def _nao_sub(mol, pre_occ, pre_nao, s=None):
if s is None:
s = mol.intor_symmetric('cint1e_ovlp_sph')
core_lst, val_lst, rydbg_lst = _core_val_ryd_list(mol)
nbf = mol.nao_nr()
cnao = numpy.empty((nbf,nbf))
if core_lst:
c = pre_nao[:,core_lst].copy()
s1 = reduce(lib.dot, (c.T, s, c))
cnao[:,core_lst] = c1 = lib.dot(c, orth.lowdin(s1))
c = pre_nao[:,val_lst].copy()
c -= reduce(lib.dot, (c1, c1.T, s, c))
else:
c = pre_nao[:,val_lst]
if val_lst:
s1 = reduce(lib.dot, (c.T, s, c))
wt = pre_occ[val_lst]
cnao[:,val_lst] = lib.dot(c, orth.weight_orth(s1, wt))
if rydbg_lst:
cvlst = core_lst + val_lst
c1 = cnao[:,cvlst].copy()
c = pre_nao[:,rydbg_lst].copy()
c -= reduce(lib.dot, (c1, c1.T, s, c))
s1 = reduce(lib.dot, (c.T, s, c))
cnao[:,rydbg_lst] = lib.dot(c, orth.lowdin(s1))
snorm = numpy.linalg.norm(reduce(lib.dot, (cnao.T, s, cnao)) - numpy.eye(nbf))
if snorm > 1e-9:
logger.warn(mol, 'Weak orthogonality for localized orbitals %s', snorm)
return cnao
def _nao_sub(mol, pre_occ, pre_nao, s=None):
if s is None:
s = mol.intor_symmetric('cint1e_ovlp_sph')
core_lst, val_lst, rydbg_lst = _core_val_ryd_list(mol)
nbf = mol.nao_nr()
cnao = numpy.empty((nbf,nbf))
if core_lst:
c = pre_nao[:,core_lst]
s1 = reduce(numpy.dot, (c.T, s, c))
cnao[:,core_lst] = c1 = numpy.dot(c, orth.lowdin(s1))
c = pre_nao[:,val_lst]
c -= reduce(numpy.dot, (c1, c1.T, s, c))
else:
c = pre_nao[:,val_lst]
s1 = reduce(numpy.dot, (c.T, s, c))
wt = pre_occ[val_lst]
cnao[:,val_lst] = numpy.dot(c, orth.weight_orth(s1, wt))
if rydbg_lst:
cvlst = core_lst + val_lst
c1 = cnao[:,cvlst]
c = pre_nao[:,rydbg_lst]
c -= reduce(numpy.dot, (c1, c1.T, s, c))
s1 = reduce(numpy.dot, (c.T, s, c))
cnao[:,rydbg_lst] = numpy.dot(c, orth.lowdin(s1))
snorm = numpy.linalg.norm(reduce(numpy.dot, (cnao.T, s, cnao)) - numpy.eye(nbf))
if snorm > 1e-9:
logger.warn(mol, 'Weak orthogonality for localized orbitals %s', snorm)
return cnao
def _nao_sub(mol, pre_occ, pre_nao):
core_lst, val_lst, rydbg_lst = _core_val_ryd_list(mol)
s = mol.intor_symmetric('cint1e_ovlp_sph')
nao = mol.nao_nr()
cnao = numpy.zeros((nao,nao))
if core_lst:
c = pre_nao[:,core_lst]
s1 = reduce(numpy.dot, (c.T, s, c))
cnao[:,core_lst] = numpy.dot(c, orth.lowdin(s1))
c1 = cnao[:,core_lst]
rm_core = numpy.eye(nao) - reduce(numpy.dot, (c1, c1.T, s))
c = numpy.dot(rm_core, pre_nao[:,val_lst])
s1 = reduce(numpy.dot, (c.T.conj(), s, c))
wt = pre_occ[val_lst]
cnao[:,val_lst] = numpy.dot(c, orth.weight_orth(s1, wt))
if rydbg_lst:
c1 = cnao[:,val_lst]
rm_val = numpy.eye(nao)-reduce(numpy.dot, (c1, c1.T, s))
c = reduce(numpy.dot, (rm_core, rm_val, pre_nao[:,rydbg_lst]))
s1 = reduce(numpy.dot, (c.T.conj(), s, c))
cnao[:,rydbg_lst] = numpy.dot(c, orth.lowdin(s1))
return cnao
def test_weight_orth(self):
numpy.random.seed(10)
n = 100
a = numpy.random.random((n,n))
s = numpy.dot(a.T, a)
weight = numpy.random.random(n)
c = orth.weight_orth(s, weight)
self.assertTrue(numpy.allclose(reduce(numpy.dot, (c.T, s, c)),
numpy.eye(n)))
self.assertAlmostEqual(numpy.linalg.norm(c), 36.56738258719514, 9)
self.assertAlmostEqual(abs(c).sum(), 1908.8535852660757, 7)
def test_weight_orth(self):
numpy.random.seed(10)
n = 100
a = numpy.random.random((n, n))
s = numpy.dot(a.T, a)
weight = numpy.random.random(n)
c = orth.weight_orth(s, weight)
self.assertTrue(
numpy.allclose(reduce(numpy.dot, (c.T, s, c)), numpy.eye(n)))
self.assertAlmostEqual(numpy.linalg.norm(c), 36.56738258719514, 8)
self.assertAlmostEqual(abs(c).sum(), 1908.8535852660757, 6)
def _nao_sub(mol, pre_occ, pre_nao, s=None):
if s is None:
if getattr(mol, 'pbc_intor', None): # whether mol object is a cell
s = mol.pbc_intor('int1e_ovlp', hermi=1)
else:
s = mol.intor_symmetric('int1e_ovlp')
core_lst, val_lst, rydbg_lst = _core_val_ryd_list(mol)
nbf = mol.nao_nr()
pre_nao = pre_nao.astype(s.dtype)
cnao = numpy.empty((nbf, nbf), dtype=s.dtype)
if core_lst:
c = pre_nao[:, core_lst].copy()
s1 = reduce(lib.dot, (c.conj().T, s, c))
cnao[:, core_lst] = c1 = lib.dot(c, orth.lowdin(s1))
c = pre_nao[:, val_lst].copy()
c -= reduce(lib.dot, (c1, c1.conj().T, s, c))
else:
c = pre_nao[:, val_lst]
if val_lst:
s1 = reduce(lib.dot, (c.conj().T, s, c))
wt = pre_occ[val_lst]
cnao[:, val_lst] = lib.dot(c, orth.weight_orth(s1, wt))
if rydbg_lst:
cvlst = core_lst + val_lst
c1 = cnao[:, cvlst].copy()
c = pre_nao[:, rydbg_lst].copy()
c -= reduce(lib.dot, (c1, c1.conj().T, s, c))
s1 = reduce(lib.dot, (c.conj().T, s, c))
cnao[:, rydbg_lst] = lib.dot(c, orth.lowdin(s1))
snorm = numpy.linalg.norm(
reduce(lib.dot, (cnao.conj().T, s, cnao)) - numpy.eye(nbf))
if snorm > 1e-9:
logger.warn(mol, 'Weak orthogonality for localized orbitals %s', snorm)
return cnao
def _nao_sub(mol, pre_occ, pre_nao, s=None):
if s is None:
if getattr(mol, 'pbc_intor', None): # whether mol object is a cell
s = mol.pbc_intor('int1e_ovlp', hermi=1)
else:
s = mol.intor_symmetric('int1e_ovlp')
core_lst, val_lst, rydbg_lst = _core_val_ryd_list(mol)
nbf = mol.nao_nr()
pre_nao = pre_nao.astype(s.dtype)
cnao = numpy.empty((nbf,nbf), dtype=s.dtype)
if core_lst:
c = pre_nao[:,core_lst].copy()
s1 = reduce(lib.dot, (c.conj().T, s, c))
cnao[:,core_lst] = c1 = lib.dot(c, orth.lowdin(s1))
c = pre_nao[:,val_lst].copy()
c -= reduce(lib.dot, (c1, c1.conj().T, s, c))
else:
c = pre_nao[:,val_lst]
if val_lst:
s1 = reduce(lib.dot, (c.conj().T, s, c))
wt = pre_occ[val_lst]
cnao[:,val_lst] = lib.dot(c, orth.weight_orth(s1, wt))
if rydbg_lst:
cvlst = core_lst + val_lst
c1 = cnao[:,cvlst].copy()
c = pre_nao[:,rydbg_lst].copy()
c -= reduce(lib.dot, (c1, c1.conj().T, s, c))
s1 = reduce(lib.dot, (c.conj().T, s, c))
cnao[:,rydbg_lst] = lib.dot(c, orth.lowdin(s1))
snorm = numpy.linalg.norm(reduce(lib.dot, (cnao.conj().T, s, cnao)) - numpy.eye(nbf))
if snorm > 1e-9:
logger.warn(mol, 'Weak orthogonality for localized orbitals %s', snorm)
return cnao