def ftsolver(h1e,g2e,norb,nelec,T,mu=0,symm='UHF', Tmin=1.e-3,\
dcompl=False,**kwargs):
if symm is 'RHF':
from pyscf.fci import direct_spin1 as fcisolver
h1e = h1e[0]
g2e = g2e[1]
elif symm is 'SOC':
from pyscf.fci import fci_slow_spinless as fcisolver
dcompl = True
elif symm is 'UHF':
from pyscf.fci import direct_uhf as fcisolver
else:
from pyscf.fci import direct_spin1 as fcisolver
if isinstance(nelec, (int, np.integer)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
na = cistring.num_strings(norb, neleca)
nb = cistring.num_strings(norb, nelecb)
nelec = (neleca, nelecb)
ne = neleca + nelecb
ndim = na * nb
if T < Tmin:
e, v = fcisolver.kernel(h1e, g2e, norb, nelec)
RDM1, RDM2 = fcisolver.make_rdm12s(v, norb, nelec)
z = np.exp(-(e - mu * ne) / T)
return np.asarray(RDM1) * ndim, np.asarray(RDM2) * ndim, e * ndim
ew, ev = diagH(h1e, g2e, norb, nelec, fcisolver)
rdm1, rdm2 = [], []
RDM1 = np.zeros((2, norb, norb))
RDM2 = np.zeros((3, norb, norb, norb, norb))
Z = np.sum(np.exp(-(ew - mu * ne) / T))
E = np.sum(np.exp(-(ew - mu * ne) / T) * ew) # not normalized
#print Z, E
for i in range(ndim):
dm1, dm2 = fcisolver.make_rdm12s(ev[:, i].copy(), norb, nelec)
RDM1 += np.asarray(dm1) * np.exp(-(ew[i] - mu * ne) / T)
RDM2 += np.asarray(dm2) * np.exp(-(ew[i] - mu * ne) / T)
if symm is not 'UHF' and len(RDM1.shape) == 3:
RDM1 = np.sum(RDM1, axis=0)
RDM2 = np.sum(RDM2, axis=0)
RDM1 /= Z
RDM2 /= Z
E /= Z
return RDM1, RDM2, E
def spin_square(fcivec, norb, nelec, mo_coeff=None, ovlp=1):
r'''General spin square operator.
... math::
<CI|S_+*S_-|CI> &= n_\alpha + \delta_{ik}\delta_{jl}Gamma_{i\alpha k\beta ,j\beta l\alpha } \\
<CI|S_-*S_+|CI> &= n_\beta + \delta_{ik}\delta_{jl}Gamma_{i\beta k\alpha ,j\alpha l\beta } \\
<CI|S_z*S_z|CI> &= \delta_{ik}\delta_{jl}(Gamma_{i\alpha k\alpha ,j\alpha l\alpha }
- Gamma_{i\alpha k\alpha ,j\beta l\beta }
- Gamma_{i\beta k\beta ,j\alpha l\alpha}
+ Gamma_{i\beta k\beta ,j\beta l\beta})
+ (n_\alpha+n_\beta)/4
Given the overlap betwen non-degenerate alpha and beta orbitals, this
function can compute the expectation value spin square operator for
UHF-FCI wavefunction
'''
from pyscf.fci import direct_spin1
if isinstance(mo_coeff, numpy.ndarray) and mo_coeff.ndim == 2:
mo_coeff = (mo_coeff, mo_coeff)
elif mo_coeff is None:
mo_coeff = (numpy.eye(norb), ) * 2
# projected overlap matrix elements for partial trace
if isinstance(ovlp, numpy.ndarray):
ovlpaa = reduce(numpy.dot, (mo_coeff[0].T, ovlp, mo_coeff[0]))
ovlpbb = reduce(numpy.dot, (mo_coeff[1].T, ovlp, mo_coeff[1]))
ovlpab = reduce(numpy.dot, (mo_coeff[0].T, ovlp, mo_coeff[1]))
ovlpba = reduce(numpy.dot, (mo_coeff[1].T, ovlp, mo_coeff[0]))
else:
ovlpaa = numpy.dot(mo_coeff[0].T, mo_coeff[0])
ovlpbb = numpy.dot(mo_coeff[1].T, mo_coeff[1])
ovlpab = numpy.dot(mo_coeff[0].T, mo_coeff[1])
ovlpba = numpy.dot(mo_coeff[1].T, mo_coeff[0])
# if ovlp=1, ssz = (neleca-nelecb)**2 * .25
(dm1a, dm1b), (dm2aa, dm2ab, dm2bb) = \
direct_spin1.make_rdm12s(fcivec, norb, nelec)
ssz =(_bi_trace(dm2aa, ovlpaa, ovlpaa)
- _bi_trace(dm2ab, ovlpaa, ovlpbb)
+ _bi_trace(dm2bb, ovlpbb, ovlpbb)
- _bi_trace(dm2ab, ovlpaa, ovlpbb)) * .25 \
+(_trace(dm1a, ovlpaa)
+ _trace(dm1b, ovlpbb)) *.25
dm2baab = _make_rdm2_baab(fcivec, norb, nelec)
dm2abba = _make_rdm2_abba(fcivec, norb, nelec)
dm2baab = rdm.reorder_rdm(dm1b, dm2baab, inplace=True)[1]
dm2abba = rdm.reorder_rdm(dm1a, dm2abba, inplace=True)[1]
ssxy =(_bi_trace(dm2abba, ovlpab, ovlpba)
+ _bi_trace(dm2baab, ovlpba, ovlpab) \
+ _trace(dm1a, ovlpaa)
+ _trace(dm1b, ovlpbb)) * .5
ss = ssxy + ssz
s = numpy.sqrt(ss + .25) - .5
multip = s * 2 + 1
return ss, multip
def test_rdm(self):
norb, nelec = 10, 4
strs = cistring.gen_strings4orblist(range(norb), nelec)
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .6
strsa = strs[mask]
mask = numpy.random.random(len(strs)) > .7
strsb = strs[mask]
ci_strs = (strsa, strsb)
ci_coeff = select_ci._as_SCIvector(
numpy.random.random((len(strsa), len(strsb))), ci_strs)
ci0 = select_ci.to_fci(ci_coeff, norb, (nelec, nelec))
dm1ref, dm2ref = direct_spin1.make_rdm12s(ci0, norb, (nelec, nelec))
dm1 = select_ci.make_rdm1s(ci_coeff, norb, (nelec, nelec))
self.assertAlmostEqual(abs(dm1[0] - dm1ref[0]).sum(), 0, 9)
self.assertAlmostEqual(abs(dm1[1] - dm1ref[1]).sum(), 0, 9)
dm2 = select_ci.make_rdm2s(ci_coeff, norb, (nelec, nelec))
self.assertAlmostEqual(abs(dm2[0] - dm2ref[0]).sum(), 0, 9)
self.assertAlmostEqual(abs(dm2[1] - dm2ref[1]).sum(), 0, 9)
self.assertAlmostEqual(abs(dm2[2] - dm2ref[2]).sum(), 0, 9)
ci1_coeff = select_ci._as_SCIvector(
numpy.random.random((len(strsa), len(strsb))), ci_strs)
ci1 = select_ci.to_fci(ci1_coeff, norb, (nelec, nelec))
dm1ref, dm2ref = direct_spin1.trans_rdm12s(ci1, ci0, norb,
(nelec, nelec))
dm1 = select_ci.trans_rdm1s(ci1_coeff, ci_coeff, norb, (nelec, nelec))
self.assertAlmostEqual(abs(dm1[0] - dm1ref[0]).sum(), 0, 9)
self.assertAlmostEqual(abs(dm1[1] - dm1ref[1]).sum(), 0, 9)
def spin_square(fcivec, norb, nelec, mo_coeff=None, ovlp=1):
from pyscf.fci import direct_spin1
if mo_coeff is None:
mo_coeff = (numpy.eye(norb), ) * 2
(dm1a, dm1b), (dm2aa, dm2ab, dm2bb) = \
direct_spin1.make_rdm12s(fcivec, norb, nelec)
return spin_square_general(dm1a, dm1b, dm2aa, dm2ab, dm2bb, mo_coeff, ovlp)
def rdm12s_ft_smpl(h1e, g2e, norb, nelec, T, \
m=50, nsmpl=20000, Tmin=1e-3, symm='RHF', **kwargs):
if symm is 'RHF':
from pyscf.fci import direct_spin1 as fcisolver
elif symm is 'SOC':
from pyscf.fci import fci_slow_spinless as fcisolver
elif symm is 'UHF':
from pyscf.fci import direct_uhf as fcisolver
else:
from pyscf.fci import direct_spin1 as fcisolver
if T < Tmin:
e, c = fcisolver.kernel(h1e, g2e, norb, nelec)
dm1, dm2 = fcisolver.make_rdm12s(c, norb, nelec)
dm1 = numpy.asarray(dm1)
dm2 = numpy.asarray(dm2)
else:
h2e = fcisolver.absorb_h1e(h1e, g2e, norb, nelec, .5)
if symm is 'SOC':
na = cistring.num_strings(norb, nelec)
ci0 = numpy.random.randn(na)
else:
na = cistring.num_strings(norb, nelec // 2)
ci0 = numpy.random.randn(na * na)
hdiag = fcisolver.make_hdiag(h1e, g2e, norb, nelec)
hdiag = hdiag - hdiag[0]
disp = numpy.exp(T) * 0.5
ci0 = ci0 / numpy.linalg.norm(ci0)
def hop(c):
hc = fcisolver.contract_2e(h2e, c, norb, nelec)
return hc.reshape(-1)
def qud(v1):
dm1, dm2 = fcisolver.make_rdm12s(v1, norb, nelec)
return dm1, dm2
dm1, dm2, e = ftsmpl.ft_smpl_rdm12s(qud,
hop,
ci0,
T,
norb,
nsamp=nsmpl,
M=m)
if symm is 'UHF':
return dm1, dm2, e
elif len(dm1.shape) == 3:
return numpy.sum(dm1, axis=0), numpy.sum(dm2, axis=0), e
else:
return dm1, dm2, e
def make_rdm12s(fcivec, norb, nelec, link_index=None, reorder=True):
return direct_spin1.make_rdm12s(fcivec, norb, nelec, link_index, reorder)
def make_rdm2_abba(fcivec, norb, nelec):
from pyscf.fci import direct_spin1
dm2aa, dm2ab, dm2bb = direct_spin1.make_rdm12s(fcivec, norb, nelec)[1]
dm2abba = -dm2ab.transpose(0, 3, 2, 1)
return dm2abba
def make_rdm2_baab(fcivec, norb, nelec):
from pyscf.fci import direct_spin1
dm2aa, dm2ab, dm2bb = direct_spin1.make_rdm12s(fcivec, norb, nelec)[1]
dm2baab = -dm2ab.transpose(2, 1, 0, 3)
return dm2baab
def rdm12s_fted(h1e,g2e,norb,nelec,T,symm='RHF',Tmin=1.e-3,\
dcompl=False,**kwargs):
if symm is 'RHF':
from pyscf.fci import direct_spin1 as fcisolver
elif symm is 'SOC':
from pyscf.fci import fci_slow_spinless as fcisolver
dcompl = True
elif symm is 'UHF':
from pyscf.fci import direct_uhf as fcisolver
else:
from pyscf.fci import direct_spin1 as fcisolver
ew, ev = diagH(h1e, g2e, norb, nelec, fcisolver)
ndim = len(ew)
rdm1, rdm2 = [], []
RDM1, RDM2 = fcisolver.make_rdm12s(ev[:, 0].copy(), norb, nelec)
RDM1 = np.asarray(RDM1, dtype=np.complex128)
RDM2 = np.asarray(RDM2, dtype=np.complex128)
if T < Tmin:
if symm is not 'UHF' and len(RDM1.shape) == 3:
RDM1 = np.sum(RDM1, axis=0)
RDM2 = np.sum(RDM2, axis=0)
if not dcompl:
return RDM1.real, RDM2.real, ew[0].real
return RDM1, RDM2, ew[0]
ew -= ew[0]
Z = np.sum(np.exp(-ew / T))
E = np.sum(np.exp(-ew / T) * ew) / Z
for i in range(ndim):
dm1, dm2 = fcisolver.make_rdm12s(ev[:, i].copy(), norb, nelec)
rdm1.append(np.asarray(dm1, dtype=np.complex128))
rdm2.append(np.asarray(dm2, dtype=np.complex128))
# rdm1 = np.asarray(rdm1)
# rdm2 = np.asarray(rdm2)
# RDM1 = np.sum(rdm1*np.exp(-1.j*ew/T))/Z
# RDM2 = np.sum(rdm2*np.exp(-1.j*ew/T))/Z
RDM1 *= 0.
RDM2 *= 0.
for i in range(ndim):
RDM1 += rdm1[i] * np.exp(-ew[i] / T)
RDM2 += rdm2[i] * np.exp(-ew[i] / T)
RDM1 /= Z
RDM2 /= Z
if symm is not 'UHF' and len(RDM1.shape) == 3:
RDM1 = np.sum(RDM1, axis=0)
RDM2 = np.sum(RDM2, axis=0)
if not dcompl:
E = (E + ew[0]).real
RDM1 = RDM1.real
RDM2 = RDM2.real
return RDM1, RDM2, E
def rdm12s_fted(h1e,g2e,norb,nelec,T,symm='RHF',Tmin=1.e-3,\
dcompl=False,**kwargs):
if symm is 'RHF':
from pyscf.fci import direct_spin1 as fcisolver
elif symm is 'SOC':
from pyscf.fci import fci_slow_spinless as fcisolver
dcompl = True
elif symm is 'UHF':
from pyscf.fci import direct_uhf as fcisolver
else:
from pyscf.fci import direct_spin1 as fcisolver
ew, ev = diagH(h1e, g2e, norb, nelec, fcisolver)
RDM1, RDM2 = fcisolver.make_rdm12s(ev[:, 0].copy(), norb, nelec)
RDM1 = np.asarray(RDM1, dtype=np.complex128)
RDM2 = np.asarray(RDM2, dtype=np.complex128)
if T < Tmin:
if symm is not 'UHF' and len(RDM1.shape) == 3:
RDM1 = np.sum(RDM1, axis=0)
RDM2 = np.sum(RDM2, axis=0)
if not dcompl:
return RDM1.real, RDM2.real, ew[0].real
return RDM1, RDM2, ew[0]
ews, evs = solve_spectrum(h1e, g2e, norb, fcisolver)
mu = solve_mu(h1e, g2e, norb, nelec, fcisolver, T, mu0=0., ews=ews)
Z = 0.
E = 0.
RDM1 *= 0.
RDM2 *= 0.
for na in range(0, norb + 1):
for nb in range(0, norb + 1):
ne = na + nb
ndim = len(ews[na, nb])
Z += np.sum(np.exp((-ews[na, nb] + mu * ne) / T))
E += np.sum(np.exp((-ews[na, nb] + mu * ne) / T) * ews[na, nb])
for i in range(ndim):
dm1, dm2 = fcisolver.make_rdm12s(evs[na, nb][:, i].copy(),
norb, (na, nb))
dm1 = np.asarray(dm1, dtype=np.complex128)
dm2 = np.asarray(dm2, dtype=np.complex128)
RDM1 += dm1 * np.exp((ne * mu - ews[na, nb][i]) / T)
RDM2 += dm2 * np.exp((ne * mu - ews[na, nb][i]) / T)
E /= Z
RDM1 /= Z
RDM2 /= Z
if symm is not 'UHF' and len(RDM1.shape) == 3:
RDM1 = np.sum(RDM1, axis=0)
RDM2 = np.sum(RDM2, axis=0)
if not dcompl:
E = E.real
RDM1 = RDM1.real
RDM2 = RDM2.real
return RDM1, RDM2, E
def rdm12s_fted(h1e,g2e,norb,nelec,beta,mu=0.0,bmax=1e3, \
dcompl=False,**kwargs):
'''
Return the expectation values of energy, RDM1 and RDM2 at temperature T.
'''
# make sure the Hamiltonians have the correct shape
# if (type(h1e) is tuple) or (type(h1e) is list):
# h1e = h1e[0]
# g2e = g2e[0]
Z = 0.
E = 0.
RDM1 = np.zeros((norb, norb))
RDM2_0 = np.zeros((norb, norb, norb, norb))
RDM2_1 = np.zeros((norb, norb, norb, norb))
if beta > bmax:
e, v = fcisolver.kernel(h1e, g2e, norb, nelec)
RDM1, RDM2 = fcisolver.make_rdm12s(v, norb, nelec)
return np.asarray(RDM1), np.asarray(RDM2), e
# check for overflow
e0, _ = fcisolver.kernel(h1e, g2e, norb, norb)
exp_max = (-e0 + mu * norb) * beta
if (exp_max > 700):
exp_shift = exp_max - 500
else:
exp_shift = 0
# Calculating E, RDM1, Z
N = 0
# na =/= nb
for na in range(0, norb + 1):
for nb in range(na + 1, norb + 1):
ne = na + nb
ew, ev = diagH(h1e, g2e, norb, (na, nb), fcisolver)
exp_ = (-ew + mu * (na + nb)) * beta
exp_ -= exp_shift
ndim = len(ew)
Z += np.sum(np.exp(exp_)) * 2
E += np.sum(np.exp(exp_) * ew) * 2
N += ne * np.sum(np.exp(exp_)) * 2
for i in range(ndim):
dm1, dm2 = fcisolver.make_rdm12s(ev[:, i].copy(), norb,
(na, nb))
RDM1 += (dm1[0] + dm1[1]) * np.exp(exp_[i])
RDM2_0 += (dm2[0] + dm2[2]) * np.exp(exp_[i])
RDM2_1 += (dm2[1] + np.transpose(dm2[1],
(2, 3, 0, 1))) * np.exp(
exp_[i])
for na in range(0, norb + 1):
nb = na
ne = na + nb
ew, ev = diagH(h1e, g2e, norb, (na, nb), fcisolver)
exp_ = (-ew + mu * (na + nb)) * beta
exp_ -= exp_shift
ndim = len(ew)
Z += np.sum(np.exp(exp_))
E += np.sum(np.exp(exp_) * ew)
N += ne * np.sum(np.exp(exp_))
for i in range(ndim):
dm1, dm2 = fcisolver.make_rdm12s(ev[:, i].copy(), norb, (na, nb))
RDM1 += dm1[0] * np.exp(exp_[i])
RDM2_0 += dm2[0] * np.exp(exp_[i])
RDM2_1 += dm2[1] * np.exp(exp_[i])
E /= Z
N /= Z
RDM1 /= Z
RDM2_0 /= Z
RDM2_1 /= Z
log.result("The expectation of electron number:")
log.result("N(total) = %10.10f" % N)
RDM1 = np.asarray([RDM1, RDM1])
RDM2 = np.asarray([RDM2_0, RDM2_1, RDM2_0])
log.result("FTED energy: %10.12f" % E)
# RDM2 order: aaaa, aabb, bbbb
return RDM1, RDM2, E
def qud(v1):
dm1, dm2 = fcisolver.make_rdm12s(v1, norb, nelec)
return dm1, dm2
def make_dm12(ci0, norb, nelec):
def des(ci0, norb, nelec, ap_id, spin):
if spin == 0:
ci1 = addons.des_a(ci0, norb, nelec, ap_id)
ne = nelec[0] - 1, nelec[1]
else:
ci1 = addons.des_b(ci0, norb, nelec, ap_id)
ne = nelec[0], nelec[1] - 1
return ci1, ne
def cre(ci0, norb, nelec, ap_id, spin):
if spin == 0:
ci1 = addons.cre_a(ci0, norb, nelec, ap_id)
ne = nelec[0] + 1, nelec[1]
else:
ci1 = addons.cre_b(ci0, norb, nelec, ap_id)
ne = nelec[0], nelec[1] + 1
return ci1, ne
dm1 = numpy.zeros((norb, 2, norb, 2))
for i in range(norb):
for j in range(norb):
for i1 in range(2):
for j1 in range(2):
if i1 == j1:
ne = nelec
ci1, ne = des(ci0, norb, ne, j, j1)
ci1, ne = cre(ci1, norb, ne, i, i1)
dm1[i, i1, j, j1] = numpy.dot(ci0.ravel(), ci1.ravel())
dm2 = numpy.zeros((norb, 2, norb, 2, norb, 2, norb, 2))
for i in range(norb):
for j in range(norb):
for k in range(norb):
for l in range(norb):
for i1 in range(2):
for j1 in range(2):
for k1 in range(2):
for l1 in range(2):
if i1 + j1 == k1 + l1:
ci1, ne = ci0, nelec
ci1, ne = des(ci1, norb, ne, k, k1)
ci1, ne = des(ci1, norb, ne, l, l1)
ci1, ne = cre(ci1, norb, ne, j, j1)
ci1, ne = cre(ci1, norb, ne, i, i1)
dm2[i, i1, j, j1, k, k1, l,
l1] = numpy.dot(
ci0.ravel(), ci1.ravel())
if 0:
dm1a = numpy.einsum('iajb->ij', dm1)
dm2a = numpy.einsum('iajbkalb->ijkl', dm2)
print abs(numpy.einsum('ipjp->ij', dm2a) / (sum(nelec) - 1) -
dm1a).sum()
(dm1a, dm1b), (dm2aa, dm2ab, dm2bb) = \
direct_spin1.make_rdm12s(ci0, norb, nelec)
print abs(dm1a - dm1[:, 0, :, 0]).sum()
print abs(dm2aa -
dm2[:, 0, :, 0, :, 0, :, 0].transpose(0, 2, 1, 3)).sum()
print abs(dm2ab -
dm2[:, 0, :, 1, :, 0, :, 1].transpose(0, 2, 1, 3)).sum()
print abs(
dm2ab.transpose(2, 3, 0, 1) -
dm2[:, 1, :, 0, :, 1, :, 0].transpose(0, 2, 1, 3)).sum()
print abs(dm2bb -
dm2[:, 1, :, 1, :, 1, :, 1].transpose(0, 2, 1, 3)).sum()
dm2baab = spin_op.make_rdm2_baab(ci0, norb, nelec)
dm2abba = spin_op.make_rdm2_abba(ci0, norb, nelec)
print abs(dm2baab -
dm2[:, 1, :, 0, :, 0, :, 1].transpose(0, 2, 1, 3)).sum()
print abs(dm2abba -
dm2[:, 0, :, 1, :, 1, :, 0].transpose(0, 2, 1, 3)).sum()
return dm1, dm2
one_sf, two_sf = find_full_casscf_12rdm(mc.fcisolver, mf.mo_coeff,
'spinfree_TwoRDM.1', norb,
nelec)
assert (numpy.allclose(
two_sf[:n_occorbs, :n_occorbs, :n_occorbs, :n_occorbs],
spinfree_2))
mc2 = mcscf.CASCI(mf, 6, 6)
# mc2.canonicalization = False
mc2.fcisolver = direct_spin1.FCISolver(mol)
emc2, e_cas2, fcivec2 = mc2.kernel()[:3]
#ss_tot = spin_op.spin_square(fcivec2, norb, nelec)[0]
# print 'ss_tot exact: ',ss_tot
(dm1a_, dm1b_), (dm2aa_, dm2ab_,
dm2bb_) = direct_spin1.make_rdm12s(fcivec2,
norb,
nelec,
reorder=False)
#f_dbg = dbg_ss_frac(dm1, dm2, norb, mo_cas, ovlp)
# dm2baab(pq,rs) = <p(beta)* q(alpha) r(alpha)* s(beta)
dm2baab_ = spin_op._make_rdm2_baab(fcivec2, norb, nelec)
# dm2abba(pq,rs) = <q(alpha)* p(beta) s(beta)* r(alpha)
dm2abba_ = spin_op._make_rdm2_abba(fcivec2, norb, nelec)
ss_tot = spin_op.spin_square(fcivec2, norb, nelec)[0]
f_opt_act = opt_ss_frac(dm1a_, dm1b_, dm2aa_, dm2ab_, dm2bb_, dm2baab_,
dm2abba_, norb, nelec, mo_cas, ovlp)
f_mag_act = opt_mag_frac(dm1a_, dm1b_, norb, nelec, mo_cas, ovlp)
if DoNECI:
f_opt_full = opt_ss_frac(dm1a, dm1b, dm2aa, dm2ab, dm2bb, dm2baab,
dm2abba, n_occorbs, nelec_full, occorbs, ovlp)
def rdm12s_ftfci(h1e,g2e,norb,nelec,T,mu,m=50,Tmin=1e-3,\
dcompl=False,symm='RHF',**kwargs):
if symm is 'RHF':
from pyscf.fci import direct_spin1 as fcisolver
elif symm is 'SOC':
from pyscf.fci import fci_slow_spinless as fcisolver
dcompl = True
elif symm is 'UHF':
from pyscf.fci import direct_uhf as fcisolver
else:
from pyscf.fci import direct_spin1 as fcisolver
if symm != 'UHF' and isinstance(h1e, tuple):
h1e = h1e[0]
g2e = g2e[1]
if T < Tmin: # only for half-filling
e, v = fcisolver.kernel(h1e, g2e, norb, nelec)
RDM1, RDM2 = fcisolver.make_rdm12s(v, norb, nelec)
return numpy.asarray(RDM1), numpy.asarray(RDM2), e
# loop over na and nb
Z = 0.
E = 0.
RDM1 = numpy.zeros((2, norb, norb), dtype=numpy.complex128)
RDM2 = numpy.zeros((3, norb, norb, norb, norb), dtype=numpy.complex128)
#for ns in range(1):
# rdm1,rdm2,e,z = lanczos_grand.ft_solver(h1e,g2e,fcisolver,norb,nelec,T,mu=0,m=m)
# RDM1 += rdm1
# RDM2 += rdm2
# E += e
# Z += z
# calculate the number of states
nstate = 0.
dN = 0
for na in range(norb / 2 - dN, norb / 2 + dN + 1):
for nb in range(norb / 2 - dN, norb / 2 + dN + 1):
nstate += cistring.num_strings(norb, na) * cistring.num_strings(
norb, nb)
for na in range(norb / 2 - dN, norb / 2 + dN + 1):
for nb in range(na, norb / 2 + dN + 1):
ne = (na, nb)
ntot = na + nb
nci = cistring.num_strings(norb, na) * cistring.num_strings(
norb, nb)
factor = numpy.exp(0 * (ntot - norb) / T)
if nci < 1e2:
rdm1, rdm2, e, z = ed_canonical.ftsolver(h1e,
g2e,
fcisolver,
norb,
ne,
T,
mu,
symm='UHF')
Z += z / nstate * factor
E += e / nstate * factor
RDM1 += rdm1 / nstate * factor
RDM2 += rdm2 / nstate * factor
else:
rdm1, rdm2, e, z = lanczos_grand.ft_solver(
h1e, g2e, fcisolver, norb, ne, T, mu)
Z += z * (nci / nstate) * factor
E += e * (nci / nstate) * factor
RDM1 += rdm1 * (nci / nstate) * factor
RDM2 += rdm2 * (nci / nstate) * factor
#if nb > na:
# Z += 2*(nci/nstate)*z*factor
# E += 2*(nci/nstate)*e*factor
# RDM1 += (nci/nstate)*rdm1*factor
# RDM1 += (nci/nstate)*permute_rdm1(rdm1)*factor
# RDM2 += 2*(nci/nstate)*rdm2*factor
#else:
# Z += (nci/nstate)*z*factor
# E += (nci/nstate)*e*factor
# RDM1 += (nci/nstate)*rdm1*factor
# #RDM1 += (nci/nstate)*permute_rdm1(rdm1)*factor/2.
# RDM2 += (nci/nstate)*rdm2*factor
#
E /= Z
RDM1 /= Z
RDM2 /= Z
if not dcompl:
E = E.real
RDM1 = RDM1.real
RDM2 = RDM2.real
return RDM1, RDM2, E
if __name__ == '__main__':
from pyscf.fci import direct_uhf as fcisolver
norb = 12
nelec = (norb / 2, norb / 2)
u = 4.0
T = 0.05
mu = 2
h1e = numpy.zeros((norb, norb))
for i in range(norb):
h1e[i, (i + 1) % norb] = -1.0
h1e[i, (i - 1) % norb] = -1.0
#h1e[0,-1] = 0.
#h1e[-1,0] = 0.
g2e_ = numpy.zeros((norb, ) * 4)
for i in range(norb):
g2e_[i, i, i, i] = u
h1e = (h1e, h1e)
g2e = (numpy.zeros((norb, ) * 4), g2e_, numpy.zeros((norb, ) * 4))
rdm1, rdm2, e = rdm12s_ftfci(h1e,g2e,norb,nelec,T,mu,m=200,Tmin=1e-3,\
dcompl=False,symm='UHF')
e0, v = fcisolver.kernel(h1e, g2e, norb, nelec, nroots=1)
rdm10, rdm20 = fcisolver.make_rdm12s(v, norb, nelec)
print e / norb - e0 / norb
print numpy.linalg.norm(rdm1 - rdm10)
print numpy.linalg.norm(rdm2 - rdm20)
print rdm1[0][:4, :4]
print rdm10[0][:4, :4]
