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ccsd_lambda.py
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ccsd_lambda.py
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#!/usr/bin/env python
# Copyright 2014-2020 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>
#
'''
Restricted CCSD implementation for real integrals. Permutation symmetry for
the 4-index integrals (ij|kl) = (ij|lk) = (ji|kl) are assumed.
Note MO integrals are treated in chemist's notation
'''
import time
from functools import reduce
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.cc import ccsd
from pyscf.cc import _ccsd
# t2,l2 as ijab
def kernel(mycc, eris=None, t1=None, t2=None, l1=None, l2=None,
max_cycle=50, tol=1e-8, verbose=logger.INFO,
fintermediates=None, fupdate=None):
if eris is None: eris = mycc.ao2mo()
cput0 = (time.clock(), time.time())
log = logger.new_logger(mycc, verbose)
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = t1
if l2 is None: l2 = t2
if fintermediates is None:
fintermediates = make_intermediates
if fupdate is None:
fupdate = update_lambda
imds = fintermediates(mycc, t1, t2, eris)
if isinstance(mycc.diis, lib.diis.DIIS):
adiis = mycc.diis
elif mycc.diis:
adiis = lib.diis.DIIS(mycc, mycc.diis_file, incore=mycc.incore_complete)
adiis.space = mycc.diis_space
else:
adiis = None
cput0 = log.timer('CCSD lambda initialization', *cput0)
conv = False
for istep in range(max_cycle):
l1new, l2new = fupdate(mycc, t1, t2, l1, l2, eris, imds)
normt = numpy.linalg.norm(mycc.amplitudes_to_vector(l1new, l2new) -
mycc.amplitudes_to_vector(l1, l2))
l1, l2 = l1new, l2new
l1new = l2new = None
l1, l2 = mycc.run_diis(l1, l2, istep, normt, 0, adiis)
log.info('cycle = %d norm(lambda1,lambda2) = %.6g', istep+1, normt)
cput0 = log.timer('CCSD iter', *cput0)
if normt < tol:
conv = True
break
return conv, l1, l2
# l2, t2 as ijab
def make_intermediates(mycc, t1, t2, eris):
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
foo = eris.fock[:nocc,:nocc]
fov = eris.fock[:nocc,nocc:]
#fvo = eris.fock[nocc:,:nocc]
fvv = eris.fock[nocc:,nocc:]
class _IMDS: pass
imds = _IMDS()
#TODO: mycc.incore_complete
imds.ftmp = lib.H5TmpFile()
imds.woooo = imds.ftmp.create_dataset('woooo', (nocc,nocc,nocc,nocc), 'f8')
imds.wvooo = imds.ftmp.create_dataset('wvooo', (nvir,nocc,nocc,nocc), 'f8')
imds.wVOov = imds.ftmp.create_dataset('wVOov', (nvir,nocc,nocc,nvir), 'f8')
imds.wvOOv = imds.ftmp.create_dataset('wvOOv', (nvir,nocc,nocc,nvir), 'f8')
imds.wvvov = imds.ftmp.create_dataset('wvvov', (nvir,nvir,nocc,nvir), 'f8')
w1 = fvv - numpy.einsum('ja,jb->ba', fov, t1)
w2 = foo + numpy.einsum('ib,jb->ij', fov, t1)
w3 = numpy.einsum('kc,jkbc->bj', fov, t2) * 2 + fov.T
w3 -= numpy.einsum('kc,kjbc->bj', fov, t2)
w3 += lib.einsum('kc,kb,jc->bj', fov, t1, t1)
w4 = fov.copy()
unit = nocc*nvir**2*6
max_memory = max(0, mycc.max_memory - lib.current_memory()[0])
blksize = min(nvir, max(ccsd.BLKMIN, int((max_memory*.95e6/8-nocc**4-nvir*nocc**3)/unit)))
log.debug1('ccsd lambda make_intermediates: block size = %d, nvir = %d in %d blocks',
blksize, nvir, int((nvir+blksize-1)//blksize))
fswap = lib.H5TmpFile()
for istep, (p0, p1) in enumerate(lib.prange(0, nvir, blksize)):
eris_ovvv = eris.get_ovvv(slice(None), slice(p0,p1))
fswap['vvov/%d'%istep] = eris_ovvv.transpose(2,3,0,1)
woooo = 0
wvooo = numpy.zeros((nvir,nocc,nocc,nocc))
for p0, p1 in lib.prange(0, nvir, blksize):
eris_ovvv = eris.get_ovvv(slice(None), slice(p0,p1))
eris_vvov = numpy.empty(((p1-p0),nvir,nocc,nvir))
for istep, (q0, q1) in enumerate(lib.prange(0, nvir, blksize)):
eris_vvov[:,:,:,q0:q1] = fswap['vvov/%d'%istep][p0:p1]
w1 += numpy.einsum('jcba,jc->ba', eris_ovvv, t1[:,p0:p1]*2)
w1[:,p0:p1] -= numpy.einsum('jabc,jc->ba', eris_ovvv, t1)
theta = t2[:,:,:,p0:p1] * 2 - t2[:,:,:,p0:p1].transpose(1,0,2,3)
w3 += lib.einsum('jkcd,kdcb->bj', theta, eris_ovvv)
theta = None
wVOov = lib.einsum('jbcd,kd->bjkc', eris_ovvv, t1)
wvOOv = lib.einsum('cbjd,kd->cjkb', eris_vvov,-t1)
g2vovv = eris_vvov.transpose(0,2,1,3) * 2 - eris_vvov.transpose(0,2,3,1)
for i0, i1 in lib.prange(0, nocc, blksize):
tau = t2[:,i0:i1] + numpy.einsum('ia,jb->ijab', t1, t1[i0:i1])
wvooo[p0:p1,i0:i1] += lib.einsum('cibd,jkbd->ckij', g2vovv, tau)
g2vovv = tau = None
# Watch out memory usage here, due to the t2 transpose
wvvov = lib.einsum('jabd,jkcd->abkc', eris_ovvv, t2) * -1.5
wvvov += eris_vvov.transpose(0,3,2,1) * 2
wvvov -= eris_vvov
g2vvov = eris_vvov * 2 - eris_ovvv.transpose(1,2,0,3)
for i0, i1 in lib.prange(0, nocc, blksize):
theta = t2[i0:i1] * 2 - t2[i0:i1].transpose(0,1,3,2)
vackb = lib.einsum('acjd,kjbd->ackb', g2vvov, theta)
wvvov[:,:,i0:i1] += vackb.transpose(0,3,2,1)
wvvov[:,:,i0:i1] -= vackb * .5
g2vvov = eris_ovvv = eris_vvov = theta = None
eris_ovoo = _cp(eris.ovoo[:,p0:p1])
w2 += numpy.einsum('kbij,kb->ij', eris_ovoo, t1[:,p0:p1]) * 2
w2 -= numpy.einsum('ibkj,kb->ij', eris_ovoo, t1[:,p0:p1])
theta = t2[:,:,p0:p1].transpose(1,0,2,3) * 2 - t2[:,:,p0:p1]
w3 -= lib.einsum('lckj,klcb->bj', eris_ovoo, theta)
tmp = lib.einsum('lc,jcik->ijkl', t1[:,p0:p1], eris_ovoo)
woooo += tmp
woooo += tmp.transpose(1,0,3,2)
theta = tmp = None
wvOOv += lib.einsum('lbjk,lc->bjkc', eris_ovoo, t1)
wVOov -= lib.einsum('jbkl,lc->bjkc', eris_ovoo, t1)
wvooo[p0:p1] += eris_ovoo.transpose(1,3,2,0) * 2
wvooo[p0:p1] -= eris_ovoo.transpose(1,0,2,3)
wvooo -= lib.einsum('klbc,iblj->ckij', t2[:,:,p0:p1], eris_ovoo*1.5)
g2ovoo = eris_ovoo * 2 - eris_ovoo.transpose(2,1,0,3)
theta = t2[:,:,:,p0:p1]*2 - t2[:,:,:,p0:p1].transpose(1,0,2,3)
vcjik = lib.einsum('jlcb,lbki->cjki', theta, g2ovoo)
wvooo += vcjik.transpose(0,3,2,1)
wvooo -= vcjik*.5
theta = g2ovoo = None
eris_voov = _cp(eris.ovvo[:,p0:p1]).transpose(1,0,3,2)
tau = t2[:,:,p0:p1] + numpy.einsum('ia,jb->ijab', t1[:,p0:p1], t1)
woooo += lib.einsum('cijd,klcd->ijkl', eris_voov, tau)
tau = None
g2voov = eris_voov*2 - eris_voov.transpose(0,2,1,3)
tmpw4 = numpy.einsum('ckld,ld->kc', g2voov, t1)
w1 -= lib.einsum('ckja,kjcb->ba', g2voov, t2[:,:,p0:p1])
w1[:,p0:p1] -= numpy.einsum('ja,jb->ba', tmpw4, t1)
w2 += lib.einsum('jkbc,bikc->ij', t2[:,:,p0:p1], g2voov)
w2 += numpy.einsum('ib,jb->ij', tmpw4, t1[:,p0:p1])
w3 += reduce(numpy.dot, (t1.T, tmpw4, t1[:,p0:p1].T))
w4[:,p0:p1] += tmpw4
wvOOv += lib.einsum('bljd,kd,lc->bjkc', eris_voov, t1, t1)
wVOov -= lib.einsum('bjld,kd,lc->bjkc', eris_voov, t1, t1)
VOov = lib.einsum('bjld,klcd->bjkc', g2voov, t2)
VOov -= lib.einsum('bjld,kldc->bjkc', eris_voov, t2)
VOov += eris_voov
vOOv = lib.einsum('bljd,kldc->bjkc', eris_voov, t2)
vOOv -= _cp(eris.oovv[:,:,p0:p1]).transpose(2,1,0,3)
wVOov += VOov
wvOOv += vOOv
imds.wVOov[p0:p1] = wVOov
imds.wvOOv[p0:p1] = wvOOv
ov1 = vOOv*2 + VOov
ov2 = VOov*2 + vOOv
vOOv = VOov = None
wvooo -= lib.einsum('jb,bikc->ckij', t1[:,p0:p1], ov1)
wvooo += lib.einsum('kb,bijc->ckij', t1[:,p0:p1], ov2)
w3 += numpy.einsum('ckjb,kc->bj', ov2, t1[:,p0:p1])
wvvov += lib.einsum('ajkc,jb->abkc', ov1, t1)
wvvov -= lib.einsum('ajkb,jc->abkc', ov2, t1)
eris_ovoo = _cp(eris.ovoo[:,p0:p1])
g2ovoo = eris_ovoo * 2 - eris_ovoo.transpose(2,1,0,3)
tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
wvvov += lib.einsum('laki,klbc->abic', g2ovoo, tau)
imds.wvvov[p0:p1] = wvvov
wvvov = ov1 = ov2 = g2ovoo = None
woooo += _cp(eris.oooo).transpose(0,2,1,3)
imds.woooo[:] = woooo
imds.wvooo[:] = wvooo
woooo = wvooo = None
w3 += numpy.einsum('bc,jc->bj', w1, t1)
w3 -= numpy.einsum('kj,kb->bj', w2, t1)
fswap = None
imds.w1 = w1
imds.w2 = w2
imds.w3 = w3
imds.w4 = w4
imds.ftmp.flush()
return imds
# update L1, L2
def update_lambda(mycc, t1, t2, l1, l2, eris=None, imds=None):
if imds is None: imds = make_intermediates(mycc, t1, t2, eris)
time0 = time.clock(), time.time()
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
fov = eris.fock[:nocc,nocc:]
mo_e_o = eris.mo_energy[:nocc]
mo_e_v = eris.mo_energy[nocc:] + mycc.level_shift
theta = t2*2 - t2.transpose(0,1,3,2)
mba = lib.einsum('klca,klcb->ba', l2, theta)
mij = lib.einsum('ikcd,jkcd->ij', l2, theta)
theta = None
mba1 = numpy.einsum('jc,jb->bc', l1, t1) + mba
mij1 = numpy.einsum('kb,jb->kj', l1, t1) + mij
mia1 = t1 + numpy.einsum('kc,jkbc->jb', l1, t2) * 2
mia1 -= numpy.einsum('kc,jkcb->jb', l1, t2)
mia1 -= reduce(numpy.dot, (t1, l1.T, t1))
mia1 -= numpy.einsum('bd,jd->jb', mba, t1)
mia1 -= numpy.einsum('lj,lb->jb', mij, t1)
l2new = mycc._add_vvvv(None, l2, eris, with_ovvv=False, t2sym='jiba')
l1new = numpy.einsum('ijab,jb->ia', l2new, t1) * 2
l1new -= numpy.einsum('jiab,jb->ia', l2new, t1)
l2new *= .5 # *.5 because of l2+l2.transpose(1,0,3,2) in the end
tmp = tmp1 = None
w1 = imds.w1 - numpy.diag(mo_e_v)
w2 = imds.w2 - numpy.diag(mo_e_o)
l1new += fov
l1new += numpy.einsum('ib,ba->ia', l1, w1)
l1new -= numpy.einsum('ja,ij->ia', l1, w2)
l1new -= numpy.einsum('ik,ka->ia', mij, imds.w4)
l1new -= numpy.einsum('ca,ic->ia', mba, imds.w4)
l1new += numpy.einsum('ijab,bj->ia', l2, imds.w3) * 2
l1new -= numpy.einsum('ijba,bj->ia', l2, imds.w3)
l2new += numpy.einsum('ia,jb->ijab', l1, imds.w4)
l2new += lib.einsum('jibc,ca->jiba', l2, w1)
l2new -= lib.einsum('jk,kiba->jiba', w2, l2)
eris_ovoo = _cp(eris.ovoo)
l1new -= numpy.einsum('iajk,kj->ia', eris_ovoo, mij1) * 2
l1new += numpy.einsum('jaik,kj->ia', eris_ovoo, mij1)
l2new -= lib.einsum('jbki,ka->jiba', eris_ovoo, l1)
eris_ovoo = None
tau = _ccsd.make_tau(t2, t1, t1)
l2tau = lib.einsum('ijcd,klcd->ijkl', l2, tau)
tau = None
l2t1 = lib.einsum('jidc,kc->ijkd', l2, t1)
max_memory = max(0, mycc.max_memory - lib.current_memory()[0])
unit = nocc*nvir**2*5
blksize = min(nocc, max(ccsd.BLKMIN, int(max_memory*.95e6/8/unit)))
log.debug1('block size = %d, nocc = %d is divided into %d blocks',
blksize, nocc, int((nocc+blksize-1)/blksize))
l1new -= numpy.einsum('jb,jiab->ia', l1, _cp(eris.oovv))
for p0, p1 in lib.prange(0, nvir, blksize):
eris_ovvv = eris.get_ovvv(slice(None), slice(p0,p1))
l1new[:,p0:p1] += numpy.einsum('iabc,bc->ia', eris_ovvv, mba1) * 2
l1new -= numpy.einsum('ibca,bc->ia', eris_ovvv, mba1[p0:p1])
l2new[:,:,p0:p1] += lib.einsum('jbac,ic->jiba', eris_ovvv, l1)
m4 = lib.einsum('ijkd,kadb->ijab', l2t1, eris_ovvv)
l2new[:,:,p0:p1] -= m4
l1new[:,p0:p1] -= numpy.einsum('ijab,jb->ia', m4, t1) * 2
l1new -= numpy.einsum('ijab,ia->jb', m4, t1[:,p0:p1]) * 2
l1new[:,p0:p1] += numpy.einsum('jiab,jb->ia', m4, t1)
l1new += numpy.einsum('jiab,ia->jb', m4, t1[:,p0:p1])
eris_ovvv = m4 = None
eris_voov = _cp(eris.ovvo[:,p0:p1].transpose(1,0,3,2))
l1new[:,p0:p1] += numpy.einsum('jb,aijb->ia', l1, eris_voov) * 2
l2new[:,:,p0:p1] += eris_voov.transpose(1,2,0,3) * .5
l2new[:,:,p0:p1] -= lib.einsum('bjic,ca->jiba', eris_voov, mba1)
l2new[:,:,p0:p1] -= lib.einsum('bjka,ik->jiba', eris_voov, mij1)
l1new[:,p0:p1] += numpy.einsum('aijb,jb->ia', eris_voov, mia1) * 2
l1new -= numpy.einsum('bija,jb->ia', eris_voov, mia1[:,p0:p1])
m4 = lib.einsum('ijkl,aklb->ijab', l2tau, eris_voov)
l2new[:,:,p0:p1] += m4 * .5
l1new[:,p0:p1] += numpy.einsum('ijab,jb->ia', m4, t1) * 2
l1new -= numpy.einsum('ijba,jb->ia', m4, t1[:,p0:p1])
saved_wvooo = _cp(imds.wvooo[p0:p1])
l1new -= lib.einsum('ckij,jkca->ia', saved_wvooo, l2[:,:,p0:p1])
saved_wvovv = _cp(imds.wvvov[p0:p1])
# Watch out memory usage here, due to the l2 transpose
l1new[:,p0:p1] += lib.einsum('abkc,kibc->ia', saved_wvovv, l2)
saved_wvooo = saved_wvovv = None
saved_wvOOv = _cp(imds.wvOOv[p0:p1])
tmp_voov = _cp(imds.wVOov[p0:p1]) * 2
tmp_voov += saved_wvOOv
tmp = l2.transpose(0,2,1,3) - l2.transpose(0,3,1,2)*.5
l2new[:,:,p0:p1] += lib.einsum('iakc,bjkc->jiba', tmp, tmp_voov)
tmp = None
tmp = lib.einsum('jkca,bikc->jiba', l2, saved_wvOOv)
l2new[:,:,p0:p1] += tmp
l2new[:,:,p0:p1] += tmp.transpose(1,0,2,3) * .5
saved_wvOOv = tmp = None
saved_woooo = _cp(imds.woooo)
m3 = lib.einsum('ijkl,klab->ijab', saved_woooo, l2)
l2new += m3 * .5
l1new += numpy.einsum('ijab,jb->ia', m3, t1) * 2
l1new -= numpy.einsum('ijba,jb->ia', m3, t1)
saved_woooo = m3 = None
#time1 = log.timer_debug1('lambda pass [%d:%d]'%(p0, p1), *time1)
eia = lib.direct_sum('i-a->ia', mo_e_o, mo_e_v)
l1new /= eia
# l2new = l2new + l2new.transpose(1,0,3,2)
# l2new /= lib.direct_sum('ia+jb->ijab', eia, eia)
# l2new += l2
for i in range(nocc):
if i > 0:
l2new[i,:i] += l2new[:i,i].transpose(0,2,1)
l2new[i,:i] /= lib.direct_sum('a,jb->jab', eia[i], eia[:i])
l2new[:i,i] = l2new[i,:i].transpose(0,2,1)
l2new[i,i] = l2new[i,i] + l2new[i,i].T
l2new[i,i] /= lib.direct_sum('a,b->ab', eia[i], eia[i])
time0 = log.timer_debug1('update l1 l2', *time0)
return l1new, l2new
def _cp(a):
return numpy.array(a, copy=False, order='C')
if __name__ == '__main__':
from pyscf import gto
from pyscf import scf
from pyscf import ao2mo
mol = gto.M()
mf = scf.RHF(mol)
mcc = ccsd.CCSD(mf)
numpy.random.seed(12)
nocc = 5
nmo = 12
nvir = nmo - nocc
eri0 = numpy.random.random((nmo,nmo,nmo,nmo))
eri0 = ao2mo.restore(1, ao2mo.restore(8, eri0, nmo), nmo)
fock0 = numpy.random.random((nmo,nmo))
fock0 = fock0 + fock0.T + numpy.diag(range(nmo))*2
t1 = numpy.random.random((nocc,nvir))
t2 = numpy.random.random((nocc,nocc,nvir,nvir))
t2 = t2 + t2.transpose(1,0,3,2)
l1 = numpy.random.random((nocc,nvir))
l2 = numpy.random.random((nocc,nocc,nvir,nvir))
l2 = l2 + l2.transpose(1,0,3,2)
eris = ccsd._ChemistsERIs()
eris.oooo = eri0[:nocc,:nocc,:nocc,:nocc].copy()
eris.ovoo = eri0[:nocc,nocc:,:nocc,:nocc].copy()
eris.oovv = eri0[:nocc,:nocc,nocc:,nocc:].copy()
eris.ovvo = eri0[:nocc,nocc:,nocc:,:nocc].copy()
idx = numpy.tril_indices(nvir)
eris.ovvv = eri0[:nocc,nocc:,nocc:,nocc:][:,:,idx[0],idx[1]].copy()
eris.vvvv = ao2mo.restore(4,eri0[nocc:,nocc:,nocc:,nocc:],nvir)
eris.fock = fock0
eris.mo_energy = fock0.diagonal()
imds = make_intermediates(mcc, t1, t2, eris)
l1new, l2new = update_lambda(mcc, t1, t2, l1, l2, eris, imds)
print(lib.finger(l1new) - -6699.5335665027187)
print(lib.finger(l2new) - -514.7001243502192 )
print(abs(l2new-l2new.transpose(1,0,3,2)).sum())
mcc.max_memory = 0
imds = make_intermediates(mcc, t1, t2, eris)
l1new, l2new = update_lambda(mcc, t1, t2, l1, l2, eris, imds)
print(lib.finger(l1new) - -6699.5335665027187)
print(lib.finger(l2new) - -514.7001243502192 )
print(abs(l2new-l2new.transpose(1,0,3,2)).sum())
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
[8 , (0. , 0. , 0.)],
[1 , (0. , -0.757 , 0.587)],
[1 , (0. , 0.757 , 0.587)]]
mol.basis = 'cc-pvdz'
mol.build()
rhf = scf.RHF(mol)
rhf.conv_tol = 1e-16
rhf.scf()
mcc = ccsd.CCSD(rhf)
mcc.conv_tol = 1e-12
ecc, t1, t2 = mcc.kernel()
nmo = rhf.mo_energy.size
fock0 = numpy.diag(rhf.mo_energy)
nocc = mol.nelectron // 2
nvir = nmo - nocc
eris = mcc.ao2mo()
conv, l1, l2 = kernel(mcc, eris, t1, t2, tol=1e-8)
print(numpy.linalg.norm(l1)-0.0132626841292)
print(numpy.linalg.norm(l2)-0.212575609057)
from pyscf.cc import ccsd_rdm
dm1 = ccsd_rdm.make_rdm1(mcc, t1, t2, l1, l2)
dm2 = ccsd_rdm.make_rdm2(mcc, t1, t2, l1, l2)
h1 = reduce(numpy.dot, (rhf.mo_coeff.T, rhf.get_hcore(), rhf.mo_coeff))
eri = ao2mo.full(rhf._eri, rhf.mo_coeff)
eri = ao2mo.restore(1, eri, nmo).reshape((nmo,)*4)
e1 = numpy.einsum('pq,pq', h1, dm1)
e2 = numpy.einsum('pqrs,pqrs', eri, dm2) * .5
print(e1+e2+mol.energy_nuc() - rhf.e_tot - ecc)