def ecp_int(cell, kpts=None): if rank == 0: comm.bcast(cell.dumps()) else: cell = pgto.loads(comm.bcast(None)) if kpts is None: kpts_lst = numpy.zeros((1,3)) else: kpts_lst = numpy.reshape(kpts, (-1,3)) ecpcell = gto.Mole() ecpcell._atm = cell._atm # append a fictitious s function to mimic the auxiliary index in pbc.incore. # ptr2last_env_idx to force PBCnr3c_fill_* function to copy the entire "env" ptr2last_env_idx = len(cell._env) - 1 ecpbas = numpy.vstack([[0, 0, 1, 1, 0, ptr2last_env_idx, 0, 0], cell._ecpbas]).astype(numpy.int32) ecpcell._bas = ecpbas ecpcell._env = cell._env # In pbc.incore _ecpbas is appended to two sets of cell._bas and the # fictitious s function. cell._env[AS_ECPBAS_OFFSET] = cell.nbas * 2 + 1 cell._env[AS_NECPBAS] = len(cell._ecpbas) kptij_lst = numpy.hstack((kpts_lst,kpts_lst)).reshape(-1,2,3) nkpts = len(kpts_lst) if abs(kpts_lst).sum() < 1e-9: # gamma_point dtype = numpy.double else: dtype = numpy.complex128 ao_loc = cell.ao_loc_nr() nao = ao_loc[-1] mat = numpy.zeros((nkpts,nao,nao), dtype=dtype) intor = cell._add_suffix('ECPscalar') int3c = incore.wrap_int3c(cell, ecpcell, intor, kptij_lst=kptij_lst) # shls_slice of auxiliary index (0,1) corresponds to the fictitious s function tasks = [(i, i+1, j, j+1, 0, 1) # shls_slice for i in range(cell.nbas) for j in range(i+1)] for shls_slice in mpi.work_stealing_partition(tasks): i0 = ao_loc[shls_slice[0]] i1 = ao_loc[shls_slice[1]] j0 = ao_loc[shls_slice[2]] j1 = ao_loc[shls_slice[3]] buf = numpy.empty((nkpts,i1-i0,j1-j0), dtype=dtype) mat[:,i0:i1,j0:j1] = int3c(shls_slice, buf) buf = mpi.reduce(mat) if rank == 0: mat = [] for k, kpt in enumerate(kpts_lst): v = lib.unpack_tril(lib.pack_tril(buf[k]), lib.HERMITIAN) if abs(kpt).sum() < 1e-9: # gamma_point: v = v.real mat.append(v) if kpts is None or numpy.shape(kpts) == (3,): mat = mat[0] return mat
def _make_j3c(mydf, cell, auxcell, kptij_lst, cderi_file): log = logger.Logger(mydf.stdout, mydf.verbose) t1 = t0 = (time.clock(), time.time()) fused_cell, fuse = fuse_auxcell(mydf, mydf.auxcell) ao_loc = cell.ao_loc_nr() nao = ao_loc[-1] naux = auxcell.nao_nr() nkptij = len(kptij_lst) mesh = mydf.mesh Gv, Gvbase, kws = cell.get_Gv_weights(mesh) b = cell.reciprocal_vectors() gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase]) ngrids = gxyz.shape[0] kptis = kptij_lst[:, 0] kptjs = kptij_lst[:, 1] kpt_ji = kptjs - kptis uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji) log.debug('Num uniq kpts %d', len(uniq_kpts)) log.debug2('uniq_kpts %s', uniq_kpts) # j2c ~ (-kpt_ji | kpt_ji) j2c = fused_cell.pbc_intor('int2c2e', hermi=1, kpts=uniq_kpts) j2ctags = [] t1 = log.timer_debug1('2c2e', *t1) swapfile = tempfile.NamedTemporaryFile(dir=os.path.dirname(cderi_file)) fswap = lib.H5TmpFile(swapfile.name) # Unlink swapfile to avoid trash swapfile = None mem_now = max(comm.allgather(lib.current_memory()[0])) max_memory = max(2000, mydf.max_memory - mem_now) blksize = max(2048, int(max_memory * .5e6 / 16 / fused_cell.nao_nr())) log.debug2('max_memory %s (MB) blocksize %s', max_memory, blksize) for k, kpt in enumerate(uniq_kpts): coulG = mydf.weighted_coulG(kpt, False, mesh) j2c_k = numpy.zeros_like(j2c[k]) for p0, p1 in mydf.prange(0, ngrids, blksize): aoaux = ft_ao.ft_ao(fused_cell, Gv[p0:p1], None, b, gxyz[p0:p1], Gvbase, kpt).T LkR = numpy.asarray(aoaux.real, order='C') LkI = numpy.asarray(aoaux.imag, order='C') aoaux = None if is_zero(kpt): # kpti == kptj j2c_k[naux:] += lib.ddot(LkR[naux:] * coulG[p0:p1], LkR.T) j2c_k[naux:] += lib.ddot(LkI[naux:] * coulG[p0:p1], LkI.T) else: j2cR, j2cI = zdotCN(LkR[naux:] * coulG[p0:p1], LkI[naux:] * coulG[p0:p1], LkR.T, LkI.T) j2c_k[naux:] += j2cR + j2cI * 1j kLR = kLI = None j2c_k[:naux, naux:] = j2c_k[naux:, :naux].conj().T j2c[k] -= mpi.allreduce(j2c_k) j2c[k] = fuse(fuse(j2c[k]).T).T try: fswap['j2c/%d' % k] = scipy.linalg.cholesky(j2c[k], lower=True) j2ctags.append('CD') except scipy.linalg.LinAlgError as e: #msg =('===================================\n' # 'J-metric not positive definite.\n' # 'It is likely that mesh is not enough.\n' # '===================================') #log.error(msg) #raise scipy.linalg.LinAlgError('\n'.join([str(e), msg])) w, v = scipy.linalg.eigh(j2c[k]) log.debug2('metric linear dependency for kpt %s', k) log.debug2('cond = %.4g, drop %d bfns', w[0] / w[-1], numpy.count_nonzero(w < mydf.linear_dep_threshold)) v1 = v[:, w > mydf.linear_dep_threshold].T.conj() v1 /= numpy.sqrt(w[w > mydf.linear_dep_threshold]).reshape(-1, 1) fswap['j2c/%d' % k] = v1 if cell.dimension == 2 and cell.low_dim_ft_type != 'inf_vacuum': idx = numpy.where(w < -mydf.linear_dep_threshold)[0] if len(idx) > 0: fswap['j2c-/%d' % k] = (v[:, idx] / numpy.sqrt(-w[idx])).conj().T w = v = v1 = None j2ctags.append('eig') j2c = coulG = None aosym_s2 = numpy.einsum('ix->i', abs(kptis - kptjs)) < 1e-9 j_only = numpy.all(aosym_s2) if gamma_point(kptij_lst): dtype = 'f8' else: dtype = 'c16' t1 = log.timer_debug1('aoaux and int2c', *t1) # Estimates the buffer size based on the last contraction in G-space. # This contraction requires to hold nkptj copies of (naux,?) array # simultaneously in memory. mem_now = max(comm.allgather(lib.current_memory()[0])) max_memory = max(2000, mydf.max_memory - mem_now) nkptj_max = max((uniq_inverse == x).sum() for x in set(uniq_inverse)) buflen = max( int( min(max_memory * .5e6 / 16 / naux / (nkptj_max + 2) / nao, nao / 3 / mpi.pool.size)), 1) chunks = (buflen, nao) j3c_jobs = grids2d_int3c_jobs(cell, auxcell, kptij_lst, chunks, j_only) log.debug1('max_memory = %d MB (%d in use) chunks %s', max_memory, mem_now, chunks) log.debug2('j3c_jobs %s', j3c_jobs) if j_only: int3c = wrap_int3c(cell, fused_cell, 'int3c2e', 's2', 1, kptij_lst) else: int3c = wrap_int3c(cell, fused_cell, 'int3c2e', 's1', 1, kptij_lst) idxb = numpy.tril_indices(nao) idxb = (idxb[0] * nao + idxb[1]).astype('i') aux_loc = fused_cell.ao_loc_nr('ssc' in 'int3c2e') def gen_int3c(job_id, ish0, ish1): dataname = 'j3c-chunks/%d' % job_id i0 = ao_loc[ish0] i1 = ao_loc[ish1] dii = i1 * (i1 + 1) // 2 - i0 * (i0 + 1) // 2 if j_only: dij = dii buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dii + dii))) else: dij = (i1 - i0) * nao buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dij + dij))) auxranges = balance_segs(aux_loc[1:] - aux_loc[:-1], buflen) buflen = max([x[2] for x in auxranges]) buf = numpy.empty(nkptij * dij * buflen, dtype=dtype) buf1 = numpy.empty(dij * buflen, dtype=dtype) naux = aux_loc[-1] for kpt_id, kptij in enumerate(kptij_lst): key = '%s/%d' % (dataname, kpt_id) if aosym_s2[kpt_id]: shape = (naux, dii) else: shape = (naux, dij) if gamma_point(kptij): fswap.create_dataset(key, shape, 'f8') else: fswap.create_dataset(key, shape, 'c16') naux0 = 0 for istep, auxrange in enumerate(auxranges): log.alldebug2("aux_e1 job_id %d step %d", job_id, istep) sh0, sh1, nrow = auxrange sub_slice = (ish0, ish1, 0, cell.nbas, sh0, sh1) mat = numpy.ndarray((nkptij, dij, nrow), dtype=dtype, buffer=buf) mat = int3c(sub_slice, mat) for k, kptij in enumerate(kptij_lst): h5dat = fswap['%s/%d' % (dataname, k)] v = lib.transpose(mat[k], out=buf1) if not j_only and aosym_s2[k]: idy = idxb[i0 * (i0 + 1) // 2:i1 * (i1 + 1) // 2] - i0 * nao out = numpy.ndarray((nrow, dii), dtype=v.dtype, buffer=mat[k]) v = numpy.take(v, idy, axis=1, out=out) if gamma_point(kptij): h5dat[naux0:naux0 + nrow] = v.real else: h5dat[naux0:naux0 + nrow] = v naux0 += nrow def ft_fuse(job_id, uniq_kptji_id, sh0, sh1): kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0] adapted_kptjs = kptjs[adapted_ji_idx] nkptj = len(adapted_kptjs) j2c = numpy.asarray(fswap['j2c/%d' % uniq_kptji_id]) j2ctag = j2ctags[uniq_kptji_id] naux0 = j2c.shape[0] if ('j2c-/%d' % uniq_kptji_id) in fswap: j2c_negative = numpy.asarray(fswap['j2c-/%d' % uniq_kptji_id]) else: j2c_negative = None if is_zero(kpt): aosym = 's2' else: aosym = 's1' if aosym == 's2' and cell.dimension == 3: vbar = fuse(mydf.auxbar(fused_cell)) ovlp = cell.pbc_intor('int1e_ovlp', hermi=1, kpts=adapted_kptjs) ovlp = [lib.pack_tril(s) for s in ovlp] j3cR = [None] * nkptj j3cI = [None] * nkptj i0 = ao_loc[sh0] i1 = ao_loc[sh1] for k, idx in enumerate(adapted_ji_idx): key = 'j3c-chunks/%d/%d' % (job_id, idx) v = numpy.asarray(fswap[key]) if aosym == 's2' and cell.dimension == 3: for i in numpy.where(vbar != 0)[0]: v[i] -= vbar[i] * ovlp[k][i0 * (i0 + 1) // 2:i1 * (i1 + 1) // 2].ravel() j3cR[k] = numpy.asarray(v.real, order='C') if v.dtype == numpy.complex128: j3cI[k] = numpy.asarray(v.imag, order='C') v = None ncol = j3cR[0].shape[1] Gblksize = max(16, int(max_memory * 1e6 / 16 / ncol / (nkptj + 1))) # +1 for pqkRbuf/pqkIbuf Gblksize = min(Gblksize, ngrids, 16384) pqkRbuf = numpy.empty(ncol * Gblksize) pqkIbuf = numpy.empty(ncol * Gblksize) buf = numpy.empty(nkptj * ncol * Gblksize, dtype=numpy.complex128) log.alldebug2('job_id %d blksize (%d,%d)', job_id, Gblksize, ncol) wcoulG = mydf.weighted_coulG(kpt, False, mesh) fused_cell_slice = (auxcell.nbas, fused_cell.nbas) if aosym == 's2': shls_slice = (sh0, sh1, 0, sh1) else: shls_slice = (sh0, sh1, 0, cell.nbas) for p0, p1 in lib.prange(0, ngrids, Gblksize): Gaux = ft_ao.ft_ao(fused_cell, Gv[p0:p1], fused_cell_slice, b, gxyz[p0:p1], Gvbase, kpt) Gaux *= wcoulG[p0:p1, None] kLR = Gaux.real.copy('C') kLI = Gaux.imag.copy('C') Gaux = None dat = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym, b, gxyz[p0:p1], Gvbase, kpt, adapted_kptjs, out=buf) nG = p1 - p0 for k, ji in enumerate(adapted_ji_idx): aoao = dat[k].reshape(nG, ncol) pqkR = numpy.ndarray((ncol, nG), buffer=pqkRbuf) pqkI = numpy.ndarray((ncol, nG), buffer=pqkIbuf) pqkR[:] = aoao.real.T pqkI[:] = aoao.imag.T lib.dot(kLR.T, pqkR.T, -1, j3cR[k][naux:], 1) lib.dot(kLI.T, pqkI.T, -1, j3cR[k][naux:], 1) if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])): lib.dot(kLR.T, pqkI.T, -1, j3cI[k][naux:], 1) lib.dot(kLI.T, pqkR.T, 1, j3cI[k][naux:], 1) kLR = kLI = None for k, idx in enumerate(adapted_ji_idx): if is_zero(kpt) and gamma_point(adapted_kptjs[k]): v = fuse(j3cR[k]) else: v = fuse(j3cR[k] + j3cI[k] * 1j) if j2ctag == 'CD': v = scipy.linalg.solve_triangular(j2c, v, lower=True, overwrite_b=True) fswap['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = v else: fswap['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = lib.dot( j2c, v) # low-dimension systems if j2c_negative is not None: fswap['j3c-/%d/%d' % (job_id, idx)] = lib.dot(j2c_negative, v) _assemble(mydf, kptij_lst, j3c_jobs, gen_int3c, ft_fuse, cderi_file, fswap, log)
def aux_e1(cell, auxcell, erifile, intor='int3c2e', aosym='s2ij', comp=None, kptij_lst=None, dataname='eri_mo', shls_slice=None, max_memory=2000, verbose=0): r'''3-center AO integrals (L|ij) with double lattice sum: \sum_{lm} (L[0]|i[l]j[m]), where L is the auxiliary basis. Three-index integral tensor (kptij_idx, naux, nao_pair) or four-index integral tensor (kptij_idx, comp, naux, nao_pair) are stored on disk. Args: kptij_lst : (*,2,3) array A list of (kpti, kptj) ''' intor, comp = gto.moleintor._get_intor_and_comp(cell._add_suffix(intor), comp) if isinstance(erifile, h5py.Group): feri = erifile elif h5py.is_hdf5(erifile): feri = h5py.File(erifile, 'a') else: feri = h5py.File(erifile, 'w') if dataname in feri: del (feri[dataname]) if dataname + '-kptij' in feri: del (feri[dataname + '-kptij']) 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(auxcell.cart or '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) feri.create_dataset(key, shape, dtype) 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 if not isinstance(erifile, h5py.Group): feri.close() return erifile
def _aux_e2(cell, auxcell, erifile, intor='int3c2e', aosym='s2ij', comp=None, 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. Three-index integral tensor (kptij_idx, nao_pair, naux) or four-index integral tensor (kptij_idx, comp, nao_pair, naux) are stored on disk. **This function should be only used by df and mdf initialization function _make_j3c** Args: kptij_lst : (*,2,3) array A list of (kpti, kptj) ''' intor, comp = gto.moleintor._get_intor_and_comp(cell._add_suffix(intor), comp) if isinstance(erifile, h5py.Group): feri = erifile elif h5py.is_hdf5(erifile): feri = h5py.File(erifile, 'a') else: feri = h5py.File(erifile, 'w') if dataname in feri: del (feri[dataname]) if dataname + '-kptij' in feri: del (feri[dataname + '-kptij']) 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(auxcell.cart or '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' 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 * .47e6 / 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_like(buf) int3c = wrap_int3c(cell, auxcell, intor, aosym, comp, kptij_lst) kptis = kptij_lst[:, 0] kptjs = kptij_lst[:, 1] kpt_ji = kptjs - kptis uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji) # sorted_ij_idx: Sort and group the kptij_lst according to the ordering in # df._make_j3c to reduce the data fragment in the hdf5 file. When datasets # are written to hdf5, they are saved sequentially. If the integral data are # saved as the order of kptij_lst, removing the datasets in df._make_j3c will # lead to holes that can not be reused. sorted_ij_idx = numpy.hstack( [numpy.where(uniq_inverse == k)[0] for k, kpt in enumerate(uniq_kpts)]) tril_idx = numpy.tril_indices(ni) tril_idx = tril_idx[0] * ni + tril_idx[1] def save(istep, mat): for k in sorted_ij_idx: v = mat[k] if gamma_point(kptij_lst[k]): v = v.real if aosym_ks2[k] and nao_pair == ni**2: v = v[:, tril_idx] feri['%s/%d/%d' % (dataname, k, istep)] = v with lib.call_in_background(save) as bsave: 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) bsave(istep, int3c(sub_slice, mat)) buf, buf1 = buf1, buf if not isinstance(erifile, h5py.Group): feri.close() return erifile
def _make_j3c(mydf, cell, auxcell, kptij_lst, cderi_file): log = logger.Logger(mydf.stdout, mydf.verbose) t1 = t0 = (time.clock(), time.time()) fused_cell, fuse = fuse_auxcell(mydf, mydf.auxcell) ao_loc = cell.ao_loc_nr() nao = ao_loc[-1] naux = auxcell.nao_nr() nkptij = len(kptij_lst) gs = mydf.gs Gv, Gvbase, kws = cell.get_Gv_weights(gs) b = cell.reciprocal_vectors() gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase]) ngs = gxyz.shape[0] kptis = kptij_lst[:, 0] kptjs = kptij_lst[:, 1] kpt_ji = kptjs - kptis uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji) log.debug('Num uniq kpts %d', len(uniq_kpts)) log.debug2('uniq_kpts %s', uniq_kpts) # j2c ~ (-kpt_ji | kpt_ji) j2c = fused_cell.pbc_intor('int2c2e_sph', hermi=1, kpts=uniq_kpts) j2ctags = [] nauxs = [] t1 = log.timer_debug1('2c2e', *t1) if h5py.is_hdf5(cderi_file): feri = h5py.File(cderi_file) else: feri = h5py.File(cderi_file, 'w') for k, kpt in enumerate(uniq_kpts): aoaux = ft_ao.ft_ao(fused_cell, Gv, None, b, gxyz, Gvbase, kpt).T coulG = numpy.sqrt(mydf.weighted_coulG(kpt, False, gs)) kLR = (aoaux.real * coulG).T kLI = (aoaux.imag * coulG).T if not kLR.flags.c_contiguous: kLR = lib.transpose(kLR.T) if not kLI.flags.c_contiguous: kLI = lib.transpose(kLI.T) aoaux = None kLR1 = numpy.asarray(kLR[:, naux:], order='C') kLI1 = numpy.asarray(kLI[:, naux:], order='C') if is_zero(kpt): # kpti == kptj for p0, p1 in mydf.mpi_prange(0, ngs): j2cR = lib.ddot(kLR1[p0:p1].T, kLR[p0:p1]) j2cR = lib.ddot(kLI1[p0:p1].T, kLI[p0:p1], 1, j2cR, 1) j2c[k][naux:] -= mpi.allreduce(j2cR) j2c[k][:naux, naux:] = j2c[k][naux:, :naux].T else: for p0, p1 in mydf.mpi_prange(0, ngs): j2cR, j2cI = zdotCN(kLR1[p0:p1].T, kLI1[p0:p1].T, kLR[p0:p1], kLI[p0:p1]) j2cR = mpi.allreduce(j2cR) j2cI = mpi.allreduce(j2cI) j2c[k][naux:] -= j2cR + j2cI * 1j j2c[k][:naux, naux:] = j2c[k][naux:, :naux].T.conj() j2c[k] = fuse(fuse(j2c[k]).T).T try: feri['j2c/%d' % k] = scipy.linalg.cholesky(j2c[k], lower=True) j2ctags.append('CD') nauxs.append(naux) except scipy.linalg.LinAlgError as e: #msg =('===================================\n' # 'J-metric not positive definite.\n' # 'It is likely that gs is not enough.\n' # '===================================') #log.error(msg) #raise scipy.linalg.LinAlgError('\n'.join([e.message, msg])) w, v = scipy.linalg.eigh(j2c) log.debug2('metric linear dependency for kpt %s', uniq_kptji_id) log.debug2('cond = %.4g, drop %d bfns', w[0] / w[-1], numpy.count_nonzero(w < LINEAR_DEP_THR)) v = v[:, w > LINEAR_DEP_THR].T.conj() v /= numpy.sqrt(w[w > LINEAR_DEP_THR]).reshape(-1, 1) feri['j2c/%d' % k] = v j2ctags.append('eig') nauxs.append(v.shape[0]) kLR = kLI = kLR1 = kLI1 = coulG = None j2c = None aosym_s2 = numpy.einsum('ix->i', abs(kptis - kptjs)) < 1e-9 j_only = numpy.all(aosym_s2) if gamma_point(kptij_lst): dtype = 'f8' else: dtype = 'c16' vbar = mydf.auxbar(fused_cell) vbar = fuse(vbar) ovlp = cell.pbc_intor('int1e_ovlp_sph', hermi=1, kpts=kptjs[aosym_s2]) ovlp = [lib.pack_tril(s) for s in ovlp] t1 = log.timer_debug1('aoaux and int2c', *t1) # Estimates the buffer size based on the last contraction in G-space. # This contraction requires to hold nkptj copies of (naux,?) array # simultaneously in memory. mem_now = max(comm.allgather(lib.current_memory()[0])) max_memory = max(2000, mydf.max_memory - mem_now) nkptj_max = max((uniq_inverse == x).sum() for x in set(uniq_inverse)) buflen = max( int( min(max_memory * .5e6 / 16 / naux / (nkptj_max + 2) / nao, nao / 3 / mpi.pool.size)), 1) chunks = (buflen, nao) j3c_jobs = grids2d_int3c_jobs(cell, auxcell, kptij_lst, chunks, j_only) log.debug1('max_memory = %d MB (%d in use) chunks %s', max_memory, mem_now, chunks) log.debug2('j3c_jobs %s', j3c_jobs) if j_only: int3c = wrap_int3c(cell, fused_cell, 'int3c2e_sph', 's2', 1, kptij_lst) else: int3c = wrap_int3c(cell, fused_cell, 'int3c2e_sph', 's1', 1, kptij_lst) idxb = numpy.tril_indices(nao) idxb = (idxb[0] * nao + idxb[1]).astype('i') aux_loc = fused_cell.ao_loc_nr('ssc' in 'int3c2e_sph') def gen_int3c(auxcell, job_id, ish0, ish1): dataname = 'j3c-chunks/%d' % job_id if dataname in feri: del (feri[dataname]) i0 = ao_loc[ish0] i1 = ao_loc[ish1] dii = i1 * (i1 + 1) // 2 - i0 * (i0 + 1) // 2 dij = (i1 - i0) * nao if j_only: buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dii + dii))) else: buflen = max(8, int(max_memory * 1e6 / 16 / (nkptij * dij + dij))) auxranges = balance_segs(aux_loc[1:] - aux_loc[:-1], buflen) buflen = max([x[2] for x in auxranges]) buf = numpy.empty(nkptij * dij * buflen, dtype=dtype) buf1 = numpy.empty(dij * buflen, dtype=dtype) naux = aux_loc[-1] for kpt_id, kptij in enumerate(kptij_lst): key = '%s/%d' % (dataname, kpt_id) if aosym_s2[kpt_id]: shape = (naux, dii) else: shape = (naux, dij) if gamma_point(kptij): feri.create_dataset(key, shape, 'f8') else: feri.create_dataset(key, shape, 'c16') naux0 = 0 for istep, auxrange in enumerate(auxranges): log.alldebug2("aux_e2 job_id %d step %d", job_id, istep) sh0, sh1, nrow = auxrange sub_slice = (ish0, ish1, 0, cell.nbas, sh0, sh1) if j_only: mat = numpy.ndarray((nkptij, dii, nrow), dtype=dtype, buffer=buf) else: mat = numpy.ndarray((nkptij, dij, nrow), dtype=dtype, buffer=buf) mat = int3c(sub_slice, mat) for k, kptij in enumerate(kptij_lst): h5dat = feri['%s/%d' % (dataname, k)] v = lib.transpose(mat[k], out=buf1) if not j_only and aosym_s2[k]: idy = idxb[i0 * (i0 + 1) // 2:i1 * (i1 + 1) // 2] - i0 * nao out = numpy.ndarray((nrow, dii), dtype=v.dtype, buffer=mat[k]) v = numpy.take(v, idy, axis=1, out=out) if gamma_point(kptij): h5dat[naux0:naux0 + nrow] = v.real else: h5dat[naux0:naux0 + nrow] = v naux0 += nrow def ft_fuse(job_id, uniq_kptji_id, sh0, sh1): kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0] adapted_kptjs = kptjs[adapted_ji_idx] nkptj = len(adapted_kptjs) shls_slice = (auxcell.nbas, fused_cell.nbas) Gaux = ft_ao.ft_ao(fused_cell, Gv, shls_slice, b, gxyz, Gvbase, kpt) Gaux *= mydf.weighted_coulG(kpt, False, gs).reshape(-1, 1) kLR = Gaux.real.copy('C') kLI = Gaux.imag.copy('C') j2c = numpy.asarray(feri['j2c/%d' % uniq_kptji_id]) j2ctag = j2ctags[uniq_kptji_id] naux0 = j2c.shape[0] if is_zero(kpt): aosym = 's2' else: aosym = 's1' j3cR = [None] * nkptj j3cI = [None] * nkptj i0 = ao_loc[sh0] i1 = ao_loc[sh1] for k, idx in enumerate(adapted_ji_idx): key = 'j3c-chunks/%d/%d' % (job_id, idx) v = numpy.asarray(feri[key]) if is_zero(kpt): for i, c in enumerate(vbar): if c != 0: v[i] -= c * ovlp[k][i0 * (i0 + 1) // 2:i1 * (i1 + 1) // 2].ravel() j3cR[k] = numpy.asarray(v.real, order='C') if v.dtype == numpy.complex128: j3cI[k] = numpy.asarray(v.imag, order='C') v = None ncol = j3cR[0].shape[1] Gblksize = max(16, int(max_memory * 1e6 / 16 / ncol / (nkptj + 1))) # +1 for pqkRbuf/pqkIbuf Gblksize = min(Gblksize, ngs, 16384) pqkRbuf = numpy.empty(ncol * Gblksize) pqkIbuf = numpy.empty(ncol * Gblksize) buf = numpy.empty(nkptj * ncol * Gblksize, dtype=numpy.complex128) log.alldebug2(' blksize (%d,%d)', Gblksize, ncol) shls_slice = (sh0, sh1, 0, cell.nbas) for p0, p1 in lib.prange(0, ngs, Gblksize): dat = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym, b, gxyz[p0:p1], Gvbase, kpt, adapted_kptjs, out=buf) nG = p1 - p0 for k, ji in enumerate(adapted_ji_idx): aoao = dat[k].reshape(nG, ncol) pqkR = numpy.ndarray((ncol, nG), buffer=pqkRbuf) pqkI = numpy.ndarray((ncol, nG), buffer=pqkIbuf) pqkR[:] = aoao.real.T pqkI[:] = aoao.imag.T lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k][naux:], 1) lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k][naux:], 1) if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])): lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k][naux:], 1) lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k][naux:], 1) for k, idx in enumerate(adapted_ji_idx): if is_zero(kpt) and gamma_point(adapted_kptjs[k]): v = fuse(j3cR[k]) else: v = fuse(j3cR[k] + j3cI[k] * 1j) if j2ctag == 'CD': v = scipy.linalg.solve_triangular(j2c, v, lower=True, overwrite_b=True) else: v = lib.dot(j2c, v) feri['j3c-chunks/%d/%d' % (job_id, idx)][:naux0] = v t2 = t1 j3c_workers = numpy.zeros(len(j3c_jobs), dtype=int) #for job_id, ish0, ish1 in mpi.work_share_partition(j3c_jobs): for job_id, ish0, ish1 in mpi.work_stealing_partition(j3c_jobs): gen_int3c(fused_cell, job_id, ish0, ish1) t2 = log.alltimer_debug2('int j3c %d' % job_id, *t2) for k, kpt in enumerate(uniq_kpts): ft_fuse(job_id, k, ish0, ish1) t2 = log.alltimer_debug2('ft-fuse %d k %d' % (job_id, k), *t2) j3c_workers[job_id] = rank j3c_workers = mpi.allreduce(j3c_workers) log.debug2('j3c_workers %s', j3c_workers) j2c = kLRs = kLIs = ovlp = vbar = fuse = gen_int3c = ft_fuse = None t1 = log.timer_debug1('int3c and fuse', *t1) def get_segs_loc(aosym): off0 = numpy.asarray([ao_loc[i0] for x, i0, i1 in j3c_jobs]) off1 = numpy.asarray([ao_loc[i1] for x, i0, i1 in j3c_jobs]) if aosym: # s2 dims = off1 * (off1 + 1) // 2 - off0 * (off0 + 1) // 2 else: dims = (off1 - off0) * nao #dims = numpy.asarray([ao_loc[i1]-ao_loc[i0] for x,i0,i1 in j3c_jobs]) dims = numpy.hstack( [dims[j3c_workers == w] for w in range(mpi.pool.size)]) job_idx = numpy.hstack( [numpy.where(j3c_workers == w)[0] for w in range(mpi.pool.size)]) segs_loc = numpy.append(0, numpy.cumsum(dims)) segs_loc = [(segs_loc[j], segs_loc[j + 1]) for j in numpy.argsort(job_idx)] return segs_loc segs_loc_s1 = get_segs_loc(False) segs_loc_s2 = get_segs_loc(True) if 'j3c' in feri: del (feri['j3c']) segsize = (max(nauxs) + mpi.pool.size - 1) // mpi.pool.size naux0 = rank * segsize for k, kptij in enumerate(kptij_lst): naux1 = min(nauxs[uniq_inverse[k]], naux0 + segsize) nrow = max(0, naux1 - naux0) if gamma_point(kptij): dtype = 'f8' else: dtype = 'c16' if aosym_s2[k]: nao_pair = nao * (nao + 1) // 2 else: nao_pair = nao * nao feri.create_dataset('j3c/%d' % k, (nrow, nao_pair), dtype, maxshape=(None, nao_pair)) def load(k, p0, p1): naux1 = nauxs[uniq_inverse[k]] slices = [(min(i * segsize + p0, naux1), min(i * segsize + p1, naux1)) for i in range(mpi.pool.size)] segs = [] for p0, p1 in slices: val = [] for job_id, worker in enumerate(j3c_workers): if rank == worker: key = 'j3c-chunks/%d/%d' % (job_id, k) val.append(feri[key][p0:p1].ravel()) if val: segs.append(numpy.hstack(val)) else: segs.append(numpy.zeros(0)) return segs def save(k, p0, p1, segs): segs = mpi.alltoall(segs) naux1 = nauxs[uniq_inverse[k]] loc0, loc1 = min(p0, naux1 - naux0), min(p1, naux1 - naux0) nL = loc1 - loc0 if nL > 0: if aosym_s2[k]: segs = numpy.hstack([ segs[i0 * nL:i1 * nL].reshape(nL, -1) for i0, i1 in segs_loc_s2 ]) else: segs = numpy.hstack([ segs[i0 * nL:i1 * nL].reshape(nL, -1) for i0, i1 in segs_loc_s1 ]) feri['j3c/%d' % k][loc0:loc1] = segs mem_now = max(comm.allgather(lib.current_memory()[0])) max_memory = max(2000, min(8000, mydf.max_memory - mem_now)) if numpy.all(aosym_s2): if gamma_point(kptij_lst): blksize = max(16, int(max_memory * .5e6 / 8 / nao**2)) else: blksize = max(16, int(max_memory * .5e6 / 16 / nao**2)) else: blksize = max(16, int(max_memory * .5e6 / 16 / nao**2 / 2)) log.debug1('max_momory %d MB (%d in use), blksize %d', max_memory, mem_now, blksize) t2 = t1 with lib.call_in_background(save) as async_write: for k, kptji in enumerate(kptij_lst): for p0, p1 in lib.prange(0, segsize, blksize): segs = load(k, p0, p1) async_write(k, p0, p1, segs) t2 = log.timer_debug1( 'assemble k=%d %d:%d (in %d)' % (k, p0, p1, segsize), *t2) if 'j3c-chunks' in feri: del (feri['j3c-chunks']) if 'j3c-kptij' in feri: del (feri['j3c-kptij']) feri['j3c-kptij'] = kptij_lst t1 = log.alltimer_debug1('assembling j3c', *t1) feri.close()
def _make_j3c(mydf, cell, auxcell, kptij_lst, cderi_file): log = logger.Logger(mydf.stdout, mydf.verbose) t1 = t0 = (time.clock(), time.time()) fused_cell, fuse = fuse_auxcell(mydf, mydf.auxcell) ao_loc = cell.ao_loc_nr() nao = ao_loc[-1] naux = auxcell.nao_nr() nkptij = len(kptij_lst) mesh = mydf.mesh Gv, Gvbase, kws = cell.get_Gv_weights(mesh) b = cell.reciprocal_vectors() gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase]) ngrids = gxyz.shape[0] kptis = kptij_lst[:,0] kptjs = kptij_lst[:,1] kpt_ji = kptjs - kptis uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji) log.debug('Num uniq kpts %d', len(uniq_kpts)) log.debug2('uniq_kpts %s', uniq_kpts) # j2c ~ (-kpt_ji | kpt_ji) j2c = fused_cell.pbc_intor('int2c2e', hermi=1, kpts=uniq_kpts) j2ctags = [] t1 = log.timer_debug1('2c2e', *t1) swapfile = tempfile.NamedTemporaryFile(dir=os.path.dirname(cderi_file)) fswap = lib.H5TmpFile(swapfile.name) # Unlink swapfile to avoid trash swapfile = None for k, kpt in enumerate(uniq_kpts): coulG = mydf.weighted_coulG(kpt, False, mesh) j2c[k] = fuse(fuse(j2c[k]).T).T.copy() j2c_k = numpy.zeros_like(j2c[k]) for p0, p1 in mydf.mpi_prange(0, ngrids): aoaux = ft_ao.ft_ao(fused_cell, Gv[p0:p1], None, b, gxyz[p0:p1], Gvbase, kpt).T aoaux = fuse(aoaux) LkR = numpy.asarray(aoaux.real, order='C') LkI = numpy.asarray(aoaux.imag, order='C') aoaux = None if is_zero(kpt): # kpti == kptj j2cR = lib.dot(LkR*coulG[p0:p1], LkR.T) j2c_k += lib.dot(LkI*coulG[p0:p1], LkI.T, 1, j2cR, 1) else: # aoaux ~ kpt_ij, aoaux.conj() ~ kpt_kl j2cR, j2cI = zdotCN(LkR*coulG[p0:p1], LkI*coulG[p0:p1], LkR.T, LkI.T) j2c_k += j2cR + j2cI * 1j LkR = LkI = None j2c[k] -= mpi.allreduce(j2c_k) try: fswap['j2c/%d'%k] = scipy.linalg.cholesky(j2c[k], lower=True) j2ctags.append('CD') except scipy.linalg.LinAlgError: w, v = scipy.linalg.eigh(j2c[k]) log.debug2('metric linear dependency for kpt %s', k) log.debug2('cond = %.4g, drop %d bfns', w[0]/w[-1], numpy.count_nonzero(w<mydf.linear_dep_threshold)) v1 = v[:,w>mydf.linear_dep_threshold].T.conj() v1 /= numpy.sqrt(w[w>mydf.linear_dep_threshold]).reshape(-1,1) fswap['j2c/%d'%k] = v1 if cell.dimension == 2 and cell.low_dim_ft_type != 'inf_vacuum': idx = numpy.where(w < -mydf.linear_dep_threshold)[0] if len(idx) > 0: fswap['j2c-/%d'%k] = (v[:,idx]/numpy.sqrt(-w[idx])).conj().T w = v = v1 = v2 = None j2ctags.append('eig') aoaux = kLR = kLI = j2cR = j2cI = coulG = None j2c = None aosym_s2 = numpy.einsum('ix->i', abs(kptis-kptjs)) < 1e-9 j_only = numpy.all(aosym_s2) if gamma_point(kptij_lst): dtype = 'f8' else: dtype = 'c16' t1 = log.timer_debug1('aoaux and int2c', *t1) # Estimates the buffer size based on the last contraction in G-space. # This contraction requires to hold nkptj copies of (naux,?) array # simultaneously in memory. mem_now = max(comm.allgather(lib.current_memory()[0])) max_memory = max(2000, mydf.max_memory - mem_now) nkptj_max = max((uniq_inverse==x).sum() for x in set(uniq_inverse)) buflen = max(int(min(max_memory*.5e6/16/naux/(nkptj_max+2)/nao, nao/3/mpi.pool.size)), 1) chunks = (buflen, nao) j3c_jobs = mpi_df.grids2d_int3c_jobs(cell, auxcell, kptij_lst, chunks, j_only) log.debug1('max_memory = %d MB (%d in use) chunks %s', max_memory, mem_now, chunks) log.debug2('j3c_jobs %s', j3c_jobs) if j_only: int3c = wrap_int3c(cell, fused_cell, 'int3c2e', 's2', 1, kptij_lst) else: int3c = wrap_int3c(cell, fused_cell, 'int3c2e', 's1', 1, kptij_lst) idxb = numpy.tril_indices(nao) idxb = (idxb[0] * nao + idxb[1]).astype('i') aux_loc = fused_cell.ao_loc_nr(fused_cell.cart) def gen_int3c(job_id, ish0, ish1): dataname = 'j3c-chunks/%d' % job_id i0 = ao_loc[ish0] i1 = ao_loc[ish1] dii = i1*(i1+1)//2 - i0*(i0+1)//2 dij = (i1 - i0) * nao if j_only: buflen = max(8, int(max_memory*1e6/16/(nkptij*dii+dii))) else: buflen = max(8, int(max_memory*1e6/16/(nkptij*dij+dij))) auxranges = balance_segs(aux_loc[1:]-aux_loc[:-1], buflen) buflen = max([x[2] for x in auxranges]) buf = numpy.empty(nkptij*dij*buflen, dtype=dtype) buf1 = numpy.empty(dij*buflen, dtype=dtype) naux = aux_loc[-1] for kpt_id, kptij in enumerate(kptij_lst): key = '%s/%d' % (dataname, kpt_id) if aosym_s2[kpt_id]: shape = (naux, dii) else: shape = (naux, dij) if gamma_point(kptij): fswap.create_dataset(key, shape, 'f8') else: fswap.create_dataset(key, shape, 'c16') naux0 = 0 for istep, auxrange in enumerate(auxranges): log.alldebug2("aux_e1 job_id %d step %d", job_id, istep) sh0, sh1, nrow = auxrange sub_slice = (ish0, ish1, 0, cell.nbas, sh0, sh1) if j_only: mat = numpy.ndarray((nkptij,dii,nrow), dtype=dtype, buffer=buf) else: mat = numpy.ndarray((nkptij,dij,nrow), dtype=dtype, buffer=buf) mat = int3c(sub_slice, mat) for k, kptij in enumerate(kptij_lst): h5dat = fswap['%s/%d'%(dataname,k)] v = lib.transpose(mat[k], out=buf1) if not j_only and aosym_s2[k]: idy = idxb[i0*(i0+1)//2:i1*(i1+1)//2] - i0 * nao out = numpy.ndarray((nrow,dii), dtype=v.dtype, buffer=mat[k]) v = numpy.take(v, idy, axis=1, out=out) if gamma_point(kptij): h5dat[naux0:naux0+nrow] = v.real else: h5dat[naux0:naux0+nrow] = v naux0 += nrow def ft_fuse(job_id, uniq_kptji_id, sh0, sh1): kpt = uniq_kpts[uniq_kptji_id] # kpt = kptj - kpti adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0] adapted_kptjs = kptjs[adapted_ji_idx] nkptj = len(adapted_kptjs) Gaux = ft_ao.ft_ao(fused_cell, Gv, None, b, gxyz, Gvbase, kpt).T Gaux = fuse(Gaux) Gaux *= mydf.weighted_coulG(kpt, False, mesh) kLR = lib.transpose(numpy.asarray(Gaux.real, order='C')) kLI = lib.transpose(numpy.asarray(Gaux.imag, order='C')) j2c = numpy.asarray(fswap['j2c/%d'%uniq_kptji_id]) j2ctag = j2ctags[uniq_kptji_id] naux0 = j2c.shape[0] if ('j2c-/%d' % uniq_kptji_id) in fswap: j2c_negative = numpy.asarray(fswap['j2c-/%d'%uniq_kptji_id]) else: j2c_negative = None if is_zero(kpt): aosym = 's2' else: aosym = 's1' if aosym == 's2' and cell.dimension == 3: vbar = fuse(mydf.auxbar(fused_cell)) ovlp = cell.pbc_intor('int1e_ovlp', hermi=1, kpts=adapted_kptjs) ovlp = [lib.pack_tril(s) for s in ovlp] j3cR = [None] * nkptj j3cI = [None] * nkptj i0 = ao_loc[sh0] i1 = ao_loc[sh1] for k, idx in enumerate(adapted_ji_idx): key = 'j3c-chunks/%d/%d' % (job_id, idx) v = fuse(numpy.asarray(fswap[key])) if aosym == 's2' and cell.dimension == 3: for i in numpy.where(vbar != 0)[0]: v[i] -= vbar[i] * ovlp[k][i0*(i0+1)//2:i1*(i1+1)//2].ravel() j3cR[k] = numpy.asarray(v.real, order='C') if v.dtype == numpy.complex128: j3cI[k] = numpy.asarray(v.imag, order='C') v = None ncol = j3cR[0].shape[1] Gblksize = max(16, int(max_memory*1e6/16/ncol/(nkptj+1))) # +1 for pqkRbuf/pqkIbuf Gblksize = min(Gblksize, ngrids, 16384) pqkRbuf = numpy.empty(ncol*Gblksize) pqkIbuf = numpy.empty(ncol*Gblksize) buf = numpy.empty(nkptj*ncol*Gblksize, dtype=numpy.complex128) log.alldebug2(' blksize (%d,%d)', Gblksize, ncol) if aosym == 's2': shls_slice = (sh0, sh1, 0, sh1) else: shls_slice = (sh0, sh1, 0, cell.nbas) for p0, p1 in lib.prange(0, ngrids, Gblksize): dat = ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym, b, gxyz[p0:p1], Gvbase, kpt, adapted_kptjs, out=buf) nG = p1 - p0 for k, ji in enumerate(adapted_ji_idx): aoao = dat[k].reshape(nG,ncol) pqkR = numpy.ndarray((ncol,nG), buffer=pqkRbuf) pqkI = numpy.ndarray((ncol,nG), buffer=pqkIbuf) pqkR[:] = aoao.real.T pqkI[:] = aoao.imag.T lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k], 1) lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k], 1) if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])): lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k], 1) lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k], 1) for k, idx in enumerate(adapted_ji_idx): if is_zero(kpt) and gamma_point(adapted_kptjs[k]): v = j3cR[k] else: v = j3cR[k] + j3cI[k] * 1j if j2ctag == 'CD': v = scipy.linalg.solve_triangular(j2c, v, lower=True, overwrite_b=True) fswap['j3c-chunks/%d/%d'%(job_id,idx)][:naux0] = v else: fswap['j3c-chunks/%d/%d'%(job_id,idx)][:naux0] = lib.dot(j2c, v) # low-dimension systems if j2c_negative is not None: fswap['j3c-/%d/%d'%(job_id,idx)] = lib.dot(j2c_negative, v) mpi_df._assemble(mydf, kptij_lst, j3c_jobs, gen_int3c, ft_fuse, cderi_file, fswap, log)
def aux_e1(cell, auxcell, erifile, intor='int3c2e', aosym='s2ij', comp=None, kptij_lst=None, dataname='eri_mo', shls_slice=None, max_memory=2000, verbose=0): r'''3-center AO integrals (L|ij) with double lattice sum: \sum_{lm} (L[0]|i[l]j[m]), where L is the auxiliary basis. Three-index integral tensor (kptij_idx, naux, nao_pair) or four-index integral tensor (kptij_idx, comp, naux, nao_pair) are stored on disk. Args: kptij_lst : (*,2,3) array A list of (kpti, kptj) ''' intor, comp = gto.moleintor._get_intor_and_comp(cell._add_suffix(intor), comp) if isinstance(erifile, h5py.Group): feri = erifile elif h5py.is_hdf5(erifile): feri = h5py.File(erifile) else: feri = h5py.File(erifile, 'w') if dataname in feri: del(feri[dataname]) if dataname+'-kptij' in feri: del(feri[dataname+'-kptij']) 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(auxcell.cart or '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) feri.create_dataset(key, shape, dtype) 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 if not isinstance(erifile, h5py.Group): feri.close() return erifile
def _aux_e2(cell, auxcell, erifile, intor='int3c2e', aosym='s2ij', comp=None, 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. Three-index integral tensor (kptij_idx, nao_pair, naux) or four-index integral tensor (kptij_idx, comp, nao_pair, naux) are stored on disk. **This function should be only used by df and mdf initialization function _make_j3c** Args: kptij_lst : (*,2,3) array A list of (kpti, kptj) ''' intor, comp = gto.moleintor._get_intor_and_comp(cell._add_suffix(intor), comp) if isinstance(erifile, h5py.Group): feri = erifile elif h5py.is_hdf5(erifile): feri = h5py.File(erifile) else: feri = h5py.File(erifile, 'w') if dataname in feri: del(feri[dataname]) if dataname+'-kptij' in feri: del(feri[dataname+'-kptij']) 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(auxcell.cart or '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' 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*.47e6/16/(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_like(buf) int3c = wrap_int3c(cell, auxcell, intor, aosym, comp, kptij_lst) kptis = kptij_lst[:,0] kptjs = kptij_lst[:,1] kpt_ji = kptjs - kptis uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji) # sorted_ij_idx: Sort and group the kptij_lst according to the ordering in # df._make_j3c to reduce the data fragment in the hdf5 file. When datasets # are written to hdf5, they are saved sequentially. If the integral data are # saved as the order of kptij_lst, removing the datasets in df._make_j3c will # lead to holes that can not be reused. sorted_ij_idx = numpy.hstack([numpy.where(uniq_inverse == k)[0] for k, kpt in enumerate(uniq_kpts)]) tril_idx = numpy.tril_indices(ni) tril_idx = tril_idx[0] * ni + tril_idx[1] def save(istep, mat): for k in sorted_ij_idx: v = mat[k] if gamma_point(kptij_lst[k]): v = v.real if aosym_ks2[k] and nao_pair == ni**2: v = v[:,tril_idx] feri['%s/%d/%d' % (dataname,k,istep)] = v with lib.call_in_background(save) as bsave: 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) bsave(istep, int3c(sub_slice, mat)) buf, buf1 = buf1, buf if not isinstance(erifile, h5py.Group): feri.close() return erifile