Source code for pyscf.ao2mo.incore

#!/usr/bin/env python
# Copyright 2014-2018 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Qiming Sun <osirpt.sun@gmail.com>
#

import sys
import numpy
import ctypes
from pyscf import lib
from pyscf.lib import logger
from pyscf.ao2mo import _ao2mo

BLOCK = 56

[docs]def full(eri_ao, mo_coeff, verbose=0, compact=True, **kwargs): r'''MO integral transformation for the given orbital. Args: eri_ao : ndarray AO integrals, can be either 8-fold or 4-fold symmetry. mo_coeff : ndarray Transform (ij|kl) with the same set of orbitals. Kwargs: verbose : int Print level compact : bool When compact is True, the returned MO integrals have 4-fold symmetry. Otherwise, return the "plain" MO integrals. Returns: 2D array of transformed MO integrals. The MO integrals may or may not have the permutation symmetry (controlled by the kwargs compact) Examples: >>> from pyscf import gto >>> from pyscf.scf import _vhf >>> from pyscf import ao2mo >>> mol = gto.M(atom='O 0 0 0; H 0 1 0; H 0 0 1', basis='sto3g') >>> eri = mol.intor('int2e_sph', aosym='s8') >>> mo1 = numpy.random.random((mol.nao_nr(), 10)) >>> eri1 = ao2mo.incore.full(eri, mo1) >>> print(eri1.shape) (55, 55) >>> eri1 = ao2mo.incore.full(eri, mo1, compact=False) >>> print(eri1.shape) (100, 100) ''' return general(eri_ao, (mo_coeff,)*4, verbose, compact)
# It consumes two times of the memory needed by MO integrals
[docs]def general(eri_ao, mo_coeffs, verbose=0, compact=True, **kwargs): r'''For the given four sets of orbitals, transfer the 8-fold or 4-fold 2e AO integrals to MO integrals. Args: eri_ao : ndarray AO integrals, can be either 8-fold or 4-fold symmetry. mo_coeffs : 4-item list of ndarray Four sets of orbital coefficients, corresponding to the four indices of (ij|kl) Kwargs: verbose : int Print level compact : bool When compact is True, depending on the four oribital sets, the returned MO integrals has (up to 4-fold) permutation symmetry. If it's False, the function will abandon any permutation symmetry, and return the "plain" MO integrals Returns: 2D array of transformed MO integrals. The MO integrals may or may not have the permutation symmetry, depending on the given orbitals, and the kwargs compact. If the four sets of orbitals are identical, the MO integrals will at most have 4-fold symmetry. Examples: >>> from pyscf import gto >>> from pyscf.scf import _vhf >>> from pyscf import ao2mo >>> mol = gto.M(atom='O 0 0 0; H 0 1 0; H 0 0 1', basis='sto3g') >>> eri = mol.intor('int2e_sph', aosym='s8') >>> mo1 = numpy.random.random((mol.nao_nr(), 10)) >>> mo2 = numpy.random.random((mol.nao_nr(), 8)) >>> mo3 = numpy.random.random((mol.nao_nr(), 6)) >>> mo4 = numpy.random.random((mol.nao_nr(), 4)) >>> eri1 = ao2mo.incore.general(eri, (mo1,mo2,mo3,mo4)) >>> print(eri1.shape) (80, 24) >>> eri1 = ao2mo.incore.general(eri, (mo1,mo2,mo3,mo3)) >>> print(eri1.shape) (80, 21) >>> eri1 = ao2mo.incore.general(eri, (mo1,mo2,mo3,mo3), compact=False) >>> print(eri1.shape) (80, 36) >>> eri1 = ao2mo.incore.general(eri, (mo1,mo1,mo2,mo2)) >>> print(eri1.shape) (55, 36) >>> eri1 = ao2mo.incore.general(eri, (mo1,mo2,mo1,mo2)) >>> print(eri1.shape) (80, 80) ''' log = logger.new_logger(sys, verbose) nao = mo_coeffs[0].shape[0] nao_pair = nao*(nao+1)//2 if eri_ao.size == nao**4: return lib.einsum('pqrs,pi,qj,rk,sl->ijkl', eri_ao.reshape([nao]*4), mo_coeffs[0].conj(), mo_coeffs[1], mo_coeffs[2].conj(), mo_coeffs[3]) # transform e1 eri1 = half_e1(eri_ao, mo_coeffs, compact) klmosym, nkl_pair, mokl, klshape = _conc_mos(mo_coeffs[2], mo_coeffs[3], compact) if eri1.shape[0] == 0 or nkl_pair == 0: # 0 dimension causes error in certain BLAS implementations return numpy.zeros((eri1.shape[0],nkl_pair)) # if nij_pair > nkl_pair: # log.warn('low efficiency for AO to MO trans!') # transform e2 eri1 = _ao2mo.nr_e2(eri1, mokl, klshape, aosym='s4', mosym=klmosym) return eri1
[docs]def half_e1(eri_ao, mo_coeffs, compact=True): r'''Given two set of orbitals, half transform the (ij| pair of 8-fold or 4-fold AO integrals (ij|kl) Args: eri_ao : ndarray AO integrals, can be either 8-fold or 4-fold symmetry. mo_coeffs : list of ndarray Two sets of orbital coefficients, corresponding to the i, j indices of (ij|kl) Kwargs: compact : bool When compact is True, the returned MO integrals uses the highest possible permutation symmetry. If it's False, the function will abandon any permutation symmetry, and return the "plain" MO integrals Returns: ndarray of transformed MO integrals. The MO integrals may or may not have the permutation symmetry, depending on the given orbitals, and the kwargs compact. Examples: >>> from pyscf import gto >>> from pyscf import ao2mo >>> mol = gto.M(atom='O 0 0 0; H 0 1 0; H 0 0 1', basis='sto3g') >>> eri = mol.intor('int2e_sph', aosym='s8') >>> mo1 = numpy.random.random((mol.nao_nr(), 10)) >>> mo2 = numpy.random.random((mol.nao_nr(), 8)) >>> eri1 = ao2mo.incore.half_e1(eri, (mo1,mo2)) >>> eri1 = ao2mo.incore.half_e1(eri, (mo1,mo2)) >>> print(eri1.shape) (80, 28) >>> eri1 = ao2mo.incore.half_e1(eri, (mo1,mo2), compact=False) >>> print(eri1.shape) (80, 28) >>> eri1 = ao2mo.incore.half_e1(eri, (mo1,mo1)) >>> print(eri1.shape) (55, 28) ''' eri_ao = numpy.asarray(eri_ao, order='C') nao, nmoi = mo_coeffs[0].shape nmoj = mo_coeffs[1].shape[1] nao_pair = nao*(nao+1)//2 ijmosym, nij_pair, moij, ijshape = _conc_mos(mo_coeffs[0], mo_coeffs[1], compact) ijshape = (ijshape[0], ijshape[1]-ijshape[0], ijshape[2], ijshape[3]-ijshape[2]) eri1 = numpy.empty((nij_pair,nao_pair)) if nij_pair == 0: return eri1 if eri_ao.size == nao_pair**2: # 4-fold symmetry ftrans = _ao2mo.libao2mo.AO2MOtranse1_incore_s4 elif eri_ao.size == nao_pair*(nao_pair+1)//2: ftrans = _ao2mo.libao2mo.AO2MOtranse1_incore_s8 else: from pyscf.ao2mo.addons import restore eri_ao = restore(4, eri_ao, nao) ftrans = _ao2mo.libao2mo.AO2MOtranse1_incore_s4 if ijmosym == 's2': fmmm = _ao2mo.libao2mo.AO2MOmmm_nr_s2_s2 elif nmoi <= nmoj: fmmm = _ao2mo.libao2mo.AO2MOmmm_nr_s2_iltj else: fmmm = _ao2mo.libao2mo.AO2MOmmm_nr_s2_igtj fdrv = getattr(_ao2mo.libao2mo, 'AO2MOnr_e1incore_drv') bufs = numpy.empty((BLOCK, nij_pair)) for blk0 in range(0, nao_pair, BLOCK): blk1 = min(blk0+BLOCK, nao_pair) buf = bufs[:blk1-blk0] fdrv(ftrans, fmmm, buf.ctypes.data_as(ctypes.c_void_p), eri_ao.ctypes.data_as(ctypes.c_void_p), moij.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(blk0), ctypes.c_int(blk1-blk0), ctypes.c_int(nao), ctypes.c_int(ijshape[0]), ctypes.c_int(ijshape[1]), ctypes.c_int(ijshape[2]), ctypes.c_int(ijshape[3])) eri1[:,blk0:blk1] = buf.T return eri1
def iden_coeffs(mo1, mo2): return (id(mo1) == id(mo2) or (mo1.shape==mo2.shape and numpy.linalg.norm(mo1-mo2) < 1e-13)) def _conc_mos(moi, moj, compact=False): nmoi = moi.shape[1] nmoj = moj.shape[1] if compact and iden_coeffs(moi, moj): ijmosym = 's2' nij_pair = nmoi * (nmoi+1) // 2 moij = numpy.asarray(moi, order='F') ijshape = (0, nmoi, 0, nmoi) else: ijmosym = 's1' nij_pair = nmoi * nmoj moij = numpy.asarray(numpy.hstack((moi,moj)), order='F') ijshape = (0, nmoi, nmoi, nmoi+nmoj) return ijmosym, nij_pair, moij, ijshape if __name__ == '__main__': from pyscf import scf from pyscf import gto mol = gto.Mole() mol.verbose = 5 mol.output = 'out_h2o' mol.atom = [ ["O" , (0. , 0. , 0.)], [1 , (0. , -0.757 , 0.587)], [1 , (0. , 0.757 , 0.587)]] mol.basis = {'H': 'cc-pvtz', 'O': 'cc-pvtz',} mol.build() rhf = scf.RHF(mol) rhf.scf() import time print(time.clock()) eri0 = full(rhf._eri, rhf.mo_coeff) print(abs(eri0).sum()-5384.460843787659) # should = 0 eri0 = general(rhf._eri, (rhf.mo_coeff,)*4) print(abs(eri0).sum()-5384.460843787659) print(time.clock())