def update_amps(cc, t1, t2, eris):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nkpts, nocc, nvir = t1.shape
fock = eris.fock
mo_e_o = [e[:nocc] for e in eris.mo_energy]
mo_e_v = [e[nocc:] + cc.level_shift for e in eris.mo_energy]
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(cc, kind="split")
fov = fock[:, :nocc, nocc:].copy()
foo = fock[:, :nocc, :nocc].copy()
fvv = fock[:, nocc:, nocc:].copy()
# Get the momentum conservation array
# Note: chemist's notation for momentum conserving t2(ki,kj,ka,kb), even though
# integrals are in physics notation
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
tau = imdk.make_tau(cc, t2, t1, t1, kconserv)
Fvv = imdk.cc_Fvv(cc, t1, t2, eris, kconserv)
Foo = imdk.cc_Foo(cc, t1, t2, eris, kconserv)
Fov = imdk.cc_Fov(cc, t1, t2, eris, kconserv)
Woooo = imdk.cc_Woooo(cc, t1, t2, eris, kconserv)
Wvvvv = imdk.cc_Wvvvv(cc, t1, t2, eris, kconserv)
Wovvo = imdk.cc_Wovvo(cc, t1, t2, eris, kconserv)
# Move energy terms to the other side
for k in range(nkpts):
Foo[k][numpy.diag_indices(nocc)] -= mo_e_o[k]
Fvv[k][numpy.diag_indices(nvir)] -= mo_e_v[k]
eris_ovvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nvir, nvir,
nocc),
dtype=t2.dtype)
eris_oovo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nocc, nvir,
nocc),
dtype=t2.dtype)
eris_vvvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nvir, nvir, nvir,
nocc),
dtype=t2.dtype)
for km, kb, ke in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ke, kb]
# <mb||je> -> -<mb||ej>
eris_ovvo[km, kb, ke] = -eris.ovov[km, kb, kj].transpose(0, 1, 3, 2)
# <mn||je> -> -<mn||ej>
# let kb = kn as a dummy variable
eris_oovo[km, kb, ke] = -eris.ooov[km, kb, kj].transpose(0, 1, 3, 2)
# <ma||be> -> - <be||am>*
# let kj = ka as a dummy variable
kj = kconserv[km, ke, kb]
eris_vvvo[ke, kj,
kb] = -eris.ovvv[km, kb, ke].transpose(2, 3, 1, 0).conj()
# T1 equation
t1new = numpy.zeros(shape=t1.shape, dtype=t1.dtype)
for ka in range(nkpts):
ki = ka
t1new[ka] += numpy.array(fov[ka, :, :]).conj()
t1new[ka] += einsum('ie,ae->ia', t1[ka], Fvv[ka])
t1new[ka] += -einsum('ma,mi->ia', t1[ka], Foo[ka])
for km in range(nkpts):
t1new[ka] += einsum('imae,me->ia', t2[ka, km, ka], Fov[km])
t1new[ka] += -einsum('nf,naif->ia', t1[km], eris.ovov[km, ka, ki])
for kn in range(nkpts):
ke = kconserv[km, ki, kn]
t1new[ka] += -0.5 * einsum('imef,maef->ia', t2[ki, km, ke],
eris.ovvv[km, ka, ke])
t1new[ka] += -0.5 * einsum('mnae,nmei->ia', t2[km, kn, ka],
eris_oovo[kn, km, ke])
# T2 equation
t2new = numpy.array(eris.oovv).conj()
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki, ka, kj]
Ftmp = Fvv[kb] - 0.5 * einsum('mb,me->be', t1[kb], Fov[kb])
tmp = einsum('ijae,be->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] += tmp
#t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
Ftmp = Fvv[ka] - 0.5 * einsum('ma,me->ae', t1[ka], Fov[ka])
tmp = einsum('ijbe,ae->ijab', t2[ki, kj, kb], Ftmp)
t2new[ki, kj, ka] -= tmp
Ftmp = Foo[kj] + 0.5 * einsum('je,me->mj', t1[kj], Fov[kj])
tmp = einsum('imab,mj->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] -= tmp
#t2new[kj,ki,ka] += tmp.transpose(1,0,2,3)
Ftmp = Foo[ki] + 0.5 * einsum('ie,me->mi', t1[ki], Fov[ki])
tmp = einsum('jmab,mi->ijab', t2[kj, ki, ka], Ftmp)
t2new[ki, kj, ka] += tmp
for km in range(nkpts):
# Wminj
# - km - kn + ka + kb = 0
# => kn = ka - km + kb
kn = kconserv[ka, km, kb]
t2new[ki, kj, ka] += 0.5 * einsum(
'mnab,mnij->ijab', tau[km, kn, ka], Woooo[km, kn, ki])
ke = km
t2new[ki, kj, ka] += 0.5 * einsum(
'ijef,abef->ijab', tau[ki, kj, ke], Wvvvv[ka, kb, ke])
# Wmbej
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
ke = kconserv[km, kj, kb]
tmp = einsum('imae,mbej->ijab', t2[ki, km, ka], Wovvo[km, kb, ke])
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
#
# t[i,e] => ki = ke
# t[m,a] => km = ka
if km == ka and ke == ki:
tmp -= einsum('ie,ma,mbej->ijab', t1[ki], t1[km],
eris_ovvo[km, kb, ke])
t2new[ki, kj, ka] += tmp
t2new[ki, kj, kb] -= tmp.transpose(0, 1, 3, 2)
t2new[kj, ki, ka] -= tmp.transpose(1, 0, 2, 3)
t2new[kj, ki, kb] += tmp.transpose(1, 0, 3, 2)
ke = ki
tmp = einsum('ie,abej->ijab', t1[ki], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] += tmp
# P(ij) term
ke = kj
tmp = einsum('je,abei->ijab', t1[kj], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] -= tmp
km = ka
tmp = einsum('ma,mbij->ijab', t1[ka], eris.ovoo[km, kb, ki])
t2new[ki, kj, ka] -= tmp
# P(ab) term
km = kb
tmp = einsum('mb,maij->ijab', t1[kb], eris.ovoo[km, ka, ki])
t2new[ki, kj, ka] += tmp
for ki in range(nkpts):
ka = ki
# Remove zero/padded elements from denominator
eia = LARGE_DENOM * numpy.ones(
(nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:, None] - mo_e_v[ka])[n0_ovp_ia]
t1new[ki] /= eia
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
# For LARGE_DENOM, see t1new update above
eia = LARGE_DENOM * numpy.ones(
(nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:, None] - mo_e_v[ka])[n0_ovp_ia]
ejb = LARGE_DENOM * numpy.ones(
(nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_jb = numpy.ix_(nonzero_opadding[kj], nonzero_vpadding[kb])
ejb[n0_ovp_jb] = (mo_e_o[kj][:, None] - mo_e_v[kb])[n0_ovp_jb]
eijab = eia[:, None, :, None] + ejb[:, None, :]
t2new[ki, kj, ka] /= eijab
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)
nkpts, nocc, nvir = t1.shape
#nov = nocc*nvir
fock = eris.fock
#t1new = numpy.zeros_like(t1)
#t2new = numpy.zeros_like(t2)
fov = fock[:,:nocc,nocc:].copy()
foo = fock[:,:nocc,:nocc].copy()
fvv = fock[:,nocc:,nocc:].copy()
#mo_e = eris.fock.diagonal()
#eia = mo_e[:nocc,None] - mo_e[None,nocc:]
#eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
tau = imdk.make_tau(cc,t2,t1,t1)
### From eom-cc hackathon code ###
Fvv = imdk.cc_Fvv(cc,t1,t2,eris)
Foo = imdk.cc_Foo(cc,t1,t2,eris)
Fov = imdk.cc_Fov(cc,t1,t2,eris)
Woooo = imdk.cc_Woooo(cc,t1,t2,eris)
Wvvvv = imdk.cc_Wvvvv(cc,t1,t2,eris)
Wovvo = imdk.cc_Wovvo(cc,t1,t2,eris)
# Move energy terms to the other side
Fvv -= fvv
Foo -= foo
# Get the momentum conservation array
# Note: chemist's notation for momentum conserving t2(ki,kj,ka,kb), even though
# integrals are in physics notation
kconserv = tools.get_kconserv(cc._scf.cell, cc.kpts)
eris_ovvo = numpy.zeros(shape=(nkpts,nkpts,nkpts,nocc,nvir,nvir,nocc), dtype=t2.dtype)
eris_oovo = numpy.zeros(shape=(nkpts,nkpts,nkpts,nocc,nocc,nvir,nocc), dtype=t2.dtype)
eris_vvvo = numpy.zeros(shape=(nkpts,nkpts,nkpts,nvir,nvir,nvir,nocc), dtype=t2.dtype)
for km in range(nkpts):
for kb in range(nkpts):
for ke in range(nkpts):
kj = kconserv[km,ke,kb]
# <mb||je> -> -<mb||ej>
eris_ovvo[km,kb,ke] = -eris.ovov[km,kb,kj].transpose(0,1,3,2)
# <mn||je> -> -<mn||ej>
# let kb = kn as a dummy variable
eris_oovo[km,kb,ke] = -eris.ooov[km,kb,kj].transpose(0,1,3,2)
# <ma||be> -> - <be||am>*
# let kj = ka as a dummy variable
kj = kconserv[km,ke,kb]
eris_vvvo[ke,kj,kb] = -eris.ovvv[km,kb,ke].transpose(2,3,1,0).conj()
# T1 equation
t1new = numpy.zeros(shape=t1.shape, dtype=t1.dtype)
for ka in range(nkpts):
ki = ka
# TODO: Does this fov need a conj()? Usually zero w/ canonical HF.
t1new[ka] += fov[ka,:,:]
t1new[ka] += einsum('ie,ae->ia',t1[ka],Fvv[ka])
t1new[ka] += -einsum('ma,mi->ia',t1[ka],Foo[ka])
for km in range(nkpts):
t1new[ka] += einsum('imae,me->ia',t2[ka,km,ka],Fov[km])
t1new[ka] += -einsum('nf,naif->ia',t1[km],eris.ovov[km,ka,ki])
for kn in range(nkpts):
ke = kconserv[km,ki,kn]
t1new[ka] += -0.5*einsum('imef,maef->ia',t2[ki,km,ke],eris.ovvv[km,ka,ke])
t1new[ka] += -0.5*einsum('mnae,nmei->ia',t2[km,kn,ka],eris_oovo[kn,km,ke])
# T2 equation
# For conj(), see Hirata and Bartlett, Eq. (36)
t2new = eris.oovv.copy().conj()
for ki in range(nkpts):
for kj in range(nkpts):
for ka in range(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki,ka,kj]
Ftmp = Fvv[kb] - 0.5*einsum('mb,me->be',t1[kb],Fov[kb])
tmp = einsum('ijae,be->ijab',t2[ki,kj,ka],Ftmp)
t2new[ki,kj,ka] += tmp
Ftmp = Fvv[ka] - 0.5*einsum('ma,me->ae',t1[ka],Fov[ka])
tmp = einsum('ijbe,ae->ijab',t2[ki,kj,kb],Ftmp)
t2new[ki,kj,ka] -= tmp
#t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
Ftmp = Foo[kj] + 0.5*einsum('je,me->mj',t1[kj],Fov[kj])
tmp = einsum('imab,mj->ijab',t2[ki,kj,ka],Ftmp)
t2new[ki,kj,ka] -= tmp
Ftmp = Foo[ki] + 0.5*einsum('ie,me->mi',t1[ki],Fov[ki])
tmp = einsum('jmab,mi->ijab',t2[kj,ki,ka],Ftmp)
t2new[ki,kj,ka] += tmp
#t2new[kj,ki,ka] += tmp.transpose(1,0,2,3)
for km in range(nkpts):
# Wminj
# - km - kn + ka + kb = 0
# => kn = ka - km + kb
kn = kconserv[ka,km,kb]
t2new[ki,kj,ka] += 0.5*einsum('mnab,mnij->ijab',tau[km,kn,ka],Woooo[km,kn,ki])
ke = km
t2new[ki,kj,ka] += 0.5*einsum('ijef,abef->ijab',tau[ki,kj,ke],Wvvvv[ka,kb,ke])
# Wmbej
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
ke = kconserv[km,kj,kb]
tmp = einsum('imae,mbej->ijab',t2[ki,km,ka],Wovvo[km,kb,ke])
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
#
# t[i,e] => ki = ke
# t[m,a] => km = ka
if km == ka and ke == ki:
tmp -= einsum('ie,ma,mbej->ijab',t1[ki],t1[km],eris_ovvo[km,kb,ke])
t2new[ki,kj,ka] += tmp
t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
t2new[kj,ki,ka] -= tmp.transpose(1,0,2,3)
t2new[kj,ki,kb] += tmp.transpose(1,0,3,2)
ke = ki
tmp = einsum('ie,abej->ijab',t1[ki],eris_vvvo[ka,kb,ke])
t2new[ki,kj,ka] += tmp
# P(ij) term
ke = kj
tmp = einsum('je,abei->ijab',t1[kj],eris_vvvo[ka,kb,ke])
t2new[ki,kj,ka] -= tmp
km = ka
tmp = einsum('ma,mbij->ijab',t1[ka],eris.ovoo[km,kb,ki])
t2new[ki,kj,ka] -= tmp
# P(ab) term
km = kb
tmp = einsum('mb,maij->ijab',t1[kb],eris.ovoo[km,ka,ki])
t2new[ki,kj,ka] += tmp
eia = numpy.zeros(shape=t1new.shape, dtype=t1new.dtype)
for ki in range(nkpts):
for i in range(nocc):
for a in range(nvir):
eia[ki,i,a] = foo[ki,i,i] - fvv[ki,a,a]
t1new[ki] /= eia[ki]
eijab = numpy.zeros(shape=t2new.shape, dtype=t2new.dtype)
kconserv = tools.get_kconserv(cc._scf.cell, cc.kpts)
for ki in range(nkpts):
for kj in range(nkpts):
for ka in range(nkpts):
kb = kconserv[ki,ka,kj]
for i in range(nocc):
for a in range(nvir):
for j in range(nocc):
for b in range(nvir):
eijab[ki,kj,ka,i,j,a,b] = ( foo[ki,i,i] + foo[kj,j,j]
- fvv[ka,a,a] - fvv[kb,b,b] )
t2new[ki,kj,ka] /= eijab[ki,kj,ka]
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def update_amps(cc, t1, t2, eris):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nkpts, nocc, nvir = t1.shape
fock = eris.fock
mo_e_o = [e[:nocc] for e in eris.mo_energy]
mo_e_v = [e[nocc:] + cc.level_shift for e in eris.mo_energy]
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(cc, kind="split")
fov = fock[:, :nocc, nocc:].copy()
foo = fock[:, :nocc, :nocc].copy()
fvv = fock[:, nocc:, nocc:].copy()
# Get the momentum conservation array
# Note: chemist's notation for momentum conserving t2(ki,kj,ka,kb), even though
# integrals are in physics notation
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
tau = imdk.make_tau(cc, t2, t1, t1, kconserv)
Fvv = imdk.cc_Fvv(cc, t1, t2, eris, kconserv)
Foo = imdk.cc_Foo(cc, t1, t2, eris, kconserv)
Fov = imdk.cc_Fov(cc, t1, t2, eris, kconserv)
Woooo = imdk.cc_Woooo(cc, t1, t2, eris, kconserv)
Wvvvv = imdk.cc_Wvvvv(cc, t1, t2, eris, kconserv)
Wovvo = imdk.cc_Wovvo(cc, t1, t2, eris, kconserv)
# Move energy terms to the other side
for k in range(nkpts):
Foo[k][numpy.diag_indices(nocc)] -= mo_e_o[k]
Fvv[k][numpy.diag_indices(nvir)] -= mo_e_v[k]
eris_ovvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nvir, nvir, nocc), dtype=t2.dtype)
eris_oovo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nocc, nvir, nocc), dtype=t2.dtype)
eris_vvvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nvir, nvir, nvir, nocc), dtype=t2.dtype)
for km, kb, ke in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ke, kb]
# <mb||je> -> -<mb||ej>
eris_ovvo[km, kb, ke] = -eris.ovov[km, kb, kj].transpose(0, 1, 3, 2)
# <mn||je> -> -<mn||ej>
# let kb = kn as a dummy variable
eris_oovo[km, kb, ke] = -eris.ooov[km, kb, kj].transpose(0, 1, 3, 2)
# <ma||be> -> - <be||am>*
# let kj = ka as a dummy variable
kj = kconserv[km, ke, kb]
eris_vvvo[ke, kj, kb] = -eris.ovvv[km, kb, ke].transpose(2, 3, 1, 0).conj()
# T1 equation
t1new = numpy.zeros(shape=t1.shape, dtype=t1.dtype)
for ka in range(nkpts):
ki = ka
t1new[ka] += numpy.array(fov[ka, :, :]).conj()
t1new[ka] += einsum('ie,ae->ia', t1[ka], Fvv[ka])
t1new[ka] += -einsum('ma,mi->ia', t1[ka], Foo[ka])
for km in range(nkpts):
t1new[ka] += einsum('imae,me->ia', t2[ka, km, ka], Fov[km])
t1new[ka] += -einsum('nf,naif->ia', t1[km], eris.ovov[km, ka, ki])
for kn in range(nkpts):
ke = kconserv[km, ki, kn]
t1new[ka] += -0.5 * einsum('imef,maef->ia', t2[ki, km, ke], eris.ovvv[km, ka, ke])
t1new[ka] += -0.5 * einsum('mnae,nmei->ia', t2[km, kn, ka], eris_oovo[kn, km, ke])
# T2 equation
t2new = numpy.array(eris.oovv).conj()
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki, ka, kj]
Ftmp = Fvv[kb] - 0.5 * einsum('mb,me->be', t1[kb], Fov[kb])
tmp = einsum('ijae,be->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] += tmp
#t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
Ftmp = Fvv[ka] - 0.5 * einsum('ma,me->ae', t1[ka], Fov[ka])
tmp = einsum('ijbe,ae->ijab', t2[ki, kj, kb], Ftmp)
t2new[ki, kj, ka] -= tmp
Ftmp = Foo[kj] + 0.5 * einsum('je,me->mj', t1[kj], Fov[kj])
tmp = einsum('imab,mj->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] -= tmp
#t2new[kj,ki,ka] += tmp.transpose(1,0,2,3)
Ftmp = Foo[ki] + 0.5 * einsum('ie,me->mi', t1[ki], Fov[ki])
tmp = einsum('jmab,mi->ijab', t2[kj, ki, ka], Ftmp)
t2new[ki, kj, ka] += tmp
for km in range(nkpts):
# Wminj
# - km - kn + ka + kb = 0
# => kn = ka - km + kb
kn = kconserv[ka, km, kb]
t2new[ki, kj, ka] += 0.5 * einsum('mnab,mnij->ijab', tau[km, kn, ka], Woooo[km, kn, ki])
ke = km
t2new[ki, kj, ka] += 0.5 * einsum('ijef,abef->ijab', tau[ki, kj, ke], Wvvvv[ka, kb, ke])
# Wmbej
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
ke = kconserv[km, kj, kb]
tmp = einsum('imae,mbej->ijab', t2[ki, km, ka], Wovvo[km, kb, ke])
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
#
# t[i,e] => ki = ke
# t[m,a] => km = ka
if km == ka and ke == ki:
tmp -= einsum('ie,ma,mbej->ijab', t1[ki], t1[km], eris_ovvo[km, kb, ke])
t2new[ki, kj, ka] += tmp
t2new[ki, kj, kb] -= tmp.transpose(0, 1, 3, 2)
t2new[kj, ki, ka] -= tmp.transpose(1, 0, 2, 3)
t2new[kj, ki, kb] += tmp.transpose(1, 0, 3, 2)
ke = ki
tmp = einsum('ie,abej->ijab', t1[ki], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] += tmp
# P(ij) term
ke = kj
tmp = einsum('je,abei->ijab', t1[kj], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] -= tmp
km = ka
tmp = einsum('ma,mbij->ijab', t1[ka], eris.ovoo[km, kb, ki])
t2new[ki, kj, ka] -= tmp
# P(ab) term
km = kb
tmp = einsum('mb,maij->ijab', t1[kb], eris.ovoo[km, ka, ki])
t2new[ki, kj, ka] += tmp
for ki in range(nkpts):
ka = ki
# Remove zero/padded elements from denominator
eia = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:,None] - mo_e_v[ka])[n0_ovp_ia]
t1new[ki] /= eia
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
# For LARGE_DENOM, see t1new update above
eia = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:,None] - mo_e_v[ka])[n0_ovp_ia]
ejb = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_jb = numpy.ix_(nonzero_opadding[kj], nonzero_vpadding[kb])
ejb[n0_ovp_jb] = (mo_e_o[kj][:,None] - mo_e_v[kb])[n0_ovp_jb]
eijab = eia[:, None, :, None] + ejb[:, None, :]
t2new[ki, kj, ka] /= eijab
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)
nkpts, nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:, :nocc, nocc:].copy()
foo = fock[:, :nocc, :nocc].copy()
fvv = fock[:, nocc:, nocc:].copy()
#mo_e = eris.fock.diagonal()
#eia = mo_e[:nocc,None] - mo_e[None,nocc:]
#eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
tau = imdk.make_tau(cc, t2, t1, t1)
Fvv = imdk.cc_Fvv(cc, t1, t2, eris)
Foo = imdk.cc_Foo(cc, t1, t2, eris)
Fov = imdk.cc_Fov(cc, t1, t2, eris)
Woooo = imdk.cc_Woooo(cc, t1, t2, eris)
Wvvvv = imdk.cc_Wvvvv(cc, t1, t2, eris)
Wovvo = imdk.cc_Wovvo(cc, t1, t2, eris)
# Move energy terms to the other side
for k in range(nkpts):
Fvv[k] -= numpy.diag(numpy.diag(fvv[k]))
Foo[k] -= numpy.diag(numpy.diag(foo[k]))
# Get the momentum conservation array
# Note: chemist's notation for momentum conserving t2(ki,kj,ka,kb), even though
# integrals are in physics notation
kconserv = tools.get_kconserv(cc._scf.cell, cc.kpts)
eris_ovvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nvir, nvir,
nocc),
dtype=t2.dtype)
eris_oovo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nocc, nvir,
nocc),
dtype=t2.dtype)
eris_vvvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nvir, nvir, nvir,
nocc),
dtype=t2.dtype)
for km in range(nkpts):
for kb in range(nkpts):
for ke in range(nkpts):
kj = kconserv[km, ke, kb]
# <mb||je> -> -<mb||ej>
eris_ovvo[km, kb,
ke] = -eris.ovov[km, kb, kj].transpose(0, 1, 3, 2)
# <mn||je> -> -<mn||ej>
# let kb = kn as a dummy variable
eris_oovo[km, kb,
ke] = -eris.ooov[km, kb, kj].transpose(0, 1, 3, 2)
# <ma||be> -> - <be||am>*
# let kj = ka as a dummy variable
kj = kconserv[km, ke, kb]
eris_vvvo[ke, kj, kb] = -eris.ovvv[km, kb, ke].transpose(
2, 3, 1, 0).conj()
# T1 equation
t1new = numpy.zeros(shape=t1.shape, dtype=t1.dtype)
for ka in range(nkpts):
ki = ka
t1new[ka] += numpy.array(fov[ka, :, :]).conj()
t1new[ka] += einsum('ie,ae->ia', t1[ka], Fvv[ka])
t1new[ka] += -einsum('ma,mi->ia', t1[ka], Foo[ka])
for km in range(nkpts):
t1new[ka] += einsum('imae,me->ia', t2[ka, km, ka], Fov[km])
t1new[ka] += -einsum('nf,naif->ia', t1[km], eris.ovov[km, ka, ki])
for kn in range(nkpts):
ke = kconserv[km, ki, kn]
t1new[ka] += -0.5 * einsum('imef,maef->ia', t2[ki, km, ke],
eris.ovvv[km, ka, ke])
t1new[ka] += -0.5 * einsum('mnae,nmei->ia', t2[km, kn, ka],
eris_oovo[kn, km, ke])
# T2 equation
t2new = numpy.array(eris.oovv).conj()
for ki in range(nkpts):
for kj in range(nkpts):
for ka in range(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki, ka, kj]
Ftmp = Fvv[kb] - 0.5 * einsum('mb,me->be', t1[kb], Fov[kb])
tmp = einsum('ijae,be->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] += tmp
#t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
Ftmp = Fvv[ka] - 0.5 * einsum('ma,me->ae', t1[ka], Fov[ka])
tmp = einsum('ijbe,ae->ijab', t2[ki, kj, kb], Ftmp)
t2new[ki, kj, ka] -= tmp
Ftmp = Foo[kj] + 0.5 * einsum('je,me->mj', t1[kj], Fov[kj])
tmp = einsum('imab,mj->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] -= tmp
#t2new[kj,ki,ka] += tmp.transpose(1,0,2,3)
Ftmp = Foo[ki] + 0.5 * einsum('ie,me->mi', t1[ki], Fov[ki])
tmp = einsum('jmab,mi->ijab', t2[kj, ki, ka], Ftmp)
t2new[ki, kj, ka] += tmp
for km in range(nkpts):
# Wminj
# - km - kn + ka + kb = 0
# => kn = ka - km + kb
kn = kconserv[ka, km, kb]
t2new[ki, kj, ka] += 0.5 * einsum(
'mnab,mnij->ijab', tau[km, kn, ka], Woooo[km, kn, ki])
ke = km
t2new[ki, kj, ka] += 0.5 * einsum(
'ijef,abef->ijab', tau[ki, kj, ke], Wvvvv[ka, kb, ke])
# Wmbej
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
ke = kconserv[km, kj, kb]
tmp = einsum('imae,mbej->ijab', t2[ki, km, ka],
Wovvo[km, kb, ke])
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
#
# t[i,e] => ki = ke
# t[m,a] => km = ka
if km == ka and ke == ki:
tmp -= einsum('ie,ma,mbej->ijab', t1[ki], t1[km],
eris_ovvo[km, kb, ke])
t2new[ki, kj, ka] += tmp
t2new[ki, kj, kb] -= tmp.transpose(0, 1, 3, 2)
t2new[kj, ki, ka] -= tmp.transpose(1, 0, 2, 3)
t2new[kj, ki, kb] += tmp.transpose(1, 0, 3, 2)
ke = ki
tmp = einsum('ie,abej->ijab', t1[ki], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] += tmp
# P(ij) term
ke = kj
tmp = einsum('je,abei->ijab', t1[kj], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] -= tmp
km = ka
tmp = einsum('ma,mbij->ijab', t1[ka], eris.ovoo[km, kb, ki])
t2new[ki, kj, ka] -= tmp
# P(ab) term
km = kb
tmp = einsum('mb,maij->ijab', t1[kb], eris.ovoo[km, ka, ki])
t2new[ki, kj, ka] += tmp
eia = numpy.zeros(shape=t1new.shape, dtype=t1new.dtype)
for ki in range(nkpts):
for i in range(nocc):
for a in range(nvir):
eia[ki, i, a] = foo[ki, i, i] - fvv[ki, a, a]
t1new[ki] /= eia[ki]
eijab = numpy.zeros(shape=t2new.shape, dtype=t2new.dtype)
kconserv = tools.get_kconserv(cc._scf.cell, cc.kpts)
for ki in range(nkpts):
for kj in range(nkpts):
for ka in range(nkpts):
kb = kconserv[ki, ka, kj]
for i in range(nocc):
for a in range(nvir):
for j in range(nocc):
for b in range(nvir):
eijab[ki, kj, ka, i, j, a,
b] = (foo[ki, i, i] + foo[kj, j, j] -
fvv[ka, a, a] - fvv[kb, b, b])
t2new[ki, kj, ka] /= eijab[ki, kj, ka]
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)
nkpts, nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:, :nocc, nocc:].copy()
foo = fock[:, :nocc, :nocc].copy()
fvv = fock[:, nocc:, nocc:].copy()
tau = imdk.make_tau(cc, t2, t1, t1)
Fvv = imdk.cc_Fvv(cc, t1, t2, eris)
Foo = imdk.cc_Foo(cc, t1, t2, eris)
Fov = imdk.cc_Fov(cc, t1, t2, eris)
Woooo = imdk.cc_Woooo(cc, t1, t2, eris)
Wvvvv = imdk.cc_Wvvvv(cc, t1, t2, eris)
Wovvo = imdk.cc_Wovvo(cc, t1, t2, eris)
# Move energy terms to the other side
for k in range(nkpts):
Fvv[k] -= numpy.diag(numpy.diag(fvv[k]))
Foo[k] -= numpy.diag(numpy.diag(foo[k]))
# Get the momentum conservation array
# Note: chemist's notation for momentum conserving t2(ki,kj,ka,kb), even though
# integrals are in physics notation
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
eris_ovvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nvir, nvir,
nocc),
dtype=t2.dtype)
eris_oovo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nocc, nvir,
nocc),
dtype=t2.dtype)
eris_vvvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nvir, nvir, nvir,
nocc),
dtype=t2.dtype)
for km, kb, ke in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ke, kb]
# <mb||je> -> -<mb||ej>
eris_ovvo[km, kb, ke] = -eris.ovov[km, kb, kj].transpose(0, 1, 3, 2)
# <mn||je> -> -<mn||ej>
# let kb = kn as a dummy variable
eris_oovo[km, kb, ke] = -eris.ooov[km, kb, kj].transpose(0, 1, 3, 2)
# <ma||be> -> - <be||am>*
# let kj = ka as a dummy variable
kj = kconserv[km, ke, kb]
eris_vvvo[ke, kj,
kb] = -eris.ovvv[km, kb, ke].transpose(2, 3, 1, 0).conj()
# T1 equation
t1new = numpy.zeros(shape=t1.shape, dtype=t1.dtype)
for ka in range(nkpts):
ki = ka
t1new[ka] += numpy.array(fov[ka, :, :]).conj()
t1new[ka] += einsum('ie,ae->ia', t1[ka], Fvv[ka])
t1new[ka] += -einsum('ma,mi->ia', t1[ka], Foo[ka])
for km in range(nkpts):
t1new[ka] += einsum('imae,me->ia', t2[ka, km, ka], Fov[km])
t1new[ka] += -einsum('nf,naif->ia', t1[km], eris.ovov[km, ka, ki])
for kn in range(nkpts):
ke = kconserv[km, ki, kn]
t1new[ka] += -0.5 * einsum('imef,maef->ia', t2[ki, km, ke],
eris.ovvv[km, ka, ke])
t1new[ka] += -0.5 * einsum('mnae,nmei->ia', t2[km, kn, ka],
eris_oovo[kn, km, ke])
# T2 equation
t2new = numpy.array(eris.oovv).conj()
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki, ka, kj]
Ftmp = Fvv[kb] - 0.5 * einsum('mb,me->be', t1[kb], Fov[kb])
tmp = einsum('ijae,be->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] += tmp
#t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
Ftmp = Fvv[ka] - 0.5 * einsum('ma,me->ae', t1[ka], Fov[ka])
tmp = einsum('ijbe,ae->ijab', t2[ki, kj, kb], Ftmp)
t2new[ki, kj, ka] -= tmp
Ftmp = Foo[kj] + 0.5 * einsum('je,me->mj', t1[kj], Fov[kj])
tmp = einsum('imab,mj->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] -= tmp
#t2new[kj,ki,ka] += tmp.transpose(1,0,2,3)
Ftmp = Foo[ki] + 0.5 * einsum('ie,me->mi', t1[ki], Fov[ki])
tmp = einsum('jmab,mi->ijab', t2[kj, ki, ka], Ftmp)
t2new[ki, kj, ka] += tmp
for km in range(nkpts):
# Wminj
# - km - kn + ka + kb = 0
# => kn = ka - km + kb
kn = kconserv[ka, km, kb]
t2new[ki, kj, ka] += 0.5 * einsum(
'mnab,mnij->ijab', tau[km, kn, ka], Woooo[km, kn, ki])
ke = km
t2new[ki, kj, ka] += 0.5 * einsum(
'ijef,abef->ijab', tau[ki, kj, ke], Wvvvv[ka, kb, ke])
# Wmbej
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
ke = kconserv[km, kj, kb]
tmp = einsum('imae,mbej->ijab', t2[ki, km, ka], Wovvo[km, kb, ke])
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
#
# t[i,e] => ki = ke
# t[m,a] => km = ka
if km == ka and ke == ki:
tmp -= einsum('ie,ma,mbej->ijab', t1[ki], t1[km],
eris_ovvo[km, kb, ke])
t2new[ki, kj, ka] += tmp
t2new[ki, kj, kb] -= tmp.transpose(0, 1, 3, 2)
t2new[kj, ki, ka] -= tmp.transpose(1, 0, 2, 3)
t2new[kj, ki, kb] += tmp.transpose(1, 0, 3, 2)
ke = ki
tmp = einsum('ie,abej->ijab', t1[ki], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] += tmp
# P(ij) term
ke = kj
tmp = einsum('je,abei->ijab', t1[kj], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] -= tmp
km = ka
tmp = einsum('ma,mbij->ijab', t1[ka], eris.ovoo[km, kb, ki])
t2new[ki, kj, ka] -= tmp
# P(ab) term
km = kb
tmp = einsum('mb,maij->ijab', t1[kb], eris.ovoo[km, ka, ki])
t2new[ki, kj, ka] += tmp
eia = numpy.zeros(shape=(nocc, nvir), dtype=t1new.dtype)
for ki in range(nkpts):
eia = foo[ki].diagonal()[:, None] - fvv[ki].diagonal()[None, :]
# When padding the occupied/virtual arrays, some fock elements will be zero
idx = numpy.where(abs(eia) < LOOSE_ZERO_TOL)[0]
eia[idx] = LARGE_DENOM
t1new[ki] /= eia
eijab = numpy.zeros(shape=(nocc, nocc, nvir, nvir), dtype=t2new.dtype)
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
eijab = (foo[ki].diagonal()[:, None, None, None] +
foo[kj].diagonal()[None, :, None, None] -
fvv[ka].diagonal()[None, None, :, None] -
fvv[kb].diagonal()[None, None, None, :])
# Due to padding; see above discussion concerning t1new in update_amps()
idx = numpy.where(abs(eijab) < LOOSE_ZERO_TOL)[0]
eijab[idx] = LARGE_DENOM
t2new[ki, kj, ka] /= eijab
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
