def guess_wfnsym(ci, norb, nelec, orbsym):
'''Guess the wavefunction symmetry based on the non-zero elements in the
given CI coefficients.
Args:
ci : 2D array
CI coefficients, row for alpha strings and column for beta strings.
norb : int
Number of orbitals.
nelec : int or 2-item list
Number of electrons, or 2-item list for (alpha, beta) electrons
orbsym : list of int
The irrep ID for each orbital.
Returns:
Irrep ID
'''
neleca, nelecb = _unpack_nelec(nelec)
strsa = numpy.asarray(cistring.make_strings(range(norb), neleca))
strsb = numpy.asarray(cistring.make_strings(range(norb), nelecb))
if isinstance(ci, numpy.ndarray) and ci.ndim <= 2:
wfnsym = _guess_wfnsym(ci, strsa, strsb, orbsym)
else:
wfnsym = [_guess_wfnsym(c, strsa, strsb, orbsym) for c in ci]
if any(wfnsym[0] != x for x in wfnsym):
warnings.warn('Different wfnsym %s found in different CI vecotrs' %
wfnsym)
wfnsym = wfnsym[0]
return wfnsym
def symmetrize_wfn(ci, norb, nelec, orbsym, wfnsym=0):
'''Symmetrize the CI wavefunction by zeroing out the determinants which
do not have the right symmetry.
Args:
ci : 2D array
CI coefficients, row for alpha strings and column for beta strings.
norb : int
Number of orbitals.
nelec : int or 2-item list
Number of electrons, or 2-item list for (alpha, beta) electrons
orbsym : list of int
The irrep ID for each orbital.
Kwags:
wfnsym : int
The irrep ID of target symmetry
Returns:
2D array which is the symmetrized CI coefficients
'''
neleca, nelecb = _unpack_nelec(nelec)
strsa = numpy.asarray(cistring.make_strings(range(norb), neleca))
strsb = numpy.asarray(cistring.make_strings(range(norb), nelecb))
return _symmetrize_wfn(ci, strsa, strsb, orbsym, wfnsym)
def gen_frag_basis (psi, ifrag, ci_f=None, nelec=None):
if ci_f is None: ci_f = psi.ci0_f
norb, norb_f, nfrag = psi.norb, psi.norb_f, psi.nfrag
ci0 = np.ones ([1,1], dtype=ci_f[0].dtype)
n = 0
for jfrag, (c, dn) in enumerate (zip (ci_f, norb_f)):
if (ifrag == jfrag): continue
n += dn
ndet = 2**n
ci0 = np.multiply.outer (c, ci0).transpose (0,2,1,3).reshape (ndet, ndet)
n = norb_f[ifrag]
ndet = 2**norb
ci1 = np.empty ((ndet, ndet), dtype=ci_f[0].dtype)
norb0 = sum (norb_f[ifrag+1:]) if ifrag+1<nfrag else 0
norb1 = norb_f[ifrag]
norb2 = sum (norb_f[:ifrag]) if ifrag>0 else 0
ndet0, ndet1, ndet2 = 2**norb0, 2**norb1, 2**norb2
deta_gen, detb_gen = range (ndet1), range (ndet1)
if nelec is not None:
nelec = _unpack_nelec (nelec)
deta_gen = make_strings (range (norb1), nelec[0])
detb_gen = make_strings (range (norb1), nelec[1])
for ideta, idetb in product (deta_gen, detb_gen):
ci1[:,:] = 0
ci1 = ci1.reshape (ndet0, ndet1, ndet2, ndet0, ndet1, ndet2)
ci1[:,ideta,:,:,idetb,:] = ci0.reshape (ndet0, ndet2, ndet0, ndet2)
ci1 = ci1.reshape (ndet, ndet)
ci1 = psi.fermion_spin_shuffle (ci1)
yield ideta, idetb, ci1
def symmetrize_wfn(ci, norb, nelec, orbsym, wfnsym=0):
'''Symmetrize the CI wavefunction by zeroing out the determinants which
do not have the right symmetry.
Args:
ci : 2D array
CI coefficients, row for alpha strings and column for beta strings.
norb : int
Number of orbitals.
nelec : int or 2-item list
Number of electrons, or 2-item list for (alpha, beta) electrons
orbsym : list of int
The irrep ID for each orbital.
Kwags:
wfnsym : int
The irrep ID of target symmetry
Returns:
2D array which is the symmetrized CI coefficients
'''
neleca, nelecb = _unpack_nelec(nelec)
strsa = numpy.asarray(cistring.make_strings(range(norb), neleca))
strsb = numpy.asarray(cistring.make_strings(range(norb), nelecb))
return _symmetrize_wfn(ci, strsa, strsb, orbsym, wfnsym)
def guess_wfnsym(self,
norb,
nelec,
fcivec=None,
orbsym=None,
wfnsym=None,
**kwargs):
'''
Guess point group symmetry of the FCI wavefunction. If fcivec is
given, the symmetry of fcivec is used. Otherwise the symmetry is
based on the HF determinant.
'''
if orbsym is None:
orbsym = self.orbsym
verbose = kwargs.get('verbose', None)
log = logger.new_logger(self, verbose)
nelec = _unpack_nelec(nelec, self.spin)
if fcivec is None:
# guess wfnsym if initial guess is not given
wfnsym = _id_wfnsym(self, norb, nelec, orbsym, wfnsym)
log.debug('Guessing CI wfn symmetry = %s', wfnsym)
elif wfnsym is None:
wfnsym = addons.guess_wfnsym(fcivec, norb, nelec, orbsym)
log.debug('Guessing CI wfn symmetry = %s', wfnsym)
else:
# verify if the input wfnsym is consistent with the symmetry of fcivec
neleca, nelecb = nelec
strsa = numpy.asarray(cistring.make_strings(range(norb), neleca))
strsb = numpy.asarray(cistring.make_strings(range(norb), nelecb))
na, nb = strsa.size, strsb.size
orbsym_in_d2h = numpy.asarray(orbsym) % 10
airreps = numpy.zeros(na, dtype=numpy.int32)
birreps = numpy.zeros(nb, dtype=numpy.int32)
for i, ir in enumerate(orbsym_in_d2h):
airreps[numpy.bitwise_and(strsa, 1 << i) > 0] ^= ir
birreps[numpy.bitwise_and(strsb, 1 << i) > 0] ^= ir
wfnsym = _id_wfnsym(self, norb, nelec, orbsym, wfnsym)
mask = (airreps.reshape(-1, 1) ^ birreps) == wfnsym
if isinstance(fcivec, numpy.ndarray) and fcivec.ndim <= 2:
fcivec = [fcivec]
if all(abs(c.reshape(na, nb)[mask]).max() < 1e-5 for c in fcivec):
raise RuntimeError(
'Input wfnsym is not consistent with fcivec coefficients')
return wfnsym
def test_spin0_contract_2e_symm(self):
norb, nelec = 7, (4,4)
strs = cistring.make_strings(range(norb), nelec[0])
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .3
strsa = strs[mask]
ci_strs = (strsa, strsa)
na = len(strsa)
ci_coeff = numpy.random.random((na,na))
ci_coeff = ci_coeff + ci_coeff.T
civec_strs = selected_ci._as_SCIvector(ci_coeff, ci_strs)
orbsym = (numpy.random.random(norb) * 4).astype(int)
nn = norb*(norb+1)//2
eri = ao2mo.restore(1, (numpy.random.random(nn*(nn+1)//2)-.2)**3, norb)
oosym = orbsym[:,None] ^ orbsym
oosym = oosym.reshape(-1,1) ^ oosym.ravel()
eri[oosym.reshape([norb]*4)!=0] = 0
ci0 = fci.selected_ci.to_fci(civec_strs, norb, nelec)
ci0 = fci.addons.symmetrize_wfn(ci0, norb, nelec, orbsym)
civec_strs = fci.selected_ci.from_fci(ci0, civec_strs._strs, norb, nelec)
myci = selected_ci_spin0_symm.SCI()
e1 = numpy.dot(civec_strs.ravel(), myci.contract_2e(eri, civec_strs, norb, nelec, orbsym=orbsym).ravel())
e2 = numpy.dot(ci0.ravel(), direct_spin1_symm.contract_2e(eri, ci0, norb, nelec, orbsym=orbsym).ravel())
self.assertAlmostEqual(e1, e2, 9)
def test_rdm_2e(self):
norb, nelec = 10, 1
strs = cistring.make_strings(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 = selected_ci._as_SCIvector(numpy.random.random((len(strsa),len(strsb))), ci_strs)
ci0 = selected_ci.to_fci(ci_coeff, norb, (nelec,nelec))
dm1ref, dm2ref = direct_spin1.make_rdm12s(ci0, norb, (nelec,nelec))
dm1 = selected_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 = selected_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 = selected_ci._as_SCIvector(numpy.random.random((len(strsa),len(strsb))), ci_strs)
ci1 = selected_ci.to_fci(ci1_coeff, norb, (nelec,nelec))
dm1ref, dm2ref = direct_spin1.trans_rdm12s(ci1, ci0, norb, (nelec,nelec))
dm1 = selected_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 test_contract_2e_1(self):
myci = selected_ci.SCI()
nelec = (4,3)
strsa = cistring.make_strings(range(norb), nelec[0])
strsb = cistring.make_strings(range(norb), nelec[1])
ci0 = selected_ci._as_SCIvector(numpy.random.random((len(strsa),len(strsb))), (strsa,strsb))
h2 = ao2mo.restore(1, eri, norb)
c1 = myci.contract_2e(h2, ci0, norb, nelec)
c2 = direct_spin1.contract_2e(h2, ci0, norb, nelec)
self.assertAlmostEqual(float(abs(c1-c2).sum()), 0, 9)
dm1_1 = myci.make_rdm1(c1, norb, nelec)
dm1_2 = direct_spin1.make_rdm1(c2, norb, nelec)
self.assertAlmostEqual(abs(dm1_1 - dm1_2).sum(), 0, 9)
dm2_1 = myci.make_rdm12(c1, norb, nelec)[1]
dm2_2 = direct_spin1.make_rdm12(c2, norb, nelec)[1]
self.assertAlmostEqual(abs(dm2_1 - dm2_2).sum(), 0, 9)
def test_spin0_contract_2e_symm(self):
norb, nelec = 7, (4, 4)
strs = cistring.make_strings(range(norb), nelec[0])
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .3
strsa = strs[mask]
ci_strs = (strsa, strsa)
na = len(strsa)
ci_coeff = numpy.random.random((na, na))
ci_coeff = ci_coeff + ci_coeff.T
civec_strs = selected_ci._as_SCIvector(ci_coeff, ci_strs)
orbsym = (numpy.random.random(norb) * 4).astype(int)
nn = norb * (norb + 1) // 2
eri = ao2mo.restore(1,
(numpy.random.random(nn * (nn + 1) // 2) - .2)**3,
norb)
oosym = orbsym[:, None] ^ orbsym
oosym = oosym.reshape(-1, 1) ^ oosym.ravel()
eri[oosym.reshape([norb] * 4) != 0] = 0
ci0 = fci.selected_ci.to_fci(civec_strs, norb, nelec)
ci0 = fci.addons.symmetrize_wfn(ci0, norb, nelec, orbsym)
civec_strs = fci.selected_ci.from_fci(ci0, civec_strs._strs, norb,
nelec)
myci = selected_ci_spin0_symm.SCI()
e1 = numpy.dot(
civec_strs.ravel(),
myci.contract_2e(eri, civec_strs, norb, nelec,
orbsym=orbsym).ravel())
e2 = numpy.dot(
ci0.ravel(),
direct_spin1_symm.contract_2e(eri, ci0, norb, nelec,
orbsym=orbsym).ravel())
self.assertAlmostEqual(e1, e2, 9)
def test_guess_wfnsym(self):
norb, nelec = 7, (4, 4)
strs = cistring.make_strings(range(norb), nelec[0])
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .3
strsa = strs[mask]
mask = numpy.random.random(len(strs)) > .2
strsb = strs[mask]
ci_strs = (strsa, strsb)
ci0 = selected_ci._as_SCIvector(
numpy.random.random((len(strsa), len(strsb))), ci_strs)
fake_mol = gto.M()
fake_mol.groupname = 'C2v'
cis = selected_ci_symm.SelectedCI(fake_mol)
cis.orbsym = orbsym = (numpy.random.random(norb) * 4).astype(int)
self.assertEqual(cis.guess_wfnsym(norb, nelec), 0)
self.assertEqual(cis.guess_wfnsym(norb, nelec, ci0), 3)
self.assertEqual(cis.guess_wfnsym(norb, nelec, ci0, wfnsym=0), 0)
self.assertEqual(cis.guess_wfnsym(norb, nelec, ci0, wfnsym='B2'), 3)
ci0[:] = 0
self.assertRaises(RuntimeError,
cis.guess_wfnsym,
norb,
nelec,
ci0,
wfnsym=1)
def test_rdm_2e(self):
norb, nelec = 10, 1
strs = cistring.make_strings(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 = selected_ci._as_SCIvector(
numpy.random.random((len(strsa), len(strsb))), ci_strs)
ci0 = selected_ci.to_fci(ci_coeff, norb, (nelec, nelec))
dm1ref, dm2ref = direct_spin1.make_rdm12s(ci0, norb, (nelec, nelec))
dm1 = selected_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 = selected_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 = selected_ci._as_SCIvector(
numpy.random.random((len(strsa), len(strsb))), ci_strs)
ci1 = selected_ci.to_fci(ci1_coeff, norb, (nelec, nelec))
dm1ref, dm2ref = direct_spin1.trans_rdm12s(ci1, ci0, norb,
(nelec, nelec))
dm1 = selected_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 test_des_linkstr1(self):
norb, nelec = 10, 4
strs = cistring.make_strings(range(norb), nelec)
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .6
strs = strs[mask]
c_index0 = gen_cre_linkstr(strs, norb, nelec)
c_index1 = selected_ci.gen_cre_linkstr(strs, norb, nelec)
c_index1[:, :, 1] = 0
self.assertTrue(numpy.all(c_index0 == c_index1))
def test_des_linkstr(self):
norb, nelec = 10, 4
strs = cistring.make_strings(range(norb), nelec)
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .6
strs = strs[mask]
c_index0 = gen_cre_linkstr(strs, norb, nelec)
c_index1 = selected_ci.gen_cre_linkstr(strs, norb, nelec)
c_index1[:,:,1] = 0
self.assertTrue(numpy.all(c_index0 == c_index1))
def guess_wfnsym(ci, norb, nelec, orbsym):
'''Guess the wavefunction symmetry based on the non-zero elements in the
given CI coefficients.
Args:
ci : 2D array
CI coefficients, row for alpha strings and column for beta strings.
norb : int
Number of orbitals.
nelec : int or 2-item list
Number of electrons, or 2-item list for (alpha, beta) electrons
orbsym : list of int
The irrep ID for each orbital.
Returns:
Irrep ID
'''
neleca, nelecb = _unpack_nelec(nelec)
strsa = numpy.asarray(cistring.make_strings(range(norb), neleca))
strsb = numpy.asarray(cistring.make_strings(range(norb), nelecb))
return _guess_wfnsym(ci, strsa, strsb, orbsym)
def guess_wfnsym(ci, norb, nelec, orbsym):
'''Guess the wavefunction symmetry based on the non-zero elements in the
given CI coefficients.
Args:
ci : 2D array
CI coefficients, row for alpha strings and column for beta strings.
norb : int
Number of orbitals.
nelec : int or 2-item list
Number of electrons, or 2-item list for (alpha, beta) electrons
orbsym : list of int
The irrep ID for each orbital.
Returns:
Irrep ID
'''
neleca, nelecb = _unpack_nelec(nelec)
strsa = numpy.asarray(cistring.make_strings(range(norb), neleca))
strsb = numpy.asarray(cistring.make_strings(range(norb), nelecb))
return _guess_wfnsym(ci, strsa, strsb, orbsym)
def test_des_des_linkstr(self):
norb, nelec = 10, 4
strs = cistring.make_strings(range(norb), nelec)
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .4
strs = strs[mask]
dd_index0 = des_des_linkstr(strs, norb, nelec)
dd_index1 = selected_ci.des_des_linkstr(strs, norb, nelec)
self.assertTrue(numpy.all(dd_index0 == dd_index1))
dd_index0 = des_des_linkstr_tril(strs, norb, nelec)
dd_index1 = selected_ci.des_des_linkstr_tril(strs, norb, nelec)
dd_index1[:,:,1] = 0
self.assertTrue(numpy.all(dd_index0 == dd_index1))
def test_des_des_linkstr(self):
norb, nelec = 10, 4
strs = cistring.make_strings(range(norb), nelec)
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .4
strs = strs[mask]
dd_index0 = des_des_linkstr(strs, norb, nelec)
dd_index1 = selected_ci.des_des_linkstr(strs, norb, nelec)
self.assertTrue(numpy.all(dd_index0 == dd_index1))
dd_index0 = des_des_linkstr_tril(strs, norb, nelec)
dd_index1 = selected_ci.des_des_linkstr_tril(strs, norb, nelec)
dd_index1[:, :, 1] = 0
self.assertTrue(numpy.all(dd_index0 == dd_index1))
def test_spin_square(self):
norb, nelec = 10, 4
strs = cistring.make_strings(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 = selected_ci._as_SCIvector(numpy.random.random((len(strsa),len(strsb))), ci_strs)
ci0 = selected_ci.to_fci(ci_coeff, norb, (nelec,nelec))
ss0 = selected_ci.spin_square(ci_coeff, norb, (nelec,nelec))
ss1 = spin_op.spin_square0(ci0, norb, (nelec,nelec))
self.assertAlmostEqual(ss0[0], ss1[0], 9)
def test_select_strs(self):
myci = selected_ci.SCI()
myci.select_cutoff = 1e-3
norb, nelec = 10, 4
strs = cistring.make_strings(range(norb), nelec)
numpy.random.seed(11)
mask = numpy.random.random(len(strs)) > .8
strs = strs[mask]
nn = norb*(norb+1)//2
eri = (numpy.random.random(nn*(nn+1)//2)-.2)**3
eri[eri<.1] *= 3e-3
eri = ao2mo.restore(1, eri, norb)
eri_pq_max = abs(eri.reshape(norb**2,-1)).max(axis=1).reshape(norb,norb)
civec_max = numpy.random.random(len(strs))
strs_add0 = select_strs(myci, eri, eri_pq_max, civec_max, strs, norb, nelec)
strs_add1 = selected_ci.select_strs(myci, eri, eri_pq_max, civec_max,
strs, norb, nelec)
self.assertTrue(numpy.all(strs_add0 == strs_add1))
def transform_ci(ci, nelec, u):
'''Transform CI coefficients to the representation in new one-particle basis.
Solving CI problem for Hamiltonian h1, h2 defined in old basis,
CI_old = fci.kernel(h1, h2, ...)
Given orbital rotation u, the CI problem can be either solved by
transforming the Hamiltonian, or transforming the coefficients.
CI_new = fci.kernel(u^T*h1*u, ...) = transform_ci_for_orbital_rotation(CI_old, u)
Args:
u : 2D array or a list of 2D array
the orbital rotation to transform the old one-particle basis to new
one-particle basis. If u is not a squared matrix, the resultant CI
coefficients array may have different shape to the input CI
coefficients.
'''
neleca, nelecb = _unpack_nelec(nelec)
if isinstance(u, numpy.ndarray) and u.ndim == 2:
ua = ub = u
assert ua.shape == ub.shape
else:
ua, ub = u
norb_old, norb_new = ua.shape
na_old = cistring.num_strings(norb_old, neleca)
nb_old = cistring.num_strings(norb_old, nelecb)
na_new = cistring.num_strings(norb_new, neleca)
nb_new = cistring.num_strings(norb_new, nelecb)
ci = ci.reshape(na_old, nb_old)
one_particle_strs_old = numpy.asarray([1 << i for i in range(norb_old)])
one_particle_strs_new = numpy.asarray([1 << i for i in range(norb_new)])
if neleca == 0:
trans_ci_a = numpy.ones((1, 1))
else:
trans_ci_a = numpy.zeros((na_old, na_new))
strs_old = numpy.asarray(cistring.make_strings(range(norb_old),
neleca))
# Unitary transformation array trans_ci is the overlap between two sets of CI basis.
occ_masks_old = (strs_old[:, None] & one_particle_strs_old) != 0
if norb_old == norb_new:
occ_masks_new = occ_masks_old
else:
strs_new = numpy.asarray(
cistring.make_strings(range(norb_new), neleca))
occ_masks_new = (strs_new[:, None] & one_particle_strs_new) != 0
# Perform
#for i in range(na_old): # old basis
# for j in range(na_new): # new basis
# uij = u[occ_masks_old[i]][:,occ_masks_new[j]]
# trans_ci_a[i,j] = numpy.linalg.det(uij)
occ_idx_all_strs = numpy.where(occ_masks_new)[1].reshape(
na_new, neleca)
for i in range(na_old):
ui = ua[occ_masks_old[i]].T.copy()
minors = ui[occ_idx_all_strs]
trans_ci_a[i, :] = numpy.linalg.det(minors)
if neleca == nelecb and numpy.allclose(ua, ub):
trans_ci_b = trans_ci_a
elif nelecb == 0:
trans_ci_b = numpy.ones((1, 1))
else:
trans_ci_b = numpy.zeros((nb_old, nb_new))
strs_old = numpy.asarray(cistring.make_strings(range(norb_old),
nelecb))
occ_masks_old = (strs_old[:, None] & one_particle_strs_old) != 0
if norb_old == norb_new:
occ_masks_new = occ_masks_old
else:
strs_new = numpy.asarray(
cistring.make_strings(range(norb_new), nelecb))
occ_masks_new = (strs_new[:, None] & one_particle_strs_new) != 0
occ_idx_all_strs = numpy.where(occ_masks_new)[1].reshape(
nb_new, nelecb)
for i in range(nb_old):
ui = ub[occ_masks_old[i]].T.copy()
minors = ui[occ_idx_all_strs]
trans_ci_b[i, :] = numpy.linalg.det(minors)
# Transform old basis to new basis for all alpha-electron excitations
ci = lib.dot(trans_ci_a.T, ci)
# Transform old basis to new basis for all beta-electron excitations
ci = lib.dot(ci, trans_ci_b)
return ci
def transform_ci_for_orbital_rotation(ci, norb, nelec, u):
'''Transform CI coefficients to the representation in new one-particle basis.
Solving CI problem for Hamiltonian h1, h2 defined in old basis,
CI_old = fci.kernel(h1, h2, ...)
Given orbital rotation u, the CI problem can be either solved by
transforming the Hamiltonian, or transforming the coefficients.
CI_new = fci.kernel(u^T*h1*u, ...) = transform_ci_for_orbital_rotation(CI_old, u)
Args:
u : 2D array or a list of 2D array
the orbital rotation to transform the old one-particle basis to new
one-particle basis
'''
neleca, nelecb = _unpack(nelec)
strsa = numpy.asarray(cistring.make_strings(range(norb), neleca))
strsb = numpy.asarray(cistring.make_strings(range(norb), nelecb))
one_particle_strs = numpy.asarray([1 << i for i in range(norb)])
na = len(strsa)
nb = len(strsb)
if isinstance(u, numpy.ndarray) and u.ndim == 2:
ua = ub = u
else:
ua, ub = u
if neleca == 0:
trans_ci_a = numpy.ones((1, 1))
else:
# Unitary transformation array trans_ci is the overlap between two sets of CI basis.
occ_masks = (strsa[:, None] & one_particle_strs) != 0
trans_ci_a = numpy.zeros((na, na))
#for i in range(na): # for old basis
# for j in range(na):
# uij = u[occ_masks[i]][:,occ_masks[j]]
# trans_ci_a[i,j] = numpy.linalg.det(uij)
occ_idx_all_strs = numpy.where(occ_masks)[1].reshape(na, neleca)
for i in range(na):
ui = ua[occ_masks[i]].T.copy()
minors = ui[occ_idx_all_strs]
trans_ci_a[i, :] = numpy.linalg.det(minors)
if neleca == nelecb and numpy.allclose(ua, ub):
trans_ci_b = trans_ci_a
else:
if nelecb == 0:
trans_ci_b = numpy.ones((1, 1))
else:
occ_masks = (strsb[:, None] & one_particle_strs) != 0
trans_ci_b = numpy.zeros((nb, nb))
#for i in range(nb):
# for j in range(nb):
# uij = u[occ_masks[i]][:,occ_masks[j]]
# trans_ci_b[i,j] = numpy.linalg.det(uij)
occ_idx_all_strs = numpy.where(occ_masks)[1].reshape(nb, nelecb)
for i in range(nb):
ui = ub[occ_masks[i]].T.copy()
minors = ui[occ_idx_all_strs]
trans_ci_b[i, :] = numpy.linalg.det(minors)
# Transform old basis to new basis for all alpha-electron excitations
ci = lib.dot(trans_ci_a.T, ci.reshape(na, nb))
# Transform old basis to new basis for all beta-electron excitations
ci = lib.dot(ci.reshape(na, nb), trans_ci_b)
return ci
def transform_ci_for_orbital_rotation(ci, norb, nelec, u):
'''Transform CI coefficients to the representation in new one-particle basis.
Solving CI problem for Hamiltonian h1, h2 defined in old basis,
CI_old = fci.kernel(h1, h2, ...)
Given orbital rotation u, the CI problem can be either solved by
transforming the Hamiltonian, or transforming the coefficients.
CI_new = fci.kernel(u^T*h1*u, ...) = transform_ci_for_orbital_rotation(CI_old, u)
Args:
u : 2D array or a list of 2D array
the orbital rotation to transform the old one-particle basis to new
one-particle basis
'''
neleca, nelecb = _unpack_nelec(nelec)
strsa = numpy.asarray(cistring.make_strings(range(norb), neleca))
strsb = numpy.asarray(cistring.make_strings(range(norb), nelecb))
one_particle_strs = numpy.asarray([1<<i for i in range(norb)])
na = len(strsa)
nb = len(strsb)
assert(ci.shape == (na, nb))
if isinstance(u, numpy.ndarray) and u.ndim == 2:
ua = ub = u
else:
ua, ub = u
if neleca == 0:
trans_ci_a = numpy.ones((1,1))
else:
# Unitary transformation array trans_ci is the overlap between two sets of CI basis.
occ_masks = (strsa[:,None] & one_particle_strs) != 0
trans_ci_a = numpy.zeros((na,na))
#for i in range(na): # for old basis
# for j in range(na):
# uij = u[occ_masks[i]][:,occ_masks[j]]
# trans_ci_a[i,j] = numpy.linalg.det(uij)
occ_idx_all_strs = numpy.where(occ_masks)[1].reshape(na,neleca)
for i in range(na):
ui = ua[occ_masks[i]].T.copy()
minors = ui[occ_idx_all_strs]
trans_ci_a[i,:] = numpy.linalg.det(minors)
if neleca == nelecb and numpy.allclose(ua, ub):
trans_ci_b = trans_ci_a
else:
if nelecb == 0:
trans_ci_b = numpy.ones((1,1))
else:
occ_masks = (strsb[:,None] & one_particle_strs) != 0
trans_ci_b = numpy.zeros((nb,nb))
#for i in range(nb):
# for j in range(nb):
# uij = u[occ_masks[i]][:,occ_masks[j]]
# trans_ci_b[i,j] = numpy.linalg.det(uij)
occ_idx_all_strs = numpy.where(occ_masks)[1].reshape(nb,nelecb)
for i in range(nb):
ui = ub[occ_masks[i]].T.copy()
minors = ui[occ_idx_all_strs]
trans_ci_b[i,:] = numpy.linalg.det(minors)
# Transform old basis to new basis for all alpha-electron excitations
ci = lib.dot(trans_ci_a.T, ci.reshape(na,nb))
# Transform old basis to new basis for all beta-electron excitations
ci = lib.dot(ci.reshape(na,nb), trans_ci_b)
return ci