def gamma2_intermediates(mycc, t1, t2, l1, l2, eris=None):
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
ccsd_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = ccsd._ERIS(mycc)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
mo_e = mycc._scf.mo_energy
eia = lib.direct_sum('i-a->ia',mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w =(numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = p6_(w)
v = p6_(v)
rw = r6_(w)
rwv = r6_(w*2+v)
dovov += numpy.einsum('kc,ijkabc->iajb', t1, rw) * .5
dooov -= numpy.einsum('mkbc,ijkabc->jmia', t2, rwv)
# Note "dovvv +=" also changes the value of dvvov
dovvv += numpy.einsum('kjcf,ijkabc->iabf', t2, rwv)
dvvov = dovvv.transpose(2,3,0,1)
return dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov
def add_wvvVV_(self, t1, t2, eris, t2new_tril, max_memory=2000):
time0 = time.clock(), time.time()
nocc, nvir = t1.shape
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: t2new += numpy.einsum('ijcd,acdb->ijab', tau, vvvv)
tau = numpy.empty((nocc*(nocc+1)//2,nvir,nvir))
p0 = 0
for i in range(nocc):
tau[p0:p0+i+1] = numpy.einsum('a,jb->jab', t1[i], t1[:i+1])
tau[p0:p0+i+1] += t2[i,:i+1]
p0 += i + 1
time0 = logger.timer_debug1(self, 'vvvv-tau', *time0)
p0 = 0
outbuf = numpy.empty((nvir,nvir,nvir))
for a in range(nvir):
buf = _ccsd.unpack_tril(eris.vvvv[p0:p0+a+1], out=outbuf[:a+1])
#: t2new_tril[i,:i+1, a] += numpy.einsum('xcd,cdb->xb', tau[:,:a+1], buf)
lib.numpy_helper._dgemm('N', 'N', nocc*(nocc+1)//2, nvir, (a+1)*nvir,
tau.reshape(-1,nvir*nvir), buf.reshape(-1,nvir),
t2new_tril.reshape(-1,nvir*nvir), 1, 1,
0, 0, a*nvir)
#: t2new_tril[i,:i+1,:a] += numpy.einsum('xd,abd->xab', tau[:,a], buf[:a])
if a > 0:
lib.numpy_helper._dgemm('N', 'T', nocc*(nocc+1)//2, a*nvir, nvir,
tau.reshape(-1,nvir*nvir), buf.reshape(-1,nvir),
t2new_tril.reshape(-1,nvir*nvir), 1, 1,
a*nvir, 0, 0)
p0 += a+1
time0 = logger.timer_debug1(self, 'vvvv %d'%a, *time0)
return t2new_tril
def gamma1_intermediates(mycc, t1, t2, l1, l2, eris=None):
doo, dov, dvo, dvv = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = ccsd._ERIS(mycc)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
mo_e = mycc._scf.mo_energy
eia = lib.direct_sum('i-a->ia',mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w =(numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = p6_(w)
v = p6_(v)
wv = w+v
rw = r6_(w)
goo =-numpy.einsum('iklabc,jklabc->ij', wv, rw) * .5
gvv = numpy.einsum('ijkacd,ijkbcd->ab', wv, rw) * .5
doo += goo
dvv += gvv
return doo, dov, dvo, dvv
def make_intermediates(mycc, t1, t2, eris):
saved = ccsd_lambda.make_intermediates(mycc, t1, t2, eris)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
mo_e = mycc._scf.mo_energy
eia = lib.direct_sum('i-a->ia',mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w =(numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = ccsd_t.p6_(w)
v = ccsd_t.p6_(v)
rwv = ccsd_t.r6_(w*2+v)
jov = numpy.einsum('jbkc,ijkabc->ia', eris.ovov, ccsd_t.r6_(w))
joovv = numpy.einsum('iabf,ijkabc->kjcf', eris_ovvv, rwv)
joovv-= numpy.einsum('iajm,ijkabc->mkbc', eris.ovoo, rwv)
joovv = joovv + joovv.transpose(1,0,3,2)
saved.jov = jov
saved.joovv = joovv
return saved
def kernel(cc, eris, t1=None, t2=None, max_memory=2000, verbose=logger.INFO):
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(cc.stdout, verbose)
if t1 is None: t1 = cc.t1
if t2 is None: t2 = cc.t2
nocc, nvir = t1.shape
nmo = nocc + nvir
mo_e = cc._scf.mo_energy
eia = mo_e[:nocc,None] - mo_e[nocc:]
eiajb = eia.reshape(-1,1) + eia.reshape(-1)
d3 = eia.reshape(-1,1) + eiajb.reshape(-1)
d3 = d3.reshape(nocc,nvir,nocc,nvir,nocc,nvir).transpose(0,2,4,1,3,5)
eris_ovvv = _ccsd.unpack_tril(eris.ovvv.reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
eris_ovoo = eris.ovoo
eris_ovov = eris.ovov
w =(numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2))
#r = r6_(w)
#v = numpy.einsum('iajb,kc->ijkabc', eris_ovov, t1)
#wvd = p6_(w + .5 * v) / d3
#et = numpy.einsum('ijkabc,ijkabc', wvd, r) * 2
# wvd = (w + .5 * v) / d3
# et =(numpy.einsum('ijkabc,ijkabc', wvd, r)
# + numpy.einsum('ikjacb,ijkabc', wvd, r)
# + numpy.einsum('jikbac,ijkabc', wvd, r)
# + numpy.einsum('jkibca,ijkabc', wvd, r)
# + numpy.einsum('kijcab,ijkabc', wvd, r)
# + numpy.einsum('kjicba,ijkabc', wvd, r)) * 2
r = r6_(p6_(w))
v = numpy.einsum('iajb,kc->ijkabc', eris_ovov, t1)
wvd = p6_(w + .5 * v) / d3
wt = numpy.zeros((nvir,nvir,nvir))
for i in range(nvir):
for j in range(i+1):
for k in range(j+1):
wt[i,j,k] = 1
if i == j or j == k:
wt[i,j,k] = 1./2
if i == k:
wt[i,j,k] *= 1./3
et = numpy.einsum('ijkabc,ijkabc,abc', wvd, r, wt) * 2
return et
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if d1 is None:
doo, dvv = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
else:
doo, dvv = d1
if d2 is None:
d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2)
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
# Note Ioo, Ivv are not hermitian
Ioo = numpy.zeros((nocc,nocc))
Ivv = numpy.zeros((nvir,nvir))
Ivo = numpy.zeros((nvir,nocc))
Xvo = numpy.zeros((nvir,nocc))
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
d_oooo = _cp(doooo)
d_oooo = _cp(d_oooo + d_oooo.transpose(1,0,2,3))
#:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2
Ioo += lib.dot(eris_oooo.reshape(nocc,-1), d_oooo.reshape(nocc,-1).T, 2)
d_oooo = _cp(d_oooo.transpose(0,2,3,1))
#:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2
Xvo += lib.dot(eris_ooov.reshape(-1,nvir).T, d_oooo.reshape(nocc,-1).T, 2)
Xvo +=(numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4
- numpy.einsum('kj,ikja->ai', doo+doo.T, eris_ooov))
eris_oooo = eris_ooov = d_oooo = None
d_ooov = _cp(dooov)
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
#:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov)
#:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo)
Ivv += lib.dot(eris_ooov.reshape(-1,nvir).T, d_ooov.reshape(-1,nvir))
Ivo += lib.dot(d_ooov.reshape(-1,nvir).T, eris_oooo.reshape(-1,nocc))
#:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv)
eris_oovv = _cp(eris.oovv)
tmp = _cp(d_ooov.transpose(0,1,3,2).reshape(-1,nocc))
tmpooov = _cp(eris_ooov.transpose(0,1,3,2))
Ioo += lib.dot(tmpooov.reshape(-1,nocc).T, tmp)
Xvo += lib.dot(eris_oovv.reshape(-1,nvir).T, tmp)
eris_oooo = tmp = None
d_ooov = d_ooov + d_ooov.transpose(1,0,2,3)
eris_ovov = _cp(eris.ovov)
#:Ioo += numpy.einsum('jlka,ilka->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('ijkb,kbja->ai', d_ooov, eris.ovov)
Ioo += lib.dot(eris_ooov.reshape(nocc,-1), d_ooov.reshape(nocc,-1).T)
Xvo += lib.dot(eris_ovov.reshape(-1,nvir).T,
_cp(d_ooov.transpose(0,2,3,1).reshape(nocc,-1)).T)
d_ooov = None
#:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv)
#:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv)
#:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov)
d_oovv = _cp(doovv + doovv.transpose(1,0,3,2))
for i in range(nocc):
Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1), d_oovv[i].reshape(nocc,-1).T)
Ivv += lib.dot(eris_oovv.reshape(-1,nvir).T, d_oovv.reshape(-1,nvir))
Ivo += lib.dot(d_oovv.reshape(-1,nvir).T, tmpooov.reshape(-1,nocc))
d_oovv = _ccsd.precontract(d_oovv.reshape(-1,nvir,nvir)).reshape(nocc,nocc,-1)
eris_ooov = tmpooov = None
blksize = 4
d_ovov = numpy.empty((nocc,nvir,nocc,nvir))
for p0, p1 in prange(0, nocc, blksize):
d_ovov[p0:p1] = _cp(dovov[p0:p1])
d_ovvo = _cp(dovvo[p0:p1])
for i in range(p0,p1):
d_ovov[i] += d_ovvo[i-p0].transpose(0,2,1)
d_ovvo = None
#:d_ovov = d_ovov + d_ovov.transpose(2,3,0,1)
lib.transpose_sum(d_ovov.reshape(nov,nov), inplace=True)
#:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo)
Ivo += lib.dot(d_ovov.reshape(-1,nvir).T, _cp(eris.ovoo).reshape(-1,nocc))
#:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov)
#:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov)
Ioo += lib.dot(eris_ovov.reshape(nocc,-1), d_ovov.reshape(nocc,-1).T)
Ivv += lib.dot(eris_ovov.reshape(-1,nvir).T, d_ovov.reshape(-1,nvir))
nvir_pair = nvir * (nvir+1) // 2
bufe_ovvv = numpy.empty((blksize,nvir,nvir,nvir))
bufc_ovvv = numpy.empty((blksize,nvir,nvir_pair))
bufc_ovvv.data = bufe_ovvv.data
c_vvvo = numpy.empty((nvir_pair,nvir,nocc))
for p0, p1 in prange(0, nocc, blksize):
d_ovvv = numpy.empty((p1-p0,nvir,nvir,nvir))
#:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv)
for i in range(p1-p0):
lib.dot(dovvv[p0+i].reshape(nvir,-1),
eris_oovv[p0+i].reshape(nocc,-1).T, 1, Ivo, 1)
c_ovvv = bufc_ovvv[:p1-p0]
# tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2))
_ccsd.precontract(dovvv[p0:p1].reshape(-1,nvir,nvir), out=c_ovvv)
for i0, i1, in prange(0, nvir_pair, BLKSIZE):
for j0, j1 in prange(0, nvir, BLKSIZE//(p1-p0)+1):
c_vvvo[i0:i1,j0:j1,p0:p1] = c_ovvv[:,j0:j1,i0:i1].transpose(2,1,0)
eris_ovx = _cp(eris.ovvv[p0:p1])
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
#:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv)
for i in range(p1-p0):
lib.dot(eris_ovx[i].reshape(nvir,-1),
d_oovv[p0+i].reshape(nocc,-1).T, 1, Xvo, 1)
lib.dot(eris_ovx[i].reshape(nvir,-1),
c_ovvv[i].reshape(nvir,-1).T, 1, Ivv, 1)
eris_ovvv = bufe_ovvv[:p1-p0]
_ccsd.unpack_tril(eris_ovx.reshape(-1,nvir_pair),
out=eris_ovvv.reshape(-1,nvir**2))
eris_ovx = None
#:Xvo += numpy.einsum('icjb,acjb->ai', d_ovov, eris_vvov)
d_ovvo = _cp(d_ovov[p0:p1].transpose(0,1,3,2))
lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvo.reshape(-1,nocc), 1, Xvo, 1)
e_ovvo, d_ovvo = d_ovvo, None
for i in range(p1-p0):
d_ovvv[i] = _ccsd.sum021(dovvv[p0+i])
e_ovvo[i] = eris_ovov[p0+i].transpose(0,2,1)
#:Ivo += numpy.einsum('jcab,jcib->ai', d_ovvv, eris_ovov)
#:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv)
lib.dot(d_ovvv.reshape(-1,nvir).T,
e_ovvo[:p1-p0].reshape(-1,nocc), 1, Ivo, 1)
lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvv.reshape(-1,nvir), 1, Ivv, 1)
Xvo[:,p0:p1] +=(numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4
- numpy.einsum('cb,icba->ai', dvv+dvv.T, eris_ovvv))
d_oovv = d_ovvv = bufc_ovvv = bufe_ovvv = None
eris_ovov = eris_ovvv = eris_oovv = e_ovvo = None
eris_ovvv = _cp(eris.ovvv)
bufe_vvvo = numpy.empty((blksize*nvir,nvir,nocc))
bufe_vvvv = numpy.empty((blksize*nvir,nvir,nvir))
bufd_vvvv = numpy.empty((blksize*nvir,nvir,nvir))
for p0, p1 in prange(0, nvir, blksize):
off0 = p0*(p0+1)//2
off1 = p1*(p1+1)//2
d_vvvv = _cp(dvvvv[off0:off1]) * 4
for i in range(p0, p1):
d_vvvv[i*(i+1)//2+i-off0] *= .5
d_vvvv = _ccsd.unpack_tril(d_vvvv, out=bufd_vvvv[:off1-off0])
eris_vvvv = _ccsd.unpack_tril(eris.vvvv[off0:off1], out=bufe_vvvv[:off1-off0])
#:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2
#:Xvo += numpy.einsum('icdb,acdb->ai', d_ovvv, eris_vvvv)
lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvv.reshape(-1,nvir), 2, Ivv, 1)
d_vvvo = _cp(c_vvvo[off0:off1])
lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvo.reshape(-1,nocc), 1, Xvo, 1)
#:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo)
#:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2
eris_vvvo = bufe_vvvo[:off1-off0]
for i0, i1 in prange(off0, off1, BLKSIZE):
for j0, j1, in prange(0, nvir, BLKSIZE//nocc+1):
eris_vvvo[i0-off0:i1-off0,j0:j1,:] = eris_ovvv[:,j0:j1,i0:i1].transpose(2,1,0)
lib.dot(eris_vvvo.reshape(-1,nocc).T, d_vvvo.reshape(-1,nocc), 1, Ioo, 1)
lib.dot(d_vvvv.reshape(-1,nvir).T, eris_vvvo.reshape(-1,nocc), 2, Ivo, 1)
Ioo *= -1
Ivv *= -1
Ivo *= -1
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def _rdm2_mo2ao(mycc, d2, dm1, mo_coeff, fsave=None, max_memory=2000):
log = logger.Logger(mycc.stdout, mycc.verbose)
if fsave is None:
_dm2file = tempfile.NamedTemporaryFile()
fsave = h5py.File(_dm2file.name, 'w')
else:
_dm2file = None
time1 = time.clock(), time.time()
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
nocc, nvir = dovov.shape[:2]
nov = nocc * nvir
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao+1) // 2
nvir_pair = nvir * (nvir+1) //2
mo_coeff = numpy.asarray(mo_coeff, order='F')
def _trans(vin, i0, icount, j0, jcount, out=None):
nrow = vin.shape[0]
if out is None:
out = numpy.empty((nrow,nao_pair))
fdrv = getattr(_ccsd.libcc, 'AO2MOnr_e2_drv')
pao_loc = ctypes.POINTER(ctypes.c_void_p)()
ftrans = ctypes.c_void_p(_ctypes.dlsym(_ccsd.libcc._handle, 'AO2MOtranse2_nr_s1'))
fmmm = ctypes.c_void_p(_ctypes.dlsym(_ccsd.libcc._handle, 'CCmmm_transpose_sum'))
fdrv(ftrans, fmmm,
out.ctypes.data_as(ctypes.c_void_p),
vin.ctypes.data_as(ctypes.c_void_p),
mo_coeff.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nrow), ctypes.c_int(nao),
ctypes.c_int(i0), ctypes.c_int(icount),
ctypes.c_int(j0), ctypes.c_int(jcount),
pao_loc, ctypes.c_int(0))
return out
# transform dm2_ij to get lower triangular (dm2+dm2.transpose(0,1,3,2))
_tmpfile = tempfile.NamedTemporaryFile()
fswap = h5py.File(_tmpfile.name)
max_memory1 = max_memory - lib.current_memory()[0]
blksize = max(1, int(max_memory1*1e6/8/(nmo*nao_pair+nmo**3+nvir**3)))
iobuflen = int(256e6/8/(blksize*nmo))
log.debug1('_rdm2_mo2ao pass 1: blksize = %d, iobuflen = %d', blksize, iobuflen)
fswap.create_group('o') # for h5py old version
pool1 = numpy.empty((blksize,nmo,nmo,nmo))
pool2 = numpy.empty((blksize,nmo,nao_pair))
bufd_ovvv = numpy.empty((blksize,nvir,nvir,nvir))
for istep, (p0, p1) in enumerate(prange(0, nocc, blksize)):
buf1 = pool1[:p1-p0]
buf1[:,:nocc,:nocc,:nocc] = doooo[p0:p1]
buf1[:,:nocc,:nocc,nocc:] = dooov[p0:p1]
buf1[:,:nocc,nocc:,:nocc] = 0
buf1[:,:nocc,nocc:,nocc:] = doovv[p0:p1]
buf1[:,nocc:,:nocc,:nocc] = 0
buf1[:,nocc:,:nocc,nocc:] = dovov[p0:p1]
buf1[:,nocc:,nocc:,:nocc] = dovvo[p0:p1]
d_ovvv = bufd_ovvv[:p1-p0]
ao2mo.outcore._load_from_h5g(dovvv, p0*nvir, p1*nvir,
d_ovvv.reshape(-1,nvir**2))
buf1[:,nocc:,nocc:,nocc:] = d_ovvv
for i in range(p0, p1):
buf1[i-p0,i,:,:] += dm1
buf1[i-p0,:,:,i] -= dm1 * .5
buf2 = pool2[:p1-p0].reshape(-1,nao_pair)
_trans(buf1.reshape(-1,nmo**2), 0, nmo, 0, nmo, buf2)
ao2mo.outcore._transpose_to_h5g(fswap, 'o/%d'%istep, buf2, iobuflen)
pool1 = pool2 = bufd_ovvv = None
time1 = log.timer_debug1('_rdm2_mo2ao pass 1', *time1)
fswap.create_group('v') # for h5py old version
pool1 = numpy.empty((blksize*nvir,nao_pair))
pool2 = numpy.empty((blksize*nvir,nvir,nvir))
for istep, (p0, p1) in enumerate(prange(0, nvir_pair, blksize*nvir)):
buf1 = _cp(dvvvv[p0:p1])
buf2 = _ccsd.unpack_tril(buf1, out=pool2[:p1-p0])
buf1 = _trans(buf2, nocc, nvir, nocc, nvir, out=pool1[:p1-p0])
ao2mo.outcore._transpose_to_h5g(fswap, 'v/%d'%istep, buf1, iobuflen)
pool1 = pool2 = None
time1 = log.timer_debug1('_rdm2_mo2ao pass 2', *time1)
# transform dm2_kl then dm2 + dm2.transpose(2,3,0,1)
max_memory1 = max_memory - lib.current_memory()[0]
blksize = max(nao, int(max_memory1*1e6/8/(nao_pair+nmo**2)))
iobuflen = int(256e6/8/blksize)
log.debug1('_rdm2_mo2ao pass 3: blksize = %d, iobuflen = %d', blksize, iobuflen)
gsave = fsave.create_group('dm2')
for istep, (p0, p1) in enumerate(prange(0, nao_pair, blksize)):
gsave.create_dataset(str(istep), (nao_pair,p1-p0), 'f8')
diagidx = numpy.arange(nao)
diagidx = diagidx*(diagidx+1)//2 + diagidx
pool1 = numpy.empty((blksize,nmo,nmo))
pool2 = numpy.empty((blksize,nvir_pair))
pool3 = numpy.empty((blksize,nvir,nvir))
pool4 = numpy.empty((blksize,nao_pair))
for istep, (p0, p1) in enumerate(prange(0, nao_pair, blksize)):
buf1 = pool1[:p1-p0]
ao2mo.outcore._load_from_h5g(fswap['o'], p0, p1,
buf1[:,:nocc].reshape(p1-p0,-1))
buf2 = ao2mo.outcore._load_from_h5g(fswap['v'], p0, p1, pool2[:p1-p0])
buf3 = _ccsd.unpack_tril(buf2, out=pool3[:p1-p0])
buf1[:,nocc:,nocc:] = buf3
buf1[:,nocc:,:nocc] = 0
buf2 = _trans(buf1, 0, nmo, 0, nmo, out=pool4[:p1-p0])
ic = 0
idx = diagidx[diagidx<p1]
if p0 > 0:
buf1 = _cp(gsave[str(istep)][:p0])
for i0, i1 in prange(0, p1-p0, BLKSIZE):
for j0, j1, in prange(0, p0, BLKSIZE):
buf1[j0:j1,i0:i1] += buf2[i0:i1,j0:j1].T
buf2[i0:i1,j0:j1] = buf1[j0:j1,i0:i1].T
buf1[:,idx[p0<=idx]-p0] *= .5
gsave[str(istep)][:p0] = buf1
lib.transpose_sum(buf2[:,p0:p1], inplace=True)
buf2[:,idx] *= .5
for ic, (i0, i1) in enumerate(prange(0, nao_pair, blksize)):
gsave[str(ic)][p0:p1] = buf2[:,i0:i1]
time1 = log.timer_debug1('_rdm2_mo2ao pass 3', *time1)
del(fswap['o'])
del(fswap['v'])
fswap.close()
_tmpfile = None
time1 = log.timer_debug1('_rdm2_mo2ao cleanup', *time1)
if _dm2file is not None:
nvir_pair = nvir * (nvir+1) // 2
dm2 = numpy.empty((nvir_pair, nvir_pair))
ao2mo.outcore._load_from_h5g(fsave['dm2'], 0, nvir_pair, dm2)
fsave.close()
_dm2file = None
return dm2
else:
return fsave
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None,
max_memory=2000):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if d1 is None:
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2, max_memory)
doo, dov, dvo, dvv = d1
if d2 is None:
_d2tmpfile = tempfile.NamedTemporaryFile()
fd2intermediate = h5py.File(_d2tmpfile.name, 'w')
ccsd_rdm.gamma2_outcore(mycc, t1, t2, l1, l2, fd2intermediate, max_memory)
dovov = fd2intermediate['dovov']
dvvvv = fd2intermediate['dvvvv']
doooo = fd2intermediate['doooo']
doovv = fd2intermediate['doovv']
dovvo = fd2intermediate['dovvo']
dovvv = fd2intermediate['dovvv']
dooov = fd2intermediate['dooov']
else:
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
nvir_pair = nvir * (nvir+1) //2
_tmpfile = tempfile.NamedTemporaryFile()
fswap = h5py.File(_tmpfile.name, 'w')
fswap.create_group('e_vvov')
fswap.create_group('c_vvov')
# Note Ioo, Ivv are not hermitian
Ioo = numpy.zeros((nocc,nocc))
Ivv = numpy.zeros((nvir,nvir))
Ivo = numpy.zeros((nvir,nocc))
Xvo = numpy.zeros((nvir,nocc))
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
d_oooo = _cp(doooo)
d_oooo = _cp(d_oooo + d_oooo.transpose(1,0,2,3))
#:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2
Ioo += lib.dot(eris_oooo.reshape(nocc,-1), d_oooo.reshape(nocc,-1).T, 2)
d_oooo = _cp(d_oooo.transpose(0,2,3,1))
#:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2
Xvo += lib.dot(eris_ooov.reshape(-1,nvir).T, d_oooo.reshape(nocc,-1).T, 2)
Xvo +=(numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4
- numpy.einsum('kj,ikja->ai', doo+doo.T, eris_ooov))
eris_oooo = eris_ooov = d_oooo = None
d_ovov = numpy.empty((nocc,nvir,nocc,nvir))
blksize = 8
for p0, p1 in prange(0, nocc, blksize):
d_ovov[p0:p1] = _cp(dovov[p0:p1])
d_ovvo = _cp(dovvo[p0:p1])
for i in range(p0,p1):
d_ovov[i] += d_ovvo[i-p0].transpose(0,2,1)
d_ovvo = None
d_ovov = lib.transpose_sum(d_ovov.reshape(nov,nov)).reshape(nocc,nvir,nocc,nvir)
#:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo)
Ivo += lib.dot(d_ovov.reshape(-1,nvir).T, _cp(eris.ovoo).reshape(-1,nocc))
eris_ovov = _cp(eris.ovov)
#:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov)
#:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov)
Ioo += lib.dot(eris_ovov.reshape(nocc,-1), d_ovov.reshape(nocc,-1).T)
Ivv += lib.dot(eris_ovov.reshape(-1,nvir).T, d_ovov.reshape(-1,nvir))
eris_ovov = None
fswap['dovvo'] = d_ovov.transpose(0,1,3,2)
d_ovov = None
max_memory1 = max_memory - lib.current_memory()[0]
unit = max(nvir**3*2.5, nvir**3*2+nocc*nvir**2)
blksize = max(ccsd.BLKMIN, int(max_memory1*1e6/8/unit))
iobuflen = int(256e6/8/(blksize*nvir))
log.debug1('IX_intermediates pass 1: block size = %d, nocc = %d in %d blocks',
blksize, nocc, int((nocc+blksize-1)/blksize))
for istep, (p0, p1) in enumerate(prange(0, nocc, blksize)):
d_ooov = _cp(dooov[p0:p1])
eris_oooo = _cp(eris.oooo[p0:p1])
eris_ooov = _cp(eris.ooov[p0:p1])
#:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov)
#:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo)
Ivv += lib.dot(eris_ooov.reshape(-1,nvir).T, d_ooov.reshape(-1,nvir))
Ivo += lib.dot(d_ooov.reshape(-1,nvir).T, eris_oooo.reshape(-1,nocc))
#:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv)
eris_oovv = _cp(eris.oovv[p0:p1])
tmp = _cp(d_ooov.transpose(0,1,3,2).reshape(-1,nocc))
Ioo += lib.dot(_cp(eris_ooov.transpose(0,1,3,2).reshape(-1,nocc)).T, tmp)
Xvo += lib.dot(eris_oovv.reshape(-1,nvir).T, tmp)
eris_oooo = tmp = None
d_ooov = d_ooov + dooov[:,p0:p1].transpose(1,0,2,3)
eris_ovov = _cp(eris.ovov[p0:p1])
#:Ioo += numpy.einsum('ljka,lika->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('jikb,jakb->ai', d_ooov, eris_ovov)
for i in range(p1-p0):
lib.dot(eris_ooov[i].reshape(nocc,-1),
d_ooov[i].reshape(nocc,-1).T, 1, Ioo, 1)
lib.dot(eris_ovov[i].reshape(nvir,-1),
d_ooov[i].reshape(nocc,-1).T, 1, Xvo, 1)
d_ooov = None
#:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv)
#:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv)
#:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov)
d_oovv = _cp(doovv[p0:p1]) + doovv[:,p0:p1].transpose(1,0,3,2)
for i in range(p1-p0):
Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1), d_oovv[i].reshape(nocc,-1).T)
Ivv += lib.dot(eris_oovv.reshape(-1,nvir).T, d_oovv.reshape(-1,nvir))
Ivo += lib.dot(d_oovv.reshape(-1,nvir).T,
_cp(eris_ooov.transpose(0,1,3,2).reshape(-1,nocc)))
eris_ooov = None
d_oovv = _ccsd.precontract(d_oovv.reshape(-1,nvir,nvir)).reshape(p1-p0,nocc,-1)
d_ovvv = numpy.empty((p1-p0,nvir,nvir,nvir))
ao2mo.outcore._load_from_h5g(dovvv, p0*nvir, p1*nvir,
d_ovvv.reshape(-1,nvir**2))
#:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv)
for i in range(p1-p0):
Ivo += lib.dot(d_ovvv[i].reshape(nvir,-1), eris_oovv[i].reshape(nocc,-1).T)
eris_oovv = None
# tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2))
c_ovvv = _ccsd.precontract(d_ovvv.reshape(-1,nvir,nvir))
ao2mo.outcore._transpose_to_h5g(fswap, 'c_vvov/%d'%istep, c_ovvv, iobuflen)
c_ovvv = c_ovvv.reshape(-1,nvir,nvir_pair)
eris_ovx = _cp(eris.ovvv[p0:p1])
ao2mo.outcore._transpose_to_h5g(fswap, 'e_vvov/%d'%istep,
eris_ovx.reshape(-1,nvir_pair), iobuflen)
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
#:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv)
for i in range(p1-p0):
lib.dot(eris_ovx[i].reshape(nvir,-1),
d_oovv[i].reshape(nocc,-1).T, 1, Xvo, 1)
lib.dot(eris_ovx[i].reshape(nvir,-1),
c_ovvv[i].reshape(nvir,-1).T, 1, Ivv, 1)
c_ovvv = d_oovv = None
eris_ovvo = numpy.empty((p1-p0,nvir,nvir,nocc))
for i in range(p1-p0):
d_ovvv[i] = _ccsd.sum021(d_ovvv[i])
eris_ovvo[i] = eris_ovov[i].transpose(0,2,1)
#:Ivo += numpy.einsum('abjc,ibjc->ai', d_ovvv, eris_ovov)
Ivo += lib.dot(d_ovvv.reshape(-1,nvir).T, eris_ovvo.reshape(-1,nocc))
eris_ovvo = eris_ovov = None
eris_ovvv = _ccsd.unpack_tril(eris_ovx.reshape(-1,nvir_pair))
eris_ovx = None
eris_ovvv = eris_ovvv.reshape(p1-p0,nvir,nvir,nvir)
#:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv)
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
Ivv += lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvv.reshape(-1,nvir))
Xvo[:,p0:p1] +=(numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4
- numpy.einsum('cb,icba->ai', dvv+dvv.T, eris_ovvv))
d_ovvo = _cp(fswap['dovvo'][p0:p1])
#:Xvo += numpy.einsum('jbic,jbca->ai', d_ovov, eris_ovvv)
lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvo.reshape(-1,nocc), 1, Xvo, 1)
d_ovvv = d_ovvo = eris_ovvv = None
max_memory1 = max_memory - lib.current_memory()[0]
unit = nocc*nvir**2 + nvir**3*2.5
blksize = max(ccsd.BLKMIN, int(max_memory1*1e6/8/unit))
log.debug1('IX_intermediates pass 2: block size = %d, nocc = %d in %d blocks',
blksize, nocc, int((nocc+blksize-1)/blksize))
for p0, p1 in prange(0, nvir, blksize):
off0 = p0*(p0+1)//2
off1 = p1*(p1+1)//2
d_vvvv = _cp(dvvvv[off0:off1]) * 4
for i in range(p0, p1):
d_vvvv[i*(i+1)//2+i-off0] *= .5
d_vvvv = _ccsd.unpack_tril(d_vvvv)
eris_vvvv = _ccsd.unpack_tril(_cp(eris.vvvv[off0:off1]))
#:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2
#:Xvo += numpy.einsum('dbic,dbca->ai', d_vvov, eris_vvvv)
lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvv.reshape(-1,nvir), 2, Ivv, 1)
#:d_vvvv = _cp(d_vvvv + d_vvvv.transpose(0,1,3,2))
d_vvov = numpy.empty((off1-off0,nocc,nvir))
ao2mo.outcore._load_from_h5g(fswap['c_vvov'], off0, off1, d_vvov.reshape(-1,nov))
d_vvvo = _cp(d_vvov.transpose(0,2,1))
lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvo.reshape(-1,nocc), 1, Xvo, 1)
d_vvov = eris_vvvv = None
eris_vvov = numpy.empty((off1-off0,nocc,nvir))
ao2mo.outcore._load_from_h5g(fswap['e_vvov'], off0, off1,
eris_vvov.reshape(-1,nov))
eris_vvvo = _cp(eris_vvov.transpose(0,2,1))
#:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo)
#:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2
lib.dot(d_vvvv.reshape(-1,nvir).T, eris_vvvo.reshape(-1,nocc), 2, Ivo, 1)
lib.dot(eris_vvvo.reshape(-1,nocc).T, d_vvvo.reshape(-1,nocc), 1, Ioo, 1)
eris_vvov = eris_vovv = d_vvvv = None
del(fswap['e_vvov'])
del(fswap['c_vvov'])
del(fswap['dovvo'])
fswap.close()
_tmpfile = None
if d2 is None:
for key in fd2intermediate.keys():
del(fd2intermediate[key])
fd2intermediate.close()
_d2tmpfile = None
Ioo *= -1
Ivv *= -1
Ivo *= -1
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def make_intermediates(mycc, t1, t2, eris):
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
foo = eris.fock[:nocc,:nocc]
fov = eris.fock[:nocc,nocc:]
fvv = eris.fock[nocc:,nocc:]
class _Saved(object):
pass
saved = _Saved()
# As we don't have l2 in memory, hold tau temporarily in memory
w1 = fvv - numpy.einsum('ja,jb->ba', fov, t1)
w2 = foo + numpy.einsum('ib,jb->ij', fov, t1)
w3 = _cp(numpy.einsum('kc,jkbc->bj', fov, t2) * 2 + fov.T)
w3 -= numpy.einsum('kc,kjbc->bj', fov, t2)
w3 += reduce(numpy.dot, (t1.T, fov, t1.T))
w4 = fov.copy()
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nov,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
wovvv = numpy.empty((nocc,nvir,nvir,nvir))
t2tmp = numpy.empty((nocc,nvir,nocc,nvir))
for i in range(nocc):
wovvv[i] = eris_ovvv[i].transpose(1,0,2) * 2
t2tmp[i] = t2[i].transpose(2,0,1)
#:wovvv += numpy.einsum('jabd,kjdc->kabc', eris_ovvv, t2) * -1.5
tmp = lib.dot(t2tmp.reshape(nov,-1), wovvv.reshape(-1,nvir**2),
-1.5/2).reshape(-1,nvir,nvir,nvir)
g2ovvv = tmp
for i in range(nocc):
wovvv[i] -= eris_ovvv[i].transpose(1,2,0)
wovvv[i] += tmp[i].transpose(1,2,0)
g2ovvv[i] = eris_ovvv[i]*2
g2ovvv[i] -= eris_ovvv[i].transpose(1,2,0)
tmp = t2tmp = None
w1 += numpy.einsum('jcba,jc->ba', eris_ovvv, t1*2)
w1 -= numpy.einsum('jabc,jc->ba', eris_ovvv, t1)
#:w3 += numpy.einsum('kdcb,kjdc->bj', eris_ovvv, theta)
theta = numpy.empty(t2.shape)
for i in range(nocc):
theta[i] = t2[i] * 2
theta[i] -= t2[i].transpose(0,2,1)
lib.dot(eris_ovvv[i].reshape(-1,nvir).T,
_cp(theta[i].reshape(nocc,-1)).T, 1, w3, 1)
theta = _cp(theta.transpose(0,2,1,3))
#:vkbca = numpy.einsum('jdca,kbjd->kbca', g2ovvv, theta)
vkbca = lib.dot(_cp(theta.reshape(nov,-1)),
g2ovvv.reshape(-1,nvir*nvir)).reshape(-1,nvir,nvir,nvir)
for i in range(nocc):
wovvv[i] += vkbca[i].transpose(2,0,1)
wovvv[i] -= vkbca[i].transpose(2,1,0) * .5
vkabc = None
#:wOVov = numpy.einsum('jbcd,kd->jbkc', eris_ovvv, t1)
#:wOvOv = numpy.einsum('jdcb,kd->jbkc', eris_ovvv, -t1)
wOVov = lib.dot(eris_ovvv.reshape(-1,nvir),
t1.T).reshape(-1,nvir,nvir,nocc).transpose(0,1,3,2).copy()
for i in range(nocc):
g2ovvv[i] = eris_ovvv[i].transpose(1,2,0) * 2
wOvOv = lib.dot(g2ovvv.reshape(-1,nvir),
-t1.T, .5).reshape(-1,nvir,nvir,nocc).transpose(0,1,3,2).copy()
for i in range(nocc):
g2ovvv[i] -= eris_ovvv[i].transpose(1,0,2)
eris_ovov = _cp(_cp(eris.ovov).transpose(0,2,1,3))
tau = _ccsd.make_tau(t2, t1, t1)
#:wooov[:,j0:j1] = numpy.einsum('icbd,jkbd->ijkc', g2ovvv, tau)
#:woooo[:,:,j0:j1] = numpy.einsum('icjd,klcd->ijkl', eris_ovov, tau)
tmp = lib.dot(g2ovvv.reshape(-1,nvir**2), tau.reshape(-1,nvir**2).T)
wooov = _cp(tmp.reshape(-1,nvir,nocc,nocc).transpose(0,2,3,1))
woooo = lib.dot(eris_ovov.reshape(-1,nvir**2),
tau.reshape(-1,nvir**2).T).reshape(-1,nocc,nocc,nocc)
eris_ovov = eris_ovvv = g2ovvv = tau = tmp = None
eris_ooov = _cp(eris.ooov)
eris_ovoo = _cp(eris.ovoo)
#:woooo += numpy.einsum('icjl,kc->ijkl', eris_ovoo, t1)
#:wOVov += numpy.einsum('jblk,lc->jbkc', eris_ovoo, -t1)
for i in range(nocc):
woooo[i] += lib.dot(t1, eris_ovoo[i].reshape(nvir,-1)).reshape((nocc,)*3).transpose(1,0,2)
lib.dot(eris_ovoo.reshape(-1,nocc), t1, -1, wOVov.reshape(-1,nvir), 1)
#:wooov -= numpy.einsum('ibjl,lkcb->ijkc', eris_ovoo*1.5, t2)
t2tmp = numpy.empty((nocc,nvir,nocc,nvir))
for i in range(nocc):
t2tmp[i] = t2[i].transpose(2,0,1)
tmp_ooov = _cp(-eris_ooov.transpose(2,0,1,3)).reshape(-1,nov)
lib.dot(tmp_ooov, t2tmp.reshape(nov,-1), 1.5, wooov.reshape(-1,nov), 1)
t2tmp = None
g2ooov, tmp_ooov = tmp_ooov.reshape(nocc,nocc,nocc,nvir), None
g2ooov += eris_ooov * 2
#:vikjc = numpy.einsum('iklb,jlcb->ikjc', g2ooov, theta)
vikjc = lib.dot(g2ooov.reshape(-1,nov), theta.reshape(-1,nov).T)
vikjc = vikjc.reshape(nocc,nocc,nocc,nvir)
wooov += vikjc.transpose(0,2,1,3)
wooov -= vikjc*.5
g2ooov = vikjc = eris_ovoo = None
w2 += numpy.einsum('ijkb,kb->ij', eris_ooov, t1) * 2
w2 -= numpy.einsum('kjib,kb->ij', eris_ooov, t1)
#:w3 -= numpy.einsum('kjlc,klbc->bj', eris_ooov, theta)
for i in range(nocc):
lib.dot(_cp(theta[i].transpose(1,2,0)).reshape(-1,nvir).T,
eris_ooov[i].reshape(nocc,-1).T, -1, w3, 1)
#:woooo += numpy.einsum('ikjc,lc->ijkl', eris_ooov, t1)
#:wOvOv += numpy.einsum('jklb,lc->jbkc', eris_ooov, t1)
woooo += lib.dot(eris_ooov.reshape(-1,nvir),
t1.T).reshape((-1,nocc,nocc,nocc)).transpose(0,2,1,3)
for i in range(nocc):
lib.dot(_cp(eris_ooov[i].transpose(2,0,1)).reshape(-1,nocc),
t1, 1, wOvOv[i].reshape(-1,nvir), 1)
wooov[i] += eris_ooov[i].transpose(1,0,2)*2
wooov[i] -= eris_ooov[i]
eris_ooov = theta = None
eris_ovov = _cp(eris.ovov)
g2ovov = numpy.empty((nocc,nocc,nvir,nvir))
for i in range(nocc):
g2ovov[i] = eris_ovov[i].transpose(1,0,2)*2
g2ovov[i] -= eris_ovov[i].transpose(1,2,0)
tmpw4 = numpy.einsum('klcd,ld->kc', g2ovov, t1)
#:w1 -= numpy.einsum('kcja,kjcb->ba', g2ovov, t2)
w1 -= lib.dot(t2.reshape(-1,nvir).T, g2ovov.reshape(-1,nvir))
w1 -= numpy.einsum('ja,jb->ba', tmpw4, t1)
#:w2 += numpy.einsum('ibkc,jkbc->ij', g2ovov, t2)
w2 += lib.dot(g2ovov.reshape(nocc,-1), t2.reshape(nocc,-1).T)
w2 += numpy.einsum('ib,jb->ij', tmpw4, t1)
w3 += reduce(numpy.dot, (t1.T, tmpw4, t1.T))
w4 += tmpw4
vOVov = eris_ovov.copy()
#:vOVov += numpy.einsum('jbld,klcd->jbkc', g2ovov, t2)
#:vOVov -= numpy.einsum('jbld,kldc->jbkc', eris_ovov, t2)
lib.dot(_cp(g2ovov.transpose(0,2,1,3)).reshape(-1,nov),
_cp(t2.transpose(0,2,1,3).reshape(nov,-1).T), 1,
vOVov.reshape(nov,-1), 1)
lib.dot(eris_ovov.reshape(-1,nov),
_cp(t2.transpose(0,3,1,2).reshape(nov,-1).T), -1,
vOVov.reshape(nov,-1), 1)
g2ovov = None
#:tmp = numpy.einsum('jbld,kd->ljbk', eris_ovov, t1)
#:wOVov -= numpy.einsum('ljbk,lc->jbkc', tmp, t1)
#:tmp = numpy.einsum('jdlb,kd->ljbk', eris_ovov, t1)
#:wOvOv += numpy.einsum('ljbk,lc->jbkc', tmp, t1)
tmp = numpy.empty((nocc,nvir,nocc))
for j in range(nocc):
lib.dot(_cp(eris_ovov[j].transpose(1,0,2)).reshape(-1,nvir),
t1.T, 1, tmp.reshape(-1,nocc))
lib.dot(tmp.reshape(nocc,-1).T, t1, -1, wOVov[j].reshape(-1,nvir), 1)
lib.dot(eris_ovov[j].reshape(nvir,-1).T, t1.T, 1,
tmp.reshape(-1,nocc))
lib.dot(tmp.reshape(nocc,-1).T, t1, 1, wOvOv[j].reshape(-1,nvir), 1)
tmp = None
#:vOvOv = numpy.einsum('jdlb,kldc->jbkc', eris_ovov, t2)
ovovtmp = _cp(eris_ovov.transpose(0,3,2,1).reshape(-1,nov))
vOvOv = numpy.empty((nocc,nvir,nocc,nvir))
for j in range(nocc):
lib.dot(t2[j].reshape(-1,nvir).T, ovovtmp.T, 1,
vOvOv[j].reshape(nvir,-1))
vOvOv[j] -= eris.oovv[j].transpose(2,0,1)
ovovtmp = eris_ovov = None
vOvOv = lib.transpose(vOvOv.reshape(nov,-1)).reshape(nocc,nvir,nocc,nvir)
wOVov += vOVov
wOvOv += vOvOv
saved.wOVov = wOVov
saved.wOvOv = wOvOv
ovovtmp = wOVov = wOvOv = eris_ovov = None
ov2 = vOVov*2 + vOvOv
w3 += numpy.einsum('kcjb,kc->bj', ov2, t1)
#:wooov += numpy.einsum('ibjc,kb->ijkc', ov2, t1)
#:wovvv -= numpy.einsum('jakb,jc->kabc', ov2, t1)
for i in range(nocc):
wooov[i] += lib.dot(t1, ov2[i].reshape(nvir,-1)).reshape(nocc,nocc,nvir).transpose(1,0,2)
lib.dot(_cp(ov2.transpose(0,2,1,3).reshape(nocc,-1)).T,
t1, -1, wovvv.reshape(-1,nvir), 1)
ov2 = None
ov1 = vOvOv*2 + vOVov
#:wooov -= numpy.einsum('ibkc,jb->ijkc', ov1, t1)
#:wovvv += numpy.einsum('jakc,jb->kabc', ov1, t1)
for i in range(nocc):
lib.dot(t1, ov1[i].reshape(nvir,-1), -1, wooov[i].reshape(nocc,-1), 1)
wovvv += lib.dot(_cp(ov1.reshape(nocc,-1)).T,
t1).reshape(nvir,-1,nvir,nvir).transpose(1,0,3,2)
ov1 = None
woooo += _cp(eris.oooo).transpose(0,2,1,3)
saved.woooo = woooo
saved.wooov = wooov
woooo = wooov = None
w3 += numpy.einsum('bc,jc->bj', w1, t1)
w3 -= numpy.einsum('kj,kb->bj', w2, t1)
eris_ooov = _cp(eris.ooov)
g2ooov = eris_ooov * 2
g2ooov -= eris_ooov.transpose(2,0,1,3)
#:tmp = numpy.einsum('kjla,jb->kabl', g2ooov, t1)
#:wovvv = numpy.einsum('kabl,lc->kabc', tmp, t1)
#:wovvv += numpy.einsum('kjla,jlbc->kabc', g2ooov, t2)
tmp = lib.dot(g2ooov.reshape(nocc,-1).T, t1).reshape(-1,nocc,nvir,nvir).transpose(0,2,3,1)
lib.dot(_cp(tmp.reshape(-1,nocc)), t1, 1, wovvv.reshape(-1,nvir), 1)
tmp = None
lib.dot(_cp(g2ooov.transpose(0,2,1,3).reshape(nocc**2,-1)).T,
t2.reshape(nocc**2,-1), 1, wovvv.reshape(nov,-1), 1)
g2ooov = eris_ooov = vOVov = vOvOv = None
saved.wovvv = wovvv
saved.w1 = w1
saved.w2 = w2
saved.w3 = w3
saved.w4 = w4
return saved
l1, l2 = ccsd_t_lambda.kernel(mcc, eris, t1, t2)[1:]
print(ecc, e3ref)
eri_mo = ao2mo.kernel(mf._eri, mf.mo_coeff, compact=False)
nmo = mf.mo_coeff.shape[1]
eri_mo = eri_mo.reshape(nmo,nmo,nmo,nmo)
dm1 = make_rdm1(mcc, t1, t2, l1, l2, eris=eris)
dm2 = make_rdm2(mcc, t1, t2, l1, l2, eris=eris)
h1 = reduce(numpy.dot, (mf.mo_coeff.T, mf.get_hcore(), mf.mo_coeff))
e3 =(numpy.einsum('ij,ij->', h1, dm1)
+ numpy.einsum('ijkl,ijkl->', eri_mo, dm2)*.5 + mf.mol.energy_nuc())
#print e3ref, e3-(mf.e_tot+ecc)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
mo_e = mcc._scf.mo_energy
eia = lib.direct_sum('i-a->ia',mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w =(numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = ccsd_t.p6_(w)
v = ccsd_t.p6_(v)
rw = ccsd_t.r6_(w)
rwv = ccsd_t.r6_(w*2+v*0)
dovov = numpy.einsum('kc,ijkabc->iajb', t1, rw)
dooov =-numpy.einsum('mkbc,ijkabc->jmia', t2, rwv)
dovvv = numpy.einsum('kjcf,ijkabc->iabf', t2, rwv)
def update_amps(mycc, t1, t2, l1, l2, eris=None, saved=None):
if saved is None:
saved = make_intermediates(mycc, t1, t2, eris)
time1 = time0 = time.clock(), time.time()
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
foo = eris.fock[:nocc, :nocc]
fov = eris.fock[:nocc, nocc:]
fvv = eris.fock[:nocc, :nocc]
#:mba = numpy.einsum('klca,klcb->ba', l2, t2*2-t2.transpose(0,1,3,2))
#:mij = numpy.einsum('ikcd,jkcd->ij', l2, t2*2-t2.transpose(0,1,3,2))
#:theta = t2*2 - t2.transpose(0,1,3,2)
theta = _ccsd.make_0132(t2, t2, 2, -1)
mba = lib.dot(theta.reshape(-1, nvir).T, l2.reshape(-1, nvir))
mij = lib.dot(l2.reshape(nocc, -1), theta.reshape(nocc, -1).T)
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 -
numpy.einsum('kc,jkcb->jb', l1, t2) -
reduce(numpy.dot,
(t1, l1.T, t1)) - numpy.einsum('bd,jd->jb', mba, t1) -
numpy.einsum('lj,lb->jb', mij, t1))
tmp = mycc.add_wvvVV(numpy.zeros_like(l1), l2, eris)
l2new = numpy.empty((nocc, nocc, nvir, nvir))
ij = 0
for i in range(nocc):
for j in range(i):
tmp1 = tmp[ij] * .5 # *.5 because of l2+l2.transpose(1,0,3,2) later
l2new[i, j] = tmp1
l2new[j, i] = tmp1.T
ij += 1
l2new[i, i] = tmp[ij] * .5
ij += 1
l1new = (numpy.einsum('ijab,jb->ia', l2new, t1) * 4 -
numpy.einsum('jiab,jb->ia', l2new, t1) * 2)
tmp = tmp1 = None
l1new += eris.fock[:nocc, nocc:]
l1new += numpy.einsum('ib,ba->ia', l1, saved.w1)
l1new -= numpy.einsum('ja,ij->ia', l1, saved.w2)
l1new -= numpy.einsum('ik,ka->ia', mij, saved.w4)
l1new -= numpy.einsum('ca,ic->ia', mba, saved.w4)
l1new += numpy.einsum('ijab,bj->ia', l2, saved.w3) * 2
l1new -= numpy.einsum('ijba,bj->ia', l2, saved.w3)
l2new += numpy.einsum('ia,jb->ijab', l1, saved.w4)
#:l2new += numpy.einsum('jibc,ca->jiba', l2, saved.w1)
#:l2new -= numpy.einsum('kiba,jk->jiba', l2, saved.w2)
lib.dot(l2.reshape(-1, nvir), saved.w1, 1, l2new.reshape(-1, nvir), 1)
lib.dot(saved.w2, l2.reshape(nocc, -1), -1, l2new.reshape(nocc, -1), 1)
eris_ooov = _cp(eris.ooov)
l1new -= numpy.einsum('jkia,kj->ia', eris_ooov, mij1) * 2
l1new += numpy.einsum('ikja,kj->ia', eris_ooov, mij1)
#:l2new -= numpy.einsum('ka,kijb->jiba', l1, eris_ooov)
lib.dot(
_cp(eris_ooov.transpose(0, 2, 1, 3).reshape(nocc, -1)).T, l1, -1,
l2new.reshape(-1, nvir), 1)
eris_ooov = None
tau = _ccsd.make_tau(t2, t1, t1)
#:l2tau = numpy.einsum('ijcd,klcd->ijkl', l2, tau)
l2tau = lib.dot(l2.reshape(nocc**2, -1),
tau.reshape(nocc**2, -1).T).reshape((nocc, ) * 4)
tau = None
l2t1 = numpy.einsum('ijcd,kc->ijkd', l2, t1)
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nov, -1))
eris_ovvv = eris_ovvv.reshape(nocc, nvir, nvir, nvir)
l1new += numpy.einsum('iabc,bc->ia', eris_ovvv, mba1) * 2
l1new -= numpy.einsum('ibca,bc->ia', eris_ovvv, mba1)
#:l2new += numpy.einsum('ic,jbac->jiba', l1, eris_ovvv)
tmp = lib.dot(l1,
eris_ovvv.reshape(-1, nvir).T).reshape(nocc, -1, nvir, nvir)
for i in range(nocc):
l2new[i] += tmp[i].transpose(0, 2, 1)
#:m4 = numpy.einsum('ijkd,kadb->ijab', l2t1, eris_ovvv)
m4 = tmp
lib.dot(_cp(l2t1.reshape(nocc * nocc, -1)),
_cp(eris_ovvv.transpose(0, 2, 1, 3).reshape(-1, nvir**2)), 1,
m4.reshape(nocc * nocc, -1))
l2new -= m4
l1new -= numpy.einsum('ijab,jb->ia', m4, t1) * 2
l1new -= numpy.einsum('ijab,ia->jb', m4, t1) * 2
l1new += numpy.einsum('jiab,jb->ia', m4, t1)
l1new += numpy.einsum('jiab,ia->jb', m4, t1)
eris_ovvv = tmp = None
eris_ovov = _cp(eris.ovov)
l1new += numpy.einsum('jb,iajb->ia', l1, eris_ovov) * 2
#:l2new -= numpy.einsum('jbic,ca->jiba', eris_ovov, mba1)
#:l2new -= numpy.einsum('kajb,ik->ijab', eris_ovov, mij1)
tmp = lib.dot(eris_ovov.reshape(-1, nvir),
mba1).reshape(nocc, nvir, nocc, nvir)
lib.dot(mij1, eris_ovov.reshape(nocc, -1), 1, tmp.reshape(nocc, -1), 1)
tmp_oovv = numpy.empty((nocc, nocc, nvir, nvir))
for i in range(nocc):
tmp_oovv[i] = eris_ovov[i].transpose(1, 0, 2) * .5
l2new[i] += tmp_oovv[i]
l2new[i] -= tmp[i].transpose(1, 0, 2)
tmp = None
l1new += numpy.einsum('iajb,jb->ia', eris_ovov, mia1) * 2
l1new -= numpy.einsum('ibja,jb->ia', eris_ovov, mia1)
#:m4 = numpy.einsum('kalb,ijkl->ijab', eris_ovov, l2tau)
lib.dot(l2tau.reshape(nocc * nocc, -1), tmp_oovv.reshape(-1, nvir**2), 1,
m4.reshape(nocc**2, -1))
l2new += m4
l1new += numpy.einsum('ijab,jb->ia', m4, t1) * 4
l1new -= numpy.einsum('ijba,jb->ia', m4, t1) * 2
eris_ovov = m4 = tmp_oovv = None
eris_oovv = _cp(eris.oovv)
l1new -= numpy.einsum('jb,ijba->ia', l1, eris_oovv)
eris_oovv = None
saved_wooov = _cp(saved.wooov)
#:l1new -= numpy.einsum('jkca,ijkc->ia', l2, saved_wooov)
l1new -= lib.dot(saved_wooov.reshape(nocc, -1), l2.reshape(-1, nvir))
saved_wovvv = _cp(saved.wovvv)
#:l1new += numpy.einsum('kibc,kabc->ia', l2, saved_wovvv)
for j in range(nocc):
l1new += lib.dot(l2[j].reshape(nocc, -1),
saved_wovvv[j].reshape(nvir, -1).T)
saved_wooov = saved_wovvv = None
saved_wOvOv = _cp(saved.wOvOv)
tmp_ovov = _cp(saved.wOVov) * 2
tmp_ovov += saved_wOvOv
#:tmp = l2.transpose(0,2,1,3) - l2.transpose(0,3,1,2)*.5
#:l2new += numpy.einsum('kcia,kcjb->jiba', tmp, tmp_ovov)
tmp = numpy.empty((nocc, nvir, nocc, nvir))
for i in range(nocc):
tmp[i] = l2[i].transpose(2, 0, 1) * -.5
tmp[i] += l2[i].transpose(1, 0, 2)
tmp = lib.dot(tmp_ovov.reshape(-1, nov),
tmp.reshape(nov, -1)).reshape(-1, nvir, nocc, nvir)
#:tmp = numpy.einsum('jkca,ibkc->ijab', l2, saved_wOvOv)
for i in range(nocc):
l2new[i] += tmp[i].transpose(1, 0, 2)
tmp_ovov[i] = l2[i].transpose(2, 0, 1)
lib.dot(saved_wOvOv.reshape(-1, nov), tmp_ovov.reshape(nov, -1), 1,
tmp.reshape(nov, -1))
for i in range(nocc):
l2new[i] += tmp[i].transpose(1, 2, 0)
l2new[i] += tmp[i].transpose(1, 0, 2) * .5
saved_wOvOv = tmp = tmp_ovov = None
saved_woooo = _cp(saved.woooo)
#:m3 = numpy.einsum('klab,ijkl->ijab', l2, saved_woooo)
m3 = lib.dot(saved_woooo.reshape(-1, nocc**2), l2.reshape(nocc**2, -1),
.5).reshape(-1, nocc, nvir, nvir)
l2new += m3
l1new += numpy.einsum('ijab,jb->ia', m3, t1) * 4
l1new -= numpy.einsum('ijba,jb->ia', m3, t1) * 2
saved_woooo = m3 = None
mo_e = eris.fock.diagonal()
eia = lib.direct_sum('i-j->ij', mo_e[:nocc], mo_e[nocc:])
l1new /= eia
l1new += l1
# l2new = l2new + l2new.transpose(1,0,3,2)
# l2new /= lib.direct_sum('ia+jb->ijab', eia, eia)
# l2new += l2
ij = 0
for i in range(nocc):
for j in range(i):
dab = lib.direct_sum('a+b->ab', eia[i], eia[j])
tmp = (l2new[i, j] + l2new[j, i].T) / dab + l2[i, j]
l2new[i, j] = tmp
l2new[j, i] = tmp.T
ij += 1
dab = lib.direct_sum('a+b->ab', eia[i], eia[i])
l2new[i, i] = (l2new[i, i] + l2new[i, i].T) / dab + l2[i, i]
ij += 1
time0 = log.timer_debug1('update l1 l2', *time0)
return l1new, l2new
def make_intermediates(mycc, t1, t2, eris, max_memory=2000):
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
foo = eris.fock[:nocc, :nocc]
fov = eris.fock[:nocc, nocc:]
fvv = eris.fock[nocc:, nocc:]
class _Saved(object):
def __init__(self):
self._tmpfile = tempfile.NamedTemporaryFile()
self.ftmp = h5py.File(self._tmpfile.name)
def __del__(self):
if hasattr(self, 'ftmp'):
self.ftmp.close()
self._tmpfile = None
saved = _Saved()
saved.woooo = saved.ftmp.create_dataset('woooo', (nocc, nocc, nocc, nocc),
'f8')
saved.wooov = saved.ftmp.create_dataset('wooov', (nocc, nocc, nocc, nvir),
'f8')
saved.wOVov = saved.ftmp.create_dataset('wOVov', (nocc, nvir, nocc, nvir),
'f8')
saved.wOvOv = saved.ftmp.create_dataset('wOvOv', (nocc, nvir, nocc, nvir),
'f8')
saved.wovvv = saved.ftmp.create_dataset('wovvv', (nocc, nvir, nvir, nvir),
'f8')
# As we don't have l2 in memory, hold tau temporarily in memory
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 += reduce(numpy.dot, (t1.T, fov, t1.T))
w4 = fov.copy()
_tmpfile = tempfile.NamedTemporaryFile()
fswap = h5py.File(_tmpfile.name)
time1 = time.clock(), time.time()
max_memory = max_memory - lib.current_memory()[0]
unit = max(nocc * nvir**2 * 4 + nvir**3 * 2, nvir**3 * 3 + nocc * nvir**2,
nocc * nvir**2 * 6 + nocc**2 * nvir + nocc**3 + nocc**2 * nvir)
blksize = max(ccsd.BLKMIN, int(max_memory * .95e6 / 8 / unit))
log.debug1(
'ccsd lambda make_intermediates: block size = %d, nocc = %d in %d blocks',
blksize, nocc, int((nocc + blksize - 1) // blksize))
for istep, (p0, p1) in enumerate(prange(0, nocc, blksize)):
eris_ovvv = _cp(eris.ovvv[p0:p1])
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape((p1 - p0) * nvir, -1))
eris_ovvv = eris_ovvv.reshape(p1 - p0, nvir, nvir, nvir)
w1 += numpy.einsum('jcba,jc->ba', eris_ovvv, t1[p0:p1] * 2)
w1 -= numpy.einsum('jabc,jc->ba', eris_ovvv, t1[p0:p1])
#:w3 += numpy.einsum('kdcb,kjdc->bj', eris_ovvv, theta)
for i in range(p1 - p0):
theta = t2[p0 + i] * 2
theta -= t2[p0 + i].transpose(0, 2, 1)
w3 += lib.dot(eris_ovvv[i].reshape(-1, nvir).T,
_cp(theta.reshape(nocc, -1)).T)
theta = None
#:wOVov = numpy.einsum('jbcd,kd->jbkc', eris_ovvv, t1)
#:wOvOv = numpy.einsum('jdcb,kd->jbkc', eris_ovvv, -t1)
wOVov = lib.dot(eris_ovvv.reshape(-1, nvir),
t1.T).reshape(-1, nvir, nvir,
nocc).transpose(0, 1, 3, 2).copy()
g2ovvv = _cp(eris_ovvv.transpose(0, 2, 3, 1))
wOvOv = lib.dot(g2ovvv.reshape(-1, nvir),
-t1.T).reshape(-1, nvir, nvir,
nocc).transpose(0, 1, 3, 2).copy()
for i in range(p1 - p0):
g2ovvv[i] *= 2
g2ovvv[i] -= eris_ovvv[i].transpose(1, 0, 2)
wooov = numpy.empty((p1 - p0, nocc, nocc, nvir))
woooo = numpy.empty((p1 - p0, nocc, nocc, nocc))
eris_ovov = _cp(_cp(eris.ovov[p0:p1]).transpose(0, 2, 1, 3))
for j0, j1 in prange(0, nocc, blksize):
tau = _ccsd.make_tau(t2[j0:j1], t1[j0:j1], t1)
#:wooov[:,j0:j1] = numpy.einsum('icbd,jkbd->ijkc', g2ovvv, tau)
#:woooo[:,:,j0:j1] = numpy.einsum('icjd,klcd->ijkl', eris_ovov, tau)
tmp = lib.dot(g2ovvv.reshape(-1, nvir**2),
tau.reshape(-1, nvir**2).T)
wooov[:, j0:j1] = tmp.reshape(-1, nvir, j1 - j0,
nocc).transpose(0, 2, 3, 1)
woooo[:, :, j0:j1] = lib.dot(eris_ovov.reshape(-1, nvir**2),
tau.reshape(-1, nvir**2).T).reshape(
-1, nocc, j1 - j0, nocc)
eris_ovov = eris_ovvv = g2ovvv = tau = tmp = None
#==== mem usage nocc*nvir**2*2 + nocc**2*nvir + nocc**3 + nvir**3*2 + nocc*nvir**2*2
eris_ooov = _cp(eris.ooov[p0:p1])
w2[p0:p1] += numpy.einsum('ijkb,kb->ij', eris_ooov, t1) * 2
w2 -= numpy.einsum('kjib,kb->ij', eris_ooov, t1[p0:p1])
#:w3 -= numpy.einsum('kjlc,klbc->bj', eris_ooov, theta)
for i in range(p1 - p0):
theta = t2[p0 + i].transpose(0, 2, 1) * 2
theta -= t2[p0 + i]
w3 -= lib.dot(
theta.reshape(-1, nvir).T, eris_ooov[i].reshape(nocc, -1).T)
theta = None
#:woooo += numpy.einsum('ikjc,lc->ijkl', eris_ooov, t1)
#:wOvOv += numpy.einsum('jklb,lc->jbkc', eris_ooov, t1)
woooo += lib.dot(eris_ooov.reshape(-1, nvir), t1.T).reshape(
(-1, nocc, nocc, nocc)).transpose(0, 2, 1, 3)
for i in range(p1 - p0):
lib.dot(
_cp(eris_ooov[i].transpose(2, 0, 1)).reshape(-1, nocc), t1, 1,
wOvOv[i].reshape(-1, nvir), 1)
wooov[i] += eris_ooov[i].transpose(1, 0, 2) * 2
wooov[i] -= eris_ooov[i]
eris_ovoo = _cp(eris.ovoo[p0:p1])
#:woooo += numpy.einsum('icjl,kc->ijkl', eris_ovoo, t1)
#:wOVov += numpy.einsum('jbkl,lc->jbkc', eris_ovoo, -t1)
for i in range(p1 - p0):
woooo[i] += lib.dot(t1, eris_ovoo[i].reshape(nvir, -1)).reshape(
(nocc, ) * 3).transpose(1, 0, 2)
lib.dot(eris_ovoo.reshape(-1, nocc), t1, -1, wOVov.reshape(-1, nvir),
1)
#:wooov -= numpy.einsum('iblj,klbc->ijkc', eris_ovoo*1.5, t2)
tmp_ovoo = _cp(-eris_ovoo.transpose(0, 2, 3, 1)).reshape(-1, nov)
for j in range(nocc):
wooov[:, :, j] += lib.dot(tmp_ovoo, t2[j].reshape(-1, nvir),
1.5).reshape(-1, nocc, nvir)
#:g2ooov = eris_ooov * 2 - eris_ovoo.transpose(0,3,2,1)
g2ooov, tmp_ovoo = tmp_ovoo.reshape(p1 - p0, nocc, nocc, nvir), None
g2ooov += eris_ooov * 2
thetabuf = numpy.empty((blksize, nvir, nocc, nvir))
vikjc = numpy.empty((p1 - p0, nocc, blksize, nvir))
for j0, j1 in prange(0, nocc, blksize):
theta = thetabuf[:j1 - j0]
for i in range(j1 - j0):
theta[i] = t2[j0 + i].transpose(
1, 0, 2) * 2 - t2[j0 + i].transpose(2, 0, 1)
#:vikjc = numpy.einsum('iklb,jlcb->ikjc', g2ooov, theta)
if j1 == j0 + blksize:
lib.dot(g2ooov.reshape(-1, nov),
_cp(theta.reshape(-1, nov)).T, 1,
vikjc.reshape((p1 - p0) * nocc, -1), 0)
else:
vikjc = lib.dot(g2ooov.reshape(-1, nov),
_cp(theta.reshape(-1, nov)).T)
vikjc = vikjc.reshape(p1 - p0, nocc, j1 - j0, nvir)
wooov[:, j0:j1, :] += vikjc.transpose(0, 2, 1, 3)
wooov[:, :, j0:j1] -= vikjc * .5
eris_ooov = eris_ovoo = g2ooov = vikjc = theta = thetabuf = None
#==== mem usage nocc*nvir**2*3 + nocc**2*nvir + nocc**3 + nocc*nvir**2 + nocc**2*nvir*3
eris_ovov = _cp(eris.ovov[p0:p1])
g2ovov = eris_ovov * 2
g2ovov -= eris_ovov.transpose(0, 3, 2, 1)
tmpw4 = numpy.einsum('kcld,ld->kc', g2ovov, t1)
#:w1 -= numpy.einsum('kcja,kjcb->ba', g2ovov, t2[p0:p1])
w1 -= lib.dot(t2[p0:p1].reshape(-1, nvir).T,
_cp(g2ovov.transpose(0, 2, 1, 3).reshape(-1, nvir)))
w1 -= numpy.einsum('ja,jb->ba', tmpw4, t1[p0:p1])
#:w2[p0:p1] += numpy.einsum('ibkc,jkbc->ij', g2ovov, t2)
w2[p0:p1] += lib.dot(
_cp(g2ovov.transpose(0, 2, 1, 3)).reshape(p1 - p0, -1),
t2.reshape(nocc, -1).T)
w2[p0:p1] += numpy.einsum('ib,jb->ij', tmpw4, t1)
w3 += reduce(numpy.dot, (t1[p0:p1].T, tmpw4, t1.T))
w4[p0:p1] += tmpw4
vOVov = numpy.empty((nocc, nvir, p1 - p0, nvir))
#:vOVov += numpy.einsum('jbld,klcd->kcjb', g2ovov, t2)
#:vOVov -= numpy.einsum('jbld,kldc->kcjb', eris_ovov, t2)
for j in range(nocc):
lib.dot(
_cp(t2[j].transpose(1, 0, 2)).reshape(-1, nov),
g2ovov.reshape(-1, nov).T, 1, vOVov[j].reshape(nvir, -1))
lib.dot(t2[j].reshape(nov, -1).T,
eris_ovov.reshape(-1, nov).T, -1,
vOVov[j].reshape(nvir, -1), 1)
vOVov = lib.transpose(vOVov.reshape(nov, -1)).reshape(
p1 - p0, nvir, nocc, nvir)
vOVov += eris_ovov
g2ovov = tmp = tmpw4 = None
#==== mem usage nocc*nvir**2*4 + nocc**2*nvir + nocc**3 + nocc*nvir**2
#:tmp = numpy.einsum('jbld,kd->jlbk', eris_ovov, t1)
#:wOVov -= numpy.einsum('jlbk,lc->jbkc', tmp, t1)
#:tmp = numpy.einsum('jdlb,kd->jlbk', eris_ovov, t1)
#:wOvOv += numpy.einsum('jlbk,lc->jbkc', tmp, t1)
tmp = numpy.empty((nocc, nvir, nocc))
for j in range(p1 - p0):
lib.dot(
_cp(eris_ovov[j].transpose(1, 0, 2)).reshape(-1, nvir), t1.T,
1, tmp.reshape(-1, nocc))
lib.dot(
tmp.reshape(nocc, -1).T, t1, -1, wOVov[j].reshape(-1, nvir), 1)
lib.dot(eris_ovov[j].reshape(nvir, -1).T, t1.T, 1,
tmp.reshape(-1, nocc))
lib.dot(
tmp.reshape(nocc, -1).T, t1, 1, wOvOv[j].reshape(-1, nvir), 1)
tmp = None
#:vOvOv = numpy.einsum('jdlb,kldc->kcjb', eris_ovov, t2)
ovovtmp = _cp(eris_ovov.transpose(0, 3, 2, 1)).reshape(-1, nov)
vOvOv = numpy.empty((nocc, nvir, p1 - p0, nvir))
for j in range(nocc):
lib.dot(t2[j].reshape(-1, nvir).T, ovovtmp.T, 1,
vOvOv[j].reshape(nvir, -1))
ovovtmp = eris_ovov = None
vOvOv = lib.transpose(vOvOv.reshape(nov, -1)).reshape(
p1 - p0, nvir, nocc, nvir)
vOvOv -= _cp(eris.oovv[p0:p1]).transpose(0, 3, 1, 2)
wOVov += vOVov
wOvOv += vOvOv
saved.wOVov[p0:p1] = wOVov
saved.wOvOv[p0:p1] = wOvOv
wOVov = wOvOv = None
#==== mem usage nocc*nvir**2*6 + nocc**2*nvir + nocc**3 + nocc**2*nvir
ov1 = vOvOv * 2 + vOVov
#:wooov -= numpy.einsum('ibkc,jb->ijkc', ov1, t1)
for i in range(p1 - p0):
lib.dot(t1, ov1[i].reshape(nvir, -1), -1,
wooov[i].reshape(nocc, -1), 1)
ov1 = lib.transpose(ov1.reshape(-1, nov))
fswap['2vOvOv/%d' % istep] = ov1.reshape(nocc, nvir, -1, nvir)
ov1 = None
ov2 = vOVov * 2 + vOvOv
w3 += numpy.einsum('kcjb,kc->bj', ov2, t1[p0:p1])
#:wooov += numpy.einsum('ibjc,kb->ijkc', ov2, t1)
for i in range(p1 - p0):
wooov[i] += lib.dot(t1, ov2[i].reshape(nvir, -1)).reshape(
nocc, nocc, nvir).transpose(1, 0, 2)
ov2 = lib.transpose(ov2.reshape(-1, nov))
fswap['2vovOV/%d' % istep] = ov2.reshape(nocc, nvir, -1, nvir)
vOVov = vOvOv = None
ov2 = None
#==== mem usage nocc*nvir**2*5 + nocc**2*nvir + nocc**3
woooo += _cp(eris.oooo[p0:p1]).transpose(0, 2, 1, 3)
saved.woooo[p0:p1] = woooo
saved.wooov[p0:p1] = wooov
woooo = wooov = None
time1 = log.timer_debug1('pass1 [%d:%d]' % (p0, p1), *time1)
w3 += numpy.einsum('bc,jc->bj', w1, t1)
w3 -= numpy.einsum('kj,kb->bj', w2, t1)
for p0, p1 in prange(0, nocc, blksize):
eris_ooov = _cp(eris.ooov[p0:p1])
g2ooov = eris_ooov * 2
g2ooov -= eris_ooov.transpose(0, 2, 1, 3)
#:tmp = numpy.einsum('kjla,jb->kabl', g2ooov, t1)
#:wovvv = numpy.einsum('kabl,lc->kabc', tmp, t1)
#:wovvv += numpy.einsum('kjla,jlbc->kabc', g2ooov, t2)
tmp = lib.dot(
_cp(g2ooov.transpose(1, 0, 2, 3).reshape(nocc, -1)).T,
t1).reshape(-1, nocc, nvir, nvir).transpose(0, 2, 3, 1)
wovvv = lib.dot(_cp(tmp.reshape(-1, nocc)),
t1).reshape(-1, nvir, nvir, nvir)
wovvv += lib.dot(
_cp(g2ooov.transpose(0, 3, 1, 2).reshape(-1, nocc**2)),
t2.reshape(nocc**2, -1)).reshape(-1, nvir, nvir, nvir)
tmp = g2ooov = None
ov1 = numpy.empty((p1 - p0, nvir, nocc, nvir))
ov2 = numpy.empty((p1 - p0, nvir, nocc, nvir))
for istep, (j0, j1) in enumerate(prange(0, nocc, blksize)):
ov1[:, :, j0:j1] = fswap['2vOvOv/%d' % istep][p0:p1]
ov2[:, :, j0:j1] = fswap['2vovOV/%d' % istep][p0:p1]
#:wovvv += numpy.einsum('kcja,jb->kabc', ov1, t1)
#:wovvv -= numpy.einsum('kbja,jc->kabc', ov2, t1)
wovvv += lib.dot(_cp(ov1.transpose(0, 1, 3, 2).reshape(-1, nocc)),
t1).reshape(-1, nvir, nvir,
nvir).transpose(0, 2, 3, 1)
wovvv -= lib.dot(_cp(ov2.transpose(0, 1, 3, 2).reshape(-1, nocc)),
t1).reshape(-1, nvir, nvir,
nvir).transpose(0, 2, 1, 3)
#==== mem usage nvir**3 + nocc*nvir**2*2
eris_ooov = ov1 = ov2 = None
for j0, j1 in prange(0, nocc, blksize):
eris_ovvv = _cp(eris.ovvv[j0:j1])
eris_ovvv = _ccsd.unpack_tril(
eris_ovvv.reshape((j1 - j0) * nvir, -1))
eris_ovvv = eris_ovvv.reshape(j1 - j0, nvir, nvir, nvir)
#:wovvv += numpy.einsum('jabd,kjdc->kabc', eris_ovvv, t2[p0:p1,j0:j1]) * -1.5
tmp_ovvv = numpy.empty((j1 - j0, nvir, nvir, nvir))
for i in range(j1 - j0):
tmp_ovvv[i] = eris_ovvv[i].transpose(1, 0, 2) * 2
tmp = lib.dot(
_cp(t2[p0:p1, j0:j1].transpose(0, 3, 1, 2).reshape(
(p1 - p0) * nvir, -1)), tmp_ovvv.reshape(-1, nvir**2),
-1.5 / 2).reshape(-1, nvir, nvir, nvir)
wovvv += tmp.transpose(0, 2, 3, 1)
if p0 == j0:
for i in range(p1 - p0):
tmp_ovvv[i] -= eris_ovvv[i].transpose(1, 2, 0)
wovvv[i] += tmp_ovvv[i]
tmp = tmp_ovvv = None
g2ovvv = numpy.empty((j1 - j0, nvir, nvir, nvir))
for i in range(j1 - j0):
g2ovvv[i] = eris_ovvv[i] * 2
g2ovvv[i] -= eris_ovvv[i].transpose(1, 2, 0)
#==== mem usage nvir**3*3
eris_ovvv = None
theta = _cp(t2[p0:p1, j0:j1].transpose(0, 2, 1, 3) * 2)
for i in range(p1 - p0):
theta[i] -= t2[p0 + i, j0:j1].transpose(2, 0, 1)
#:vkbca = numpy.einsum('jdca,kbjd->kbca', g2ovvv, theta)
vkbca = lib.dot(theta.reshape((p1 - p0) * nvir, -1),
g2ovvv.reshape(-1, nvir * nvir)).reshape(
-1, nvir, nvir, nvir)
wovvv += vkbca.transpose(0, 3, 1, 2)
wovvv -= vkbca.transpose(0, 3, 2, 1) * .5
#==== mem usage nvir**3*3 + nocc*nvir**2
g2ovvv = theta = vkabc = None
saved.wovvv[p0:p1] = wovvv
time1 = log.timer_debug1('pass2 [%d:%d]' % (p0, p1), *time1)
fswap.close()
saved.w1 = w1
saved.w2 = w2
saved.w3 = w3
saved.w4 = w4
saved.ftmp.flush()
return saved
l1, l2 = ccsd_t_lambda.kernel(mcc, eris, t1, t2)[1:]
print(ecc, e3ref)
eri_mo = ao2mo.kernel(mf._eri, mf.mo_coeff, compact=False)
nmo = mf.mo_coeff.shape[1]
eri_mo = eri_mo.reshape(nmo,nmo,nmo,nmo)
dm1 = make_rdm1(mcc, t1, t2, l1, l2, eris=eris)
dm2 = make_rdm2(mcc, t1, t2, l1, l2, eris=eris)
h1 = reduce(numpy.dot, (mf.mo_coeff.T, mf.get_hcore(), mf.mo_coeff))
e3 =(numpy.einsum('ij,ij->', h1, dm1)
+ numpy.einsum('ijkl,ijkl->', eri_mo, dm2)*.5 + mf.mol.energy_nuc())
#print e3ref, e3-(mf.e_tot+ecc)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
mo_e = mcc._scf.mo_energy
eia = lib.direct_sum('i-a->ia',mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w =(numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = ccsd_t.p6_(w)
v = ccsd_t.p6_(v)
rw = ccsd_t.r6_(w)
rwv = ccsd_t.r6_(w*2+v*0)
dovov = numpy.einsum('kc,ijkabc->iajb', t1, rw)
dooov =-numpy.einsum('mkbc,ijkabc->jmia', t2, rwv)
dovvv = numpy.einsum('kjcf,ijkabc->iabf', t2, rwv)
def update_amps(cc, t1, t2, eris, max_memory=2000):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
fock = eris.fock
t1new = numpy.zeros_like(t1)
t2new = numpy.zeros_like(t2)
#** make_inter_F
fov = fock[:nocc, nocc:].copy()
foo = fock[:nocc, :nocc].copy()
foo[range(nocc), range(nocc)] = 0
foo += .5 * numpy.einsum('ia,ja->ij', fock[:nocc, nocc:], t1)
fvv = fock[nocc:, nocc:].copy()
fvv[range(nvir), range(nvir)] = 0
fvv -= .5 * numpy.einsum('ia,ib->ab', t1, fock[:nocc, nocc:])
#: woooo = numpy.einsum('la,ikja->ikjl', t1, eris.ooov)
eris_ooov = _cp(eris.ooov)
foo += numpy.einsum('kc,jikc->ij', 2 * t1, eris_ooov)
foo += numpy.einsum('kc,jkic->ij', -t1, eris_ooov)
woooo = lib.dot(eris_ooov.reshape(-1, nvir), t1.T).reshape((nocc, ) * 4)
woooo = lib.transpose_sum(woooo.reshape(nocc * nocc, -1), inplace=True)
woooo += _cp(eris.oooo).reshape(nocc**2, -1)
woooo = _cp(woooo.reshape(nocc, nocc, nocc, nocc).transpose(0, 2, 1, 3))
eris_ooov = None
time1 = log.timer_debug1('woooo', *time0)
unit = _memory_usage_inloop(nocc, nvir) * 1e6 / 8
max_memory = max_memory - lib.current_memory()[0]
blksize = max(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))
for p0, p1 in prange(0, nocc, blksize):
# ==== read eris.ovvv ====
eris_ovvv = _cp(eris.ovvv[p0:p1])
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape((p1 - p0) * nvir, -1))
eris_ovvv = eris_ovvv.reshape(p1 - p0, nvir, nvir, nvir)
fvv += numpy.einsum('kc,kcba->ab', 2 * t1[p0:p1], eris_ovvv)
fvv += numpy.einsum('kc,kbca->ab', -t1[p0:p1], eris_ovvv)
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: tmp = numpy.einsum('ijcd,kdcb->ijbk', tau, eris.ovvv)
#: t2new += numpy.einsum('ka,ijbk->ijba', -t1, tmp)
#: eris_vvov = eris_ovvv.transpose(1,2,0,3).copy()
eris_vvov = _cp(
eris_ovvv.transpose(2, 1, 0, 3).reshape(nvir * nvir, -1))
tmp = numpy.empty((nocc, nocc, p1 - p0, nvir))
taubuf = numpy.empty((blksize, nocc, nvir, nvir))
for j0, j1 in prange(0, nocc, blksize):
tau = make_tau(t2[j0:j1], t1[j0:j1], t1, 1, out=taubuf[:j1 - j0])
lib.dot(tau.reshape(-1, nvir * nvir), eris_vvov, 1,
tmp[j0:j1].reshape((j1 - j0) * nocc, -1), 0)
tmp = _cp(tmp.transpose(0, 1, 3, 2).reshape(-1, p1 - p0))
lib.dot(tmp, t1[p0:p1], -1, t2new.reshape(-1, nvir), 1)
tau = tmp = eris_vvov = None
#==== mem usage blksize*(nvir**3*2+nvir*nocc**2*2)
#: wOVov += numpy.einsum('iabc,jc->ijab', eris.ovvv, t1)
#: wOVov -= numpy.einsum('jbik,ka->jiba', eris.ovoo, t1)
#: t2new += woVoV.transpose()
#: wOVov = -numpy.einsum('jbik,ka->ijba', eris.ovoo[p0:p1], t1)
tmp = _cp(eris.ovoo[p0:p1].transpose(2, 0, 1, 3))
wOVov = lib.dot(tmp.reshape(-1, nocc), t1, -1)
tmp = None
wOVov = wOVov.reshape(nocc, p1 - p0, nvir, nvir)
#: wOVov += numpy.einsum('iabc,jc->jiab', eris_ovvv, t1)
lib.dot(t1,
eris_ovvv.reshape(-1, nvir).T, 1, wOVov.reshape(nocc, -1), 1)
t2new[p0:p1] += wOVov.transpose(1, 0, 2, 3)
eris_ooov = _cp(eris.ooov[p0:p1])
#: woVoV = numpy.einsum('ka,ijkb->ijba', t1, eris.ooov[p0:p1])
#: woVoV -= numpy.einsum('jc,icab->ijab', t1, eris_ovvv)
woVoV = lib.dot(_cp(eris_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc)),
t1)
woVoV = woVoV.reshape(p1 - p0, nocc, nvir, nvir)
for i in range(eris_ovvv.shape[0]):
lib.dot(t1, eris_ovvv[i].reshape(nvir, -1), -1,
woVoV[i].reshape(nocc, -1), 1)
#: theta = t2.transpose(0,1,3,2) * 2 - t2
#: t1new += numpy.einsum('ijcb,jcba->ia', theta, eris.ovvv)
theta = numpy.empty((p1 - p0, nocc, nvir, nvir))
for i in range(p1 - p0):
theta[i] = t2[p0 + i].transpose(0, 2, 1) * 2
theta[i] -= t2[p0 + i]
lib.dot(_cp(theta[i].transpose(0, 2, 1).reshape(nocc, -1)),
eris_ovvv[i].reshape(-1, nvir), 1, t1new, 1)
eris_ovvv = None
time2 = log.timer_debug1('ovvv [%d:%d]' % (p0, p1), *time1)
#==== mem usage blksize*(nvir**3+nocc*nvir**2*4)
# ==== read eris.ovov ====
eris_ovov = _cp(eris.ovov[p0:p1])
#==== mem usage blksize*(nocc*nvir**2*4)
for i in range(p1 - p0):
t2new[p0 + i] += eris_ovov[i].transpose(1, 0, 2) * .5
fov[p0:p1] += numpy.einsum('kc,iakc->ia', t1, eris_ovov) * 2
fov[p0:p1] -= numpy.einsum('kc,icka->ia', t1, eris_ovov)
#: theta = t2.transpose(1,0,2,3) * 2 - t2
#: t1new += numpy.einsum('jb,ijba->ia', fov, theta)
#: t1new -= numpy.einsum('kijb,kjba->ia', eris_ooov, theta)
t1new += numpy.einsum('jb,jiab->ia', fov[p0:p1], theta)
#: t1new -= numpy.einsum('kijb,kjab->ia', eris.ooov[p0:p1], theta)
lib.dot(_cp(eris_ooov.transpose(1, 0, 2, 3).reshape(nocc, -1)),
theta.reshape(-1, nvir), -1, t1new, 1)
eris_ooov = None
#: wOVov += eris.ovov.transpose(0,1,3,2)
#: theta = t2.transpose(1,0,2,3) * 2 - t2
#: tau = theta - numpy.einsum('ic,kb->ikcb', t1, t1*2)
#: wOVov += .5 * numpy.einsum('jakc,ikcb->jiba', eris.ovov, tau)
#: wOVov -= .5 * numpy.einsum('jcka,ikcb->jiba', eris.ovov, t2)
#: t2new += numpy.einsum('ikca,kjbc->ijba', theta, wOVov)
theta = _cp(theta.transpose(0, 3, 1, 2))
wOVov = _cp(wOVov.transpose(0, 3, 1, 2))
eris_OVov = lib.transpose(eris_ovov.reshape(-1, nov)).reshape(
nocc, nvir, -1, nvir)
eris_OvoV = _cp(eris_OVov.transpose(0, 3, 2, 1))
wOVov += eris_OVov
for j0, j1 in prange(0, nocc, blksize):
t2iajb = t2[j0:j1].transpose(0, 2, 1, 3).copy()
#: wOVov[j0:j1] -= .5 * numpy.einsum('iack,jkbc->jbai', eris_ovov, t2)
lib.dot(t2iajb.reshape(-1, nov), eris_OvoV.reshape(nov, -1), -.5,
wOVov[j0:j1].reshape((j1 - j0) * nvir, -1), 1)
tau, t2iajb = t2iajb, None
for i in range(j1 - j0):
tau[i] *= 2
tau[i] -= t2[j0 + i].transpose(2, 0, 1)
tau[i] -= numpy.einsum('a,jb->bja', t1[j0 + i] * 2, t1)
#: wOVov[j0:j1] += .5 * numpy.einsum('iakc,jbkc->jbai', eris_ovov, tau)
lib.dot(tau.reshape(-1, nov), eris_OVov.reshape(nov, -1), .5,
wOVov[j0:j1].reshape((j1 - j0) * nvir, -1), 1)
#theta = t2[p0:p1] * 2 - t2[p0:p1].transpose(0,1,3,2)
#: t2new[j0:j1] += numpy.einsum('iack,jbck->jiba', theta, wOVov[j0:j1])
tmp, tau = tau, None
lib.dot(wOVov[j0:j1].reshape((j1 - j0) * nvir, -1),
theta.reshape(-1, nov), 1, tmp.reshape(-1, nov))
for i in range(j1 - j0):
t2new[j0 + i] += tmp[i].transpose(1, 0, 2)
tmp = None
#==== mem usage blksize*(nocc*nvir**2*8)
theta = wOVov = eris_OvoV = eris_OVov = None
time2 = log.timer_debug1('wOVov [%d:%d]' % (p0, p1), *time2)
#==== mem usage blksize*(nocc*nvir**2*2)
#: fvv -= numpy.einsum('ijca,ibjc->ab', theta, eris.ovov)
#: foo += numpy.einsum('iakb,jkba->ij', eris.ovov, theta)
for i in range(p1 - p0):
tau = numpy.einsum('a,jb->jab', t1[p0 + i] * .5, t1)
tau += t2[p0 + i]
theta = tau.transpose(0, 2, 1) * 2
theta -= tau
lib.dot(
_cp(eris_ovov[i].transpose(1, 2, 0)).reshape(nocc, -1),
theta.reshape(nocc, -1).T, 1, foo, 1)
lib.dot(
theta.reshape(-1, nvir).T, eris_ovov[i].reshape(nvir, -1).T,
-1, fvv, 1)
tau = theta = None
# ==== read eris.oovv ====
eris_oovv = _cp(eris.oovv[p0:p1])
#==== mem usage blksize*(nocc*nvir**2*3)
#:tmp = numpy.einsum('ic,jkbc->jibk', t1, eris_oovv)
#:t2new[p0:p1] += numpy.einsum('ka,jibk->jiab', -t1, tmp)
#:tmp = numpy.einsum('ic,jbkc->jibk', t1, eris_ovov)
#:t2new[p0:p1] += numpy.einsum('ka,jibk->jiba', -t1, tmp)
for j in range(p1 - p0):
tmp = lib.dot(t1, eris_oovv[j].reshape(-1, nvir).T)
tmp = _cp(tmp.reshape(nocc, nocc, nvir).transpose(0, 2, 1))
t2new[p0 + j] += lib.dot(tmp.reshape(-1, nocc), t1,
-1).reshape(nocc, nvir,
nvir).transpose(0, 2, 1)
lib.dot(t1, eris_ovov[j].reshape(-1, nvir).T, 1,
tmp.reshape(nocc, -1))
lib.dot(tmp.reshape(-1, nocc), t1, -1,
t2new[p0 + j].reshape(-1, nvir), 1)
tmp = None
#: g2 = 2 * eris.oOVv - eris.oovv
#: t1new += numpy.einsum('jb,ijba->ia', t1, g2)
t1new[p0:p1] += numpy.einsum('jb,iajb->ia', 2 * t1, eris_ovov)
t1new[p0:p1] += numpy.einsum('jb,ijba->ia', -t1, eris_oovv)
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: woooo += numpy.einsum('ijba,klab->ijkl', eris.oOVv, tau)
#: woVoV -= eris.oovv
#: tau = .5*t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: woVoV += numpy.einsum('ka,ijkb->ijab', t1, eris.ooov)
#: woVoV += numpy.einsum('jkca,ikbc->ijab', tau, eris.oOVv)
woVoV -= eris_oovv
woVoV = woVoV.transpose(1, 3, 0, 2).copy()
eris_oVOv = _cp(eris_ovov.transpose(0, 3, 2, 1))
eris_oOvV = _cp(eris_ovov.transpose(0, 2, 1, 3))
#==== mem usage blksize*(nocc*nvir**2*4)
taubuf = numpy.empty((blksize, nocc, nvir, nvir))
for j0, j1 in prange(0, nocc, blksize):
tau = make_tau(t2[j0:j1], t1[j0:j1], t1, 1, out=taubuf[:j1 - j0])
#: woooo[p0:p1,:,j0:j1] += numpy.einsum('ijab,klab->ijkl', eris_oOvV, tau)
lib.numpy_helper._dgemm('N', 'T', (p1 - p0) * nocc,
(j1 - j0) * nocc, nvir * nvir,
eris_oOvV.reshape(-1, nvir * nvir),
tau.reshape(-1, nvir * nvir),
woooo[p0:p1].reshape(-1, nocc * nocc), 1,
1, 0, 0, j0 * nocc)
for i in range(j1 - j0):
tau[i] -= t2[j0 + i] * .5
#: woVoV[j0:j1] += numpy.einsum('jkca,ickb->jiab', tau, eris_ovov)
lib.dot(_cp(tau.transpose(0, 3, 1, 2).reshape(-1, nov)),
eris_oVOv.reshape(-1, nov).T, 1, woVoV[j0:j1].reshape(
(j1 - j0) * nvir, -1), 1)
#==== mem usage blksize*(nocc*nvir**2*6)
time2 = log.timer_debug1('woVoV [%d:%d]' % (p0, p1), *time2)
tau = make_tau(t2[p0:p1], t1[p0:p1], t1, 1, out=taubuf[:p1 - p0])
#: t2new += .5 * numpy.einsum('klij,klab->ijab', woooo[p0:p1], tau)
lib.dot(woooo[p0:p1].reshape(-1, nocc * nocc).T,
tau.reshape(-1, nvir * nvir), .5,
t2new.reshape(nocc * nocc, -1), 1)
eris_oovv = eris_ovov = eris_oVOv = eris_oOvV = taubuf = tau = None
#==== mem usage blksize*(nocc*nvir**2*1)
t2iajb = _cp(t2[p0:p1].transpose(0, 2, 1, 3))
t2ibja = _cp(t2[p0:p1].transpose(0, 3, 1, 2))
tmp = numpy.empty((blksize, nvir, nocc, nvir))
for j0, j1 in prange(0, nocc, blksize):
#: t2new[j0:j1] += numpy.einsum('ibkc,kcja->ijab', woVoV[j0:j1], t2ibja)
lib.dot(woVoV[j0:j1].reshape((j1 - j0) * nvir, -1),
t2ibja.reshape(-1, nov), 1, tmp[:j1 - j0].reshape(-1, nov))
for i in range(j1 - j0):
t2new[j0 + i] += tmp[i].transpose(1, 2, 0)
#: t2new[j0:j1] += numpy.einsum('iakc,kcjb->ijab', woVoV[j0:j1], t2iajb)
lib.dot(woVoV[j0:j1].reshape((j1 - j0) * nvir, -1),
t2iajb.reshape(-1, nov), 1, tmp[:j1 - j0].reshape(-1, nov))
for i in range(j1 - j0):
t2new[j0 + i] += tmp[i].transpose(1, 0, 2)
t2ibja = t2iajb = woVoV = tmp = None
#==== mem usage blksize*(nocc*nvir**2*3)
time1 = log.timer_debug1('contract occ [%d:%d]' % (p0, p1), *time1)
# ==================
time1 = log.timer_debug1('contract loop', *time0)
woooo = None
ft_ij = foo + numpy.einsum('ja,ia->ij', .5 * t1, fov)
ft_ab = fvv - numpy.einsum('ia,ib->ab', .5 * t1, fov)
#: t2new += numpy.einsum('ijac,bc->ijab', t2, ft_ab)
#: t2new -= numpy.einsum('ki,kjab->ijab', ft_ij, t2)
lib.dot(t2.reshape(-1, nvir), ft_ab.T, 1, t2new.reshape(-1, nvir), 1)
lib.dot(ft_ij.T, t2.reshape(nocc, -1), -1, t2new.reshape(nocc, -1), 1)
#: t2new = t2new + t2new.transpose(1,0,3,2)
t2new_tril = numpy.empty((nocc * (nocc + 1) // 2, nvir, nvir))
ij = 0
for i in range(nocc):
for j in range(i + 1):
t2new_tril[ij] = t2new[i, j]
t2new_tril[ij] += t2new[j, i].T
ij += 1
t2new = None
time1 = log.timer_debug1('t2 tril', *time1)
cc.add_wvvVV_(t1, t2, eris, t2new_tril, max_memory)
time1 = log.timer_debug1('vvvv', *time1)
mo_e = fock.diagonal()
eia = mo_e[:nocc, None] - mo_e[None, nocc:]
p0 = 0
for i in range(nocc):
t2new_tril[p0:p0 + i + 1] /= lib.direct_sum('a,jb->jab', eia[i],
eia[:i + 1])
p0 += i + 1
time1 = log.timer_debug1('g2/dijab', *time1)
t2new = numpy.empty((nocc, nocc, nvir, nvir))
ij = 0
for i in range(nocc):
for j in range(i):
t2new[i, j] = t2new_tril[ij]
t2new[j, i] = t2new_tril[ij].T
ij += 1
t2new[i, i] = t2new_tril[ij]
ij += 1
t2new_tril = None
#** update_amp_t1
t1new += fock[:nocc,nocc:] \
+ numpy.einsum('ib,ab->ia', t1, fvv) \
- numpy.einsum('ja,ji->ia', t1, foo)
mo_e = fock.diagonal()
eia = mo_e[:nocc, None] - mo_e[None, nocc:]
t1new /= eia
#** end update_amp_t1
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def __init__(self, cc, mo_coeff=None, method='incore'):
cput0 = (time.clock(), time.time())
moidx = numpy.ones(cc.mo_energy.size, dtype=numpy.bool)
if isinstance(cc.frozen, (int, numpy.integer)):
moidx[:cc.frozen] = False
elif len(cc.frozen) > 0:
moidx[numpy.asarray(cc.frozen)] = False
if mo_coeff is None:
self.mo_coeff = mo_coeff = cc.mo_coeff[:, moidx]
self.fock = numpy.diag(cc.mo_energy[moidx])
else: # If mo_coeff is not canonical orbital
self.mo_coeff = mo_coeff = mo_coeff[:, moidx]
dm = cc._scf.make_rdm1(cc.mo_coeff, cc.mo_occ)
fockao = cc._scf.get_hcore() + cc._scf.get_veff(cc.mol, dm)
self.fock = reduce(numpy.dot, (mo_coeff.T, fockao, mo_coeff))
nocc = cc.nocc()
nmo = cc.nmo()
nvir = nmo - nocc
mem_incore, mem_outcore, mem_basic = _mem_usage(nocc, nvir)
mem_now = pyscf.lib.current_memory()[0]
log = logger.Logger(cc.stdout, cc.verbose)
if (method == 'incore' and cc._scf._eri is not None and
(mem_incore + mem_now < cc.max_memory) or cc.mol.incore_anyway):
eri1 = pyscf.ao2mo.incore.full(cc._scf._eri, mo_coeff)
#:eri1 = pyscf.ao2mo.restore(1, eri1, nmo)
#:self.oooo = eri1[:nocc,:nocc,:nocc,:nocc].copy()
#:self.ooov = eri1[:nocc,:nocc,:nocc,nocc:].copy()
#:self.ovoo = eri1[:nocc,nocc:,:nocc,:nocc].copy()
#:self.oovv = eri1[:nocc,:nocc,nocc:,nocc:].copy()
#:self.ovov = eri1[:nocc,nocc:,:nocc,nocc:].copy()
#:ovvv = eri1[:nocc,nocc:,nocc:,nocc:].copy()
#:self.ovvv = numpy.empty((nocc,nvir,nvir*(nvir+1)//2))
#:for i in range(nocc):
#: for j in range(nvir):
#: self.ovvv[i,j] = lib.pack_tril(ovvv[i,j])
#:self.vvvv = pyscf.ao2mo.restore(4, eri1[nocc:,nocc:,nocc:,nocc:], nvir)
nvir_pair = nvir * (nvir + 1) // 2
self.oooo = numpy.empty((nocc, nocc, nocc, nocc))
self.ooov = numpy.empty((nocc, nocc, nocc, nvir))
self.ovoo = numpy.empty((nocc, nvir, nocc, nocc))
self.oovv = numpy.empty((nocc, nocc, nvir, nvir))
self.ovov = numpy.empty((nocc, nvir, nocc, nvir))
self.ovvv = numpy.empty((nocc, nvir, nvir_pair))
self.vvvv = numpy.empty((nvir_pair, nvir_pair))
ij = 0
outbuf = numpy.empty((nmo, nmo, nmo))
for i in range(nocc):
buf = _ccsd.unpack_tril(eri1[ij:ij + i + 1],
out=outbuf[:i + 1])
for j in range(i + 1):
self.oooo[i, j] = self.oooo[j, i] = buf[j, :nocc, :nocc]
self.ooov[i, j] = self.ooov[j, i] = buf[j, :nocc, nocc:]
self.oovv[i, j] = self.oovv[j, i] = buf[j, nocc:, nocc:]
ij += i + 1
ij1 = 0
for i in range(nocc, nmo):
buf = _ccsd.unpack_tril(eri1[ij:ij + i + 1],
out=outbuf[:i + 1])
self.ovoo[:, i - nocc] = buf[:nocc, :nocc, :nocc]
self.ovov[:, i - nocc] = buf[:nocc, :nocc, nocc:]
for j in range(nocc):
self.ovvv[j, i - nocc] = lib.pack_tril(
_cp(buf[j, nocc:, nocc:]))
for j in range(nocc, i + 1):
self.vvvv[ij1] = lib.pack_tril(_cp(buf[j, nocc:, nocc:]))
ij1 += 1
ij += i + 1
else:
cput1 = time.clock(), time.time()
_tmpfile1 = tempfile.NamedTemporaryFile()
_tmpfile2 = tempfile.NamedTemporaryFile()
self.feri1 = h5py.File(_tmpfile1.name)
orbo = mo_coeff[:, :nocc]
orbv = mo_coeff[:, nocc:]
nvpair = nvir * (nvir + 1) // 2
self.oooo = self.feri1.create_dataset('oooo',
(nocc, nocc, nocc, nocc),
'f8')
self.ooov = self.feri1.create_dataset('ooov',
(nocc, nocc, nocc, nvir),
'f8')
self.ovoo = self.feri1.create_dataset('ovoo',
(nocc, nvir, nocc, nocc),
'f8')
self.oovv = self.feri1.create_dataset('oovv',
(nocc, nocc, nvir, nvir),
'f8')
self.ovov = self.feri1.create_dataset('ovov',
(nocc, nvir, nocc, nvir),
'f8')
self.ovvv = self.feri1.create_dataset('ovvv', (nocc, nvir, nvpair),
'f8')
max_memory = max(2000,
cc.max_memory - pyscf.lib.current_memory()[0])
self.feri2 = h5py.File(_tmpfile2.name, 'w')
pyscf.ao2mo.full(cc.mol,
orbv,
self.feri2,
max_memory=max_memory,
verbose=log)
self.vvvv = self.feri2['eri_mo']
cput1 = log.timer_debug1('transforming vvvv', *cput1)
tmpfile3 = tempfile.NamedTemporaryFile()
with h5py.File(tmpfile3.name, 'w') as feri:
max_memory = max(2000,
cc.max_memory - pyscf.lib.current_memory()[0])
pyscf.ao2mo.general(cc.mol,
(orbo, mo_coeff, mo_coeff, mo_coeff),
feri,
max_memory=max_memory,
verbose=log)
cput1 = log.timer_debug1('transforming oppp', *cput1)
eri1 = feri['eri_mo']
outbuf = numpy.empty((nmo, nmo, nmo))
for i in range(nocc):
buf = _ccsd.unpack_tril(_cp(eri1[i * nmo:(i + 1) * nmo]),
out=outbuf)
self.oooo[i] = buf[:nocc, :nocc, :nocc]
self.ooov[i] = buf[:nocc, :nocc, nocc:]
self.ovoo[i] = buf[nocc:, :nocc, :nocc]
self.oovv[i] = buf[:nocc, nocc:, nocc:]
self.ovov[i] = buf[nocc:, :nocc, nocc:]
self.ovvv[i] = _ccsd.pack_tril(
_cp(buf[nocc:, nocc:, nocc:]))
cput1 = log.timer_debug1('sorting %d' % i, *cput1)
for key in feri.keys():
del (feri[key])
log.timer('CCSD integral transformation', *cput0)
def _rdm2_mo2ao(mycc, d2, dm1, mo_coeff):
log = logger.Logger(mycc.stdout, mycc.verbose)
time1 = time.clock(), time.time()
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
nocc, nvir = dovov.shape[:2]
nov = nocc * nvir
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao+1) // 2
nvir_pair = nvir * (nvir+1) //2
mo_coeff = numpy.asarray(mo_coeff, order='F')
def _trans(vin, i0, icount, j0, jcount, out=None):
nrow = vin.shape[0]
fdrv = getattr(_ccsd.libcc, 'AO2MOnr_e2_drv')
pao_loc = ctypes.POINTER(ctypes.c_void_p)()
ftrans = ctypes.c_void_p(_ctypes.dlsym(_ccsd.libcc._handle, 'AO2MOtranse2_nr_s1'))
fmmm = ctypes.c_void_p(_ctypes.dlsym(_ccsd.libcc._handle, 'CCmmm_transpose_sum'))
fdrv(ftrans, fmmm,
out.ctypes.data_as(ctypes.c_void_p),
vin.ctypes.data_as(ctypes.c_void_p),
mo_coeff.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nrow), ctypes.c_int(nao),
ctypes.c_int(i0), ctypes.c_int(icount),
ctypes.c_int(j0), ctypes.c_int(jcount),
pao_loc, ctypes.c_int(0))
return out
blksize = 4
bufop = numpy.empty((nocc*nmo,nao_pair))
bufvv = numpy.empty((nvir_pair,nao_pair))
pool = numpy.empty((blksize,nmo,nmo,nmo))
for p0, p1 in prange(0, nocc, blksize):
buf1 = pool[:p1-p0]
buf1[:,:nocc,:nocc,:nocc] = doooo[p0:p1]
buf1[:,:nocc,:nocc,nocc:] = dooov[p0:p1]
buf1[:,:nocc,nocc:,:nocc] = 0
buf1[:,:nocc,nocc:,nocc:] = doovv[p0:p1]
buf1[:,nocc:,:nocc,:nocc] = 0
buf1[:,nocc:,:nocc,nocc:] = dovov[p0:p1]
buf1[:,nocc:,nocc:,:nocc] = dovvo[p0:p1]
buf1[:,nocc:,nocc:,nocc:] = dovvv[p0:p1]
for i in range(p1-p0):
buf1[i,p0+i,:,:] += dm1
buf1[i,:,:,p0+i] -= dm1 * .5
_trans(buf1.reshape(-1,nmo**2), 0, nmo, 0, nmo, bufop[p0*nmo:p1*nmo])
pool = pool.ravel()[:blksize*nvir**3].reshape((blksize*nvir,nvir,nvir))
for p0, p1 in prange(0, nvir_pair, blksize*nvir):
buf1 = _ccsd.unpack_tril(_cp(dvvvv[p0:p1]), out=pool[:p1-p0])
_trans(buf1, nocc, nvir, nocc, nvir, bufvv[p0:p1])
pool = buf1 = None
# trans ij of d_ijkl
bufaa = numpy.empty((nao_pair,nao_pair))
tmpbuf1 = numpy.empty((BLKSIZE,nmo,nmo))
tmpbuf2 = numpy.empty((BLKSIZE,nvir_pair))
tmpbuf3 = numpy.empty((BLKSIZE,nvir,nvir))
tmpbuf1[:,nocc:,:nocc] = 0
for i0, i1 in prange(0, nao_pair, BLKSIZE):
buf1 = tmpbuf1[:i1-i0].reshape(i1-i0,-1)
for j0, j1 in prange(0, nocc*nmo, BLKSIZE):
buf1[:,j0:j1] = bufop[j0:j1,i0:i1].T
buf1 = tmpbuf1[:i1-i0]
tmp = tmpbuf2[:i1-i0]
for j0, j1 in prange(0, nvir_pair, BLKSIZE):
tmp[:,j0:j1] = bufvv[j0:j1,i0:i1].T
buf1[:,nocc:,nocc:] = _ccsd.unpack_tril(tmp, out=tmpbuf3[:i1-i0])
_trans(buf1, 0, nmo, 0, nmo, bufaa[i0:i1])
# dm2 + dm2.transpose(2,3,0,1)
for j0, j1, in prange(0, i0, BLKSIZE):
bufaa[i0:i1,j0:j1] += bufaa[j0:j1,i0:i1].T
bufaa[j0:j1,i0:i1] = bufaa[i0:i1,j0:j1].T
bufaa[i0:i1,i0:i1] = bufaa[i0:i1,i0:i1] + bufaa[i0:i1,i0:i1].T
tmpbuf1 = tmpbuf2 = tmpbuf3 = bufop = bufvv = pool = None
idx = numpy.arange(nao)
idx = idx*(idx+1)//2 + idx
bufaa[:,idx] *= .5
return bufaa
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if d1 is None:
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
if d2 is None:
d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
# Note Ioo, Ivv are not hermitian
Ioo = numpy.zeros((nocc,nocc))
Ivv = numpy.zeros((nvir,nvir))
Ivo = numpy.zeros((nvir,nocc))
Xvo = numpy.zeros((nvir,nocc))
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
d_oooo = _cp(doooo)
d_oooo = _cp(d_oooo + d_oooo.transpose(1,0,2,3))
#:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2
Ioo += lib.dot(eris_oooo.reshape(nocc,-1), d_oooo.reshape(nocc,-1).T, 2)
d_oooo = _cp(d_oooo.transpose(0,2,3,1))
#:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2
Xvo += lib.dot(eris_ooov.reshape(-1,nvir).T, d_oooo.reshape(nocc,-1).T, 2)
Xvo +=(numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4
- numpy.einsum('kj,ikja->ai', doo+doo.T, eris_ooov))
eris_oooo = eris_ooov = d_oooo = None
d_ooov = _cp(dooov)
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
#:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov)
#:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo)
Ivv += lib.dot(eris_ooov.reshape(-1,nvir).T, d_ooov.reshape(-1,nvir))
Ivo += lib.dot(d_ooov.reshape(-1,nvir).T, eris_oooo.reshape(-1,nocc))
#:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv)
eris_oovv = _cp(eris.oovv)
tmp = _cp(d_ooov.transpose(0,1,3,2).reshape(-1,nocc))
tmpooov = _cp(eris_ooov.transpose(0,1,3,2))
Ioo += lib.dot(tmpooov.reshape(-1,nocc).T, tmp)
Xvo += lib.dot(eris_oovv.reshape(-1,nvir).T, tmp)
eris_oooo = tmp = None
d_ooov = d_ooov + d_ooov.transpose(1,0,2,3)
eris_ovov = _cp(eris.ovov)
#:Ioo += numpy.einsum('jlka,ilka->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('ijkb,kbja->ai', d_ooov, eris.ovov)
Ioo += lib.dot(eris_ooov.reshape(nocc,-1), d_ooov.reshape(nocc,-1).T)
Xvo += lib.dot(eris_ovov.reshape(-1,nvir).T,
_cp(d_ooov.transpose(0,2,3,1).reshape(nocc,-1)).T)
d_ooov = None
#:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv)
#:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv)
#:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov)
d_oovv = _cp(doovv + doovv.transpose(1,0,3,2))
for i in range(nocc):
Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1), d_oovv[i].reshape(nocc,-1).T)
Ivv += lib.dot(eris_oovv.reshape(-1,nvir).T, d_oovv.reshape(-1,nvir))
Ivo += lib.dot(d_oovv.reshape(-1,nvir).T, tmpooov.reshape(-1,nocc))
d_oovv = _ccsd.precontract(d_oovv.reshape(-1,nvir,nvir)).reshape(nocc,nocc,-1)
eris_ooov = tmpooov = None
blksize = 4
d_ovov = numpy.empty((nocc,nvir,nocc,nvir))
for p0, p1 in prange(0, nocc, blksize):
d_ovov[p0:p1] = _cp(dovov[p0:p1])
d_ovvo = _cp(dovvo[p0:p1])
for i in range(p0,p1):
d_ovov[i] += d_ovvo[i-p0].transpose(0,2,1)
d_ovvo = None
#:d_ovov = d_ovov + d_ovov.transpose(2,3,0,1)
lib.transpose_sum(d_ovov.reshape(nov,nov), inplace=True)
#:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo)
Ivo += lib.dot(d_ovov.reshape(-1,nvir).T, _cp(eris.ovoo).reshape(-1,nocc))
#:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov)
#:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov)
Ioo += lib.dot(eris_ovov.reshape(nocc,-1), d_ovov.reshape(nocc,-1).T)
Ivv += lib.dot(eris_ovov.reshape(-1,nvir).T, d_ovov.reshape(-1,nvir))
nvir_pair = nvir * (nvir+1) // 2
bufe_ovvv = numpy.empty((blksize,nvir,nvir,nvir))
bufc_ovvv = numpy.empty((blksize,nvir,nvir_pair))
bufc_ovvv.data = bufe_ovvv.data
c_vvvo = numpy.empty((nvir_pair,nvir,nocc))
for p0, p1 in prange(0, nocc, blksize):
d_ovvv = numpy.empty((p1-p0,nvir,nvir,nvir))
#:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv)
for i in range(p1-p0):
lib.dot(dovvv[p0+i].reshape(nvir,-1),
eris_oovv[p0+i].reshape(nocc,-1).T, 1, Ivo, 1)
c_ovvv = bufc_ovvv[:p1-p0]
# tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2))
_ccsd.precontract(dovvv[p0:p1].reshape(-1,nvir,nvir), out=c_ovvv)
for i0, i1, in prange(0, nvir_pair, BLKSIZE):
for j0, j1 in prange(0, nvir, BLKSIZE//(p1-p0)+1):
c_vvvo[i0:i1,j0:j1,p0:p1] = c_ovvv[:,j0:j1,i0:i1].transpose(2,1,0)
eris_ovx = _cp(eris.ovvv[p0:p1])
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
#:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv)
for i in range(p1-p0):
lib.dot(eris_ovx[i].reshape(nvir,-1),
d_oovv[p0+i].reshape(nocc,-1).T, 1, Xvo, 1)
lib.dot(eris_ovx[i].reshape(nvir,-1),
c_ovvv[i].reshape(nvir,-1).T, 1, Ivv, 1)
eris_ovvv = bufe_ovvv[:p1-p0]
_ccsd.unpack_tril(eris_ovx.reshape(-1,nvir_pair),
out=eris_ovvv.reshape(-1,nvir**2))
eris_ovx = None
#:Xvo += numpy.einsum('icjb,acjb->ai', d_ovov, eris_vvov)
d_ovvo = _cp(d_ovov[p0:p1].transpose(0,1,3,2))
lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvo.reshape(-1,nocc), 1, Xvo, 1)
e_ovvo, d_ovvo = d_ovvo, None
for i in range(p1-p0):
d_ovvv[i] = _ccsd.sum021(dovvv[p0+i])
e_ovvo[i] = eris_ovov[p0+i].transpose(0,2,1)
#:Ivo += numpy.einsum('jcab,jcib->ai', d_ovvv, eris_ovov)
#:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv)
lib.dot(d_ovvv.reshape(-1,nvir).T,
e_ovvo[:p1-p0].reshape(-1,nocc), 1, Ivo, 1)
lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvv.reshape(-1,nvir), 1, Ivv, 1)
Xvo[:,p0:p1] +=(numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4
- numpy.einsum('cb,icba->ai', dvv+dvv.T, eris_ovvv))
d_oovv = d_ovvv = bufc_ovvv = bufe_ovvv = None
eris_ovov = eris_ovvv = eris_oovv = e_ovvo = None
eris_ovvv = _cp(eris.ovvv)
bufe_vvvo = numpy.empty((blksize*nvir,nvir,nocc))
bufe_vvvv = numpy.empty((blksize*nvir,nvir,nvir))
bufd_vvvv = numpy.empty((blksize*nvir,nvir,nvir))
for p0, p1 in prange(0, nvir, blksize):
off0 = p0*(p0+1)//2
off1 = p1*(p1+1)//2
d_vvvv = _cp(dvvvv[off0:off1]) * 4
for i in range(p0, p1):
d_vvvv[i*(i+1)//2+i-off0] *= .5
d_vvvv = _ccsd.unpack_tril(d_vvvv, out=bufd_vvvv[:off1-off0])
eris_vvvv = _ccsd.unpack_tril(eris.vvvv[off0:off1], out=bufe_vvvv[:off1-off0])
#:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2
#:Xvo += numpy.einsum('icdb,acdb->ai', d_ovvv, eris_vvvv)
lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvv.reshape(-1,nvir), 2, Ivv, 1)
d_vvvo = _cp(c_vvvo[off0:off1])
lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvo.reshape(-1,nocc), 1, Xvo, 1)
#:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo)
#:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2
eris_vvvo = bufe_vvvo[:off1-off0]
for i0, i1 in prange(off0, off1, BLKSIZE):
for j0, j1, in prange(0, nvir, BLKSIZE//nocc+1):
eris_vvvo[i0-off0:i1-off0,j0:j1,:] = eris_ovvv[:,j0:j1,i0:i1].transpose(2,1,0)
lib.dot(eris_vvvo.reshape(-1,nocc).T, d_vvvo.reshape(-1,nocc), 1, Ioo, 1)
lib.dot(d_vvvv.reshape(-1,nvir).T, eris_vvvo.reshape(-1,nocc), 2, Ivo, 1)
Ioo *= -1
Ivv *= -1
Ivo *= -1
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def make_intermediates(mycc, t1, t2, eris):
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
foo = eris.fock[:nocc, :nocc]
fov = eris.fock[:nocc, nocc:]
fvv = eris.fock[nocc:, nocc:]
class _Saved(object):
pass
saved = _Saved()
# As we don't have l2 in memory, hold tau temporarily in memory
w1 = fvv - numpy.einsum('ja,jb->ba', fov, t1)
w2 = foo + numpy.einsum('ib,jb->ij', fov, t1)
w3 = _cp(numpy.einsum('kc,jkbc->bj', fov, t2) * 2 + fov.T)
w3 -= numpy.einsum('kc,kjbc->bj', fov, t2)
w3 += reduce(numpy.dot, (t1.T, fov, t1.T))
w4 = fov.copy()
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nov, -1))
eris_ovvv = eris_ovvv.reshape(nocc, nvir, nvir, nvir)
wovvv = numpy.empty((nocc, nvir, nvir, nvir))
t2tmp = numpy.empty((nocc, nvir, nocc, nvir))
for i in range(nocc):
wovvv[i] = eris_ovvv[i].transpose(1, 0, 2) * 2
t2tmp[i] = t2[i].transpose(2, 0, 1)
#:wovvv += numpy.einsum('jabd,kjdc->kabc', eris_ovvv, t2) * -1.5
tmp = lib.dot(t2tmp.reshape(nov, -1), wovvv.reshape(-1, nvir**2),
-1.5 / 2).reshape(-1, nvir, nvir, nvir)
g2ovvv = tmp
for i in range(nocc):
wovvv[i] -= eris_ovvv[i].transpose(1, 2, 0)
wovvv[i] += tmp[i].transpose(1, 2, 0)
g2ovvv[i] = eris_ovvv[i] * 2
g2ovvv[i] -= eris_ovvv[i].transpose(1, 2, 0)
tmp = t2tmp = None
w1 += numpy.einsum('jcba,jc->ba', eris_ovvv, t1 * 2)
w1 -= numpy.einsum('jabc,jc->ba', eris_ovvv, t1)
#:w3 += numpy.einsum('kdcb,kjdc->bj', eris_ovvv, theta)
theta = numpy.empty(t2.shape)
for i in range(nocc):
theta[i] = t2[i] * 2
theta[i] -= t2[i].transpose(0, 2, 1)
lib.dot(eris_ovvv[i].reshape(-1, nvir).T,
_cp(theta[i].reshape(nocc, -1)).T, 1, w3, 1)
theta = _cp(theta.transpose(0, 2, 1, 3))
#:vkbca = numpy.einsum('jdca,kbjd->kbca', g2ovvv, theta)
vkbca = lib.dot(_cp(theta.reshape(nov, -1)),
g2ovvv.reshape(-1,
nvir * nvir)).reshape(-1, nvir, nvir, nvir)
for i in range(nocc):
wovvv[i] += vkbca[i].transpose(2, 0, 1)
wovvv[i] -= vkbca[i].transpose(2, 1, 0) * .5
vkabc = None
#:wOVov = numpy.einsum('jbcd,kd->jbkc', eris_ovvv, t1)
#:wOvOv = numpy.einsum('jdcb,kd->jbkc', eris_ovvv, -t1)
wOVov = lib.dot(eris_ovvv.reshape(-1, nvir),
t1.T).reshape(-1, nvir, nvir, nocc).transpose(0, 1, 3,
2).copy()
for i in range(nocc):
g2ovvv[i] = eris_ovvv[i].transpose(1, 2, 0) * 2
wOvOv = lib.dot(g2ovvv.reshape(-1, nvir), -t1.T,
.5).reshape(-1, nvir, nvir, nocc).transpose(0, 1, 3,
2).copy()
for i in range(nocc):
g2ovvv[i] -= eris_ovvv[i].transpose(1, 0, 2)
eris_ovov = _cp(_cp(eris.ovov).transpose(0, 2, 1, 3))
tau = _ccsd.make_tau(t2, t1, t1)
#:wooov[:,j0:j1] = numpy.einsum('icbd,jkbd->ijkc', g2ovvv, tau)
#:woooo[:,:,j0:j1] = numpy.einsum('icjd,klcd->ijkl', eris_ovov, tau)
tmp = lib.dot(g2ovvv.reshape(-1, nvir**2), tau.reshape(-1, nvir**2).T)
wooov = _cp(tmp.reshape(-1, nvir, nocc, nocc).transpose(0, 2, 3, 1))
woooo = lib.dot(eris_ovov.reshape(-1, nvir**2),
tau.reshape(-1, nvir**2).T).reshape(-1, nocc, nocc, nocc)
eris_ovov = eris_ovvv = g2ovvv = tau = tmp = None
eris_ooov = _cp(eris.ooov)
eris_ovoo = _cp(eris.ovoo)
#:woooo += numpy.einsum('icjl,kc->ijkl', eris_ovoo, t1)
#:wOVov += numpy.einsum('jblk,lc->jbkc', eris_ovoo, -t1)
for i in range(nocc):
woooo[i] += lib.dot(t1, eris_ovoo[i].reshape(nvir, -1)).reshape(
(nocc, ) * 3).transpose(1, 0, 2)
lib.dot(eris_ovoo.reshape(-1, nocc), t1, -1, wOVov.reshape(-1, nvir), 1)
#:wooov -= numpy.einsum('ibjl,lkcb->ijkc', eris_ovoo*1.5, t2)
t2tmp = numpy.empty((nocc, nvir, nocc, nvir))
for i in range(nocc):
t2tmp[i] = t2[i].transpose(2, 0, 1)
tmp_ooov = _cp(-eris_ooov.transpose(2, 0, 1, 3)).reshape(-1, nov)
lib.dot(tmp_ooov, t2tmp.reshape(nov, -1), 1.5, wooov.reshape(-1, nov), 1)
t2tmp = None
g2ooov, tmp_ooov = tmp_ooov.reshape(nocc, nocc, nocc, nvir), None
g2ooov += eris_ooov * 2
#:vikjc = numpy.einsum('iklb,jlcb->ikjc', g2ooov, theta)
vikjc = lib.dot(g2ooov.reshape(-1, nov), theta.reshape(-1, nov).T)
vikjc = vikjc.reshape(nocc, nocc, nocc, nvir)
wooov += vikjc.transpose(0, 2, 1, 3)
wooov -= vikjc * .5
g2ooov = vikjc = eris_ovoo = None
w2 += numpy.einsum('ijkb,kb->ij', eris_ooov, t1) * 2
w2 -= numpy.einsum('kjib,kb->ij', eris_ooov, t1)
#:w3 -= numpy.einsum('kjlc,klbc->bj', eris_ooov, theta)
for i in range(nocc):
lib.dot(
_cp(theta[i].transpose(1, 2, 0)).reshape(-1, nvir).T,
eris_ooov[i].reshape(nocc, -1).T, -1, w3, 1)
#:woooo += numpy.einsum('ikjc,lc->ijkl', eris_ooov, t1)
#:wOvOv += numpy.einsum('jklb,lc->jbkc', eris_ooov, t1)
woooo += lib.dot(eris_ooov.reshape(-1, nvir), t1.T).reshape(
(-1, nocc, nocc, nocc)).transpose(0, 2, 1, 3)
for i in range(nocc):
lib.dot(
_cp(eris_ooov[i].transpose(2, 0, 1)).reshape(-1, nocc), t1, 1,
wOvOv[i].reshape(-1, nvir), 1)
wooov[i] += eris_ooov[i].transpose(1, 0, 2) * 2
wooov[i] -= eris_ooov[i]
eris_ooov = theta = None
eris_ovov = _cp(eris.ovov)
g2ovov = numpy.empty((nocc, nocc, nvir, nvir))
for i in range(nocc):
g2ovov[i] = eris_ovov[i].transpose(1, 0, 2) * 2
g2ovov[i] -= eris_ovov[i].transpose(1, 2, 0)
tmpw4 = numpy.einsum('klcd,ld->kc', g2ovov, t1)
#:w1 -= numpy.einsum('kcja,kjcb->ba', g2ovov, t2)
w1 -= lib.dot(t2.reshape(-1, nvir).T, g2ovov.reshape(-1, nvir))
w1 -= numpy.einsum('ja,jb->ba', tmpw4, t1)
#:w2 += numpy.einsum('ibkc,jkbc->ij', g2ovov, t2)
w2 += lib.dot(g2ovov.reshape(nocc, -1), t2.reshape(nocc, -1).T)
w2 += numpy.einsum('ib,jb->ij', tmpw4, t1)
w3 += reduce(numpy.dot, (t1.T, tmpw4, t1.T))
w4 += tmpw4
vOVov = eris_ovov.copy()
#:vOVov += numpy.einsum('jbld,klcd->jbkc', g2ovov, t2)
#:vOVov -= numpy.einsum('jbld,kldc->jbkc', eris_ovov, t2)
lib.dot(
_cp(g2ovov.transpose(0, 2, 1, 3)).reshape(-1, nov),
_cp(t2.transpose(0, 2, 1, 3).reshape(nov, -1).T), 1,
vOVov.reshape(nov, -1), 1)
lib.dot(eris_ovov.reshape(-1, nov),
_cp(t2.transpose(0, 3, 1, 2).reshape(nov, -1).T), -1,
vOVov.reshape(nov, -1), 1)
g2ovov = None
#:tmp = numpy.einsum('jbld,kd->ljbk', eris_ovov, t1)
#:wOVov -= numpy.einsum('ljbk,lc->jbkc', tmp, t1)
#:tmp = numpy.einsum('jdlb,kd->ljbk', eris_ovov, t1)
#:wOvOv += numpy.einsum('ljbk,lc->jbkc', tmp, t1)
tmp = numpy.empty((nocc, nvir, nocc))
for j in range(nocc):
lib.dot(
_cp(eris_ovov[j].transpose(1, 0, 2)).reshape(-1, nvir), t1.T, 1,
tmp.reshape(-1, nocc))
lib.dot(tmp.reshape(nocc, -1).T, t1, -1, wOVov[j].reshape(-1, nvir), 1)
lib.dot(eris_ovov[j].reshape(nvir, -1).T, t1.T, 1,
tmp.reshape(-1, nocc))
lib.dot(tmp.reshape(nocc, -1).T, t1, 1, wOvOv[j].reshape(-1, nvir), 1)
tmp = None
#:vOvOv = numpy.einsum('jdlb,kldc->jbkc', eris_ovov, t2)
ovovtmp = _cp(eris_ovov.transpose(0, 3, 2, 1).reshape(-1, nov))
vOvOv = numpy.empty((nocc, nvir, nocc, nvir))
for j in range(nocc):
lib.dot(t2[j].reshape(-1, nvir).T, ovovtmp.T, 1,
vOvOv[j].reshape(nvir, -1))
vOvOv[j] -= eris.oovv[j].transpose(2, 0, 1)
ovovtmp = eris_ovov = None
vOvOv = lib.transpose(vOvOv.reshape(nov,
-1)).reshape(nocc, nvir, nocc, nvir)
wOVov += vOVov
wOvOv += vOvOv
saved.wOVov = wOVov
saved.wOvOv = wOvOv
ovovtmp = wOVov = wOvOv = eris_ovov = None
ov2 = vOVov * 2 + vOvOv
w3 += numpy.einsum('kcjb,kc->bj', ov2, t1)
#:wooov += numpy.einsum('ibjc,kb->ijkc', ov2, t1)
#:wovvv -= numpy.einsum('jakb,jc->kabc', ov2, t1)
for i in range(nocc):
wooov[i] += lib.dot(t1, ov2[i].reshape(nvir, -1)).reshape(
nocc, nocc, nvir).transpose(1, 0, 2)
lib.dot(
_cp(ov2.transpose(0, 2, 1, 3).reshape(nocc, -1)).T, t1, -1,
wovvv.reshape(-1, nvir), 1)
ov2 = None
ov1 = vOvOv * 2 + vOVov
#:wooov -= numpy.einsum('ibkc,jb->ijkc', ov1, t1)
#:wovvv += numpy.einsum('jakc,jb->kabc', ov1, t1)
for i in range(nocc):
lib.dot(t1, ov1[i].reshape(nvir, -1), -1, wooov[i].reshape(nocc, -1),
1)
wovvv += lib.dot(_cp(ov1.reshape(nocc, -1)).T,
t1).reshape(nvir, -1, nvir, nvir).transpose(1, 0, 3, 2)
ov1 = None
woooo += _cp(eris.oooo).transpose(0, 2, 1, 3)
saved.woooo = woooo
saved.wooov = wooov
woooo = wooov = None
w3 += numpy.einsum('bc,jc->bj', w1, t1)
w3 -= numpy.einsum('kj,kb->bj', w2, t1)
eris_ooov = _cp(eris.ooov)
g2ooov = eris_ooov * 2
g2ooov -= eris_ooov.transpose(2, 0, 1, 3)
#:tmp = numpy.einsum('kjla,jb->kabl', g2ooov, t1)
#:wovvv = numpy.einsum('kabl,lc->kabc', tmp, t1)
#:wovvv += numpy.einsum('kjla,jlbc->kabc', g2ooov, t2)
tmp = lib.dot(g2ooov.reshape(nocc, -1).T,
t1).reshape(-1, nocc, nvir, nvir).transpose(0, 2, 3, 1)
lib.dot(_cp(tmp.reshape(-1, nocc)), t1, 1, wovvv.reshape(-1, nvir), 1)
tmp = None
lib.dot(
_cp(g2ooov.transpose(0, 2, 1, 3).reshape(nocc**2, -1)).T,
t2.reshape(nocc**2, -1), 1, wovvv.reshape(nov, -1), 1)
g2ooov = eris_ooov = vOVov = vOvOv = None
saved.wovvv = wovvv
saved.w1 = w1
saved.w2 = w2
saved.w3 = w3
saved.w4 = w4
return saved
def _rdm2_mo2ao(mycc, d2, dm1, mo_coeff):
log = logger.Logger(mycc.stdout, mycc.verbose)
time1 = time.clock(), time.time()
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
nocc, nvir = dovov.shape[:2]
nov = nocc * nvir
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao+1) // 2
nvir_pair = nvir * (nvir+1) //2
mo_coeff = numpy.asarray(mo_coeff, order='F')
def _trans(vin, i0, icount, j0, jcount, out=None):
nrow = vin.shape[0]
fdrv = getattr(_ccsd.libcc, 'AO2MOnr_e2_drv')
pao_loc = ctypes.POINTER(ctypes.c_void_p)()
ftrans = ctypes.c_void_p(_ctypes.dlsym(_ccsd.libcc._handle, 'AO2MOtranse2_nr_s1'))
fmmm = ctypes.c_void_p(_ctypes.dlsym(_ccsd.libcc._handle, 'CCmmm_transpose_sum'))
fdrv(ftrans, fmmm,
out.ctypes.data_as(ctypes.c_void_p),
vin.ctypes.data_as(ctypes.c_void_p),
mo_coeff.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nrow), ctypes.c_int(nao),
ctypes.c_int(i0), ctypes.c_int(icount),
ctypes.c_int(j0), ctypes.c_int(jcount),
pao_loc, ctypes.c_int(0))
return out
blksize = 4
bufop = numpy.empty((nocc*nmo,nao_pair))
bufvv = numpy.empty((nvir_pair,nao_pair))
pool = numpy.empty((blksize,nmo,nmo,nmo))
for p0, p1 in prange(0, nocc, blksize):
buf1 = pool[:p1-p0]
buf1[:,:nocc,:nocc,:nocc] = doooo[p0:p1]
buf1[:,:nocc,:nocc,nocc:] = dooov[p0:p1]
buf1[:,:nocc,nocc:,:nocc] = 0
buf1[:,:nocc,nocc:,nocc:] = doovv[p0:p1]
buf1[:,nocc:,:nocc,:nocc] = 0
buf1[:,nocc:,:nocc,nocc:] = dovov[p0:p1]
buf1[:,nocc:,nocc:,:nocc] = dovvo[p0:p1]
buf1[:,nocc:,nocc:,nocc:] = dovvv[p0:p1]
for i in range(p1-p0):
buf1[i,p0+i,:,:] += dm1
buf1[i,:,:,p0+i] -= dm1 * .5
_trans(buf1.reshape(-1,nmo**2), 0, nmo, 0, nmo, bufop[p0*nmo:p1*nmo])
pool = pool.ravel()[:blksize*nvir**3].reshape((blksize*nvir,nvir,nvir))
for p0, p1 in prange(0, nvir_pair, blksize*nvir):
buf1 = _ccsd.unpack_tril(_cp(dvvvv[p0:p1]), out=pool[:p1-p0])
_trans(buf1, nocc, nvir, nocc, nvir, bufvv[p0:p1])
pool = buf1 = None
# trans ij of d_ijkl
bufaa = numpy.empty((nao_pair,nao_pair))
tmpbuf1 = numpy.empty((BLKSIZE,nmo,nmo))
tmpbuf2 = numpy.empty((BLKSIZE,nvir_pair))
tmpbuf3 = numpy.empty((BLKSIZE,nvir,nvir))
tmpbuf1[:,nocc:,:nocc] = 0
for i0, i1 in prange(0, nao_pair, BLKSIZE):
buf1 = tmpbuf1[:i1-i0].reshape(i1-i0,-1)
for j0, j1 in prange(0, nocc*nmo, BLKSIZE):
buf1[:,j0:j1] = bufop[j0:j1,i0:i1].T
buf1 = tmpbuf1[:i1-i0]
tmp = tmpbuf2[:i1-i0]
for j0, j1 in prange(0, nvir_pair, BLKSIZE):
tmp[:,j0:j1] = bufvv[j0:j1,i0:i1].T
buf1[:,nocc:,nocc:] = _ccsd.unpack_tril(tmp, out=tmpbuf3[:i1-i0])
_trans(buf1, 0, nmo, 0, nmo, bufaa[i0:i1])
# dm2 + dm2.transpose(2,3,0,1)
for j0, j1, in prange(0, i0, BLKSIZE):
bufaa[i0:i1,j0:j1] += bufaa[j0:j1,i0:i1].T
bufaa[j0:j1,i0:i1] = bufaa[i0:i1,j0:j1].T
bufaa[i0:i1,i0:i1] = bufaa[i0:i1,i0:i1] + bufaa[i0:i1,i0:i1].T
tmpbuf1 = tmpbuf2 = tmpbuf3 = bufop = bufvv = pool = None
idx = numpy.arange(nao)
idx = idx*(idx+1)//2 + idx
bufaa[:,idx] *= .5
return bufaa
def update_amps(mycc, t1, t2, l1, l2, eris=None, saved=None, max_memory=2000):
if saved is None:
saved = make_intermediates(mycc, t1, t2, eris)
time1 = time0 = time.clock(), time.time()
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
foo = eris.fock[:nocc, :nocc]
fov = eris.fock[:nocc, nocc:]
fvv = eris.fock[:nocc, :nocc]
#:mba = numpy.einsum('klca,klcb->ba', l2, t2*2-t2.transpose(0,1,3,2))
#:mij = numpy.einsum('ikcd,jkcd->ij', l2, t2*2-t2.transpose(0,1,3,2))
#:theta = t2*2 - t2.transpose(0,1,3,2)
theta = _ccsd.make_0132(t2, t2, 2, -1)
mba = lib.dot(theta.reshape(-1, nvir).T, l2.reshape(-1, nvir))
mij = lib.dot(l2.reshape(nocc, -1), theta.reshape(nocc, -1).T)
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 -
numpy.einsum('kc,jkcb->jb', l1, t2) -
reduce(numpy.dot,
(t1, l1.T, t1)) - numpy.einsum('bd,jd->jb', mba, t1) -
numpy.einsum('lj,lb->jb', mij, t1))
tmp = mycc.add_wvvVV(numpy.zeros_like(l1), l2, eris, max_memory)
l2new = numpy.empty((nocc, nocc, nvir, nvir))
ij = 0
for i in range(nocc):
for j in range(i):
tmp1 = tmp[ij] * .5 # *.5 because of l2+l2.transpose(1,0,3,2) later
l2new[i, j] = tmp1
l2new[j, i] = tmp1.T
ij += 1
l2new[i, i] = tmp[ij] * .5
ij += 1
l1new = (numpy.einsum('ijab,jb->ia', l2new, t1) * 4 -
numpy.einsum('jiab,jb->ia', l2new, t1) * 2)
tmp = tmp1 = None
l1new += fov
l1new += numpy.einsum('ib,ba->ia', l1, saved.w1)
l1new -= numpy.einsum('ja,ij->ia', l1, saved.w2)
l1new -= numpy.einsum('ik,ka->ia', mij, saved.w4)
l1new -= numpy.einsum('ca,ic->ia', mba, saved.w4)
l1new += numpy.einsum('ijab,bj->ia', l2, saved.w3) * 2
l1new -= numpy.einsum('ijba,bj->ia', l2, saved.w3)
l2new += numpy.einsum('ia,jb->ijab', l1, saved.w4)
#:l2new += numpy.einsum('jibc,ca->jiba', l2, saved.w1)
#:l2new -= numpy.einsum('kiba,jk->jiba', l2, saved.w2)
lib.dot(l2.reshape(-1, nvir), saved.w1, 1, l2new.reshape(-1, nvir), 1)
lib.dot(saved.w2, l2.reshape(nocc, -1), -1, l2new.reshape(nocc, -1), 1)
eris_ooov = _cp(eris.ooov)
l1new -= numpy.einsum('jkia,kj->ia', eris_ooov, mij1) * 2
l1new += numpy.einsum('ikja,kj->ia', eris_ooov, mij1)
#:l2new -= numpy.einsum('ka,kijb->jiba', l1, eris_ooov)
lib.dot(
_cp(eris_ooov.transpose(0, 2, 1, 3).reshape(nocc, -1)).T, l1, -1,
l2new.reshape(-1, nvir), 1)
eris_ooov = None
tau = _ccsd.make_tau(t2, t1, t1)
#:l2tau = numpy.einsum('ijcd,klcd->ijkl', l2, tau)
l2tau = lib.dot(l2.reshape(nocc**2, -1),
tau.reshape(nocc**2, -1).T).reshape((nocc, ) * 4)
tau = None
#:l2t1 = numpy.einsum('jidc,kc->ijkd', l2, t1)
l2t1 = lib.dot(l2.reshape(-1, nvir), t1.T).reshape(nocc, nocc, nvir, nocc)
l2t1 = _cp(l2t1.transpose(1, 0, 3, 2))
max_memory = max_memory - lib.current_memory()[0]
unit = max(nvir**3 * 2 + nocc * nvir**2, 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))
for p0, p1 in prange(0, nocc, blksize):
eris_ovvv = _cp(eris.ovvv[p0:p1])
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape((p1 - p0) * nvir, -1))
eris_ovvv = eris_ovvv.reshape(p1 - p0, nvir, nvir, nvir)
l1new[p0:p1] += numpy.einsum('iabc,bc->ia', eris_ovvv, mba1) * 2
l1new[p0:p1] -= numpy.einsum('ibca,bc->ia', eris_ovvv, mba1)
#:l2new[p0:p1] += numpy.einsum('ic,jbac->jiba', l1, eris_ovvv)
tmp = lib.dot(l1, eris_ovvv.reshape(-1, nvir).T)
l2new[p0:p1] += tmp.reshape(nocc, -1, nvir, nvir).transpose(1, 0, 2, 3)
tmp = None
m4buf = numpy.empty((blksize, nocc, nvir, nvir))
eris_ovvv = _cp(eris_ovvv.transpose(0, 2, 1, 3).reshape(-1, nvir**2))
for j0, j1 in prange(0, nocc, blksize):
#:m4 = numpy.einsum('ijkd,kadb->ijab', l2t1[j0:j1,:,p0:p1], eris_ovvv)
m4 = m4buf[:j1 - j0]
lib.dot(_cp(l2t1[j0:j1, :, p0:p1].reshape((j1 - j0) * nocc, -1)),
eris_ovvv, 1, m4.reshape(-1, nvir**2))
l2new[j0:j1] -= m4
l1new[j0:j1] -= numpy.einsum('ijab,jb->ia', m4, t1) * 2
l1new -= numpy.einsum('ijab,ia->jb', m4, t1[j0:j1]) * 2
l1new += numpy.einsum('jiab,jb->ia', m4, t1[j0:j1])
l1new[j0:j1] += numpy.einsum('jiab,ia->jb', m4, t1)
eris_ovvv = m4buf = m4 = None
#==== mem usage nvir**3*2 + nocc*nvir**2
eris_ovov = _cp(eris.ovov[p0:p1])
l1new[p0:p1] += numpy.einsum('jb,iajb->ia', l1, eris_ovov) * 2
for i in range(p1 - p0):
l2new[p0 + i] += eris_ovov[i].transpose(1, 0, 2) * .5
#:l2new[p0:p1] -= numpy.einsum('icjb,ca->ijab', eris_ovov, mba1)
#:l2new[p0:p1] -= numpy.einsum('jbka,ik->jiba', eris_ovov, mij1)
tmp = numpy.empty((nocc, nvir, nvir))
for j in range(p0, p1):
lib.dot(eris_ovov[j - p0].reshape(nvir, -1).T, mba1, 1,
tmp.reshape(-1, nvir))
l2new[j] -= tmp.transpose(0, 2, 1)
lib.dot(
mij1,
_cp(eris_ovov[j - p0].transpose(1, 0, 2).reshape(nocc, -1)),
-1, l2new[j].reshape(nocc, -1), 1)
tmp = None
l1new[p0:p1] += numpy.einsum('iajb,jb->ia', eris_ovov, mia1) * 2
l1new[p0:p1] -= numpy.einsum('ibja,jb->ia', eris_ovov, mia1)
m4buf = numpy.empty((blksize, nocc, nvir, nvir))
for j0, j1 in prange(0, nocc, blksize):
#:m4 = numpy.einsum('kalb,ijkl->ijab', eris_ovov, l2tau[j0:j1,:,p0:p1])
m4 = m4buf[:j1 - j0]
lib.dot(
l2tau[j0:j1, :, p0:p1].reshape((j1 - j0) * nocc, -1).copy(),
_cp(eris_ovov.transpose(0, 2, 1, 3).reshape(-1, nvir**2)), .5,
m4.reshape(-1, nvir**2))
l2new[j0:j1] += m4
l1new[j0:j1] += numpy.einsum('ijab,jb->ia', m4, t1) * 4
l1new[j0:j1] -= numpy.einsum('ijba,jb->ia', m4, t1) * 2
eris_ovov = m4buf = m4 = None
#==== mem usage nocc*nvir**2 * 3
eris_oovv = _cp(eris.oovv[p0:p1])
l1new[p0:p1] -= numpy.einsum('jb,ijba->ia', l1, eris_oovv)
eris_oovv = None
saved_wooov = _cp(saved.wooov[p0:p1])
#:l1new[p0:p1] -= numpy.einsum('jkca,ijkc->ia', l2, saved_wooov)
l1new[p0:p1] -= lib.dot(saved_wooov.reshape(p1 - p0, -1),
l2.reshape(-1, nvir))
saved_wovvv = _cp(saved.wovvv[p0:p1])
#:l1new += numpy.einsum('kibc,kabc->ia', l2[p0:p1], saved_wovvv)
for j in range(p1 - p0):
lib.dot(l2[p0 + j].reshape(nocc, -1),
saved_wovvv[j].reshape(nvir, -1).T, 1, l1new, 1)
saved_wooov = saved_wovvv = None
#==== mem usage nvir**3 + nocc**2*nvir
saved_wOvOv = _cp(saved.wOvOv[p0:p1])
tmp_ovov = _cp(saved.wOVov[p0:p1]) * 2
tmp_ovov += saved_wOvOv
tmp_ovov = lib.transpose(tmp_ovov.reshape(-1, nov)).reshape(
nocc, nvir, -1, nvir)
tmp1 = numpy.empty((p1 - p0, nvir, nocc, nvir))
tmp = numpy.empty((blksize, nvir, nocc, nvir))
for j0, j1 in prange(0, nocc, blksize):
#:tmp = l2[j0:j1].transpose(0,2,1,3) - l2[j0:j1].transpose(0,3,1,2)*.5
#:l2new[p0:p1] += numpy.einsum('kcia,kcjb->jiba', tmp, tmp_ovov[j0:j1])
for i in range(j1 - j0):
tmp[i] = -.5 * l2[j0 + i].transpose(2, 0, 1)
tmp[i] += l2[j0 + i].transpose(1, 0, 2)
lib.dot(tmp_ovov[j0:j1].reshape((j1 - j0) * nvir, -1).T,
tmp[:j1 - j0].reshape((j1 - j0) * nvir, -1), 1,
tmp1.reshape(-1, nov))
l2new[p0:p1] += tmp1.transpose(0, 2, 1, 3)
tmp = tmp1 = tmp_ovov = None
#==== mem usage nocc*nvir**2 * 5
#:tmp = numpy.einsum('jkca,ibkc->ijab', l2, saved_wOvOv)
tmp = numpy.empty((p1 - p0, nvir, nvir))
for j in range(nocc):
lib.dot(saved_wOvOv.reshape(-1, nov), l2[j].reshape(nov, -1), 1,
tmp.reshape(-1, nvir))
l2new[p0:p1, j] += tmp.transpose(0, 2, 1)
l2new[p0:p1, j] += tmp * .5
saved_wOvOv = tmp = None
saved_woooo = _cp(saved.woooo[p0:p1])
#:m3 = numpy.einsum('klab,ijkl->ijab', l2, saved_woooo)
m3 = lib.dot(saved_woooo.reshape(-1, nocc**2), l2.reshape(nocc**2, -1),
.5).reshape(-1, nocc, nvir, nvir)
l2new[p0:p1] += m3
l1new[p0:p1] += numpy.einsum('ijab,jb->ia', m3, t1) * 4
l1new[p0:p1] -= numpy.einsum('ijba,jb->ia', m3, t1) * 2
saved_woooo = m3 = None
time1 = log.timer_debug1('lambda pass [%d:%d]' % (p0, p1), *time1)
mo_e = eris.fock.diagonal()
eia = lib.direct_sum('i-a->ia', mo_e[:nocc], mo_e[nocc:])
l1new /= eia
l1new += l1
# l2new = l2new + l2new.transpose(1,0,3,2)
# l2new /= lib.direct_sum('ia+jb->ijab', eia, eia)
# l2new += l2
ij = 0
for i in range(nocc):
for j in range(i):
dab = lib.direct_sum('a+b->ab', eia[i], eia[j])
tmp = (l2new[i, j] + l2new[j, i].T) / dab + l2[i, j]
l2new[i, j] = tmp
l2new[j, i] = tmp.T
ij += 1
dab = lib.direct_sum('a+b->ab', eia[i], eia[i])
l2new[i, i] = (l2new[i, i] + l2new[i, i].T) / dab + l2[i, i]
ij += 1
time0 = log.timer_debug1('update l1 l2', *time0)
return l1new, l2new
def make_intermediates(mycc, t1, t2, eris, max_memory=2000):
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
foo = eris.fock[:nocc,:nocc]
fov = eris.fock[:nocc,nocc:]
fvv = eris.fock[nocc:,nocc:]
class _Saved(object):
def __init__(self):
self._tmpfile = tempfile.NamedTemporaryFile()
self.ftmp = h5py.File(self._tmpfile.name)
def __del__(self):
if hasattr(self, 'ftmp'):
self.ftmp.close()
self._tmpfile = None
saved = _Saved()
saved.woooo = saved.ftmp.create_dataset('woooo', (nocc,nocc,nocc,nocc), 'f8')
saved.wooov = saved.ftmp.create_dataset('wooov', (nocc,nocc,nocc,nvir), 'f8')
saved.wOVov = saved.ftmp.create_dataset('wOVov', (nocc,nvir,nocc,nvir), 'f8')
saved.wOvOv = saved.ftmp.create_dataset('wOvOv', (nocc,nvir,nocc,nvir), 'f8')
saved.wovvv = saved.ftmp.create_dataset('wovvv', (nocc,nvir,nvir,nvir), 'f8')
# As we don't have l2 in memory, hold tau temporarily in memory
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 += reduce(numpy.dot, (t1.T, fov, t1.T))
w4 = fov.copy()
_tmpfile = tempfile.NamedTemporaryFile()
fswap = h5py.File(_tmpfile.name)
time1 = time.clock(), time.time()
max_memory = max_memory - lib.current_memory()[0]
unit = max(nocc*nvir**2*4 + nvir**3*2,
nvir**3*3 + nocc*nvir**2,
nocc*nvir**2*6 + nocc**2*nvir + nocc**3 + nocc**2*nvir)
blksize = max(ccsd.BLKMIN, int(max_memory*.95e6/8/unit))
log.debug1('ccsd lambda make_intermediates: block size = %d, nocc = %d in %d blocks',
blksize, nocc, int((nocc+blksize-1)//blksize))
for istep, (p0, p1) in enumerate(prange(0, nocc, blksize)):
eris_ovvv = _cp(eris.ovvv[p0:p1])
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape((p1-p0)*nvir,-1))
eris_ovvv = eris_ovvv.reshape(p1-p0,nvir,nvir,nvir)
w1 += numpy.einsum('jcba,jc->ba', eris_ovvv, t1[p0:p1]*2)
w1 -= numpy.einsum('jabc,jc->ba', eris_ovvv, t1[p0:p1])
#:w3 += numpy.einsum('kdcb,kjdc->bj', eris_ovvv, theta)
for i in range(p1-p0):
theta = t2[p0+i] * 2
theta -= t2[p0+i].transpose(0,2,1)
w3 += lib.dot(eris_ovvv[i].reshape(-1,nvir).T,
_cp(theta.reshape(nocc,-1)).T)
theta = None
#:wOVov = numpy.einsum('jbcd,kd->jbkc', eris_ovvv, t1)
#:wOvOv = numpy.einsum('jdcb,kd->jbkc', eris_ovvv, -t1)
wOVov = lib.dot(eris_ovvv.reshape(-1,nvir),
t1.T).reshape(-1,nvir,nvir,nocc).transpose(0,1,3,2).copy()
g2ovvv = _cp(eris_ovvv.transpose(0,2,3,1))
wOvOv = lib.dot(g2ovvv.reshape(-1,nvir),
-t1.T).reshape(-1,nvir,nvir,nocc).transpose(0,1,3,2).copy()
for i in range(p1-p0):
g2ovvv[i] *= 2
g2ovvv[i] -= eris_ovvv[i].transpose(1,0,2)
wooov = numpy.empty((p1-p0,nocc,nocc,nvir))
woooo = numpy.empty((p1-p0,nocc,nocc,nocc))
eris_ovov = _cp(_cp(eris.ovov[p0:p1]).transpose(0,2,1,3))
for j0, j1 in prange(0, nocc, blksize):
tau = _ccsd.make_tau(t2[j0:j1], t1[j0:j1], t1)
#:wooov[:,j0:j1] = numpy.einsum('icbd,jkbd->ijkc', g2ovvv, tau)
#:woooo[:,:,j0:j1] = numpy.einsum('icjd,klcd->ijkl', eris_ovov, tau)
tmp = lib.dot(g2ovvv.reshape(-1,nvir**2), tau.reshape(-1,nvir**2).T)
wooov[:,j0:j1] = tmp.reshape(-1,nvir,j1-j0,nocc).transpose(0,2,3,1)
woooo[:,:,j0:j1] = lib.dot(eris_ovov.reshape(-1,nvir**2),
tau.reshape(-1,nvir**2).T).reshape(-1,nocc,j1-j0,nocc)
eris_ovov = eris_ovvv = g2ovvv = tau = tmp = None
#==== mem usage nocc*nvir**2*2 + nocc**2*nvir + nocc**3 + nvir**3*2 + nocc*nvir**2*2
eris_ooov = _cp(eris.ooov[p0:p1])
w2[p0:p1] += numpy.einsum('ijkb,kb->ij', eris_ooov, t1) * 2
w2 -= numpy.einsum('kjib,kb->ij', eris_ooov, t1[p0:p1])
#:w3 -= numpy.einsum('kjlc,klbc->bj', eris_ooov, theta)
for i in range(p1-p0):
theta = t2[p0+i].transpose(0,2,1) * 2
theta -= t2[p0+i]
w3 -= lib.dot(theta.reshape(-1,nvir).T, eris_ooov[i].reshape(nocc,-1).T)
theta = None
#:woooo += numpy.einsum('ikjc,lc->ijkl', eris_ooov, t1)
#:wOvOv += numpy.einsum('jklb,lc->jbkc', eris_ooov, t1)
woooo += lib.dot(eris_ooov.reshape(-1,nvir),
t1.T).reshape((-1,nocc,nocc,nocc)).transpose(0,2,1,3)
for i in range(p1-p0):
lib.dot(_cp(eris_ooov[i].transpose(2,0,1)).reshape(-1,nocc),
t1, 1, wOvOv[i].reshape(-1,nvir), 1)
wooov[i] += eris_ooov[i].transpose(1,0,2)*2
wooov[i] -= eris_ooov[i]
eris_ovoo = _cp(eris.ovoo[p0:p1])
#:woooo += numpy.einsum('icjl,kc->ijkl', eris_ovoo, t1)
#:wOVov += numpy.einsum('jbkl,lc->jbkc', eris_ovoo, -t1)
for i in range(p1-p0):
woooo[i] += lib.dot(t1, eris_ovoo[i].reshape(nvir,-1)).reshape((nocc,)*3).transpose(1,0,2)
lib.dot(eris_ovoo.reshape(-1,nocc), t1, -1, wOVov.reshape(-1,nvir), 1)
#:wooov -= numpy.einsum('iblj,klbc->ijkc', eris_ovoo*1.5, t2)
tmp_ovoo = _cp(-eris_ovoo.transpose(0,2,3,1)).reshape(-1,nov)
for j in range(nocc):
wooov[:,:,j] += lib.dot(tmp_ovoo, t2[j].reshape(-1,nvir),
1.5).reshape(-1,nocc,nvir)
#:g2ooov = eris_ooov * 2 - eris_ovoo.transpose(0,3,2,1)
g2ooov, tmp_ovoo = tmp_ovoo.reshape(p1-p0,nocc,nocc,nvir), None
g2ooov += eris_ooov * 2
thetabuf = numpy.empty((blksize,nvir,nocc,nvir))
vikjc = numpy.empty((p1-p0,nocc,blksize,nvir))
for j0, j1 in prange(0, nocc, blksize):
theta = thetabuf[:j1-j0]
for i in range(j1-j0):
theta[i] = t2[j0+i].transpose(1,0,2)*2 - t2[j0+i].transpose(2,0,1)
#:vikjc = numpy.einsum('iklb,jlcb->ikjc', g2ooov, theta)
if j1 == j0 + blksize:
lib.dot(g2ooov.reshape(-1,nov), _cp(theta.reshape(-1,nov)).T,
1, vikjc.reshape((p1-p0)*nocc,-1), 0)
else:
vikjc = lib.dot(g2ooov.reshape(-1,nov),
_cp(theta.reshape(-1,nov)).T)
vikjc = vikjc.reshape(p1-p0,nocc,j1-j0,nvir)
wooov[:,j0:j1,:] += vikjc.transpose(0,2,1,3)
wooov[:,:,j0:j1] -= vikjc*.5
eris_ooov = eris_ovoo = g2ooov = vikjc = theta = thetabuf = None
#==== mem usage nocc*nvir**2*3 + nocc**2*nvir + nocc**3 + nocc*nvir**2 + nocc**2*nvir*3
eris_ovov = _cp(eris.ovov[p0:p1])
g2ovov = eris_ovov*2
g2ovov -= eris_ovov.transpose(0,3,2,1)
tmpw4 = numpy.einsum('kcld,ld->kc', g2ovov, t1)
#:w1 -= numpy.einsum('kcja,kjcb->ba', g2ovov, t2[p0:p1])
w1 -= lib.dot(t2[p0:p1].reshape(-1,nvir).T,
_cp(g2ovov.transpose(0,2,1,3).reshape(-1,nvir)))
w1 -= numpy.einsum('ja,jb->ba', tmpw4, t1[p0:p1])
#:w2[p0:p1] += numpy.einsum('ibkc,jkbc->ij', g2ovov, t2)
w2[p0:p1] += lib.dot(_cp(g2ovov.transpose(0,2,1,3)).reshape(p1-p0,-1),
t2.reshape(nocc,-1).T)
w2[p0:p1] += numpy.einsum('ib,jb->ij', tmpw4, t1)
w3 += reduce(numpy.dot, (t1[p0:p1].T, tmpw4, t1.T))
w4[p0:p1] += tmpw4
vOVov = numpy.empty((nocc,nvir,p1-p0,nvir))
#:vOVov += numpy.einsum('jbld,klcd->kcjb', g2ovov, t2)
#:vOVov -= numpy.einsum('jbld,kldc->kcjb', eris_ovov, t2)
for j in range(nocc):
lib.dot(_cp(t2[j].transpose(1,0,2)).reshape(-1,nov),
g2ovov.reshape(-1,nov).T, 1, vOVov[j].reshape(nvir,-1))
lib.dot(t2[j].reshape(nov,-1).T, eris_ovov.reshape(-1,nov).T,
-1, vOVov[j].reshape(nvir,-1), 1)
vOVov = lib.transpose(vOVov.reshape(nov,-1)).reshape(p1-p0,nvir,nocc,nvir)
vOVov += eris_ovov
g2ovov = tmp = tmpw4 = None
#==== mem usage nocc*nvir**2*4 + nocc**2*nvir + nocc**3 + nocc*nvir**2
#:tmp = numpy.einsum('jbld,kd->jlbk', eris_ovov, t1)
#:wOVov -= numpy.einsum('jlbk,lc->jbkc', tmp, t1)
#:tmp = numpy.einsum('jdlb,kd->jlbk', eris_ovov, t1)
#:wOvOv += numpy.einsum('jlbk,lc->jbkc', tmp, t1)
tmp = numpy.empty((nocc,nvir,nocc))
for j in range(p1-p0):
lib.dot(_cp(eris_ovov[j].transpose(1,0,2)).reshape(-1,nvir),
t1.T, 1, tmp.reshape(-1,nocc))
lib.dot(tmp.reshape(nocc,-1).T, t1, -1, wOVov[j].reshape(-1,nvir), 1)
lib.dot(eris_ovov[j].reshape(nvir,-1).T, t1.T, 1,
tmp.reshape(-1,nocc))
lib.dot(tmp.reshape(nocc,-1).T, t1, 1, wOvOv[j].reshape(-1,nvir), 1)
tmp = None
#:vOvOv = numpy.einsum('jdlb,kldc->kcjb', eris_ovov, t2)
ovovtmp = _cp(eris_ovov.transpose(0,3,2,1)).reshape(-1,nov)
vOvOv = numpy.empty((nocc,nvir,p1-p0,nvir))
for j in range(nocc):
lib.dot(t2[j].reshape(-1,nvir).T, ovovtmp.T, 1,
vOvOv[j].reshape(nvir,-1))
ovovtmp = eris_ovov = None
vOvOv = lib.transpose(vOvOv.reshape(nov,-1)).reshape(p1-p0,nvir,nocc,nvir)
vOvOv -= _cp(eris.oovv[p0:p1]).transpose(0,3,1,2)
wOVov += vOVov
wOvOv += vOvOv
saved.wOVov[p0:p1] = wOVov
saved.wOvOv[p0:p1] = wOvOv
wOVov = wOvOv = None
#==== mem usage nocc*nvir**2*6 + nocc**2*nvir + nocc**3 + nocc**2*nvir
ov1 = vOvOv*2 + vOVov
#:wooov -= numpy.einsum('ibkc,jb->ijkc', ov1, t1)
for i in range(p1-p0):
lib.dot(t1, ov1[i].reshape(nvir,-1), -1, wooov[i].reshape(nocc,-1), 1)
ov1 = lib.transpose(ov1.reshape(-1,nov))
fswap['2vOvOv/%d'%istep] = ov1.reshape(nocc,nvir,-1,nvir)
ov1 = None
ov2 = vOVov*2 + vOvOv
w3 += numpy.einsum('kcjb,kc->bj', ov2, t1[p0:p1])
#:wooov += numpy.einsum('ibjc,kb->ijkc', ov2, t1)
for i in range(p1-p0):
wooov[i] += lib.dot(t1, ov2[i].reshape(nvir,-1)).reshape(nocc,nocc,nvir).transpose(1,0,2)
ov2 = lib.transpose(ov2.reshape(-1,nov))
fswap['2vovOV/%d'%istep] = ov2.reshape(nocc,nvir,-1,nvir)
vOVov = vOvOv = None
ov2 = None
#==== mem usage nocc*nvir**2*5 + nocc**2*nvir + nocc**3
woooo += _cp(eris.oooo[p0:p1]).transpose(0,2,1,3)
saved.woooo[p0:p1] = woooo
saved.wooov[p0:p1] = wooov
woooo = wooov = None
time1 = log.timer_debug1('pass1 [%d:%d]'%(p0, p1), *time1)
w3 += numpy.einsum('bc,jc->bj', w1, t1)
w3 -= numpy.einsum('kj,kb->bj', w2, t1)
for p0, p1 in prange(0, nocc, blksize):
eris_ooov = _cp(eris.ooov[p0:p1])
g2ooov = eris_ooov * 2
g2ooov -= eris_ooov.transpose(0,2,1,3)
#:tmp = numpy.einsum('kjla,jb->kabl', g2ooov, t1)
#:wovvv = numpy.einsum('kabl,lc->kabc', tmp, t1)
#:wovvv += numpy.einsum('kjla,jlbc->kabc', g2ooov, t2)
tmp = lib.dot(_cp(g2ooov.transpose(1,0,2,3).reshape(nocc,-1)).T,
t1).reshape(-1,nocc,nvir,nvir).transpose(0,2,3,1)
wovvv = lib.dot(_cp(tmp.reshape(-1,nocc)), t1).reshape(-1,nvir,nvir,nvir)
wovvv += lib.dot(_cp(g2ooov.transpose(0,3,1,2).reshape(-1,nocc**2)),
t2.reshape(nocc**2,-1)).reshape(-1,nvir,nvir,nvir)
tmp = g2ooov = None
ov1 = numpy.empty((p1-p0,nvir,nocc,nvir))
ov2 = numpy.empty((p1-p0,nvir,nocc,nvir))
for istep, (j0, j1) in enumerate(prange(0, nocc, blksize)):
ov1[:,:,j0:j1] = fswap['2vOvOv/%d'%istep][p0:p1]
ov2[:,:,j0:j1] = fswap['2vovOV/%d'%istep][p0:p1]
#:wovvv += numpy.einsum('kcja,jb->kabc', ov1, t1)
#:wovvv -= numpy.einsum('kbja,jc->kabc', ov2, t1)
wovvv += lib.dot(_cp(ov1.transpose(0,1,3,2).reshape(-1,nocc)),
t1).reshape(-1,nvir,nvir,nvir).transpose(0,2,3,1)
wovvv -= lib.dot(_cp(ov2.transpose(0,1,3,2).reshape(-1,nocc)),
t1).reshape(-1,nvir,nvir,nvir).transpose(0,2,1,3)
#==== mem usage nvir**3 + nocc*nvir**2*2
eris_ooov = ov1 = ov2 = None
for j0, j1 in prange(0, nocc, blksize):
eris_ovvv = _cp(eris.ovvv[j0:j1])
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape((j1-j0)*nvir,-1))
eris_ovvv = eris_ovvv.reshape(j1-j0,nvir,nvir,nvir)
#:wovvv += numpy.einsum('jabd,kjdc->kabc', eris_ovvv, t2[p0:p1,j0:j1]) * -1.5
tmp_ovvv = numpy.empty((j1-j0,nvir,nvir,nvir))
for i in range(j1-j0):
tmp_ovvv[i] = eris_ovvv[i].transpose(1,0,2)*2
tmp = lib.dot(_cp(t2[p0:p1,j0:j1].transpose(0,3,1,2).reshape((p1-p0)*nvir,-1)),
tmp_ovvv.reshape(-1,nvir**2), -1.5/2).reshape(-1,nvir,nvir,nvir)
wovvv += tmp.transpose(0,2,3,1)
if p0 == j0:
for i in range(p1-p0):
tmp_ovvv[i] -= eris_ovvv[i].transpose(1,2,0)
wovvv[i] += tmp_ovvv[i]
tmp = tmp_ovvv = None
g2ovvv = numpy.empty((j1-j0,nvir,nvir,nvir))
for i in range(j1-j0):
g2ovvv[i] = eris_ovvv[i] * 2
g2ovvv[i] -= eris_ovvv[i].transpose(1,2,0)
#==== mem usage nvir**3*3
eris_ovvv = None
theta = _cp(t2[p0:p1,j0:j1].transpose(0,2,1,3)*2)
for i in range(p1-p0):
theta[i] -= t2[p0+i,j0:j1].transpose(2,0,1)
#:vkbca = numpy.einsum('jdca,kbjd->kbca', g2ovvv, theta)
vkbca = lib.dot(theta.reshape((p1-p0)*nvir,-1),
g2ovvv.reshape(-1,nvir*nvir)).reshape(-1,nvir,nvir,nvir)
wovvv += vkbca.transpose(0,3,1,2)
wovvv -= vkbca.transpose(0,3,2,1) * .5
#==== mem usage nvir**3*3 + nocc*nvir**2
g2ovvv = theta = vkabc = None
saved.wovvv[p0:p1] = wovvv
time1 = log.timer_debug1('pass2 [%d:%d]'%(p0, p1), *time1)
fswap.close()
saved.w1 = w1
saved.w2 = w2
saved.w3 = w3
saved.w4 = w4
saved.ftmp.flush()
return saved
def update_amps(mycc, t1, t2, l1, l2, eris=None, saved=None, max_memory=2000):
if saved is None:
saved = make_intermediates(mycc, t1, t2, eris)
time1 = time0 = time.clock(), time.time()
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
foo = eris.fock[:nocc,:nocc]
fov = eris.fock[:nocc,nocc:]
fvv = eris.fock[:nocc,:nocc]
#:mba = numpy.einsum('klca,klcb->ba', l2, t2*2-t2.transpose(0,1,3,2))
#:mij = numpy.einsum('ikcd,jkcd->ij', l2, t2*2-t2.transpose(0,1,3,2))
#:theta = t2*2 - t2.transpose(0,1,3,2)
theta = _ccsd.make_0132(t2, t2, 2, -1)
mba = lib.dot(theta.reshape(-1,nvir).T, l2.reshape(-1,nvir))
mij = lib.dot(l2.reshape(nocc,-1), theta.reshape(nocc,-1).T)
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
- numpy.einsum('kc,jkcb->jb', l1, t2)
- reduce(numpy.dot, (t1, l1.T, t1))
- numpy.einsum('bd,jd->jb', mba, t1)
- numpy.einsum('lj,lb->jb', mij, t1))
tmp = mycc.add_wvvVV(numpy.zeros_like(l1), l2, eris, max_memory)
l2new = numpy.empty((nocc,nocc,nvir,nvir))
ij = 0
for i in range(nocc):
for j in range(i):
tmp1 = tmp[ij] * .5 # *.5 because of l2+l2.transpose(1,0,3,2) later
l2new[i,j] = tmp1
l2new[j,i] = tmp1.T
ij += 1
l2new[i,i] = tmp[ij] * .5
ij += 1
l1new =(numpy.einsum('ijab,jb->ia', l2new, t1) * 4
- numpy.einsum('jiab,jb->ia', l2new, t1) * 2)
tmp = tmp1 = None
l1new += fov
l1new += numpy.einsum('ib,ba->ia', l1, saved.w1)
l1new -= numpy.einsum('ja,ij->ia', l1, saved.w2)
l1new -= numpy.einsum('ik,ka->ia', mij, saved.w4)
l1new -= numpy.einsum('ca,ic->ia', mba, saved.w4)
l1new += numpy.einsum('ijab,bj->ia', l2, saved.w3) * 2
l1new -= numpy.einsum('ijba,bj->ia', l2, saved.w3)
l2new += numpy.einsum('ia,jb->ijab', l1, saved.w4)
#:l2new += numpy.einsum('jibc,ca->jiba', l2, saved.w1)
#:l2new -= numpy.einsum('kiba,jk->jiba', l2, saved.w2)
lib.dot(l2.reshape(-1,nvir), saved.w1, 1, l2new.reshape(-1,nvir), 1)
lib.dot(saved.w2, l2.reshape(nocc,-1),-1, l2new.reshape(nocc,-1), 1)
eris_ooov = _cp(eris.ooov)
l1new -= numpy.einsum('jkia,kj->ia', eris_ooov, mij1) * 2
l1new += numpy.einsum('ikja,kj->ia', eris_ooov, mij1)
#:l2new -= numpy.einsum('ka,kijb->jiba', l1, eris_ooov)
lib.dot(_cp(eris_ooov.transpose(0,2,1,3).reshape(nocc,-1)).T,
l1, -1, l2new.reshape(-1,nvir), 1)
eris_ooov = None
tau = _ccsd.make_tau(t2, t1, t1)
#:l2tau = numpy.einsum('ijcd,klcd->ijkl', l2, tau)
l2tau = lib.dot(l2.reshape(nocc**2,-1),
tau.reshape(nocc**2,-1).T).reshape((nocc,)*4)
tau = None
#:l2t1 = numpy.einsum('jidc,kc->ijkd', l2, t1)
l2t1 = lib.dot(l2.reshape(-1,nvir), t1.T).reshape(nocc,nocc,nvir,nocc)
l2t1 = _cp(l2t1.transpose(1,0,3,2))
max_memory = max_memory - lib.current_memory()[0]
unit = max(nvir**3*2+nocc*nvir**2, 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))
for p0, p1 in prange(0, nocc, blksize):
eris_ovvv = _cp(eris.ovvv[p0:p1])
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape((p1-p0)*nvir,-1))
eris_ovvv = eris_ovvv.reshape(p1-p0,nvir,nvir,nvir)
l1new[p0:p1] += numpy.einsum('iabc,bc->ia', eris_ovvv, mba1) * 2
l1new[p0:p1] -= numpy.einsum('ibca,bc->ia', eris_ovvv, mba1)
#:l2new[p0:p1] += numpy.einsum('ic,jbac->jiba', l1, eris_ovvv)
tmp = lib.dot(l1, eris_ovvv.reshape(-1,nvir).T)
l2new[p0:p1] += tmp.reshape(nocc,-1,nvir,nvir).transpose(1,0,2,3)
tmp = None
m4buf = numpy.empty((blksize,nocc,nvir,nvir))
eris_ovvv = _cp(eris_ovvv.transpose(0,2,1,3).reshape(-1,nvir**2))
for j0, j1 in prange(0, nocc, blksize):
#:m4 = numpy.einsum('ijkd,kadb->ijab', l2t1[j0:j1,:,p0:p1], eris_ovvv)
m4 = m4buf[:j1-j0]
lib.dot(_cp(l2t1[j0:j1,:,p0:p1].reshape((j1-j0)*nocc,-1)),
eris_ovvv, 1, m4.reshape(-1,nvir**2))
l2new[j0:j1] -= m4
l1new[j0:j1] -= numpy.einsum('ijab,jb->ia', m4, t1) * 2
l1new -= numpy.einsum('ijab,ia->jb', m4, t1[j0:j1]) * 2
l1new += numpy.einsum('jiab,jb->ia', m4, t1[j0:j1])
l1new[j0:j1] += numpy.einsum('jiab,ia->jb', m4, t1)
eris_ovvv = m4buf = m4 = None
#==== mem usage nvir**3*2 + nocc*nvir**2
eris_ovov = _cp(eris.ovov[p0:p1])
l1new[p0:p1] += numpy.einsum('jb,iajb->ia', l1, eris_ovov) * 2
for i in range(p1-p0):
l2new[p0+i] += eris_ovov[i].transpose(1,0,2) * .5
#:l2new[p0:p1] -= numpy.einsum('icjb,ca->ijab', eris_ovov, mba1)
#:l2new[p0:p1] -= numpy.einsum('jbka,ik->jiba', eris_ovov, mij1)
tmp = numpy.empty((nocc,nvir,nvir))
for j in range(p0,p1):
lib.dot(eris_ovov[j-p0].reshape(nvir,-1).T, mba1, 1,
tmp.reshape(-1,nvir))
l2new[j] -= tmp.transpose(0,2,1)
lib.dot(mij1, _cp(eris_ovov[j-p0].transpose(1,0,2).reshape(nocc,-1)),
-1, l2new[j].reshape(nocc,-1), 1)
tmp = None
l1new[p0:p1] += numpy.einsum('iajb,jb->ia', eris_ovov, mia1) * 2
l1new[p0:p1] -= numpy.einsum('ibja,jb->ia', eris_ovov, mia1)
m4buf = numpy.empty((blksize,nocc,nvir,nvir))
for j0, j1 in prange(0, nocc, blksize):
#:m4 = numpy.einsum('kalb,ijkl->ijab', eris_ovov, l2tau[j0:j1,:,p0:p1])
m4 = m4buf[:j1-j0]
lib.dot(l2tau[j0:j1,:,p0:p1].reshape((j1-j0)*nocc,-1).copy(),
_cp(eris_ovov.transpose(0,2,1,3).reshape(-1,nvir**2)),
.5, m4.reshape(-1,nvir**2))
l2new[j0:j1] += m4
l1new[j0:j1] += numpy.einsum('ijab,jb->ia', m4, t1) * 4
l1new[j0:j1] -= numpy.einsum('ijba,jb->ia', m4, t1) * 2
eris_ovov = m4buf = m4 = None
#==== mem usage nocc*nvir**2 * 3
eris_oovv = _cp(eris.oovv[p0:p1])
l1new[p0:p1] -= numpy.einsum('jb,ijba->ia', l1, eris_oovv)
eris_oovv = None
saved_wooov = _cp(saved.wooov[p0:p1])
#:l1new[p0:p1] -= numpy.einsum('jkca,ijkc->ia', l2, saved_wooov)
l1new[p0:p1] -= lib.dot(saved_wooov.reshape(p1-p0,-1),
l2.reshape(-1,nvir))
saved_wovvv = _cp(saved.wovvv[p0:p1])
#:l1new += numpy.einsum('kibc,kabc->ia', l2[p0:p1], saved_wovvv)
for j in range(p1-p0):
lib.dot(l2[p0+j].reshape(nocc,-1),
saved_wovvv[j].reshape(nvir,-1).T, 1, l1new, 1)
saved_wooov = saved_wovvv = None
#==== mem usage nvir**3 + nocc**2*nvir
saved_wOvOv = _cp(saved.wOvOv[p0:p1])
tmp_ovov = _cp(saved.wOVov[p0:p1]) * 2
tmp_ovov += saved_wOvOv
tmp_ovov = lib.transpose(tmp_ovov.reshape(-1,nov)).reshape(nocc,nvir,-1,nvir)
tmp1 = numpy.empty((p1-p0,nvir,nocc,nvir))
tmp = numpy.empty((blksize,nvir,nocc,nvir))
for j0, j1 in prange(0, nocc, blksize):
#:tmp = l2[j0:j1].transpose(0,2,1,3) - l2[j0:j1].transpose(0,3,1,2)*.5
#:l2new[p0:p1] += numpy.einsum('kcia,kcjb->jiba', tmp, tmp_ovov[j0:j1])
for i in range(j1-j0):
tmp[i] = -.5 * l2[j0+i].transpose(2,0,1)
tmp[i] += l2[j0+i].transpose(1,0,2)
lib.dot(tmp_ovov[j0:j1].reshape((j1-j0)*nvir,-1).T,
tmp[:j1-j0].reshape((j1-j0)*nvir,-1), 1, tmp1.reshape(-1,nov))
l2new[p0:p1] += tmp1.transpose(0,2,1,3)
tmp = tmp1 = tmp_ovov = None
#==== mem usage nocc*nvir**2 * 5
#:tmp = numpy.einsum('jkca,ibkc->ijab', l2, saved_wOvOv)
tmp = numpy.empty((p1-p0,nvir,nvir))
for j in range(nocc):
lib.dot(saved_wOvOv.reshape(-1,nov), l2[j].reshape(nov,-1), 1,
tmp.reshape(-1,nvir))
l2new[p0:p1,j] += tmp.transpose(0,2,1)
l2new[p0:p1,j] += tmp * .5
saved_wOvOv = tmp = None
saved_woooo = _cp(saved.woooo[p0:p1])
#:m3 = numpy.einsum('klab,ijkl->ijab', l2, saved_woooo)
m3 = lib.dot(saved_woooo.reshape(-1,nocc**2),
l2.reshape(nocc**2,-1), .5).reshape(-1,nocc,nvir,nvir)
l2new[p0:p1] += m3
l1new[p0:p1] += numpy.einsum('ijab,jb->ia', m3, t1) * 4
l1new[p0:p1] -= numpy.einsum('ijba,jb->ia', m3, t1) * 2
saved_woooo = m3 = None
time1 = log.timer_debug1('lambda pass [%d:%d]'%(p0, p1), *time1)
mo_e = eris.fock.diagonal()
eia = lib.direct_sum('i-a->ia', mo_e[:nocc], mo_e[nocc:])
l1new /= eia
l1new += l1
# l2new = l2new + l2new.transpose(1,0,3,2)
# l2new /= lib.direct_sum('ia+jb->ijab', eia, eia)
# l2new += l2
ij = 0
for i in range(nocc):
for j in range(i):
dab = lib.direct_sum('a+b->ab', eia[i], eia[j])
tmp = (l2new[i,j]+l2new[j,i].T) / dab + l2[i,j]
l2new[i,j] = tmp
l2new[j,i] = tmp.T
ij += 1
dab = lib.direct_sum('a+b->ab', eia[i], eia[i])
l2new[i,i] = (l2new[i,i]+l2new[i,i].T)/dab + l2[i,i]
ij += 1
time0 = log.timer_debug1('update l1 l2', *time0)
return l1new, l2new
def IX_intermediates(mycc, t1, t2, l1, l2, d1=None, d2=None, eris=None):
if d1 is None:
doo, dov, dvo, dvv = ccsd_t_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2, eris)
else:
doo, dov, dvo, dvv = d1
if d2 is None:
# Note gamma2 are in Chemist's notation
d2 = ccsd_t_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
else:
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
if dovvv is None:
dovvv = dvvov.transpose(2,3,0,1)
elif dvvov is None:
dvvov = dovvv.transpose(2,3,0,1)
nocc, nvir = t1.shape
eris_ovvv = _ccsd.unpack_tril(_cp(eris.ovvv).reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
eris_vvvv = pyscf.ao2mo.restore(1, _cp(eris.vvvv), nvir)
dvvvv = pyscf.ao2mo.restore(1, _cp(dvvvv), nvir)
# Note Ioo is not hermitian
Ioo =(numpy.einsum('jakb,iakb->ij', dovov, eris.ovov)
+ numpy.einsum('kbja,iakb->ij', dovov, eris.ovov))
Ioo +=(numpy.einsum('jabk,iakb->ij', dovvo, eris.ovov)
+ numpy.einsum('kbaj,iakb->ij', dovvo, eris.ovov)
+ numpy.einsum('jkab,ikab->ij', doovv, eris.oovv)
+ numpy.einsum('kjba,ikab->ij', doovv, eris.oovv))
Ioo +=(numpy.einsum('jmlk,imlk->ij', doooo, eris.oooo) * 2
+ numpy.einsum('mjkl,imlk->ij', doooo, eris.oooo) * 2)
Ioo +=(numpy.einsum('jlka,ilka->ij', dooov, eris.ooov)
+ numpy.einsum('klja,klia->ij', dooov, eris.ooov))
Ioo += numpy.einsum('abjc,icab->ij', dvvov, eris_ovvv)
Ioo += numpy.einsum('ljka,lika->ij', dooov, eris.ooov)
Ioo *= -1
# Note Ivv is not hermitian
Ivv =(numpy.einsum('ibjc,iajc->ab', dovov, eris.ovov)
+ numpy.einsum('jcib,iajc->ab', dovov, eris.ovov))
Ivv +=(numpy.einsum('jcbi,iajc->ab', dovvo, eris.ovov)
+ numpy.einsum('ibcj,iajc->ab', dovvo, eris.ovov)
+ numpy.einsum('jibc,jiac->ab', doovv, eris.oovv)
+ numpy.einsum('ijcb,jiac->ab', doovv, eris.oovv))
Ivv +=(numpy.einsum('bced,aced->ab', dvvvv, eris_vvvv) * 2
+ numpy.einsum('cbde,aced->ab', dvvvv, eris_vvvv) * 2)
Ivv +=(numpy.einsum('dbic,icda->ab', dvvov, eris_ovvv)
+ numpy.einsum('dcib,iadc->ab', dvvov, eris_ovvv))
Ivv += numpy.einsum('bcid,idac->ab', dvvov, eris_ovvv)
Ivv += numpy.einsum('jikb,jika->ab', dooov, eris.ooov)
Ivv *= -1
Ivo =(numpy.einsum('kajb,kijb->ai', dovov, eris.ooov)
+ numpy.einsum('kbja,jikb->ai', dovov, eris.ooov))
Ivo +=(numpy.einsum('acbd,icbd->ai', dvvvv, eris_ovvv) * 2
+ numpy.einsum('cadb,icbd->ai', dvvvv, eris_ovvv) * 2)
Ivo +=(numpy.einsum('jbak,jbik->ai', dovvo, eris.ovoo)
+ numpy.einsum('kabj,jbik->ai', dovvo, eris.ovoo)
+ numpy.einsum('jkab,jkib->ai', doovv, eris.ooov)
+ numpy.einsum('kjba,jkib->ai', doovv, eris.ooov))
Ivo +=(numpy.einsum('dajc,idjc->ai', dvvov, eris.ovov)
+ numpy.einsum('dcja,jidc->ai', dvvov, eris.oovv))
Ivo += numpy.einsum('abjc,ibjc->ai', dvvov, eris.ovov)
Ivo += numpy.einsum('jlka,jlki->ai', dooov, eris.oooo)
Ivo *= -1
Xvo =(numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2
+ numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2
- numpy.einsum('kj,kija->ai', doo, eris.ooov)
- numpy.einsum('kj,ijka->ai', doo, eris.ooov))
Xvo +=(numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 2
+ numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 2
- numpy.einsum('cb,icab->ai', dvv, eris_ovvv)
- numpy.einsum('cb,ibca->ai', dvv, eris_ovvv))
Xvo +=(numpy.einsum('icjb,jbac->ai', dovov, eris_ovvv)
+ numpy.einsum('jcib,jcab->ai', dovov, eris_ovvv))
Xvo +=(numpy.einsum('iklj,ljka->ai', doooo, eris.ooov) * 2
+ numpy.einsum('kijl,ljka->ai', doooo, eris.ooov) * 2)
Xvo +=(numpy.einsum('ibcj,jcab->ai', dovvo, eris_ovvv)
+ numpy.einsum('jcbi,jcab->ai', dovvo, eris_ovvv)
+ numpy.einsum('ijcb,jacb->ai', doovv, eris_ovvv)
+ numpy.einsum('jibc,jacb->ai', doovv, eris_ovvv))
Xvo +=(numpy.einsum('ijkb,jakb->ai', dooov, eris.ovov)
+ numpy.einsum('kjib,kjab->ai', dooov, eris.oovv))
Xvo += numpy.einsum('dbic,dbac->ai', dvvov, eris_vvvv)
Xvo += numpy.einsum('jikb,jakb->ai', dooov, eris.ovov)
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def update_amps(cc, t1, t2, eris):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nocc, nvir = t1.shape
nov = nocc*nvir
fock = eris.fock
t1new = numpy.zeros_like(t1)
t2new = numpy.zeros_like(t2)
#** make_inter_F
fov = fock[:nocc,nocc:].copy()
foo = fock[:nocc,:nocc].copy()
foo[range(nocc),range(nocc)] = 0
foo += .5 * numpy.einsum('ia,ja->ij', fock[:nocc,nocc:], t1)
fvv = fock[nocc:,nocc:].copy()
fvv[range(nvir),range(nvir)] = 0
fvv -= .5 * numpy.einsum('ia,ib->ab', t1, fock[:nocc,nocc:])
#: woooo = numpy.einsum('la,ikja->ikjl', t1, eris.ooov)
eris_ooov = _cp(eris.ooov)
foo += numpy.einsum('kc,jikc->ij', 2*t1, eris_ooov)
foo += numpy.einsum('kc,jkic->ij', -t1, eris_ooov)
woooo = lib.dot(eris_ooov.reshape(-1,nvir), t1.T).reshape((nocc,)*4)
woooo = lib.transpose_sum(woooo.reshape(nocc*nocc,-1), inplace=True)
woooo += _cp(eris.oooo).reshape(nocc**2,-1)
woooo = _cp(woooo.reshape(nocc,nocc,nocc,nocc).transpose(0,2,1,3))
time1 = log.timer_debug1('woooo', *time0)
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nov,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
fvv += numpy.einsum('kc,kcba->ab', 2*t1, eris_ovvv)
fvv += numpy.einsum('kc,kbca->ab', -t1, eris_ovvv)
#: woVoV = numpy.einsum('ka,ijkb->ijba', t1, eris.ooov)
#: woVoV -= numpy.einsum('jc,icab->ijab', t1, eris_ovvv)
woVoV = lib.dot(_cp(eris_ooov.transpose(0,1,3,2).reshape(-1,nocc)), t1)
woVoV = woVoV.reshape(nocc,nocc,nvir,nvir)
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: tmp = numpy.einsum('ijcd,kcdb->kijb', tau, eris.ovvv)
#: t2new += numpy.einsum('ka,kijb->jiba', -t1, tmp)
tau = make_tau(t2, t1, t1)
tmp = numpy.empty((nocc,nocc,nocc,nvir))
for k in range(nocc):
tmp[k] = lib.dot(tau.reshape(-1,nvir**2),
eris_ovvv[k].reshape(-1,nvir)).reshape(nocc,nocc,nvir).transpose(1,0,2)
lib.dot(t1, eris_ovvv[k].reshape(nvir,-1), -1, woVoV[k].reshape(nocc,-1), 1)
lib.dot(tmp.reshape(nocc,-1).T, t1, -1, t2new.reshape(-1,nvir), 1)
tmp = None
#: wOVov += numpy.einsum('iabc,jc->ijab', eris.ovvv, t1)
#: wOVov -= numpy.einsum('jbik,ka->jiba', eris.ovoo, t1)
#: t2new += woVoV.transpose()
#: wOVov = -numpy.einsum('jbik,ka->ijba', eris.ovoo, t1)
wOVov, tau = tau, None
lib.dot(_cp(_cp(eris.ooov).transpose(0,2,3,1).reshape(-1,nocc)), t1,
-1, wOVov.reshape(-1,nvir))
#: wOVov += numpy.einsum('iabc,jc->jiab', eris_ovvv, t1)
lib.dot(t1, eris_ovvv.reshape(-1,nvir).T, 1, wOVov.reshape(nocc,-1), 1)
for i in range(nocc):
t2new[i] += wOVov[i].transpose(0,2,1)
#: theta = t2.transpose(0,1,3,2) * 2 - t2
#: t1new += numpy.einsum('ijcb,jcba->ia', theta, eris.ovvv)
theta = numpy.empty((nocc,nocc,nvir,nvir))
for i in range(nocc):
theta[i] = t2[i].transpose(0,2,1) * 2
theta[i] -= t2[i]
lib.dot(_cp(theta[i].transpose(0,2,1).reshape(nocc,-1)),
eris_ovvv[i].reshape(-1,nvir), 1, t1new, 1)
eris_ovvv = None
eris_ovov = _cp(eris.ovov)
for i in range(nocc):
t2new[i] += eris_ovov[i].transpose(1,0,2) * .5
fov += numpy.einsum('kc,iakc->ia', t1, eris_ovov) * 2
fov -= numpy.einsum('kc,icka->ia', t1, eris_ovov)
#: theta = t2.transpose(1,0,2,3) * 2 - t2
#: t1new += numpy.einsum('jb,ijab->ia', fov, theta)
#: t1new -= numpy.einsum('ikjb,kjab->ia', eris.ooov, theta)
t1new += numpy.einsum('jb,jiab->ia', fov, theta)
#: t1new -= numpy.einsum('kijb,kjab->ia', eris.ooov, theta)
lib.dot(_cp(eris_ooov.transpose(1,0,2,3).reshape(nocc,-1)),
theta.reshape(-1,nvir), -1, t1new, 1)
eris_ooov = None
#: wOVov += eris.ovov.transpose(0,1,3,2)
#: theta = t2.transpose(1,0,2,3) * 2 - t2
#: tau = theta - numpy.einsum('ic,kb->ikcb', t1, t1*2)
#: wOVov += .5 * numpy.einsum('jakc,ikcb->jiba', eris.ovov, tau)
#: wOVov -= .5 * numpy.einsum('jcka,ikcb->jiba', eris.ovov, t2)
#: t2new += numpy.einsum('ikca,kjbc->ijba', theta, wOVov)
wOVov = _cp(wOVov.transpose(0,3,1,2))
eris_OVov = lib.transpose(eris_ovov.reshape(-1,nov)).reshape(nocc,nvir,-1,nvir)
eris_OvoV = _cp(eris_OVov.transpose(0,3,2,1))
wOVov += eris_OVov
t2iajb = t2.transpose(0,2,1,3).copy()
#: wOVov[j0:j1] -= .5 * numpy.einsum('iakc,jkbc->jbai', eris_ovov, t2)
lib.dot(t2iajb.reshape(-1,nov), eris_OvoV.reshape(nov,-1),
-.5, wOVov.reshape(nov,-1), 1)
tau, t2iajb = t2iajb, None
for i in range(nocc):
tau[i] = tau[i]*2 - t2[i].transpose(2,0,1)
tau[i] -= numpy.einsum('a,jb->bja', t1[i]*2, t1)
#: wOVov += .5 * numpy.einsum('iakc,jbkc->jbai', eris_ovov, tau)
lib.dot(tau.reshape(-1,nov), eris_OVov.reshape(nov,-1),
.5, wOVov.reshape(nov,-1), 1)
#theta = t2 * 2 - t2.transpose(0,1,3,2)
#: t2new[j0:j1] += numpy.einsum('iack,jbck->jiba', theta, wOVov[j0:j1])
tmp, tau = tau, None
theta = _cp(theta.transpose(0,3,1,2).reshape(nov,-1))
lib.dot(wOVov.reshape(nov,-1), theta.T, 1, tmp.reshape(nov,-1))
for i in range(nocc):
t2new[i] += tmp[i].transpose(1,0,2)
tmp = wOVov = eris_OvoV = eris_OVov = None
#: fvv -= numpy.einsum('ijca,ibjc->ab', theta, eris.ovov)
#: foo += numpy.einsum('iakb,jkba->ij', eris.ovov, theta)
for i in range(nocc):
tau = numpy.einsum('a,jb->jab', t1[i]*.5, t1) + t2[i]
theta = tau.transpose(0,2,1)*2 - tau
lib.dot(_cp(eris_ovov[i].transpose(1,2,0)).reshape(nocc,-1),
theta.reshape(nocc,-1).T, 1, foo, 1)
lib.dot(theta.reshape(-1,nvir).T,
eris_ovov[i].reshape(nvir,-1).T, -1, fvv, 1)
tau = theta = None
eris_oovv = _cp(eris.oovv)
#:tmp = numpy.einsum('ic,jkbc->jibk', t1, eris_oovv)
#:t2new += numpy.einsum('ka,jibk->jiab', -t1, tmp)
#:tmp = numpy.einsum('ic,jbkc->jibk', t1, eris_ovov)
#:t2new += numpy.einsum('ka,jibk->jiba', -t1, tmp)
for j in range(nocc):
tmp = lib.dot(t1, eris_oovv[j].reshape(-1,nvir).T)
tmp = _cp(tmp.reshape(nocc,nocc,nvir).transpose(0,2,1))
t2new[j] += lib.dot(tmp.reshape(-1,nocc), t1,
-1).reshape(nocc,nvir,nvir).transpose(0,2,1)
lib.dot(t1, eris_ovov[j].reshape(-1,nvir).T, 1, tmp.reshape(nocc,-1))
lib.dot(tmp.reshape(-1,nocc), t1, -1, t2new[j].reshape(-1,nvir), 1)
tmp = None
#: g2 = 2 * eris.oOVv - eris.oovv
#: t1new += numpy.einsum('jb,ijba->ia', t1, g2)
t1new += numpy.einsum('jb,iajb->ia', 2*t1, eris_ovov)
t1new += numpy.einsum('jb,ijba->ia', -t1, eris_oovv)
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: woooo += numpy.einsum('ijba,klab->ijkl', eris.oOVv, tau)
#: woVoV -= eris.oovv
#: tau = .5*t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: woVoV += numpy.einsum('ka,ijkb->ijab', t1, eris.ooov)
#: woVoV += numpy.einsum('jkca,ikbc->ijab', tau, eris.oOVv)
woVoV -= eris_oovv
woVoV = woVoV.transpose(1,3,0,2).copy()
eris_oVOv = _cp(eris_ovov.transpose(0,3,2,1))
eris_oOvV = _cp(eris_ovov.transpose(0,2,1,3))
tau = make_tau(t2, t1, t1)
#: woooo += numpy.einsum('ijab,klab->ijkl', eris_oOvV, tau)
lib.dot(eris_oOvV.reshape(-1,nvir**2), tau.reshape(-1,nvir**2).T,
1, woooo.reshape(nocc**2,-1), 1)
#: t2new += .5 * numpy.einsum('klij,klab->ijab', woooo, tau)
lib.dot(woooo.reshape(-1,nocc*nocc).T, tau.reshape(-1,nvir*nvir),
.5, t2new.reshape(nocc*nocc,-1), 1)
for i in range(nocc):
tau[i] -= t2[i] * .5
#: woVoV[j0:j1] += numpy.einsum('jkca,ickb->jiab', tau, eris_ovov)
tau = _cp(tau.transpose(0,3,1,2))
lib.dot(tau.reshape(-1,nov), eris_oVOv.reshape(-1,nov).T,
1, woVoV.reshape(nov,-1), 1)
eris_oovv = eris_ovov = eris_oOvV = taubuf = None
tmp, tau = tau, None
t2ibja, eris_oVOv = eris_oVOv, None
for i in range(nocc):
t2ibja[i] = t2[i].transpose(2,0,1)
#: t2new += numpy.einsum('ibkc,kcja->ijab', woVoV, t2ibja)
lib.dot(woVoV.reshape(nov,-1), t2ibja.reshape(-1,nov), 1, tmp.reshape(nov,-1))
for i in range(nocc):
t2new[i] += tmp[i].transpose(1,2,0)
#: t2new[j0:j1] += numpy.einsum('iakc,kcjb->ijab', woVoV[j0:j1], t2iajb)
t2iajb = t2ibja
for i in range(nocc):
t2iajb[i] = t2[i].transpose(1,0,2)
lib.dot(woVoV.reshape(nov,-1), t2iajb.reshape(-1,nov), 1, tmp.reshape(nov,-1))
for i in range(nocc):
t2new[i] += tmp[i].transpose(1,0,2)
t2ibja = t2iajb = woVoV = tmp = None
time1 = log.timer_debug1('contract loop', *time0)
woooo = None
ft_ij = foo + numpy.einsum('ja,ia->ij', .5*t1, fov)
ft_ab = fvv - numpy.einsum('ia,ib->ab', .5*t1, fov)
#: t2new += numpy.einsum('ijac,bc->ijab', t2, ft_ab)
#: t2new -= numpy.einsum('ki,kjab->ijab', ft_ij, t2)
lib.dot(t2.reshape(-1,nvir), ft_ab.T, 1, t2new.reshape(-1,nvir), 1)
lib.dot(ft_ij.T, t2.reshape(nocc,-1),-1, t2new.reshape(nocc,-1), 1)
#: t2new = t2new + t2new.transpose(1,0,3,2)
t2new_tril = numpy.empty((nocc*(nocc+1)//2,nvir,nvir))
ij = 0
for i in range(nocc):
for j in range(i+1):
t2new_tril[ij] = t2new[i,j]
t2new_tril[ij] += t2new[j,i].T
ij += 1
t2new = None
time1 = log.timer_debug1('t2 tril', *time1)
cc.add_wvvVV_(t1, t2, eris, t2new_tril)
time1 = log.timer_debug1('vvvv', *time1)
mo_e = fock.diagonal()
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
p0 = 0
for i in range(nocc):
dajb = (eia[i].reshape(-1,1) + eia[:i+1].reshape(1,-1))
t2new_tril[p0:p0+i+1] /= dajb.reshape(nvir,i+1,nvir).transpose(1,0,2)
p0 += i+1
time1 = log.timer_debug1('g2/dijab', *time1)
t2new = numpy.empty((nocc,nocc,nvir,nvir))
ij = 0
for i in range(nocc):
for j in range(i):
t2new[i,j] = t2new_tril[ij]
t2new[j,i] = t2new_tril[ij].T
ij += 1
t2new[i,i] = t2new_tril[ij]
ij += 1
t2new_tril = None
#** update_amp_t1
t1new += fock[:nocc,nocc:] \
+ numpy.einsum('ib,ab->ia', t1, fvv) \
- numpy.einsum('ja,ji->ia', t1, foo)
mo_e = fock.diagonal()
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
t1new /= eia
#** end update_amp_t1
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def update_amps(cc, t1, t2, eris, max_memory=2000):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nocc, nvir = t1.shape
nov = nocc*nvir
fock = eris.fock
t1new = numpy.zeros_like(t1)
t2new = numpy.zeros_like(t2)
#** make_inter_F
fov = fock[:nocc,nocc:].copy()
foo = fock[:nocc,:nocc].copy()
foo[range(nocc),range(nocc)] = 0
foo += .5 * numpy.einsum('ia,ja->ij', fock[:nocc,nocc:], t1)
fvv = fock[nocc:,nocc:].copy()
fvv[range(nvir),range(nvir)] = 0
fvv -= .5 * numpy.einsum('ia,ib->ab', t1, fock[:nocc,nocc:])
#: woooo = numpy.einsum('la,ikja->ikjl', t1, eris.ooov)
eris_ooov = _cp(eris.ooov)
foo += numpy.einsum('kc,jikc->ij', 2*t1, eris_ooov)
foo += numpy.einsum('kc,jkic->ij', -t1, eris_ooov)
woooo = lib.dot(eris_ooov.reshape(-1,nvir), t1.T).reshape((nocc,)*4)
woooo = lib.transpose_sum(woooo.reshape(nocc*nocc,-1), inplace=True)
woooo += _cp(eris.oooo).reshape(nocc**2,-1)
woooo = _cp(woooo.reshape(nocc,nocc,nocc,nocc).transpose(0,2,1,3))
eris_ooov = None
time1 = log.timer_debug1('woooo', *time0)
unit = _memory_usage_inloop(nocc, nvir)*1e6/8
max_memory = max_memory - lib.current_memory()[0]
blksize = max(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))
for p0, p1 in prange(0, nocc, blksize):
# ==== read eris.ovvv ====
eris_ovvv = _cp(eris.ovvv[p0:p1])
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape((p1-p0)*nvir,-1))
eris_ovvv = eris_ovvv.reshape(p1-p0,nvir,nvir,nvir)
fvv += numpy.einsum('kc,kcba->ab', 2*t1[p0:p1], eris_ovvv)
fvv += numpy.einsum('kc,kbca->ab', -t1[p0:p1], eris_ovvv)
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: tmp = numpy.einsum('ijcd,kdcb->ijbk', tau, eris.ovvv)
#: t2new += numpy.einsum('ka,ijbk->ijba', -t1, tmp)
#: eris_vvov = eris_ovvv.transpose(1,2,0,3).copy()
eris_vvov = _cp(eris_ovvv.transpose(2,1,0,3).reshape(nvir*nvir,-1))
tmp = numpy.empty((nocc,nocc,p1-p0,nvir))
taubuf = numpy.empty((blksize,nocc,nvir,nvir))
for j0, j1 in prange(0, nocc, blksize):
tau = make_tau(t2[j0:j1], t1[j0:j1], t1, 1, out=taubuf[:j1-j0])
lib.dot(tau.reshape(-1,nvir*nvir), eris_vvov, 1,
tmp[j0:j1].reshape((j1-j0)*nocc,-1), 0)
tmp = _cp(tmp.transpose(0,1,3,2).reshape(-1,p1-p0))
lib.dot(tmp, t1[p0:p1], -1, t2new.reshape(-1,nvir), 1)
tau = tmp = eris_vvov = None
#==== mem usage blksize*(nvir**3*2+nvir*nocc**2*2)
#: wOVov += numpy.einsum('iabc,jc->ijab', eris.ovvv, t1)
#: wOVov -= numpy.einsum('jbik,ka->jiba', eris.ovoo, t1)
#: t2new += woVoV.transpose()
#: wOVov = -numpy.einsum('jbik,ka->ijba', eris.ovoo[p0:p1], t1)
tmp = _cp(eris.ovoo[p0:p1].transpose(2,0,1,3))
wOVov = lib.dot(tmp.reshape(-1,nocc), t1, -1)
tmp = None
wOVov = wOVov.reshape(nocc,p1-p0,nvir,nvir)
#: wOVov += numpy.einsum('iabc,jc->jiab', eris_ovvv, t1)
lib.dot(t1, eris_ovvv.reshape(-1,nvir).T, 1, wOVov.reshape(nocc,-1), 1)
t2new[p0:p1] += wOVov.transpose(1,0,2,3)
eris_ooov = _cp(eris.ooov[p0:p1])
#: woVoV = numpy.einsum('ka,ijkb->ijba', t1, eris.ooov[p0:p1])
#: woVoV -= numpy.einsum('jc,icab->ijab', t1, eris_ovvv)
woVoV = lib.dot(_cp(eris_ooov.transpose(0,1,3,2).reshape(-1,nocc)), t1)
woVoV = woVoV.reshape(p1-p0,nocc,nvir,nvir)
for i in range(eris_ovvv.shape[0]):
lib.dot(t1, eris_ovvv[i].reshape(nvir,-1), -1,
woVoV[i].reshape(nocc,-1), 1)
#: theta = t2.transpose(0,1,3,2) * 2 - t2
#: t1new += numpy.einsum('ijcb,jcba->ia', theta, eris.ovvv)
theta = numpy.empty((p1-p0,nocc,nvir,nvir))
for i in range(p1-p0):
theta[i] = t2[p0+i].transpose(0,2,1) * 2
theta[i] -= t2[p0+i]
lib.dot(_cp(theta[i].transpose(0,2,1).reshape(nocc,-1)),
eris_ovvv[i].reshape(-1,nvir), 1, t1new, 1)
eris_ovvv = None
time2 = log.timer_debug1('ovvv [%d:%d]'%(p0, p1), *time1)
#==== mem usage blksize*(nvir**3+nocc*nvir**2*4)
# ==== read eris.ovov ====
eris_ovov = _cp(eris.ovov[p0:p1])
#==== mem usage blksize*(nocc*nvir**2*4)
for i in range(p1-p0):
t2new[p0+i] += eris_ovov[i].transpose(1,0,2) * .5
fov[p0:p1] += numpy.einsum('kc,iakc->ia', t1, eris_ovov) * 2
fov[p0:p1] -= numpy.einsum('kc,icka->ia', t1, eris_ovov)
#: theta = t2.transpose(1,0,2,3) * 2 - t2
#: t1new += numpy.einsum('jb,ijba->ia', fov, theta)
#: t1new -= numpy.einsum('kijb,kjba->ia', eris_ooov, theta)
t1new += numpy.einsum('jb,jiab->ia', fov[p0:p1], theta)
#: t1new -= numpy.einsum('kijb,kjab->ia', eris.ooov[p0:p1], theta)
lib.dot(_cp(eris_ooov.transpose(1,0,2,3).reshape(nocc,-1)),
theta.reshape(-1,nvir), -1, t1new, 1)
eris_ooov = None
#: wOVov += eris.ovov.transpose(0,1,3,2)
#: theta = t2.transpose(1,0,2,3) * 2 - t2
#: tau = theta - numpy.einsum('ic,kb->ikcb', t1, t1*2)
#: wOVov += .5 * numpy.einsum('jakc,ikcb->jiba', eris.ovov, tau)
#: wOVov -= .5 * numpy.einsum('jcka,ikcb->jiba', eris.ovov, t2)
#: t2new += numpy.einsum('ikca,kjbc->ijba', theta, wOVov)
theta = _cp(theta.transpose(0,3,1,2))
wOVov = _cp(wOVov.transpose(0,3,1,2))
eris_OVov = lib.transpose(eris_ovov.reshape(-1,nov)).reshape(nocc,nvir,-1,nvir)
eris_OvoV = _cp(eris_OVov.transpose(0,3,2,1))
wOVov += eris_OVov
for j0, j1 in prange(0, nocc, blksize):
t2iajb = t2[j0:j1].transpose(0,2,1,3).copy()
#: wOVov[j0:j1] -= .5 * numpy.einsum('iack,jkbc->jbai', eris_ovov, t2)
lib.dot(t2iajb.reshape(-1,nov), eris_OvoV.reshape(nov,-1),
-.5, wOVov[j0:j1].reshape((j1-j0)*nvir,-1), 1)
tau, t2iajb = t2iajb, None
for i in range(j1-j0):
tau[i] *= 2
tau[i] -= t2[j0+i].transpose(2,0,1)
tau[i] -= numpy.einsum('a,jb->bja', t1[j0+i]*2, t1)
#: wOVov[j0:j1] += .5 * numpy.einsum('iakc,jbkc->jbai', eris_ovov, tau)
lib.dot(tau.reshape(-1,nov), eris_OVov.reshape(nov,-1),
.5, wOVov[j0:j1].reshape((j1-j0)*nvir,-1), 1)
#theta = t2[p0:p1] * 2 - t2[p0:p1].transpose(0,1,3,2)
#: t2new[j0:j1] += numpy.einsum('iack,jbck->jiba', theta, wOVov[j0:j1])
tmp, tau = tau, None
lib.dot(wOVov[j0:j1].reshape((j1-j0)*nvir,-1), theta.reshape(-1,nov),
1, tmp.reshape(-1,nov))
for i in range(j1-j0):
t2new[j0+i] += tmp[i].transpose(1,0,2)
tmp = None
#==== mem usage blksize*(nocc*nvir**2*8)
theta = wOVov = eris_OvoV = eris_OVov = None
time2 = log.timer_debug1('wOVov [%d:%d]'%(p0, p1), *time2)
#==== mem usage blksize*(nocc*nvir**2*2)
#: fvv -= numpy.einsum('ijca,ibjc->ab', theta, eris.ovov)
#: foo += numpy.einsum('iakb,jkba->ij', eris.ovov, theta)
for i in range(p1-p0):
tau = numpy.einsum('a,jb->jab', t1[p0+i]*.5, t1)
tau += t2[p0+i]
theta = tau.transpose(0,2,1) * 2
theta -= tau
lib.dot(_cp(eris_ovov[i].transpose(1,2,0)).reshape(nocc,-1),
theta.reshape(nocc,-1).T, 1, foo, 1)
lib.dot(theta.reshape(-1,nvir).T,
eris_ovov[i].reshape(nvir,-1).T, -1, fvv, 1)
tau = theta = None
# ==== read eris.oovv ====
eris_oovv = _cp(eris.oovv[p0:p1])
#==== mem usage blksize*(nocc*nvir**2*3)
#:tmp = numpy.einsum('ic,jkbc->jibk', t1, eris_oovv)
#:t2new[p0:p1] += numpy.einsum('ka,jibk->jiab', -t1, tmp)
#:tmp = numpy.einsum('ic,jbkc->jibk', t1, eris_ovov)
#:t2new[p0:p1] += numpy.einsum('ka,jibk->jiba', -t1, tmp)
for j in range(p1-p0):
tmp = lib.dot(t1, eris_oovv[j].reshape(-1,nvir).T)
tmp = _cp(tmp.reshape(nocc,nocc,nvir).transpose(0,2,1))
t2new[p0+j] += lib.dot(tmp.reshape(-1,nocc), t1,
-1).reshape(nocc,nvir,nvir).transpose(0,2,1)
lib.dot(t1, eris_ovov[j].reshape(-1,nvir).T, 1, tmp.reshape(nocc,-1))
lib.dot(tmp.reshape(-1,nocc), t1, -1, t2new[p0+j].reshape(-1,nvir), 1)
tmp = None
#: g2 = 2 * eris.oOVv - eris.oovv
#: t1new += numpy.einsum('jb,ijba->ia', t1, g2)
t1new[p0:p1] += numpy.einsum('jb,iajb->ia', 2*t1, eris_ovov)
t1new[p0:p1] += numpy.einsum('jb,ijba->ia', -t1, eris_oovv)
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: woooo += numpy.einsum('ijba,klab->ijkl', eris.oOVv, tau)
#: woVoV -= eris.oovv
#: tau = .5*t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: woVoV += numpy.einsum('ka,ijkb->ijab', t1, eris.ooov)
#: woVoV += numpy.einsum('jkca,ikbc->ijab', tau, eris.oOVv)
woVoV -= eris_oovv
woVoV = woVoV.transpose(1,3,0,2).copy()
eris_oVOv = _cp(eris_ovov.transpose(0,3,2,1))
eris_oOvV = _cp(eris_ovov.transpose(0,2,1,3))
#==== mem usage blksize*(nocc*nvir**2*4)
taubuf = numpy.empty((blksize,nocc,nvir,nvir))
for j0, j1 in prange(0, nocc, blksize):
tau = make_tau(t2[j0:j1], t1[j0:j1], t1, 1, out=taubuf[:j1-j0])
#: woooo[p0:p1,:,j0:j1] += numpy.einsum('ijab,klab->ijkl', eris_oOvV, tau)
lib.numpy_helper._dgemm('N', 'T', (p1-p0)*nocc, (j1-j0)*nocc, nvir*nvir,
eris_oOvV.reshape(-1,nvir*nvir),
tau.reshape(-1,nvir*nvir),
woooo[p0:p1].reshape(-1,nocc*nocc), 1, 1,
0, 0, j0*nocc)
for i in range(j1-j0):
tau[i] -= t2[j0+i] * .5
#: woVoV[j0:j1] += numpy.einsum('jkca,ickb->jiab', tau, eris_ovov)
lib.dot(_cp(tau.transpose(0,3,1,2).reshape(-1,nov)),
eris_oVOv.reshape(-1,nov).T,
1, woVoV[j0:j1].reshape((j1-j0)*nvir,-1), 1)
#==== mem usage blksize*(nocc*nvir**2*6)
time2 = log.timer_debug1('woVoV [%d:%d]'%(p0, p1), *time2)
tau = make_tau(t2[p0:p1], t1[p0:p1], t1, 1, out=taubuf[:p1-p0])
#: t2new += .5 * numpy.einsum('klij,klab->ijab', woooo[p0:p1], tau)
lib.dot(woooo[p0:p1].reshape(-1,nocc*nocc).T, tau.reshape(-1,nvir*nvir),
.5, t2new.reshape(nocc*nocc,-1), 1)
eris_oovv = eris_ovov = eris_oVOv = eris_oOvV = taubuf = tau = None
#==== mem usage blksize*(nocc*nvir**2*1)
t2iajb = _cp(t2[p0:p1].transpose(0,2,1,3))
t2ibja = _cp(t2[p0:p1].transpose(0,3,1,2))
tmp = numpy.empty((blksize,nvir,nocc,nvir))
for j0, j1 in prange(0, nocc, blksize):
#: t2new[j0:j1] += numpy.einsum('ibkc,kcja->ijab', woVoV[j0:j1], t2ibja)
lib.dot(woVoV[j0:j1].reshape((j1-j0)*nvir,-1),
t2ibja.reshape(-1,nov), 1, tmp[:j1-j0].reshape(-1,nov))
for i in range(j1-j0):
t2new[j0+i] += tmp[i].transpose(1,2,0)
#: t2new[j0:j1] += numpy.einsum('iakc,kcjb->ijab', woVoV[j0:j1], t2iajb)
lib.dot(woVoV[j0:j1].reshape((j1-j0)*nvir,-1),
t2iajb.reshape(-1,nov), 1, tmp[:j1-j0].reshape(-1,nov))
for i in range(j1-j0):
t2new[j0+i] += tmp[i].transpose(1,0,2)
t2ibja = t2iajb = woVoV = tmp = None
#==== mem usage blksize*(nocc*nvir**2*3)
time1 = log.timer_debug1('contract occ [%d:%d]'%(p0, p1), *time1)
# ==================
time1 = log.timer_debug1('contract loop', *time0)
woooo = None
ft_ij = foo + numpy.einsum('ja,ia->ij', .5*t1, fov)
ft_ab = fvv - numpy.einsum('ia,ib->ab', .5*t1, fov)
#: t2new += numpy.einsum('ijac,bc->ijab', t2, ft_ab)
#: t2new -= numpy.einsum('ki,kjab->ijab', ft_ij, t2)
lib.dot(t2.reshape(-1,nvir), ft_ab.T, 1, t2new.reshape(-1,nvir), 1)
lib.dot(ft_ij.T, t2.reshape(nocc,-1),-1, t2new.reshape(nocc,-1), 1)
#: t2new = t2new + t2new.transpose(1,0,3,2)
t2new_tril = numpy.empty((nocc*(nocc+1)//2,nvir,nvir))
ij = 0
for i in range(nocc):
for j in range(i+1):
t2new_tril[ij] = t2new[i,j]
t2new_tril[ij] += t2new[j,i].T
ij += 1
t2new = None
time1 = log.timer_debug1('t2 tril', *time1)
cc.add_wvvVV_(t1, t2, eris, t2new_tril, max_memory)
time1 = log.timer_debug1('vvvv', *time1)
mo_e = fock.diagonal()
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
p0 = 0
for i in range(nocc):
dajb = (eia[i].reshape(-1,1) + eia[:i+1].reshape(1,-1))
t2new_tril[p0:p0+i+1] /= dajb.reshape(nvir,i+1,nvir).transpose(1,0,2)
p0 += i+1
time1 = log.timer_debug1('g2/dijab', *time1)
t2new = numpy.empty((nocc,nocc,nvir,nvir))
ij = 0
for i in range(nocc):
for j in range(i):
t2new[i,j] = t2new_tril[ij]
t2new[j,i] = t2new_tril[ij].T
ij += 1
t2new[i,i] = t2new_tril[ij]
ij += 1
t2new_tril = None
#** update_amp_t1
t1new += fock[:nocc,nocc:] \
+ numpy.einsum('ib,ab->ia', t1, fvv) \
- numpy.einsum('ja,ji->ia', t1, foo)
mo_e = fock.diagonal()
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
t1new /= eia
#** end update_amp_t1
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def update_amps(mycc, t1, t2, l1, l2, eris=None, saved=None):
if saved is None:
saved = make_intermediates(mycc, t1, t2, eris)
time1 = time0 = time.clock(), time.time()
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
foo = eris.fock[:nocc,:nocc]
fov = eris.fock[:nocc,nocc:]
fvv = eris.fock[:nocc,:nocc]
#:mba = numpy.einsum('klca,klcb->ba', l2, t2*2-t2.transpose(0,1,3,2))
#:mij = numpy.einsum('ikcd,jkcd->ij', l2, t2*2-t2.transpose(0,1,3,2))
#:theta = t2*2 - t2.transpose(0,1,3,2)
theta = _ccsd.make_0132(t2, t2, 2, -1)
mba = lib.dot(theta.reshape(-1,nvir).T, l2.reshape(-1,nvir))
mij = lib.dot(l2.reshape(nocc,-1), theta.reshape(nocc,-1).T)
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
- numpy.einsum('kc,jkcb->jb', l1, t2)
- reduce(numpy.dot, (t1, l1.T, t1))
- numpy.einsum('bd,jd->jb', mba, t1)
- numpy.einsum('lj,lb->jb', mij, t1))
tmp = mycc.add_wvvVV(numpy.zeros_like(l1), l2, eris)
l2new = numpy.empty((nocc,nocc,nvir,nvir))
ij = 0
for i in range(nocc):
for j in range(i):
tmp1 = tmp[ij] * .5 # *.5 because of l2+l2.transpose(1,0,3,2) later
l2new[i,j] = tmp1
l2new[j,i] = tmp1.T
ij += 1
l2new[i,i] = tmp[ij] * .5
ij += 1
l1new =(numpy.einsum('ijab,jb->ia', l2new, t1) * 4
- numpy.einsum('jiab,jb->ia', l2new, t1) * 2)
tmp = tmp1 = None
l1new += eris.fock[:nocc,nocc:]
l1new += numpy.einsum('ib,ba->ia', l1, saved.w1)
l1new -= numpy.einsum('ja,ij->ia', l1, saved.w2)
l1new -= numpy.einsum('ik,ka->ia', mij, saved.w4)
l1new -= numpy.einsum('ca,ic->ia', mba, saved.w4)
l1new += numpy.einsum('ijab,bj->ia', l2, saved.w3) * 2
l1new -= numpy.einsum('ijba,bj->ia', l2, saved.w3)
l2new += numpy.einsum('ia,jb->ijab', l1, saved.w4)
#:l2new += numpy.einsum('jibc,ca->jiba', l2, saved.w1)
#:l2new -= numpy.einsum('kiba,jk->jiba', l2, saved.w2)
lib.dot(l2.reshape(-1,nvir), saved.w1, 1, l2new.reshape(-1,nvir), 1)
lib.dot(saved.w2, l2.reshape(nocc,-1),-1, l2new.reshape(nocc,-1), 1)
eris_ooov = _cp(eris.ooov)
l1new -= numpy.einsum('jkia,kj->ia', eris_ooov, mij1) * 2
l1new += numpy.einsum('ikja,kj->ia', eris_ooov, mij1)
#:l2new -= numpy.einsum('ka,kijb->jiba', l1, eris_ooov)
lib.dot(_cp(eris_ooov.transpose(0,2,1,3).reshape(nocc,-1)).T,
l1, -1, l2new.reshape(-1,nvir), 1)
eris_ooov = None
tau = _ccsd.make_tau(t2, t1, t1)
#:l2tau = numpy.einsum('ijcd,klcd->ijkl', l2, tau)
l2tau = lib.dot(l2.reshape(nocc**2,-1),
tau.reshape(nocc**2,-1).T).reshape((nocc,)*4)
tau = None
l2t1 = numpy.einsum('ijcd,kc->ijkd', l2, t1)
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nov,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
l1new += numpy.einsum('iabc,bc->ia', eris_ovvv, mba1) * 2
l1new -= numpy.einsum('ibca,bc->ia', eris_ovvv, mba1)
#:l2new += numpy.einsum('ic,jbac->jiba', l1, eris_ovvv)
tmp = lib.dot(l1, eris_ovvv.reshape(-1,nvir).T).reshape(nocc,-1,nvir,nvir)
for i in range(nocc):
l2new[i] += tmp[i].transpose(0,2,1)
#:m4 = numpy.einsum('ijkd,kadb->ijab', l2t1, eris_ovvv)
m4 = tmp
lib.dot(_cp(l2t1.reshape(nocc*nocc,-1)),
_cp(eris_ovvv.transpose(0,2,1,3).reshape(-1,nvir**2)),
1, m4.reshape(nocc*nocc,-1))
l2new -= m4
l1new -= numpy.einsum('ijab,jb->ia', m4, t1) * 2
l1new -= numpy.einsum('ijab,ia->jb', m4, t1) * 2
l1new += numpy.einsum('jiab,jb->ia', m4, t1)
l1new += numpy.einsum('jiab,ia->jb', m4, t1)
eris_ovvv = tmp = None
eris_ovov = _cp(eris.ovov)
l1new += numpy.einsum('jb,iajb->ia', l1, eris_ovov) * 2
#:l2new -= numpy.einsum('jbic,ca->jiba', eris_ovov, mba1)
#:l2new -= numpy.einsum('kajb,ik->ijab', eris_ovov, mij1)
tmp = lib.dot(eris_ovov.reshape(-1,nvir), mba1).reshape(nocc,nvir,nocc,nvir)
lib.dot(mij1, eris_ovov.reshape(nocc,-1), 1, tmp.reshape(nocc,-1), 1)
tmp_oovv = numpy.empty((nocc,nocc,nvir,nvir))
for i in range(nocc):
tmp_oovv[i] = eris_ovov[i].transpose(1,0,2) * .5
l2new[i] += tmp_oovv[i]
l2new[i] -= tmp[i].transpose(1,0,2)
tmp = None
l1new += numpy.einsum('iajb,jb->ia', eris_ovov, mia1) * 2
l1new -= numpy.einsum('ibja,jb->ia', eris_ovov, mia1)
#:m4 = numpy.einsum('kalb,ijkl->ijab', eris_ovov, l2tau)
lib.dot(l2tau.reshape(nocc*nocc,-1), tmp_oovv.reshape(-1,nvir**2),
1, m4.reshape(nocc**2,-1))
l2new += m4
l1new += numpy.einsum('ijab,jb->ia', m4, t1) * 4
l1new -= numpy.einsum('ijba,jb->ia', m4, t1) * 2
eris_ovov = m4 = tmp_oovv = None
eris_oovv = _cp(eris.oovv)
l1new -= numpy.einsum('jb,ijba->ia', l1, eris_oovv)
eris_oovv = None
saved_wooov = _cp(saved.wooov)
#:l1new -= numpy.einsum('jkca,ijkc->ia', l2, saved_wooov)
l1new -= lib.dot(saved_wooov.reshape(nocc,-1), l2.reshape(-1,nvir))
saved_wovvv = _cp(saved.wovvv)
#:l1new += numpy.einsum('kibc,kabc->ia', l2, saved_wovvv)
for j in range(nocc):
l1new += lib.dot(l2[j].reshape(nocc,-1),
saved_wovvv[j].reshape(nvir,-1).T)
saved_wooov = saved_wovvv = None
saved_wOvOv = _cp(saved.wOvOv)
tmp_ovov = _cp(saved.wOVov) * 2
tmp_ovov += saved_wOvOv
#:tmp = l2.transpose(0,2,1,3) - l2.transpose(0,3,1,2)*.5
#:l2new += numpy.einsum('kcia,kcjb->jiba', tmp, tmp_ovov)
tmp = numpy.empty((nocc,nvir,nocc,nvir))
for i in range(nocc):
tmp[i] = l2[i].transpose(2,0,1)*-.5
tmp[i] += l2[i].transpose(1,0,2)
tmp = lib.dot(tmp_ovov.reshape(-1,nov),
tmp.reshape(nov,-1)).reshape(-1,nvir,nocc,nvir)
#:tmp = numpy.einsum('jkca,ibkc->ijab', l2, saved_wOvOv)
for i in range(nocc):
l2new[i] += tmp[i].transpose(1,0,2)
tmp_ovov[i] = l2[i].transpose(2,0,1)
lib.dot(saved_wOvOv.reshape(-1,nov), tmp_ovov.reshape(nov,-1),
1, tmp.reshape(nov,-1))
for i in range(nocc):
l2new[i] += tmp[i].transpose(1,2,0)
l2new[i] += tmp[i].transpose(1,0,2) * .5
saved_wOvOv = tmp = tmp_ovov = None
saved_woooo = _cp(saved.woooo)
#:m3 = numpy.einsum('klab,ijkl->ijab', l2, saved_woooo)
m3 = lib.dot(saved_woooo.reshape(-1,nocc**2),
l2.reshape(nocc**2,-1), .5).reshape(-1,nocc,nvir,nvir)
l2new += m3
l1new += numpy.einsum('ijab,jb->ia', m3, t1) * 4
l1new -= numpy.einsum('ijba,jb->ia', m3, t1) * 2
saved_woooo = m3 = None
mo_e = eris.fock.diagonal()
eia = lib.direct_sum('i-j->ij', mo_e[:nocc], mo_e[nocc:])
l1new /= eia
l1new += l1
# l2new = l2new + l2new.transpose(1,0,3,2)
# l2new /= lib.direct_sum('ia+jb->ijab', eia, eia)
# l2new += l2
ij = 0
for i in range(nocc):
for j in range(i):
dab = lib.direct_sum('a+b->ab', eia[i], eia[j])
tmp = (l2new[i,j]+l2new[j,i].T) / dab + l2[i,j]
l2new[i,j] = tmp
l2new[j,i] = tmp.T
ij += 1
dab = lib.direct_sum('a+b->ab', eia[i], eia[i])
l2new[i,i] = (l2new[i,i]+l2new[i,i].T)/dab + l2[i,i]
ij += 1
time0 = log.timer_debug1('update l1 l2', *time0)
return l1new, l2new
def update_amps(cc, t1, t2, eris):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nocc, nvir = t1.shape
nov = nocc*nvir
fock = eris.fock
t1new = numpy.zeros_like(t1)
t2new = numpy.zeros_like(t2)
#** make_inter_F
fov = fock[:nocc,nocc:].copy()
foo = fock[:nocc,:nocc].copy()
foo[range(nocc),range(nocc)] = 0
foo += .5 * numpy.einsum('ia,ja->ij', fock[:nocc,nocc:], t1)
fvv = fock[nocc:,nocc:].copy()
fvv[range(nvir),range(nvir)] = 0
fvv -= .5 * numpy.einsum('ia,ib->ab', t1, fock[:nocc,nocc:])
#: woooo = numpy.einsum('la,ikja->ikjl', t1, eris.ooov)
eris_ooov = _cp(eris.ooov)
foo += numpy.einsum('kc,jikc->ij', 2*t1, eris_ooov)
foo += numpy.einsum('kc,jkic->ij', -t1, eris_ooov)
woooo = lib.dot(eris_ooov.reshape(-1,nvir), t1.T).reshape((nocc,)*4)
woooo = lib.transpose_sum(woooo.reshape(nocc*nocc,-1), inplace=True)
woooo += _cp(eris.oooo).reshape(nocc**2,-1)
woooo = _cp(woooo.reshape(nocc,nocc,nocc,nocc).transpose(0,2,1,3))
time1 = log.timer_debug1('woooo', *time0)
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nov,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
fvv += numpy.einsum('kc,kcba->ab', 2*t1, eris_ovvv)
fvv += numpy.einsum('kc,kbca->ab', -t1, eris_ovvv)
#: woVoV = numpy.einsum('ka,ijkb->ijba', t1, eris.ooov)
#: woVoV -= numpy.einsum('jc,icab->ijab', t1, eris_ovvv)
woVoV = lib.dot(_cp(eris_ooov.transpose(0,1,3,2).reshape(-1,nocc)), t1)
woVoV = woVoV.reshape(nocc,nocc,nvir,nvir)
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: tmp = numpy.einsum('ijcd,kcdb->kijb', tau, eris.ovvv)
#: t2new += numpy.einsum('ka,kijb->jiba', -t1, tmp)
tau = make_tau(t2, t1, t1)
tmp = numpy.empty((nocc,nocc,nocc,nvir))
for k in range(nocc):
tmp[k] = lib.dot(tau.reshape(-1,nvir**2),
eris_ovvv[k].reshape(-1,nvir)).reshape(nocc,nocc,nvir).transpose(1,0,2)
lib.dot(t1, eris_ovvv[k].reshape(nvir,-1), -1, woVoV[k].reshape(nocc,-1), 1)
lib.dot(tmp.reshape(nocc,-1).T, t1, -1, t2new.reshape(-1,nvir), 1)
tmp = None
#: wOVov += numpy.einsum('iabc,jc->ijab', eris.ovvv, t1)
#: wOVov -= numpy.einsum('jbik,ka->jiba', eris.ovoo, t1)
#: t2new += woVoV.transpose()
#: wOVov = -numpy.einsum('jbik,ka->ijba', eris.ovoo, t1)
wOVov, tau = tau, None
lib.dot(_cp(_cp(eris.ooov).transpose(0,2,3,1).reshape(-1,nocc)), t1,
-1, wOVov.reshape(-1,nvir))
#: wOVov += numpy.einsum('iabc,jc->jiab', eris_ovvv, t1)
lib.dot(t1, eris_ovvv.reshape(-1,nvir).T, 1, wOVov.reshape(nocc,-1), 1)
for i in range(nocc):
t2new[i] += wOVov[i].transpose(0,2,1)
#: theta = t2.transpose(0,1,3,2) * 2 - t2
#: t1new += numpy.einsum('ijcb,jcba->ia', theta, eris.ovvv)
theta = numpy.empty((nocc,nocc,nvir,nvir))
for i in range(nocc):
theta[i] = t2[i].transpose(0,2,1) * 2
theta[i] -= t2[i]
lib.dot(_cp(theta[i].transpose(0,2,1).reshape(nocc,-1)),
eris_ovvv[i].reshape(-1,nvir), 1, t1new, 1)
eris_ovvv = None
eris_ovov = _cp(eris.ovov)
for i in range(nocc):
t2new[i] += eris_ovov[i].transpose(1,0,2) * .5
fov += numpy.einsum('kc,iakc->ia', t1, eris_ovov) * 2
fov -= numpy.einsum('kc,icka->ia', t1, eris_ovov)
#: theta = t2.transpose(1,0,2,3) * 2 - t2
#: t1new += numpy.einsum('jb,ijab->ia', fov, theta)
#: t1new -= numpy.einsum('ikjb,kjab->ia', eris.ooov, theta)
t1new += numpy.einsum('jb,jiab->ia', fov, theta)
#: t1new -= numpy.einsum('kijb,kjab->ia', eris.ooov, theta)
lib.dot(_cp(eris_ooov.transpose(1,0,2,3).reshape(nocc,-1)),
theta.reshape(-1,nvir), -1, t1new, 1)
eris_ooov = None
#: wOVov += eris.ovov.transpose(0,1,3,2)
#: theta = t2.transpose(1,0,2,3) * 2 - t2
#: tau = theta - numpy.einsum('ic,kb->ikcb', t1, t1*2)
#: wOVov += .5 * numpy.einsum('jakc,ikcb->jiba', eris.ovov, tau)
#: wOVov -= .5 * numpy.einsum('jcka,ikcb->jiba', eris.ovov, t2)
#: t2new += numpy.einsum('ikca,kjbc->ijba', theta, wOVov)
wOVov = _cp(wOVov.transpose(0,3,1,2))
eris_OVov = lib.transpose(eris_ovov.reshape(-1,nov)).reshape(nocc,nvir,-1,nvir)
eris_OvoV = _cp(eris_OVov.transpose(0,3,2,1))
wOVov += eris_OVov
t2iajb = t2.transpose(0,2,1,3).copy()
#: wOVov[j0:j1] -= .5 * numpy.einsum('iakc,jkbc->jbai', eris_ovov, t2)
lib.dot(t2iajb.reshape(-1,nov), eris_OvoV.reshape(nov,-1),
-.5, wOVov.reshape(nov,-1), 1)
tau, t2iajb = t2iajb, None
for i in range(nocc):
tau[i] = tau[i]*2 - t2[i].transpose(2,0,1)
tau[i] -= numpy.einsum('a,jb->bja', t1[i]*2, t1)
#: wOVov += .5 * numpy.einsum('iakc,jbkc->jbai', eris_ovov, tau)
lib.dot(tau.reshape(-1,nov), eris_OVov.reshape(nov,-1),
.5, wOVov.reshape(nov,-1), 1)
#theta = t2 * 2 - t2.transpose(0,1,3,2)
#: t2new[j0:j1] += numpy.einsum('iack,jbck->jiba', theta, wOVov[j0:j1])
tmp, tau = tau, None
theta = _cp(theta.transpose(0,3,1,2).reshape(nov,-1))
lib.dot(wOVov.reshape(nov,-1), theta.T, 1, tmp.reshape(nov,-1))
for i in range(nocc):
t2new[i] += tmp[i].transpose(1,0,2)
tmp = wOVov = eris_OvoV = eris_OVov = None
#: fvv -= numpy.einsum('ijca,ibjc->ab', theta, eris.ovov)
#: foo += numpy.einsum('iakb,jkba->ij', eris.ovov, theta)
for i in range(nocc):
tau = numpy.einsum('a,jb->jab', t1[i]*.5, t1) + t2[i]
theta = tau.transpose(0,2,1)*2 - tau
lib.dot(_cp(eris_ovov[i].transpose(1,2,0)).reshape(nocc,-1),
theta.reshape(nocc,-1).T, 1, foo, 1)
lib.dot(theta.reshape(-1,nvir).T,
eris_ovov[i].reshape(nvir,-1).T, -1, fvv, 1)
tau = theta = None
eris_oovv = _cp(eris.oovv)
#:tmp = numpy.einsum('ic,jkbc->jibk', t1, eris_oovv)
#:t2new += numpy.einsum('ka,jibk->jiab', -t1, tmp)
#:tmp = numpy.einsum('ic,jbkc->jibk', t1, eris_ovov)
#:t2new += numpy.einsum('ka,jibk->jiba', -t1, tmp)
for j in range(nocc):
tmp = lib.dot(t1, eris_oovv[j].reshape(-1,nvir).T)
tmp = _cp(tmp.reshape(nocc,nocc,nvir).transpose(0,2,1))
t2new[j] += lib.dot(tmp.reshape(-1,nocc), t1,
-1).reshape(nocc,nvir,nvir).transpose(0,2,1)
lib.dot(t1, eris_ovov[j].reshape(-1,nvir).T, 1, tmp.reshape(nocc,-1))
lib.dot(tmp.reshape(-1,nocc), t1, -1, t2new[j].reshape(-1,nvir), 1)
tmp = None
#: g2 = 2 * eris.oOVv - eris.oovv
#: t1new += numpy.einsum('jb,ijba->ia', t1, g2)
t1new += numpy.einsum('jb,iajb->ia', 2*t1, eris_ovov)
t1new += numpy.einsum('jb,ijba->ia', -t1, eris_oovv)
#: tau = t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: woooo += numpy.einsum('ijba,klab->ijkl', eris.oOVv, tau)
#: woVoV -= eris.oovv
#: tau = .5*t2 + numpy.einsum('ia,jb->ijab', t1, t1)
#: woVoV += numpy.einsum('ka,ijkb->ijab', t1, eris.ooov)
#: woVoV += numpy.einsum('jkca,ikbc->ijab', tau, eris.oOVv)
woVoV -= eris_oovv
woVoV = woVoV.transpose(1,3,0,2).copy()
eris_oVOv = _cp(eris_ovov.transpose(0,3,2,1))
eris_oOvV = _cp(eris_ovov.transpose(0,2,1,3))
tau = make_tau(t2, t1, t1)
#: woooo += numpy.einsum('ijab,klab->ijkl', eris_oOvV, tau)
lib.dot(eris_oOvV.reshape(-1,nvir**2), tau.reshape(-1,nvir**2).T,
1, woooo.reshape(nocc**2,-1), 1)
#: t2new += .5 * numpy.einsum('klij,klab->ijab', woooo, tau)
lib.dot(woooo.reshape(-1,nocc*nocc).T, tau.reshape(-1,nvir*nvir),
.5, t2new.reshape(nocc*nocc,-1), 1)
for i in range(nocc):
tau[i] -= t2[i] * .5
#: woVoV[j0:j1] += numpy.einsum('jkca,ickb->jiab', tau, eris_ovov)
tau = _cp(tau.transpose(0,3,1,2))
lib.dot(tau.reshape(-1,nov), eris_oVOv.reshape(-1,nov).T,
1, woVoV.reshape(nov,-1), 1)
eris_oovv = eris_ovov = eris_oOvV = taubuf = None
tmp, tau = tau, None
t2ibja, eris_oVOv = eris_oVOv, None
for i in range(nocc):
t2ibja[i] = t2[i].transpose(2,0,1)
#: t2new += numpy.einsum('ibkc,kcja->ijab', woVoV, t2ibja)
lib.dot(woVoV.reshape(nov,-1), t2ibja.reshape(-1,nov), 1, tmp.reshape(nov,-1))
for i in range(nocc):
t2new[i] += tmp[i].transpose(1,2,0)
#: t2new[j0:j1] += numpy.einsum('iakc,kcjb->ijab', woVoV[j0:j1], t2iajb)
t2iajb = t2ibja
for i in range(nocc):
t2iajb[i] = t2[i].transpose(1,0,2)
lib.dot(woVoV.reshape(nov,-1), t2iajb.reshape(-1,nov), 1, tmp.reshape(nov,-1))
for i in range(nocc):
t2new[i] += tmp[i].transpose(1,0,2)
t2ibja = t2iajb = woVoV = tmp = None
time1 = log.timer_debug1('contract loop', *time0)
woooo = None
ft_ij = foo + numpy.einsum('ja,ia->ij', .5*t1, fov)
ft_ab = fvv - numpy.einsum('ia,ib->ab', .5*t1, fov)
#: t2new += numpy.einsum('ijac,bc->ijab', t2, ft_ab)
#: t2new -= numpy.einsum('ki,kjab->ijab', ft_ij, t2)
lib.dot(t2.reshape(-1,nvir), ft_ab.T, 1, t2new.reshape(-1,nvir), 1)
lib.dot(ft_ij.T, t2.reshape(nocc,-1),-1, t2new.reshape(nocc,-1), 1)
#: t2new = t2new + t2new.transpose(1,0,3,2)
t2new_tril = numpy.empty((nocc*(nocc+1)//2,nvir,nvir))
ij = 0
for i in range(nocc):
for j in range(i+1):
t2new_tril[ij] = t2new[i,j]
t2new_tril[ij] += t2new[j,i].T
ij += 1
t2new = None
time1 = log.timer_debug1('t2 tril', *time1)
cc.add_wvvVV_(t1, t2, eris, t2new_tril)
time1 = log.timer_debug1('vvvv', *time1)
mo_e = fock.diagonal()
eia = lib.direct_sum('i-a->ia', mo_e[:nocc], mo_e[nocc:])
p0 = 0
for i in range(nocc):
t2new_tril[p0:p0+i+1] /= lib.direct_sum('a+jb->jab', eia[i], eia[:i+1])
p0 += i+1
time1 = log.timer_debug1('g2/dijab', *time1)
t2new = numpy.empty((nocc,nocc,nvir,nvir))
ij = 0
for i in range(nocc):
for j in range(i):
t2new[i,j] = t2new_tril[ij]
t2new[j,i] = t2new_tril[ij].T
ij += 1
t2new[i,i] = t2new_tril[ij]
ij += 1
t2new_tril = None
#** update_amp_t1
t1new += fock[:nocc,nocc:] \
+ numpy.einsum('ib,ab->ia', t1, fvv) \
- numpy.einsum('ja,ji->ia', t1, foo)
mo_e = fock.diagonal()
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
t1new /= eia
#** end update_amp_t1
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def __init__(self, cc, mo_coeff=None, method='incore'):
cput0 = (time.clock(), time.time())
moidx = numpy.ones(cc.mo_energy.size, dtype=numpy.bool)
if isinstance(cc.frozen, (int, numpy.integer)):
moidx[:cc.frozen] = False
elif len(cc.frozen) > 0:
moidx[numpy.asarray(cc.frozen)] = False
if mo_coeff is None:
self.mo_coeff = mo_coeff = cc.mo_coeff[:,moidx]
self.fock = numpy.diag(cc.mo_energy[moidx])
else: # If mo_coeff is not canonical orbital
self.mo_coeff = mo_coeff = mo_coeff[:,moidx]
dm = cc._scf.make_rdm1(cc.mo_coeff, cc.mo_occ)
fockao = cc._scf.get_hcore() + cc._scf.get_veff(cc.mol, dm)
self.fock = reduce(numpy.dot, (mo_coeff.T, fockao, mo_coeff))
nocc = cc.nocc()
nmo = cc.nmo()
nvir = nmo - nocc
mem_incore, mem_outcore, mem_basic = _mem_usage(nocc, nvir)
mem_now = pyscf.lib.current_memory()[0]
log = logger.Logger(cc.stdout, cc.verbose)
if (method == 'incore' and cc._scf._eri is not None and
(mem_incore+mem_now < cc.max_memory) or cc.mol.incore_anyway):
eri1 = pyscf.ao2mo.incore.full(cc._scf._eri, mo_coeff)
#:eri1 = pyscf.ao2mo.restore(1, eri1, nmo)
#:self.oooo = eri1[:nocc,:nocc,:nocc,:nocc].copy()
#:self.ooov = eri1[:nocc,:nocc,:nocc,nocc:].copy()
#:self.ovoo = eri1[:nocc,nocc:,:nocc,:nocc].copy()
#:self.oovv = eri1[:nocc,:nocc,nocc:,nocc:].copy()
#:self.ovov = eri1[:nocc,nocc:,:nocc,nocc:].copy()
#:ovvv = eri1[:nocc,nocc:,nocc:,nocc:].copy()
#:self.ovvv = numpy.empty((nocc,nvir,nvir*(nvir+1)//2))
#:for i in range(nocc):
#: for j in range(nvir):
#: self.ovvv[i,j] = lib.pack_tril(ovvv[i,j])
#:self.vvvv = pyscf.ao2mo.restore(4, eri1[nocc:,nocc:,nocc:,nocc:], nvir)
nvir_pair = nvir * (nvir+1) // 2
self.oooo = numpy.empty((nocc,nocc,nocc,nocc))
self.ooov = numpy.empty((nocc,nocc,nocc,nvir))
self.ovoo = numpy.empty((nocc,nvir,nocc,nocc))
self.oovv = numpy.empty((nocc,nocc,nvir,nvir))
self.ovov = numpy.empty((nocc,nvir,nocc,nvir))
self.ovvv = numpy.empty((nocc,nvir,nvir_pair))
self.vvvv = numpy.empty((nvir_pair,nvir_pair))
ij = 0
outbuf = numpy.empty((nmo,nmo,nmo))
for i in range(nocc):
buf = _ccsd.unpack_tril(eri1[ij:ij+i+1], out=outbuf[:i+1])
for j in range(i+1):
self.oooo[i,j] = self.oooo[j,i] = buf[j,:nocc,:nocc]
self.ooov[i,j] = self.ooov[j,i] = buf[j,:nocc,nocc:]
self.oovv[i,j] = self.oovv[j,i] = buf[j,nocc:,nocc:]
ij += i + 1
ij1 = 0
for i in range(nocc,nmo):
buf = _ccsd.unpack_tril(eri1[ij:ij+i+1], out=outbuf[:i+1])
self.ovoo[:,i-nocc] = buf[:nocc,:nocc,:nocc]
self.ovov[:,i-nocc] = buf[:nocc,:nocc,nocc:]
for j in range(nocc):
self.ovvv[j,i-nocc] = lib.pack_tril(_cp(buf[j,nocc:,nocc:]))
for j in range(nocc, i+1):
self.vvvv[ij1] = lib.pack_tril(_cp(buf[j,nocc:,nocc:]))
ij1 += 1
ij += i + 1
else:
cput1 = time.clock(), time.time()
_tmpfile1 = tempfile.NamedTemporaryFile()
_tmpfile2 = tempfile.NamedTemporaryFile()
self.feri1 = h5py.File(_tmpfile1.name)
orbo = mo_coeff[:,:nocc]
orbv = mo_coeff[:,nocc:]
nvpair = nvir * (nvir+1) // 2
self.oooo = self.feri1.create_dataset('oooo', (nocc,nocc,nocc,nocc), 'f8')
self.ooov = self.feri1.create_dataset('ooov', (nocc,nocc,nocc,nvir), 'f8')
self.ovoo = self.feri1.create_dataset('ovoo', (nocc,nvir,nocc,nocc), 'f8')
self.oovv = self.feri1.create_dataset('oovv', (nocc,nocc,nvir,nvir), 'f8')
self.ovov = self.feri1.create_dataset('ovov', (nocc,nvir,nocc,nvir), 'f8')
self.ovvv = self.feri1.create_dataset('ovvv', (nocc,nvir,nvpair), 'f8')
self.feri2 = h5py.File(_tmpfile2.name, 'w')
pyscf.ao2mo.full(cc.mol, orbv, self.feri2, verbose=log)
self.vvvv = self.feri2['eri_mo']
cput1 = log.timer_debug1('transforming vvvv', *cput1)
tmpfile3 = tempfile.NamedTemporaryFile()
with h5py.File(tmpfile3.name, 'w') as feri:
pyscf.ao2mo.general(cc.mol, (orbo,mo_coeff,mo_coeff,mo_coeff),
feri, verbose=log)
cput1 = log.timer_debug1('transforming oppp', *cput1)
eri1 = feri['eri_mo']
outbuf = numpy.empty((nmo,nmo,nmo))
for i in range(nocc):
buf = _ccsd.unpack_tril(_cp(eri1[i*nmo:(i+1)*nmo]), out=outbuf)
self.oooo[i] = buf[:nocc,:nocc,:nocc]
self.ooov[i] = buf[:nocc,:nocc,nocc:]
self.ovoo[i] = buf[nocc:,:nocc,:nocc]
self.oovv[i] = buf[:nocc,nocc:,nocc:]
self.ovov[i] = buf[nocc:,:nocc,nocc:]
self.ovvv[i] = _ccsd.pack_tril(_cp(buf[nocc:,nocc:,nocc:]))
cput1 = log.timer_debug1('sorting %d'%i, *cput1)
for key in feri.keys():
del(feri[key])
log.timer('CCSD integral transformation', *cput0)
def IX_intermediates(mycc, t1, t2, l1, l2, d1=None, d2=None, eris=None):
if d1 is None:
doo, dov, dvo, dvv = ccsd_t_rdm.gamma1_intermediates(
mycc, t1, t2, l1, l2, eris)
else:
doo, dov, dvo, dvv = d1
if d2 is None:
# Note gamma2 are in Chemist's notation
d2 = ccsd_t_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
else:
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
if dovvv is None:
dovvv = dvvov.transpose(2, 3, 0, 1)
elif dvvov is None:
dvvov = dovvv.transpose(2, 3, 0, 1)
nocc, nvir = t1.shape
eris_ovvv = _ccsd.unpack_tril(_cp(eris.ovvv).reshape(nocc * nvir, -1))
eris_ovvv = eris_ovvv.reshape(nocc, nvir, nvir, nvir)
eris_vvvv = pyscf.ao2mo.restore(1, _cp(eris.vvvv), nvir)
dvvvv = pyscf.ao2mo.restore(1, _cp(dvvvv), nvir)
# Note Ioo is not hermitian
Ioo = (numpy.einsum('jakb,iakb->ij', dovov, eris.ovov) +
numpy.einsum('kbja,iakb->ij', dovov, eris.ovov))
Ioo += (numpy.einsum('jabk,iakb->ij', dovvo, eris.ovov) +
numpy.einsum('kbaj,iakb->ij', dovvo, eris.ovov) +
numpy.einsum('jkab,ikab->ij', doovv, eris.oovv) +
numpy.einsum('kjba,ikab->ij', doovv, eris.oovv))
Ioo += (numpy.einsum('jmlk,imlk->ij', doooo, eris.oooo) * 2 +
numpy.einsum('mjkl,imlk->ij', doooo, eris.oooo) * 2)
Ioo += (numpy.einsum('jlka,ilka->ij', dooov, eris.ooov) +
numpy.einsum('klja,klia->ij', dooov, eris.ooov))
Ioo += numpy.einsum('abjc,icab->ij', dvvov, eris_ovvv)
Ioo += numpy.einsum('ljka,lika->ij', dooov, eris.ooov)
Ioo *= -1
# Note Ivv is not hermitian
Ivv = (numpy.einsum('ibjc,iajc->ab', dovov, eris.ovov) +
numpy.einsum('jcib,iajc->ab', dovov, eris.ovov))
Ivv += (numpy.einsum('jcbi,iajc->ab', dovvo, eris.ovov) +
numpy.einsum('ibcj,iajc->ab', dovvo, eris.ovov) +
numpy.einsum('jibc,jiac->ab', doovv, eris.oovv) +
numpy.einsum('ijcb,jiac->ab', doovv, eris.oovv))
Ivv += (numpy.einsum('bced,aced->ab', dvvvv, eris_vvvv) * 2 +
numpy.einsum('cbde,aced->ab', dvvvv, eris_vvvv) * 2)
Ivv += (numpy.einsum('dbic,icda->ab', dvvov, eris_ovvv) +
numpy.einsum('dcib,iadc->ab', dvvov, eris_ovvv))
Ivv += numpy.einsum('bcid,idac->ab', dvvov, eris_ovvv)
Ivv += numpy.einsum('jikb,jika->ab', dooov, eris.ooov)
Ivv *= -1
Ivo = (numpy.einsum('kajb,kijb->ai', dovov, eris.ooov) +
numpy.einsum('kbja,jikb->ai', dovov, eris.ooov))
Ivo += (numpy.einsum('acbd,icbd->ai', dvvvv, eris_ovvv) * 2 +
numpy.einsum('cadb,icbd->ai', dvvvv, eris_ovvv) * 2)
Ivo += (numpy.einsum('jbak,jbik->ai', dovvo, eris.ovoo) +
numpy.einsum('kabj,jbik->ai', dovvo, eris.ovoo) +
numpy.einsum('jkab,jkib->ai', doovv, eris.ooov) +
numpy.einsum('kjba,jkib->ai', doovv, eris.ooov))
Ivo += (numpy.einsum('dajc,idjc->ai', dvvov, eris.ovov) +
numpy.einsum('dcja,jidc->ai', dvvov, eris.oovv))
Ivo += numpy.einsum('abjc,ibjc->ai', dvvov, eris.ovov)
Ivo += numpy.einsum('jlka,jlki->ai', dooov, eris.oooo)
Ivo *= -1
Xvo = (numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2 +
numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2 -
numpy.einsum('kj,kija->ai', doo, eris.ooov) -
numpy.einsum('kj,ijka->ai', doo, eris.ooov))
Xvo += (numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 2 +
numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 2 -
numpy.einsum('cb,icab->ai', dvv, eris_ovvv) -
numpy.einsum('cb,ibca->ai', dvv, eris_ovvv))
Xvo += (numpy.einsum('icjb,jbac->ai', dovov, eris_ovvv) +
numpy.einsum('jcib,jcab->ai', dovov, eris_ovvv))
Xvo += (numpy.einsum('iklj,ljka->ai', doooo, eris.ooov) * 2 +
numpy.einsum('kijl,ljka->ai', doooo, eris.ooov) * 2)
Xvo += (numpy.einsum('ibcj,jcab->ai', dovvo, eris_ovvv) +
numpy.einsum('jcbi,jcab->ai', dovvo, eris_ovvv) +
numpy.einsum('ijcb,jacb->ai', doovv, eris_ovvv) +
numpy.einsum('jibc,jacb->ai', doovv, eris_ovvv))
Xvo += (numpy.einsum('ijkb,jakb->ai', dooov, eris.ovov) +
numpy.einsum('kjib,kjab->ai', dooov, eris.oovv))
Xvo += numpy.einsum('dbic,dbac->ai', dvvov, eris_vvvv)
Xvo += numpy.einsum('jikb,jakb->ai', dooov, eris.ovov)
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo