,
aosym='s2'):
vG = numpy.sqrt(coulG[p0:p1])
pqkR *= vG
pqkI *= vG
buf = lib.transpose(pqkR, out=buf)
ijR, klR = _dtrans(buf, ijR, ijmosym, moij, ijslice, buf, klR,
klmosym, mokl, klslice, sym)
lib.ddot(ijR.T, klR, 1, eri_mo, 1)
buf = lib.transpose(pqkI, out=buf)
ijI, klI = _dtrans(buf, ijI, ijmosym, moij, ijslice, buf, klI,
klmosym, mokl, klslice, sym)
lib.ddot(ijI.T, klI, 1, eri_mo, 1)
pqkR = pqkI = None
return eri_mo
####################
# (kpt) i == j == k == l != 0
# (kpt) i == l && j == k && i != j && j != k =>
#
elif is_zero(kpti - kptl) and is_zero(kptj - kptk):
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nlk_pair, molk, lkslice = _conc_mos(mo_coeffs[3], mo_coeffs[2])[1:]
eri_mo = numpy.zeros((nij_pair, nlk_pair), dtype=numpy.complex)
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[3])
and iden_coeffs(mo_coeffs[1], mo_coeffs[2]))
zij = zlk = buf = None
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mydf.gs, kptijkl[:2], q, max_memory=max_memory):
buf = lib.transpose(pqkR + pqkI * 1j, out=buf)
buf *= numpy.sqrt(coulG[p0:p1]).reshape(-1, 1)
zij, zlk = _ztrans(buf, zij, moij, ijslice, buf, zlk, molk,
lkslice, sym)
lib.dot(zij.T, zlk.conj(), 1, eri_mo, 1)
pqkR = pqkI = None
nmok = mo_coeffs[2].shape[1]
nmol = mo_coeffs[3].shape[1]
eri_mo = lib.transpose(eri_mo.reshape(-1, nmol, nmok), axes=(0, 2, 1))
return eri_mo.reshape(nij_pair, nlk_pair)
####################
# aosym = s1, complex integrals
#
# If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave
# vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition.
# So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk
#
else:
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:]
eri_mo = numpy.zeros((nij_pair, nkl_pair), dtype=numpy.complex)
tao = []
ao_loc = None
zij = zkl = buf = None
for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \
lib.izip(mydf.pw_loop(mydf.gs, kptijkl[:2], q, max_memory=max_memory*.5),
mydf.pw_loop(mydf.gs,-kptijkl[2:], q, max_memory=max_memory*.5)):
buf = lib.transpose(pqkR + pqkI * 1j, out=buf)
zij = _ao2mo.r_e2(buf, moij, ijslice, tao, ao_loc, out=zij)
buf = lib.transpose(rskR - rskI * 1j, out=buf)
zkl = _ao2mo.r_e2(buf, mokl, klslice, tao, ao_loc, out=zkl)
zij *= coulG[p0:p1].reshape(-1, 1)
lib.dot(zij.T, zkl, 1, eri_mo, 1)
pqkR = pqkI = rskR = rskI = None
return eri_mo
def get_jk(mydf,
dm,
hermi=1,
kpt=numpy.zeros(3),
kpts_band=None,
with_j=True,
with_k=True,
exxdiv=None):
'''JK for given k-point'''
vj = vk = None
if kpts_band is not None and abs(kpt - kpts_band).sum() > 1e-9:
kpt = numpy.reshape(kpt, (1, 3))
if with_k:
vk = get_k_kpts(mydf, dm, hermi, kpt, kpts_band, exxdiv)
if with_j:
vj = get_j_kpts(mydf, dm, hermi, kpt, kpts_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)
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, input_band = _format_kpts_band(kpts_band, kpts), kpts_band
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>)
#buf1R = numpy.empty((blksize*nao**2))
#buf1I = numpy.empty((blksize*nao**2))
for aoaoks, p0, p1 in mydf.ft_loop(mydf.gs,
kpt,
kptjs,
max_memory=max_memory1):
coulG = numpy.sqrt(vkcoulG[p0:p1])
nG = p1 - p0
bufR = numpy.empty((nG * nao**2))
bufI = numpy.empty((nG * nao**2))
buf1R = numpy.empty((nG * nao**2))
buf1I = numpy.empty((nG * nao**2))
for k, aoao in enumerate(aoaoks):
ki = kpti_idx[k]
kj = kptj_idx[k]
# case 1: k_pq = (pi|iq)
#:v4 = numpy.einsum('ijL,lkL->ijkl', pqk, pqk.conj())
#:vk += numpy.einsum('ijkl,jk->il', v4, dm)
pLqR = numpy.ndarray((nao, nG, nao), buffer=bufR)
pLqI = numpy.ndarray((nao, nG, nao), buffer=bufI)
pLqR[:] = aoao.real.reshape(nG, nao, nao).transpose(1, 0, 2)
pLqI[:] = aoao.imag.reshape(nG, nao, nao).transpose(1, 0, 2)
pLqR *= coulG.reshape(1, nG, 1)
pLqI *= coulG.reshape(1, nG, 1)
iLkR = numpy.ndarray((nao * nG, nao), buffer=buf1R)
iLkI = numpy.ndarray((nao * nG, nao), buffer=buf1I)
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)
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, input_band, kpts)
def get_k_kpts(mydf,
dm_kpts,
hermi=1,
kpts=np.zeros((1, 3)),
kpts_band=None,
exxdiv=None):
'''Get the Coulomb (J) and exchange (K) AO matrices at sampled k-points.
Args:
dm_kpts : (nkpts, nao, nao) ndarray
Density matrix at each k-point
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
vk : (nkpts, nao, nao) ndarray
or list of vj and vk if the input dm_kpts is a list of DMs
'''
cell = mydf.cell
gs = mydf.gs
coords = cell.gen_uniform_grids(gs)
ngs = coords.shape[0]
kpts = np.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 / ngs)
input_band = kpts_band
kpts_band, single_kpt_band = _format_kpts_band(kpts_band, kpts)
nband = len(kpts_band)
if gamma_point(kpts_band) and gamma_point(kpts):
vk_kpts = np.zeros((nset, nband, nao, nao), dtype=dms.dtype)
else:
vk_kpts = np.zeros((nset, nband, nao, nao), dtype=np.complex128)
if input_band is None:
ao_kpts = mydf._numint.eval_ao(cell,
coords,
kpts,
non0tab=mydf.non0tab)
for k2, ao_k2 in enumerate(ao_kpts):
kpt2 = kpts[k2]
aoR_dms = [lib.dot(ao_k2, dms[i, k2]) for i in range(nset)]
for k1, ao_k1 in enumerate(ao_kpts):
kpt1 = kpts_band[k1]
vkR_k1k2 = get_vkR(mydf, cell, ao_k1, ao_k2, kpt1, kpt2,
coords, gs, exxdiv)
for i in range(nset):
tmp_Rq = np.einsum('Rqs,Rs->Rq', vkR_k1k2, aoR_dms[i])
vk_kpts[i, k1] += weight * lib.dot(ao_k1.T.conj(), tmp_Rq)
vkR_k1k2 = aoR_dms = tmp_Rq = None
else:
for k2, ao_k2 in mydf.aoR_loop(gs, kpts):
kpt2 = kpts[k2]
aoR_dms = [lib.dot(ao_k2, dms[i, k2]) for i in range(nset)]
for k1, ao_k1 in mydf.aoR_loop(gs, kpts_band):
kpt1 = kpts_band[k1]
vkR_k1k2 = get_vkR(mydf, cell, ao_k1, ao_k2, kpt1, kpt2,
coords, gs, exxdiv)
for i in range(nset):
tmp_Rq = np.einsum('Rqs,Rs->Rq', vkR_k1k2, aoR_dms[i])
vk_kpts[i, k1] += weight * lib.dot(ao_k1.T.conj(), tmp_Rq)
vkR_k1k2 = aoR_dms = tmp_Rq = None
return _format_jks(vk_kpts, dm_kpts, kpts_band, kpts, single_kpt_band)
def get_ao_pairs_G(mydf,
kpts=numpy.zeros((2, 3)),
q=None,
shls_slice=None,
compact=False):
'''Calculate forward (G|ij) FFT of all AO pairs.
Returns:
ao_pairs_G : 2D complex array
For gamma point, the shape is (ngs, nao*(nao+1)/2); otherwise the
shape is (ngs, nao*nao)
'''
if kpts is None: kpts = numpy.zeros((2, 3))
cell = mydf.cell
kpts = numpy.asarray(kpts)
coords = cell.gen_uniform_grids(mydf.gs)
ngs = len(coords)
if shls_slice is None:
i0, i1 = j0, j1 = (0, cell.nao_nr())
else:
ish0, ish1, jsh0, jsh1 = shls_slice
ao_loc = cell.ao_loc_nr()
i0 = ao_loc[ish0]
i1 = ao_loc[ish1]
j0 = ao_loc[jsh0]
j1 = ao_loc[jsh1]
def trans(aoi, aoj, fac=1):
if id(aoi) == id(aoj):
aoi = aoj = numpy.asarray(aoi.T, order='C')
else:
aoi = numpy.asarray(aoi.T, order='C')
aoj = numpy.asarray(aoj.T, order='C')
ni = aoi.shape[0]
nj = aoj.shape[0]
ao_pairs_G = numpy.empty((ni, nj, ngs), dtype=numpy.complex128)
for i in range(ni):
ao_pairs_G[i] = tools.fft(fac * aoi[i].conj() * aoj, mydf.gs)
ao_pairs_G = ao_pairs_G.reshape(-1, ngs).T
return ao_pairs_G
if compact and gamma_point(kpts): # gamma point
ao = mydf._numint.eval_ao(cell, coords, kpts[:1])[0]
ao = numpy.asarray(ao.T, order='C')
npair = i1 * (i1 + 1) // 2 - i0 * (i0 + 1) // 2
ao_pairs_G = numpy.empty((npair, ngs), dtype=numpy.complex128)
ij = 0
for i in range(i0, i1):
ao_pairs_G[ij:ij + i + 1] = tools.fft(ao[i] * ao[:i + 1], mydf.gs)
ij += i + 1
ao_pairs_G = ao_pairs_G.T
elif is_zero(kpts[0] - kpts[1]):
ao = mydf._numint.eval_ao(cell, coords, kpts[:1])[0]
ao_pairs_G = trans(ao[:, i0:i1], ao[:, j0:j1])
else:
if q is None:
q = kpts[1] - kpts[0]
aoi, aoj = mydf._numint.eval_ao(cell, coords, kpts[:2])
fac = numpy.exp(-1j * numpy.dot(coords, q))
ao_pairs_G = trans(aoi[:, i0:i1], aoj[:, j0:j1], fac)
return ao_pairs_G
def general(mydf, mo_coeffs, kpts=None, compact=False):
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2:
mo_coeffs = (mo_coeffs,) * 4
mo_coeffs = [numpy.asarray(mo, order='F') for mo in mo_coeffs]
allreal = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs)
q = kptj - kpti
coulG = tools.get_coulG(cell, q, gs=mydf.gs)
ngs = len(coulG)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl) and allreal:
mo_pairs_G = get_mo_pairs_G(mydf, mo_coeffs[:2], kptijkl[:2], q,
compact=compact)
if ((iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and
iden_coeffs(mo_coeffs[1], mo_coeffs[3]))):
mo_pairs_G *= numpy.sqrt(coulG).reshape(-1,1)
moijR = moklR = mo_pairs_G.real.copy()
moijI = moklI = mo_pairs_G.imag.copy()
mo_pairs_G = None
else:
mo_pairs_G *= coulG
moijR = mo_pairs_G.real.copy()
moijI = mo_pairs_G.imag.copy()
mo_pairs_G = None
mo_pairs_G = get_mo_pairs_G(mydf, mo_coeffs[2:], kptijkl[2:], q,
compact=compact)
moklR = mo_pairs_G.real.copy()
moklI = mo_pairs_G.imag.copy()
mo_pairs_G = None
eri = lib.dot(moijR.T, moklR, cell.vol/ngs**2)
eri = lib.dot(moijI.T, moklI, cell.vol/ngs**2, eri, 1)
return eri
####################
# (kpt) i == j == k == l != 0
# (kpt) i == l && j == k && i != j && j != k =>
#
# complex integrals, N^4 elements
elif (is_zero(kpti-kptl) and is_zero(kptj-kptk) and
iden_coeffs(mo_coeffs[0], mo_coeffs[3]) and
iden_coeffs(mo_coeffs[1], mo_coeffs[2])):
nmoi = mo_coeffs[0].shape[1]
nmoj = mo_coeffs[1].shape[1]
mo_ij_G = get_mo_pairs_G(mydf, mo_coeffs[:2], kptijkl[:2])
mo_ij_G *= numpy.sqrt(coulG).reshape(-1,1)
mo_kl_G = mo_ij_G.T.reshape(nmoi,nmoj,-1).transpose(1,0,2).conj()
mo_kl_G = mo_kl_G.reshape(-1,ngs)
return lib.dot(mo_ij_G.T, mo_kl_G.T, cell.vol/ngs**2)
####################
# aosym = s1, complex integrals
#
else:
nmok = mo_coeffs[2].shape[1]
nmol = mo_coeffs[3].shape[1]
mo_ij_G = get_mo_pairs_G(mydf, mo_coeffs[:2], kptijkl[:2], q)
mo_ij_G *= coulG.reshape(-1,1)
# mo_pairs_invG = rho_rs(-G+k_rs) = conj(rho_sr(G+k_sr)).swap(r,s)
mo_kl_G = get_mo_pairs_G(mydf, (mo_coeffs[3],mo_coeffs[2]),
(kptl,kptk), q)
mo_kl_G = mo_kl_G.T.reshape(nmol,nmok,-1).transpose(1,0,2).conj()
mo_kl_G = mo_kl_G.reshape(-1,ngs)
return lib.dot(mo_ij_G.T, mo_kl_G.T, cell.vol/ngs**2)
def get_pp(mydf, kpts=None):
'''Get the periodic pseudotential nuc-el AO matrix, with G=0 removed.
'''
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
gs = mydf.gs
SI = cell.get_SI()
Gv = cell.get_Gv(gs)
vpplocG = pseudo.get_vlocG(cell, Gv)
vpplocG = -numpy.einsum('ij,ij->j', SI, vpplocG)
vpplocG[0] = numpy.sum(
pseudo.get_alphas(cell)) # from get_jvloc_G0 function
ngs = len(vpplocG)
# vpploc evaluated in real-space
vpplocR = tools.ifft(vpplocG, cell.gs).real
vpp = [
lib.dot(aoR.T.conj() * vpplocR, aoR)
for k, aoR in mydf.aoR_loop(gs, kpts_lst)
]
# vppnonloc evaluated in reciprocal space
fakemol = gto.Mole()
fakemol._atm = numpy.zeros((1, gto.ATM_SLOTS), dtype=numpy.int32)
fakemol._bas = numpy.zeros((1, gto.BAS_SLOTS), dtype=numpy.int32)
ptr = gto.PTR_ENV_START
fakemol._env = numpy.zeros(ptr + 10)
fakemol._bas[0, gto.NPRIM_OF] = 1
fakemol._bas[0, gto.NCTR_OF] = 1
fakemol._bas[0, gto.PTR_EXP] = ptr + 3
fakemol._bas[0, gto.PTR_COEFF] = ptr + 4
# buf for SPG_lmi upto l=0..3 and nl=3
buf = numpy.empty((48, ngs), dtype=numpy.complex128)
def vppnl_by_k(kpt):
Gk = Gv + kpt
G_rad = lib.norm(Gk, axis=1)
aokG = ft_ao.ft_ao(cell, Gv, kpt=kpt) * (ngs / cell.vol)
vppnl = 0
for ia in range(cell.natm):
symb = cell.atom_symbol(ia)
if symb not in cell._pseudo:
continue
pp = cell._pseudo[symb]
p1 = 0
for l, proj in enumerate(pp[5:]):
rl, nl, hl = proj
if nl > 0:
fakemol._bas[0, gto.ANG_OF] = l
fakemol._env[ptr + 3] = .5 * rl**2
fakemol._env[ptr + 4] = rl**(l + 1.5) * numpy.pi**1.25
pYlm_part = dft.numint.eval_ao(fakemol, Gk, deriv=0)
p0, p1 = p1, p1 + nl * (l * 2 + 1)
# pYlm is real, SI[ia] is complex
pYlm = numpy.ndarray((nl, l * 2 + 1, ngs),
dtype=numpy.complex128,
buffer=buf[p0:p1])
for k in range(nl):
qkl = pseudo.pp._qli(G_rad * rl, l, k)
pYlm[k] = pYlm_part.T * qkl
#:SPG_lmi = numpy.einsum('g,nmg->nmg', SI[ia].conj(), pYlm)
#:SPG_lm_aoG = numpy.einsum('nmg,gp->nmp', SPG_lmi, aokG)
#:tmp = numpy.einsum('ij,jmp->imp', hl, SPG_lm_aoG)
#:vppnl += numpy.einsum('imp,imq->pq', SPG_lm_aoG.conj(), tmp)
if p1 > 0:
SPG_lmi = buf[:p1]
SPG_lmi *= SI[ia].conj()
SPG_lm_aoGs = lib.zdot(SPG_lmi, aokG)
p1 = 0
for l, proj in enumerate(pp[5:]):
rl, nl, hl = proj
if nl > 0:
p0, p1 = p1, p1 + nl * (l * 2 + 1)
hl = numpy.asarray(hl)
SPG_lm_aoG = SPG_lm_aoGs[p0:p1].reshape(
nl, l * 2 + 1, -1)
tmp = numpy.einsum('ij,jmp->imp', hl, SPG_lm_aoG)
vppnl += numpy.einsum('imp,imq->pq', SPG_lm_aoG.conj(),
tmp)
return vppnl * (1. / ngs**2)
for k, kpt in enumerate(kpts_lst):
vppnl = vppnl_by_k(kpt)
if gamma_point(kpt):
vpp[k] = vpp[k].real + vppnl.real
else:
vpp[k] += vppnl
if kpts is None or numpy.shape(kpts) == (3, ):
vpp = vpp[0]
return numpy.asarray(vpp)
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[0] / w[-1],
numpy.count_nonzero(w < df.LINEAR_DEP_THR))
v = v[:, w > df.LINEAR_DEP_THR].T.conj()
v /= numpy.sqrt(w[w > df.LINEAR_DEP_THR]).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
shls_slice = (bstart, bend, 0, bend)
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 aux_e2(cell,
auxcell,
erifile,
intor='int3c2e_sph',
aosym='s2ij',
comp=1,
kptij_lst=None,
dataname='eri_mo',
shls_slice=None,
max_memory=2000,
verbose=0):
r'''3-center AO integrals (ij|L) with double lattice sum:
\sum_{lm} (i[l]j[m]|L[0]), where L is the auxiliary basis.
On diks, the integrals are stored as (kptij_idx, naux, nao_pair)
Args:
kptij_lst : (*,2,3) array
A list of (kpti, kptj)
'''
intor = gto.moleintor.ascint3(intor)
if h5py.is_hdf5(erifile):
feri = h5py.File(erifile)
if dataname in feri:
del (feri[dataname])
if dataname + '-kptij' in feri:
del (feri[dataname + '-kptij'])
else:
feri = h5py.File(erifile, 'w')
if kptij_lst is None:
kptij_lst = numpy.zeros((1, 2, 3))
feri[dataname + '-kptij'] = kptij_lst
if shls_slice is None:
shls_slice = (0, cell.nbas, 0, cell.nbas, 0, auxcell.nbas)
ao_loc = cell.ao_loc_nr()
aux_loc = auxcell.ao_loc_nr('ssc' in intor)[:shls_slice[5] + 1]
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
naux = aux_loc[shls_slice[5]] - aux_loc[shls_slice[4]]
nkptij = len(kptij_lst)
nii = (ao_loc[shls_slice[1]] * (ao_loc[shls_slice[1]] + 1) // 2 -
ao_loc[shls_slice[0]] * (ao_loc[shls_slice[0]] + 1) // 2)
nij = ni * nj
kpti = kptij_lst[:, 0]
kptj = kptij_lst[:, 1]
aosym_ks2 = abs(kpti - kptj).sum(axis=1) < KPT_DIFF_TOL
j_only = numpy.all(aosym_ks2)
#aosym_ks2 &= (aosym[:2] == 's2' and shls_slice[:2] == shls_slice[2:4])
aosym_ks2 &= aosym[:2] == 's2'
for k, kptij in enumerate(kptij_lst):
key = '%s/%d' % (dataname, k)
if gamma_point(kptij):
dtype = 'f8'
else:
dtype = 'c16'
if aosym_ks2[k]:
nao_pair = nii
else:
nao_pair = nij
if comp == 1:
shape = (naux, nao_pair)
else:
shape = (comp, naux, nao_pair)
chunks = (min(256, naux), min(256, nao_pair)) # 512 KB
feri.create_dataset(key, shape, dtype, chunks=chunks)
if naux == 0:
feri.close()
return erifile
if j_only and aosym[:2] == 's2':
assert (shls_slice[2] == 0)
nao_pair = nii
else:
nao_pair = nij
if gamma_point(kptij_lst):
dtype = numpy.double
else:
dtype = numpy.complex128
buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * ni * nj * comp)))
auxdims = aux_loc[shls_slice[4] + 1:shls_slice[5] +
1] - aux_loc[shls_slice[4]:shls_slice[5]]
auxranges = balance_segs(auxdims, buflen)
buflen = max([x[2] for x in auxranges])
buf = numpy.empty(nkptij * comp * ni * nj * buflen, dtype=dtype)
buf1 = numpy.empty(ni * nj * buflen, dtype=dtype)
int3c = wrap_int3c(cell, auxcell, intor, aosym, comp, kptij_lst)
naux0 = 0
for istep, auxrange in enumerate(auxranges):
sh0, sh1, nrow = auxrange
sub_slice = (shls_slice[0], shls_slice[1], shls_slice[2],
shls_slice[3], shls_slice[4] + sh0, shls_slice[4] + sh1)
mat = numpy.ndarray((nkptij, comp, nao_pair, nrow),
dtype=dtype,
buffer=buf)
mat = int3c(sub_slice, mat)
for k, kptij in enumerate(kptij_lst):
h5dat = feri['%s/%d' % (dataname, k)]
for icomp, v in enumerate(mat[k]):
v = lib.transpose(v, out=buf1)
if gamma_point(kptij):
v = v.real
if aosym_ks2[k] and v.shape[1] == ni**2:
v = lib.pack_tril(v.reshape(-1, ni, ni))
if comp == 1:
h5dat[naux0:naux0 + nrow] = v
else:
h5dat[icomp, naux0:naux0 + nrow] = v
naux0 += nrow
feri.close()
return erifile
def wrap_int3c(cell,
auxcell,
intor='int3c2e_sph',
aosym='s1',
comp=1,
kptij_lst=numpy.zeros((1, 2, 3))):
nbas = cell.nbas
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env, cell._atm,
cell._bas, cell._env)
ao_loc = gto.moleintor.make_loc(bas, intor)
aux_loc = auxcell.ao_loc_nr('ssc' in intor)
ao_loc = numpy.asarray(numpy.hstack([ao_loc, ao_loc[-1] + aux_loc[1:]]),
dtype=numpy.int32)
atm, bas, env = gto.conc_env(atm, bas, env, auxcell._atm, auxcell._bas,
auxcell._env)
Ls = cell.get_lattice_Ls()
nimgs = len(Ls)
kpti = kptij_lst[:, 0]
kptj = kptij_lst[:, 1]
if gamma_point(kptij_lst):
kk_type = 'g'
dtype = numpy.double
nkpts = nkptij = 1
kptij_idx = numpy.array([0], dtype=numpy.int32)
expkL = numpy.ones(1)
elif is_zero(kpti - kptj): # j_only
kk_type = 'k'
dtype = numpy.complex128
kpts = kptij_idx = kpti
expkL = numpy.exp(1j * numpy.dot(kpts, Ls.T))
nkpts = nkptij = len(kpts)
else:
kk_type = 'kk'
dtype = numpy.complex128
kpts = unique(numpy.vstack([kpti, kptj]))[0]
expkL = numpy.exp(1j * numpy.dot(kpts, Ls.T))
wherei = numpy.where(
abs(kpti.reshape(-1, 1, 3) - kpts).sum(axis=2) < KPT_DIFF_TOL)[1]
wherej = numpy.where(
abs(kptj.reshape(-1, 1, 3) - kpts).sum(axis=2) < KPT_DIFF_TOL)[1]
nkpts = len(kpts)
kptij_idx = numpy.asarray(wherei * nkpts + wherej, dtype=numpy.int32)
nkptij = len(kptij_lst)
fill = 'PBCnr3c_fill_%s%s' % (kk_type, aosym[:2])
drv = libpbc.PBCnr3c_drv
cintopt = _vhf.make_cintopt(atm, bas, env, intor)
# Remove the precomputed pair data because the pair data corresponds to the
# integral of cell #0 while the lattice sum moves shls to all repeated images.
libpbc.CINTdel_pairdata_optimizer(cintopt)
def int3c(shls_slice, out):
shls_slice = (shls_slice[0], shls_slice[1], nbas + shls_slice[2],
nbas + shls_slice[3], nbas * 2 + shls_slice[4],
nbas * 2 + shls_slice[5])
drv(
getattr(libpbc, intor),
getattr(libpbc, fill),
out.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nkptij),
ctypes.c_int(nkpts),
ctypes.c_int(comp),
ctypes.c_int(nimgs),
Ls.ctypes.data_as(ctypes.c_void_p),
expkL.ctypes.data_as(ctypes.c_void_p),
kptij_idx.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int * 6)(*shls_slice),
ao_loc.ctypes.data_as(ctypes.c_void_p),
cintopt,
atm.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(cell.natm),
bas.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nbas), # need to pass cell.nbas to libpbc.PBCnr3c_drv
env.ctypes.data_as(ctypes.c_void_p))
return out
return int3c
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())
if mydf._cderi is None or not mydf.has_kpts(kpts_band):
if mydf._cderi is not None:
log.warn(
'DF integrals for band k-points were not found %s. '
'DF integrals will be rebuilt to include band k-points.',
mydf._cderi)
mydf.build(kpts_band=kpts_band)
t1 = log.timer_debug1('Init get_k_kpts', *t1)
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
kpts_band, input_band = _format_kpts_band(kpts_band, kpts), kpts_band
nband = len(kpts_band)
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')
# K_pq = ( p{k1} i{k2} | i{k2} q{k1} )
bufR = numpy.empty((mydf.blockdim * nao**2))
bufI = numpy.empty((mydf.blockdim * nao**2))
max_memory = max(2000, mydf.max_memory - lib.current_memory()[0])
def make_kpt(ki, kj, swap_2e):
kpti = kpts[ki]
kptj = kpts_band[kj]
for LpqR, LpqI in mydf.sr_loop((kpti, kptj), max_memory, False):
nrow = LpqR.shape[0]
pLqR = numpy.ndarray((nao, nrow, nao), buffer=bufR)
pLqI = numpy.ndarray((nao, nrow, nao), buffer=bufI)
tmpR = numpy.ndarray((nao, nrow * nao), buffer=LpqR)
tmpI = numpy.ndarray((nao, nrow * nao), buffer=LpqI)
pLqR[:] = LpqR.reshape(-1, nao, nao).transpose(1, 0, 2)
pLqI[:] = LpqI.reshape(-1, nao, nao).transpose(1, 0, 2)
for i in range(nset):
zdotNN(dmsR[i, ki], dmsI[i, ki], pLqR.reshape(nao, -1),
pLqI.reshape(nao, -1), 1, tmpR, tmpI)
zdotCN(
pLqR.reshape(-1, nao).T,
pLqI.reshape(-1, nao).T, tmpR.reshape(-1, nao),
tmpI.reshape(-1, nao), 1, vkR[i, kj], vkI[i, kj], 1)
if swap_2e:
tmpR = tmpR.reshape(nao * nrow, nao)
tmpI = tmpI.reshape(nao * nrow, nao)
for i in range(nset):
zdotNN(pLqR.reshape(-1, nao), pLqI.reshape(-1, nao),
dmsR[i, kj], dmsI[i, kj], 1, tmpR, tmpI)
zdotNC(tmpR.reshape(nao, -1), tmpI.reshape(nao, -1),
pLqR.reshape(nao, -1).T,
pLqI.reshape(nao, -1).T, 1, vkR[i, ki], vkI[i, ki],
1)
if kpts_band is None: # normal k-points HF/DFT
for ki in range(nkpts):
for kj in range(ki):
make_kpt(ki, kj, True)
make_kpt(ki, ki, False)
else:
for ki in range(nkpts):
for kj in range(nband):
make_kpt(ki, kj, False)
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
if exxdiv:
assert (exxdiv.lower() == 'ewald')
_ewald_exxdiv_for_G0(cell, kpts, dms, vk_kpts, kpts_band)
return _format_jks(vk_kpts, dm_kpts, input_band, kpts)
def get_k_kpts(mydf,
dm_kpts,
hermi=1,
kpts=np.zeros((1, 3)),
kpts_band=None,
exxdiv=None):
'''Get the Coulomb (J) and exchange (K) AO matrices at sampled k-points.
Args:
dm_kpts : (nkpts, nao, nao) ndarray
Density matrix at each k-point
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
vk : (nkpts, nao, nao) ndarray
or list of vj and vk if the input dm_kpts is a list of DMs
'''
cell = mydf.cell
gs = mydf.gs
coords = cell.gen_uniform_grids(gs)
ngs = coords.shape[0]
if hasattr(dm_kpts, 'mo_coeff'):
mo_coeff = dm_kpts.mo_coeff
mo_occ = dm_kpts.mo_occ
else:
mo_coeff = None
kpts = np.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 / ngs)
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 = np.zeros((nset, nband, nao, nao), dtype=dms.dtype)
else:
vk_kpts = np.zeros((nset, nband, nao, nao), dtype=np.complex128)
ao2_kpts = mydf._numint.eval_ao(cell, coords, kpts, non0tab=mydf.non0tab)
ao2_kpts = [np.asarray(ao.T, order='C') for ao in ao2_kpts]
if input_band is None:
ao1_kpts = ao2_kpts
else:
ao1_kpts = mydf._numint.eval_ao(cell,
coords,
kpts_band,
non0tab=mydf.non0tab)
ao1_kpts = [np.asarray(ao.T, order='C') for ao in ao1_kpts]
if mo_coeff is not None and nset == 1:
mo_coeff = [
mo_coeff[k][:, occ > 0] * np.sqrt(occ[occ > 0])
for k, occ in enumerate(mo_occ)
]
ao2_kpts = [np.dot(mo_coeff[k].T, ao) for k, ao in enumerate(ao2_kpts)]
naoj = ao2_kpts[0].shape[0]
else:
naoj = nao
max_memory = mydf.max_memory - lib.current_memory()[0]
blksize = int(max(max_memory * 1e6 / 16 / 2 / ngs / nao, 1))
ao1_dtype = np.result_type(*ao1_kpts)
ao2_dtype = np.result_type(*ao2_kpts)
buf = np.empty((blksize, naoj, ngs),
dtype=np.result_type(ao1_dtype, ao2_dtype))
vR_dm = np.empty((nset, nao, ngs), dtype=vk_kpts.dtype)
ao_dms = np.empty((nset, naoj, ngs), dtype=np.result_type(dms, ao2_dtype))
for k2, ao2T in enumerate(ao2_kpts):
kpt2 = kpts[k2]
if mo_coeff is None or nset > 1:
for i in range(nset):
lib.dot(dms[i, k2], ao2T.conj(), c=ao_dms[i])
else:
ao_dms = [ao2T.conj()]
for k1, ao1T in enumerate(ao1_kpts):
kpt1 = kpts_band[k1]
mydf.exxdiv = exxdiv
coulG = tools.get_coulG(cell, kpt2 - kpt1, True, mydf, gs)
if is_zero(kpt1 - kpt2):
expmikr = np.array(1.)
else:
expmikr = np.exp(-1j * np.dot(coords, kpt2 - kpt1))
for p0, p1 in lib.prange(0, nao, blksize):
rho1 = np.einsum('ig,jg->ijg',
ao1T[p0:p1].conj() * expmikr,
ao2T,
out=buf[:p1 - p0])
vG = tools.fft(rho1.reshape(-1, ngs), gs)
vG *= coulG
vR = tools.ifft(vG, gs).reshape(p1 - p0, naoj, ngs)
vG = None
if vR_dm.dtype == np.double:
vR = vR.real
for i in range(nset):
np.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)
return _format_jks(vk_kpts, dm_kpts, input_band, kpts)
def get_j_kpts(mydf,
dm_kpts,
hermi=1,
kpts=numpy.zeros((1, 3)),
kpts_band=None):
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = (time.clock(), time.time())
if mydf._cderi is None or not mydf.has_kpts(kpts_band):
if mydf._cderi is not None:
log.warn(
'DF integrals for band k-points were not found %s. '
'DF integrals will be rebuilt to include band k-points.',
mydf._cderi)
mydf.build(kpts_band=kpts_band)
t1 = log.timer_debug1('Init get_j_kpts', *t1)
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
naux = mydf.get_naoaux()
nao_pair = nao * (nao + 1) // 2
kpts_band, input_band = _format_kpts_band(kpts_band, kpts), kpts_band
nband = len(kpts_band)
j_real = gamma_point(kpts_band) and not numpy.iscomplexobj(dms)
dmsR = dms.real.transpose(0, 1, 3, 2).reshape(nset, nkpts, nao**2)
dmsI = dms.imag.transpose(0, 1, 3, 2).reshape(nset, nkpts, nao**2)
rhoR = numpy.zeros((nset, naux))
rhoI = numpy.zeros((nset, naux))
max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]))
for k, kpt in enumerate(kpts):
kptii = numpy.asarray((kpt, kpt))
p1 = 0
for LpqR, LpqI in mydf.sr_loop(kptii, max_memory, False):
p0, p1 = p1, p1 + LpqR.shape[0]
#:Lpq = (LpqR + LpqI*1j).reshape(-1,nao,nao)
#:rhoR[:,p0:p1] += numpy.einsum('Lpq,xqp->xL', Lpq, dms[:,k]).real
#:rhoI[:,p0:p1] += numpy.einsum('Lpq,xqp->xL', Lpq, dms[:,k]).imag
rhoR[:, p0:p1] += numpy.einsum('Lp,xp->xL', LpqR, dmsR[:, k])
rhoI[:, p0:p1] += numpy.einsum('Lp,xp->xL', LpqR, dmsI[:, k])
if LpqI is not None:
rhoR[:, p0:p1] -= numpy.einsum('Lp,xp->xL', LpqI, dmsI[:, k])
rhoI[:, p0:p1] += numpy.einsum('Lp,xp->xL', LpqI, dmsR[:, k])
LpqR = LpqI = None
t1 = log.timer_debug1('get_j pass 1', *t1)
weight = 1. / nkpts
rhoR *= weight
rhoI *= weight
vjR = numpy.zeros((nset, nband, nao_pair))
vjI = numpy.zeros((nset, nband, nao_pair))
for k, kpt in enumerate(kpts_band):
kptii = numpy.asarray((kpt, kpt))
p1 = 0
for LpqR, LpqI in mydf.sr_loop(kptii, max_memory, True):
p0, p1 = p1, p1 + LpqR.shape[0]
#:Lpq = (LpqR + LpqI*1j)#.reshape(-1,nao,nao)
#:vjR[:,k] += numpy.dot(rho[:,p0:p1], Lpq).real
#:vjI[:,k] += numpy.dot(rho[:,p0:p1], Lpq).imag
vjR[:, k] += numpy.dot(rhoR[:, p0:p1], LpqR)
if not j_real:
vjI[:, k] += numpy.dot(rhoI[:, p0:p1], LpqR)
if LpqI is not None:
vjR[:, k] -= numpy.dot(rhoI[:, p0:p1], LpqI)
vjI[:, k] += numpy.dot(rhoR[:, p0:p1], LpqI)
LpqR = LpqI = None
t1 = log.timer_debug1('get_j pass 2', *t1)
if j_real:
vj_kpts = vjR
else:
vj_kpts = vjR + vjI * 1j
vj_kpts = lib.unpack_tril(vj_kpts.reshape(-1, nao_pair))
vj_kpts = vj_kpts.reshape(nset, nband, nao, nao)
return _format_jks(vj_kpts, dm_kpts, input_band, kpts)
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
shls_slice = (bstart, bend, 0, bend)
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
