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
fock = eris.fock
fov = fock[:nocc, nocc:]
foo = fock[:nocc, :nocc]
fvv = fock[nocc:, nocc:]
mo_e = eris.fock.diagonal()
eia = mo_e[:nocc, None] - mo_e[None, nocc:]
eijab = lib.direct_sum('ia,jb->ijab', eia, eia)
Foo = imd.cc_Foo(t1, t2, eris)
Fvv = imd.cc_Fvv(t1, t2, eris)
Fov = imd.cc_Fov(t1, t2, eris)
Loo = imd.Loo(t1, t2, eris)
Lvv = imd.Lvv(t1, t2, eris)
Woooo = imd.cc_Woooo(t1, t2, eris)
Wvvvv = imd.cc_Wvvvv(t1, t2, eris)
Wvoov = imd.cc_Wvoov(t1, t2, eris)
Wvovo = imd.cc_Wvovo(t1, t2, eris)
# Move energy terms to the other side
Foo -= foo
Fvv -= fvv
Loo -= foo
Lvv -= fvv
# T1 equation
# TODO: Check this conj(). Hirata and Bartlett has
# f_{vo}(a,i), which should be equal to f_{ov}^*(i,a)
t1new = fov.conj().copy()
t1new += -2 * einsum('kc,ka,ic->ia', fov, t1, t1)
t1new += einsum('ac,ic->ia', Fvv, t1)
t1new += -einsum('ki,ka->ia', Foo, t1)
t1new += einsum('kc,kica->ia', Fov, 2 * t2)
t1new += einsum('kc,ikca->ia', Fov, -t2)
t1new += einsum('kc,ic,ka->ia', Fov, t1, t1)
t1new += 2 * einsum('akic,kc->ia', eris.voov, t1)
t1new += -einsum('kaic,kc->ia', eris.ovov, t1)
t1new += 2 * einsum('akcd,ikcd->ia', eris.vovv, t2)
t1new += -einsum('akdc,ikcd->ia', eris.vovv, t2)
t1new += 2 * einsum('akcd,ic,kd->ia', eris.vovv, t1, t1)
t1new += -einsum('akdc,ic,kd->ia', eris.vovv, t1, t1)
t1new += -2 * einsum('klic,klac->ia', eris.ooov, t2)
t1new += einsum('lkic,klac->ia', eris.ooov, t2)
t1new += -2 * einsum('klic,ka,lc->ia', eris.ooov, t1, t1)
t1new += einsum('lkic,ka,lc->ia', eris.ooov, t1, t1)
# T2 equation
# For conj(), see Hirata and Bartlett, Eq. (36)
t2new = np.array(eris.oovv).conj()
t2new += einsum('klij,klab->ijab', Woooo, t2)
t2new += einsum('klij,ka,lb->ijab', Woooo, t1, t1)
for a in range(nvir):
Wvvvv_a = np.array(Wvvvv[a])
t2new[:, :, a, :] += einsum('bcd,ijcd->ijb', Wvvvv_a, t2)
t2new[:, :, a, :] += einsum('bcd,ic,jd->ijb', Wvvvv_a, t1, t1)
tmp = einsum('ac,ijcb->ijab', Lvv, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp = einsum('ki,kjab->ijab', Loo, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp2 = np.array(eris.vovv).transpose(3,2,1,0).conj() \
- einsum('kbic,ka->abic',eris.ovov,t1)
tmp = einsum('abic,jc->ijab', tmp2, t1)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp2 = np.array(eris.ooov).transpose(3,2,1,0).conj() \
+ einsum('akic,jc->akij',eris.voov,t1)
tmp = einsum('akij,kb->ijab', tmp2, t1)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp = 2 * einsum('akic,kjcb->ijab', Wvoov, t2) - einsum(
'akci,kjcb->ijab', Wvovo, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp = einsum('akic,kjbc->ijab', Wvoov, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp = einsum('bkci,kjac->ijab', Wvovo, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
t1new /= eia
t2new /= eijab
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def update_amps(cc, t1, t2, eris):
# Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004) Eqs.(35)-(36)
nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:nocc, nocc:].copy()
foo = fock[:nocc, :nocc].copy()
fvv = fock[nocc:, nocc:].copy()
Foo = imd.cc_Foo(t1, t2, eris)
Fvv = imd.cc_Fvv(t1, t2, eris)
Fov = imd.cc_Fov(t1, t2, eris)
# Move energy terms to the other side
Foo -= np.diag(np.diag(foo))
Fvv -= np.diag(np.diag(fvv))
# T1 equation
t1new = np.asarray(fov).conj().copy()
t1new += -2 * einsum('kc,ka,ic->ia', fov, t1, t1)
t1new += einsum('ac,ic->ia', Fvv, t1)
t1new += -einsum('ki,ka->ia', Foo, t1)
t1new += 2 * einsum('kc,kica->ia', Fov, t2)
t1new += -einsum('kc,ikca->ia', Fov, t2)
t1new += einsum('kc,ic,ka->ia', Fov, t1, t1)
t1new += 2 * einsum('kcai,kc->ia', eris.ovvo, t1)
t1new += -einsum('kiac,kc->ia', eris.oovv, t1)
eris_ovvv = np.asarray(eris.ovvv)
t1new += 2 * einsum('kdac,ikcd->ia', eris_ovvv, t2)
t1new += -einsum('kcad,ikcd->ia', eris_ovvv, t2)
t1new += 2 * einsum('kdac,kd,ic->ia', eris_ovvv, t1, t1)
t1new += -einsum('kcad,kd,ic->ia', eris_ovvv, t1, t1)
t1new += -2 * einsum('kilc,klac->ia', eris.ooov, t2)
t1new += einsum('likc,klac->ia', eris.ooov, t2)
t1new += -2 * einsum('kilc,lc,ka->ia', eris.ooov, t1, t1)
t1new += einsum('likc,lc,ka->ia', eris.ooov, t1, t1)
# T2 equation
t2new = np.asarray(eris.ovov).conj().transpose(0, 2, 1, 3).copy()
if cc.cc2:
Woooo2 = np.asarray(eris.oooo).transpose(0, 2, 1, 3).copy()
Woooo2 += einsum('kilc,jc->klij', eris.ooov, t1)
Woooo2 += einsum('ljkc,ic->klij', eris.ooov, t1)
Woooo2 += einsum('kcld,ic,jd->klij', eris.ovov, t1, t1)
t2new += einsum('klij,ka,lb->ijab', Woooo2, t1, t1)
Wvvvv = einsum('kcbd,ka->abcd', eris_ovvv, -t1)
Wvvvv = Wvvvv + Wvvvv.transpose(1, 0, 3, 2)
Wvvvv += np.asarray(eris.vvvv).transpose(0, 2, 1, 3)
t2new += einsum('abcd,ic,jd->ijab', Wvvvv, t1, t1)
Lvv2 = fvv - einsum('kc,ka->ac', fov, t1)
Lvv2 -= np.diag(np.diag(fvv))
tmp = einsum('ac,ijcb->ijab', Lvv2, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
Loo2 = foo + einsum('kc,ic->ki', fov, t1)
Loo2 -= np.diag(np.diag(foo))
tmp = einsum('ki,kjab->ijab', Loo2, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
else:
Loo = imd.Loo(t1, t2, eris)
Lvv = imd.Lvv(t1, t2, eris)
Loo -= np.diag(np.diag(foo))
Lvv -= np.diag(np.diag(fvv))
Woooo = imd.cc_Woooo(t1, t2, eris)
Wvoov = imd.cc_Wvoov(t1, t2, eris)
Wvovo = imd.cc_Wvovo(t1, t2, eris)
Wvvvv = imd.cc_Wvvvv(t1, t2, eris)
tau = t2 + einsum('ia,jb->ijab', t1, t1)
t2new += einsum('klij,klab->ijab', Woooo, tau)
t2new += einsum('abcd,ijcd->ijab', Wvvvv, tau)
tmp = einsum('ac,ijcb->ijab', Lvv, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp = einsum('ki,kjab->ijab', Loo, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp = 2 * einsum('akic,kjcb->ijab', Wvoov, t2)
tmp -= einsum('akci,kjcb->ijab', Wvovo, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp = einsum('akic,kjbc->ijab', Wvoov, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp = einsum('bkci,kjac->ijab', Wvovo, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp2 = einsum('kibc,ka->abic', eris.oovv, -t1)
tmp2 += np.asarray(eris.ovvv).conj().transpose(1, 3, 0, 2)
tmp = einsum('abic,jc->ijab', tmp2, t1)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp2 = einsum('kcai,jc->akij', eris.ovvo, t1)
tmp2 += np.asarray(eris.ooov).transpose(3, 1, 2, 0).conj()
tmp = einsum('akij,kb->ijab', tmp2, t1)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
mo_e = eris.fock.diagonal().real
eia = mo_e[:nocc, None] - mo_e[None, nocc:]
eijab = lib.direct_sum('ia,jb->ijab', eia, eia)
t1new /= eia
t2new /= eijab
return t1new, t2new
def update_amps(cc, t1, t2, eris):
# Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004) Eqs.(35)-(36)
assert(isinstance(eris, ccsd._ChemistsERIs))
nocc, nvir = t1.shape
fock = eris.fock
mo_e_o = eris.mo_energy[:nocc]
mo_e_v = eris.mo_energy[nocc:] + cc.level_shift
fov = fock[:nocc,nocc:].copy()
foo = fock[:nocc,:nocc].copy()
fvv = fock[nocc:,nocc:].copy()
Foo = imd.cc_Foo(t1,t2,eris)
Fvv = imd.cc_Fvv(t1,t2,eris)
Fov = imd.cc_Fov(t1,t2,eris)
# Move energy terms to the other side
Foo[np.diag_indices(nocc)] -= mo_e_o
Fvv[np.diag_indices(nvir)] -= mo_e_v
#occ_act = np.arange(cc.frozen_occ,nocc)
occ_act = np.arange(nocc)
vir_act = np.arange(cc.nvir_act)
#print("occ_act =", occ_act)
#print("vir_act =", vir_act)
ia_act = np.ix_(occ_act,vir_act)
ijab_act = np.ix_(occ_act,occ_act,vir_act,vir_act)
#print("ia =", ia_act)
#print("ijab =", ijab_act)
# T1 equation
t1new = np.copy(fov.conj())
t1new[ia_act] -= 2*np.einsum('kc,ka,ic->ia', fov, t1, t1)[ia_act]
t1new[ia_act] += np.einsum('ac,ic->ia', Fvv, t1)[ia_act]
t1new[ia_act] += -np.einsum('ki,ka->ia', Foo, t1)[ia_act]
t1new[ia_act] += 2*np.einsum('kc,kica->ia', Fov, t2)[ia_act]
t1new[ia_act] += -np.einsum('kc,ikca->ia', Fov, t2)[ia_act]
t1new[ia_act] += np.einsum('kc,ic,ka->ia', Fov, t1, t1)[ia_act]
t1new[ia_act] += 2*np.einsum('kcai,kc->ia', eris.ovvo, t1)[ia_act]
t1new[ia_act] += -np.einsum('kiac,kc->ia', eris.oovv, t1)[ia_act]
eris_ovvv = np.asarray(eris.get_ovvv())
t1new[ia_act] += 2*lib.einsum('kdac,ikcd->ia', eris_ovvv, t2)[ia_act]
t1new[ia_act] += -lib.einsum('kcad,ikcd->ia', eris_ovvv, t2)[ia_act]
t1new[ia_act] += 2*lib.einsum('kdac,kd,ic->ia', eris_ovvv, t1, t1)[ia_act]
t1new[ia_act] += -lib.einsum('kcad,kd,ic->ia', eris_ovvv, t1, t1)[ia_act]
eris_ovoo = np.asarray(eris.ovoo, order='C')
t1new[ia_act] +=-2*lib.einsum('lcki,klac->ia', eris_ovoo, t2)[ia_act]
t1new[ia_act] += lib.einsum('kcli,klac->ia', eris_ovoo, t2)[ia_act]
t1new[ia_act] +=-2*lib.einsum('lcki,lc,ka->ia', eris_ovoo, t1, t1)[ia_act]
t1new[ia_act] += lib.einsum('kcli,lc,ka->ia', eris_ovoo, t1, t1)[ia_act]
# T2 equation
t2new = np.copy(np.asarray(eris.ovov).conj().transpose(0,2,1,3))
tmp2 = lib.einsum('kibc,ka->abic', eris.oovv, -t1)
tmp2 += np.asarray(eris_ovvv).conj().transpose(1,3,0,2)
tmp = lib.einsum('abic,jc->ijab', tmp2, t1)
t2new[ijab_act] += (tmp + tmp.transpose(1,0,3,2))[ijab_act]
tmp2 = lib.einsum('kcai,jc->akij', eris.ovvo, t1)
tmp2 += eris_ovoo.transpose(1,3,0,2).conj()
tmp = lib.einsum('akij,kb->ijab', tmp2, t1)
t2new[ijab_act] -= (tmp + tmp.transpose(1,0,3,2))[ijab_act]
Loo = imd.Loo(t1, t2, eris)
Lvv = imd.Lvv(t1, t2, eris)
Loo[np.diag_indices(nocc)] -= mo_e_o
Lvv[np.diag_indices(nvir)] -= mo_e_v
Woooo = imd.cc_Woooo(t1, t2, eris)
Wvoov = imd.cc_Wvoov(t1, t2, eris)
Wvovo = imd.cc_Wvovo(t1, t2, eris)
Wvvvv = imd.cc_Wvvvv(t1, t2, eris)
tau = t2 + np.einsum('ia,jb->ijab', t1, t1)
t2new[ijab_act] += lib.einsum('klij,klab->ijab', Woooo, tau)[ijab_act]
t2new[ijab_act] += lib.einsum('abcd,ijcd->ijab', Wvvvv, tau)[ijab_act]
tmp = lib.einsum('ac,ijcb->ijab', Lvv, t2)
t2new[ijab_act] += (tmp + tmp.transpose(1,0,3,2))[ijab_act]
tmp = lib.einsum('ki,kjab->ijab', Loo, t2)
t2new[ijab_act] -= (tmp + tmp.transpose(1,0,3,2))[ijab_act]
tmp = 2*lib.einsum('akic,kjcb->ijab', Wvoov, t2)
tmp -= lib.einsum('akci,kjcb->ijab', Wvovo, t2)
t2new[ijab_act] += (tmp + tmp.transpose(1,0,3,2))[ijab_act]
tmp = lib.einsum('akic,kjbc->ijab', Wvoov, t2)
t2new[ijab_act] -= (tmp + tmp.transpose(1,0,3,2))[ijab_act]
tmp = lib.einsum('bkci,kjac->ijab', Wvovo, t2)
t2new[ijab_act] -= (tmp + tmp.transpose(1,0,3,2))[ijab_act]
eia = mo_e_o[:,None] - mo_e_v
eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
t1new /= eia
t2new /= eijab
return t1new, t2new
def update_amps(cc, t1, t2, eris):
# Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004) Eqs.(35)-(36)
assert (isinstance(eris, ccsd._ChemistsERIs))
nocc, nvir = t1.shape
fock = eris.fock
mo_e_o = eris.mo_energy[:nocc]
mo_e_v = eris.mo_energy[nocc:] + cc.level_shift
fov = fock[:nocc, nocc:].copy()
foo = fock[:nocc, :nocc].copy()
fvv = fock[nocc:, nocc:].copy()
Foo = imd.cc_Foo(t1, t2, eris)
Fvv = imd.cc_Fvv(t1, t2, eris)
Fov = imd.cc_Fov(t1, t2, eris)
# Move energy terms to the other side
Foo[np.diag_indices(nocc)] -= mo_e_o
Fvv[np.diag_indices(nvir)] -= mo_e_v
# T1 equation
t1new = -2 * np.einsum('kc,ka,ic->ia', fov, t1, t1)
t1new += np.einsum('ac,ic->ia', Fvv, t1)
t1new += -np.einsum('ki,ka->ia', Foo, t1)
t1new += 2 * np.einsum('kc,kica->ia', Fov, t2)
t1new += -np.einsum('kc,ikca->ia', Fov, t2)
t1new += np.einsum('kc,ic,ka->ia', Fov, t1, t1)
t1new += fov.conj()
t1new += 2 * np.einsum('kcai,kc->ia', eris.ovvo, t1)
t1new += -np.einsum('kiac,kc->ia', eris.oovv, t1)
eris_ovvv = np.asarray(eris.get_ovvv())
t1new += 2 * lib.einsum('kdac,ikcd->ia', eris_ovvv, t2)
t1new += -lib.einsum('kcad,ikcd->ia', eris_ovvv, t2)
t1new += 2 * lib.einsum('kdac,kd,ic->ia', eris_ovvv, t1, t1)
t1new += -lib.einsum('kcad,kd,ic->ia', eris_ovvv, t1, t1)
eris_ovoo = np.asarray(eris.ovoo, order='C')
t1new += -2 * lib.einsum('lcki,klac->ia', eris_ovoo, t2)
t1new += lib.einsum('kcli,klac->ia', eris_ovoo, t2)
t1new += -2 * lib.einsum('lcki,lc,ka->ia', eris_ovoo, t1, t1)
t1new += lib.einsum('kcli,lc,ka->ia', eris_ovoo, t1, t1)
# T2 equation
tmp2 = lib.einsum('kibc,ka->abic', eris.oovv, -t1)
tmp2 += np.asarray(eris_ovvv).conj().transpose(1, 3, 0, 2)
tmp = lib.einsum('abic,jc->ijab', tmp2, t1)
t2new = tmp + tmp.transpose(1, 0, 3, 2)
tmp2 = lib.einsum('kcai,jc->akij', eris.ovvo, t1)
tmp2 += eris_ovoo.transpose(1, 3, 0, 2).conj()
tmp = lib.einsum('akij,kb->ijab', tmp2, t1)
t2new -= tmp + tmp.transpose(1, 0, 3, 2)
t2new += np.asarray(eris.ovov).conj().transpose(0, 2, 1, 3)
if cc.cc2:
Woooo2 = np.asarray(eris.oooo).transpose(0, 2, 1, 3).copy()
Woooo2 += lib.einsum('lcki,jc->klij', eris_ovoo, t1)
Woooo2 += lib.einsum('kclj,ic->klij', eris_ovoo, t1)
Woooo2 += lib.einsum('kcld,ic,jd->klij', eris.ovov, t1, t1)
t2new += lib.einsum('klij,ka,lb->ijab', Woooo2, t1, t1)
Wvvvv = lib.einsum('kcbd,ka->abcd', eris_ovvv, -t1)
Wvvvv = Wvvvv + Wvvvv.transpose(1, 0, 3, 2)
Wvvvv += np.asarray(eris.vvvv).transpose(0, 2, 1, 3)
t2new += lib.einsum('abcd,ic,jd->ijab', Wvvvv, t1, t1)
Lvv2 = fvv - np.einsum('kc,ka->ac', fov, t1)
Lvv2 -= np.diag(np.diag(fvv))
tmp = lib.einsum('ac,ijcb->ijab', Lvv2, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
Loo2 = foo + np.einsum('kc,ic->ki', fov, t1)
Loo2 -= np.diag(np.diag(foo))
tmp = lib.einsum('ki,kjab->ijab', Loo2, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
else:
Loo = imd.Loo(t1, t2, eris)
Lvv = imd.Lvv(t1, t2, eris)
Loo[np.diag_indices(nocc)] -= mo_e_o
Lvv[np.diag_indices(nvir)] -= mo_e_v
Woooo = imd.cc_Woooo(t1, t2, eris)
Wvoov = imd.cc_Wvoov(t1, t2, eris)
Wvovo = imd.cc_Wvovo(t1, t2, eris)
Wvvvv = imd.cc_Wvvvv(t1, t2, eris)
tau = t2 + np.einsum('ia,jb->ijab', t1, t1)
t2new += lib.einsum('klij,klab->ijab', Woooo, tau)
t2new += lib.einsum('abcd,ijcd->ijab', Wvvvv, tau)
tmp = lib.einsum('ac,ijcb->ijab', Lvv, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp = lib.einsum('ki,kjab->ijab', Loo, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp = 2 * lib.einsum('akic,kjcb->ijab', Wvoov, t2)
tmp -= lib.einsum('akci,kjcb->ijab', Wvovo, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp = lib.einsum('akic,kjbc->ijab', Wvoov, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp = lib.einsum('bkci,kjac->ijab', Wvovo, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
eia = mo_e_o[:, None] - mo_e_v
eijab = lib.direct_sum('ia,jb->ijab', eia, eia)
t1new /= eia
t2new /= eijab
return t1new, t2new
def update_amps(cc, t1, t2, eris):
# Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004) Eqs.(35)-(36)
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:nocc,nocc:]
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
mo_e = eris.fock.diagonal()
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
Foo = imd.cc_Foo(t1,t2,eris)
Fvv = imd.cc_Fvv(t1,t2,eris)
Fov = imd.cc_Fov(t1,t2,eris)
Loo = imd.Loo(t1,t2,eris)
Lvv = imd.Lvv(t1,t2,eris)
Woooo = imd.cc_Woooo(t1,t2,eris)
Wvvvv = imd.cc_Wvvvv(t1,t2,eris)
Wvoov = imd.cc_Wvoov(t1,t2,eris)
Wvovo = imd.cc_Wvovo(t1,t2,eris)
# Move energy terms to the other side
Foo -= np.diag(np.diag(foo))
Fvv -= np.diag(np.diag(fvv))
Loo -= np.diag(np.diag(foo))
Lvv -= np.diag(np.diag(fvv))
# T1 equation
t1new = np.array(fov).conj()
t1new += -2*einsum('kc,ka,ic->ia',fov,t1,t1)
t1new += einsum('ac,ic->ia',Fvv,t1)
t1new += -einsum('ki,ka->ia',Foo,t1)
t1new += 2*einsum('kc,kica->ia',Fov,t2)
t1new += -einsum('kc,ikca->ia',Fov,t2)
t1new += einsum('kc,ic,ka->ia',Fov,t1,t1)
t1new += 2*einsum('akic,kc->ia',eris.voov,t1)
t1new += -einsum('kaic,kc->ia',eris.ovov,t1)
t1new += 2*einsum('akcd,ikcd->ia',eris.vovv,t2)
t1new += -einsum('akdc,ikcd->ia',eris.vovv,t2)
t1new += 2*einsum('akcd,ic,kd->ia',eris.vovv,t1,t1)
t1new += -einsum('akdc,ic,kd->ia',eris.vovv,t1,t1)
t1new += -2*einsum('klic,klac->ia',eris.ooov,t2)
t1new += einsum('lkic,klac->ia',eris.ooov,t2)
t1new += -2*einsum('klic,ka,lc->ia',eris.ooov,t1,t1)
t1new += einsum('lkic,ka,lc->ia',eris.ooov,t1,t1)
# T2 equation
t2new = np.array(eris.oovv).conj()
t2new += einsum('klij,klab->ijab',Woooo,t2)
t2new += einsum('klij,ka,lb->ijab',Woooo,t1,t1)
for a in range(nvir):
Wvvvv_a = np.array(Wvvvv[a])
t2new[:,:,a,:] += einsum('bcd,ijcd->ijb',Wvvvv_a,t2)
t2new[:,:,a,:] += einsum('bcd,ic,jd->ijb',Wvvvv_a,t1,t1)
tmp = einsum('ac,ijcb->ijab',Lvv,t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('ki,kjab->ijab',Loo,t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp2 = np.array(eris.vovv).transpose(3,2,1,0).conj() \
- einsum('kbic,ka->abic',eris.ovov,t1)
tmp = einsum('abic,jc->ijab',tmp2,t1)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp2 = np.array(eris.ooov).transpose(3,2,1,0).conj() \
+ einsum('akic,jc->akij',eris.voov,t1)
tmp = einsum('akij,kb->ijab',tmp2,t1)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = 2*einsum('akic,kjcb->ijab',Wvoov,t2) - einsum('akci,kjcb->ijab',Wvovo,t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('akic,kjbc->ijab',Wvoov,t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('bkci,kjac->ijab',Wvovo,t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
t1new /= eia
t2new /= 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)
nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:nocc,nocc:]
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
mo_e = eris.fock.diagonal()
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
Foo = imd.cc_Foo(t1,t2,eris)
Fvv = imd.cc_Fvv(t1,t2,eris)
Fov = imd.cc_Fov(t1,t2,eris)
Loo = imd.Loo(t1,t2,eris)
Lvv = imd.Lvv(t1,t2,eris)
Woooo = imd.cc_Woooo(t1,t2,eris)
Wvvvv = imd.cc_Wvvvv(t1,t2,eris)
Wvoov = imd.cc_Wvoov(t1,t2,eris)
Wvovo = imd.cc_Wvovo(t1,t2,eris)
# Move energy terms to the other side
Foo -= foo
Fvv -= fvv
Loo -= foo
Lvv -= fvv
# T1 equation
# TODO: Check this conj(). Hirata and Bartlett has
# f_{vo}(a,i), which should be equal to f_{ov}^*(i,a)
t1new = fov.conj().copy()
t1new += -2*einsum('kc,ka,ic->ia',fov,t1,t1)
t1new += einsum('ac,ic->ia',Fvv,t1)
t1new += -einsum('ki,ka->ia',Foo,t1)
t1new += einsum('kc,kica->ia',Fov,2*t2)
t1new += einsum('kc,ikca->ia',Fov, -t2)
t1new += einsum('kc,ic,ka->ia',Fov,t1,t1)
t1new += 2*einsum('akic,kc->ia',eris.voov,t1)
t1new += -einsum('kaic,kc->ia',eris.ovov,t1)
t1new += 2*einsum('akcd,ikcd->ia',eris.vovv,t2)
t1new += -einsum('akdc,ikcd->ia',eris.vovv,t2)
t1new += 2*einsum('akcd,ic,kd->ia',eris.vovv,t1,t1)
t1new += -einsum('akdc,ic,kd->ia',eris.vovv,t1,t1)
t1new += -2*einsum('klic,klac->ia',eris.ooov,t2)
t1new += einsum('lkic,klac->ia',eris.ooov,t2)
t1new += -2*einsum('klic,ka,lc->ia',eris.ooov,t1,t1)
t1new += einsum('lkic,ka,lc->ia',eris.ooov,t1,t1)
# T2 equation
# For conj(), see Hirata and Bartlett, Eq. (36)
t2new = np.array(eris.oovv).conj()
t2new += einsum('klij,klab->ijab',Woooo,t2)
t2new += einsum('klij,ka,lb->ijab',Woooo,t1,t1)
for a in range(nvir):
Wvvvv_a = np.array(Wvvvv[a])
t2new[:,:,a,:] += einsum('bcd,ijcd->ijb',Wvvvv_a,t2)
t2new[:,:,a,:] += einsum('bcd,ic,jd->ijb',Wvvvv_a,t1,t1)
tmp = einsum('ac,ijcb->ijab',Lvv,t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('ki,kjab->ijab',Loo,t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp2 = np.array(eris.vovv).transpose(3,2,1,0).conj() \
- einsum('kbic,ka->abic',eris.ovov,t1)
tmp = einsum('abic,jc->ijab',tmp2,t1)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp2 = np.array(eris.ooov).transpose(3,2,1,0).conj() \
+ einsum('akic,jc->akij',eris.voov,t1)
tmp = einsum('akij,kb->ijab',tmp2,t1)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = 2*einsum('akic,kjcb->ijab',Wvoov,t2) - einsum('akci,kjcb->ijab',Wvovo,t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('akic,kjbc->ijab',Wvoov,t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('bkci,kjac->ijab',Wvovo,t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
t1new /= eia
t2new /= eijab
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def update_amps(cc, t1, t2, eris):
# Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004) Eqs.(35)-(36)
nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:nocc,nocc:].copy()
foo = fock[:nocc,:nocc].copy()
fvv = fock[nocc:,nocc:].copy()
Foo = imd.cc_Foo(t1,t2,eris)
Fvv = imd.cc_Fvv(t1,t2,eris)
Fov = imd.cc_Fov(t1,t2,eris)
# Move energy terms to the other side
Foo -= np.diag(np.diag(foo))
Fvv -= np.diag(np.diag(fvv))
# T1 equation
t1new = np.asarray(fov).conj().copy()
t1new +=-2*einsum('kc,ka,ic->ia', fov, t1, t1)
t1new += einsum('ac,ic->ia', Fvv, t1)
t1new += -einsum('ki,ka->ia', Foo, t1)
t1new += 2*einsum('kc,kica->ia', Fov, t2)
t1new += -einsum('kc,ikca->ia', Fov, t2)
t1new += einsum('kc,ic,ka->ia', Fov, t1, t1)
t1new += 2*einsum('kcai,kc->ia', eris.ovvo, t1)
t1new += -einsum('kiac,kc->ia', eris.oovv, t1)
eris_ovvv = np.asarray(eris.ovvv)
t1new += 2*einsum('kdac,ikcd->ia', eris_ovvv, t2)
t1new += -einsum('kcad,ikcd->ia', eris_ovvv, t2)
t1new += 2*einsum('kdac,kd,ic->ia', eris_ovvv, t1, t1)
t1new += -einsum('kcad,kd,ic->ia', eris_ovvv, t1, t1)
t1new +=-2*einsum('kilc,klac->ia', eris.ooov, t2)
t1new += einsum('likc,klac->ia', eris.ooov, t2)
t1new +=-2*einsum('kilc,lc,ka->ia', eris.ooov, t1, t1)
t1new += einsum('likc,lc,ka->ia', eris.ooov, t1, t1)
# T2 equation
t2new = np.asarray(eris.ovov).conj().transpose(0,2,1,3).copy()
if cc.cc2:
Woooo2 = np.asarray(eris.oooo).transpose(0,2,1,3).copy()
Woooo2 += einsum('kilc,jc->klij', eris.ooov, t1)
Woooo2 += einsum('ljkc,ic->klij', eris.ooov, t1)
Woooo2 += einsum('kcld,ic,jd->klij', eris.ovov, t1, t1)
t2new += einsum('klij,ka,lb->ijab', Woooo2, t1, t1)
Wvvvv = einsum('kcbd,ka->abcd', eris_ovvv, -t1)
Wvvvv = Wvvvv + Wvvvv.transpose(1,0,3,2)
Wvvvv += np.asarray(eris.vvvv).transpose(0,2,1,3)
t2new += einsum('abcd,ic,jd->ijab', Wvvvv, t1, t1)
Lvv2 = fvv - einsum('kc,ka->ac', fov, t1)
Lvv2 -= np.diag(np.diag(fvv))
tmp = einsum('ac,ijcb->ijab', Lvv2, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
Loo2 = foo + einsum('kc,ic->ki', fov, t1)
Loo2 -= np.diag(np.diag(foo))
tmp = einsum('ki,kjab->ijab', Loo2, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
else:
Loo = imd.Loo(t1, t2, eris)
Lvv = imd.Lvv(t1, t2, eris)
Loo -= np.diag(np.diag(foo))
Lvv -= np.diag(np.diag(fvv))
Woooo = imd.cc_Woooo(t1, t2, eris)
Wvoov = imd.cc_Wvoov(t1, t2, eris)
Wvovo = imd.cc_Wvovo(t1, t2, eris)
Wvvvv = imd.cc_Wvvvv(t1, t2, eris)
tau = t2 + einsum('ia,jb->ijab', t1, t1)
t2new += einsum('klij,klab->ijab', Woooo, tau)
t2new += einsum('abcd,ijcd->ijab', Wvvvv, tau)
tmp = einsum('ac,ijcb->ijab', Lvv, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('ki,kjab->ijab', Loo, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = 2*einsum('akic,kjcb->ijab', Wvoov, t2)
tmp -= einsum('akci,kjcb->ijab', Wvovo, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('akic,kjbc->ijab', Wvoov, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('bkci,kjac->ijab', Wvovo, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp2 = einsum('kibc,ka->abic', eris.oovv, -t1)
tmp2 += np.asarray(eris.ovvv).conj().transpose(1,3,0,2)
tmp = einsum('abic,jc->ijab', tmp2, t1)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp2 = einsum('kcai,jc->akij', eris.ovvo, t1)
tmp2 += np.asarray(eris.ooov).transpose(3,1,2,0).conj()
tmp = einsum('akij,kb->ijab', tmp2, t1)
t2new -= (tmp + tmp.transpose(1,0,3,2))
mo_e = eris.fock.diagonal().real
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
t1new /= eia
t2new /= eijab
return t1new, t2new
def update_amps(cc, t1, t2, eris):
# Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004) Eqs.(35)-(36)
nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:nocc, nocc:].copy()
foo = fock[:nocc, :nocc].copy()
fvv = fock[nocc:, nocc:].copy()
Foo = imd.cc_Foo(0 * t1, t2, eris)
Fvv = imd.cc_Fvv(0 * t1, t2, eris)
Fov = imd.cc_Fov(t1, t2, eris)
Foo -= np.diag(np.diag(foo))
Fvv -= np.diag(np.diag(fvv))
# T1 equation
t1new = np.asarray(fov).conj().copy()
t1new += lib.einsum('ac,ic->ia', Fvv, t1)
t1new += -lib.einsum('ki,ka->ia', Foo, t1)
t1new += 2 * lib.einsum('kc,kica->ia', Fov, t2)
t1new += -lib.einsum('kc,ikca->ia', Fov, t2)
t1new += 2 * lib.einsum('kcai,kc->ia', eris.ovvo, t1)
t1new += -lib.einsum('kiac,kc->ia', eris.oovv, t1)
eris_ovvv = np.asarray(eris.ovvv)
t1new += 2 * lib.einsum('kdac,ikcd->ia', eris_ovvv, t2)
t1new += -lib.einsum('kcad,ikcd->ia', eris_ovvv, t2)
t1new += -2 * lib.einsum('kilc,klac->ia', eris.ooov, t2)
t1new += lib.einsum('likc,klac->ia', eris.ooov, t2)
# T2 equation
t2new = np.asarray(eris.ovov).conj().transpose(0, 2, 1, 3).copy()
Loo = imd.Loo(0 * t1, t2, eris)
Lvv = imd.Lvv(0 * t1, t2, eris)
Loo -= np.diag(np.diag(foo))
Lvv -= np.diag(np.diag(fvv))
Woooo = imd.cc_Woooo(0 * t1, t2, eris)
Wvoov = imd.cc_Wvoov(0 * t1, t2, eris)
Wvovo = imd.cc_Wvovo(0 * t1, t2, eris)
Wvvvv = imd.cc_Wvvvv(0 * t1, t2, eris)
t2new += lib.einsum('klij,klab->ijab', Woooo, t2)
t2new += lib.einsum('abcd,ijcd->ijab', Wvvvv, t2)
tmp = lib.einsum('ac,ijcb->ijab', Lvv, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp = lib.einsum('ki,kjab->ijab', Loo, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp = 2 * lib.einsum('akic,kjcb->ijab', Wvoov, t2)
tmp -= lib.einsum('akci,kjcb->ijab', Wvovo, t2)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp = lib.einsum('akic,kjbc->ijab', Wvoov, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp = lib.einsum('bkci,kjac->ijab', Wvovo, t2)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
tmp2 = np.asarray(eris.ovvv).conj().transpose(1, 3, 0, 2)
tmp = lib.einsum('abic,jc->ijab', tmp2, t1)
t2new += (tmp + tmp.transpose(1, 0, 3, 2))
tmp2 = np.asarray(eris.ooov).transpose(3, 1, 2, 0).conj()
tmp = lib.einsum('akij,kb->ijab', tmp2, t1)
t2new -= (tmp + tmp.transpose(1, 0, 3, 2))
mo_e = eris.fock.diagonal().real
eia = mo_e[:nocc, None] - mo_e[None, nocc:]
eijab = lib.direct_sum('ia,jb->ijab', eia, eia)
t1new /= eia
t2new /= eijab
return t1new, t2new
def update_amps(cc, t1, t2, eris):
# Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004) Eqs.(35)-(36)
assert(isinstance(eris, ccsd._ChemistsERIs))
nocc, nvir = t1.shape
fock = eris.fock
mo_e_o = eris.mo_energy[:nocc]
mo_e_v = eris.mo_energy[nocc:] + cc.level_shift
fov = fock[:nocc,nocc:].copy()
foo = fock[:nocc,:nocc].copy()
fvv = fock[nocc:,nocc:].copy()
Foo = imd.cc_Foo(t1,t2,eris)
Fvv = imd.cc_Fvv(t1,t2,eris)
Fov = imd.cc_Fov(t1,t2,eris)
# Move energy terms to the other side
Foo[np.diag_indices(nocc)] -= mo_e_o
Fvv[np.diag_indices(nvir)] -= mo_e_v
# T1 equation
t1new =-2*np.einsum('kc,ka,ic->ia', fov, t1, t1)
t1new += np.einsum('ac,ic->ia', Fvv, t1)
t1new += -np.einsum('ki,ka->ia', Foo, t1)
t1new += 2*np.einsum('kc,kica->ia', Fov, t2)
t1new += -np.einsum('kc,ikca->ia', Fov, t2)
t1new += np.einsum('kc,ic,ka->ia', Fov, t1, t1)
t1new += fov.conj()
t1new += 2*np.einsum('kcai,kc->ia', eris.ovvo, t1)
t1new += -np.einsum('kiac,kc->ia', eris.oovv, t1)
eris_ovvv = np.asarray(eris.get_ovvv())
t1new += 2*lib.einsum('kdac,ikcd->ia', eris_ovvv, t2)
t1new += -lib.einsum('kcad,ikcd->ia', eris_ovvv, t2)
t1new += 2*lib.einsum('kdac,kd,ic->ia', eris_ovvv, t1, t1)
t1new += -lib.einsum('kcad,kd,ic->ia', eris_ovvv, t1, t1)
eris_ovoo = np.asarray(eris.ovoo, order='C')
t1new +=-2*lib.einsum('lcki,klac->ia', eris_ovoo, t2)
t1new += lib.einsum('kcli,klac->ia', eris_ovoo, t2)
t1new +=-2*lib.einsum('lcki,lc,ka->ia', eris_ovoo, t1, t1)
t1new += lib.einsum('kcli,lc,ka->ia', eris_ovoo, t1, t1)
# T2 equation
tmp2 = lib.einsum('kibc,ka->abic', eris.oovv, -t1)
tmp2 += np.asarray(eris_ovvv).conj().transpose(1,3,0,2)
tmp = lib.einsum('abic,jc->ijab', tmp2, t1)
t2new = tmp + tmp.transpose(1,0,3,2)
tmp2 = lib.einsum('kcai,jc->akij', eris.ovvo, t1)
tmp2 += eris_ovoo.transpose(1,3,0,2).conj()
tmp = lib.einsum('akij,kb->ijab', tmp2, t1)
t2new -= tmp + tmp.transpose(1,0,3,2)
t2new += np.asarray(eris.ovov).conj().transpose(0,2,1,3)
if cc.cc2:
Woooo2 = np.asarray(eris.oooo).transpose(0,2,1,3).copy()
Woooo2 += lib.einsum('lcki,jc->klij', eris_ovoo, t1)
Woooo2 += lib.einsum('kclj,ic->klij', eris_ovoo, t1)
Woooo2 += lib.einsum('kcld,ic,jd->klij', eris.ovov, t1, t1)
t2new += lib.einsum('klij,ka,lb->ijab', Woooo2, t1, t1)
Wvvvv = lib.einsum('kcbd,ka->abcd', eris_ovvv, -t1)
Wvvvv = Wvvvv + Wvvvv.transpose(1,0,3,2)
Wvvvv += np.asarray(eris.vvvv).transpose(0,2,1,3)
t2new += lib.einsum('abcd,ic,jd->ijab', Wvvvv, t1, t1)
Lvv2 = fvv - np.einsum('kc,ka->ac', fov, t1)
Lvv2 -= np.diag(np.diag(fvv))
tmp = lib.einsum('ac,ijcb->ijab', Lvv2, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
Loo2 = foo + np.einsum('kc,ic->ki', fov, t1)
Loo2 -= np.diag(np.diag(foo))
tmp = lib.einsum('ki,kjab->ijab', Loo2, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
else:
Loo = imd.Loo(t1, t2, eris)
Lvv = imd.Lvv(t1, t2, eris)
Loo[np.diag_indices(nocc)] -= mo_e_o
Lvv[np.diag_indices(nvir)] -= mo_e_v
Woooo = imd.cc_Woooo(t1, t2, eris)
Wvoov = imd.cc_Wvoov(t1, t2, eris)
Wvovo = imd.cc_Wvovo(t1, t2, eris)
Wvvvv = imd.cc_Wvvvv(t1, t2, eris)
tau = t2 + np.einsum('ia,jb->ijab', t1, t1)
t2new += lib.einsum('klij,klab->ijab', Woooo, tau)
t2new += lib.einsum('abcd,ijcd->ijab', Wvvvv, tau)
tmp = lib.einsum('ac,ijcb->ijab', Lvv, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = lib.einsum('ki,kjab->ijab', Loo, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = 2*lib.einsum('akic,kjcb->ijab', Wvoov, t2)
tmp -= lib.einsum('akci,kjcb->ijab', Wvovo, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = lib.einsum('akic,kjbc->ijab', Wvoov, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = lib.einsum('bkci,kjac->ijab', Wvovo, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
eia = mo_e_o[:,None] - mo_e_v
eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
t1new /= eia
t2new /= eijab
return t1new, t2new