def make_hdiag(h1e, eri, norb, nelec):
'''Diagonal Hamiltonian for Davidson preconditioner
'''
if h1e.dtype == numpy.complex or eri.dtype == numpy.complex:
raise NotImplementedError('Complex Hamiltonian')
neleca, nelecb = _unpack_nelec(nelec)
h1e = numpy.asarray(h1e, order='C')
eri = ao2mo.restore(1, eri, norb)
occslsta = occslstb = cistring._gen_occslst(range(norb), neleca)
if neleca != nelecb:
occslstb = cistring._gen_occslst(range(norb), nelecb)
na = len(occslsta)
nb = len(occslstb)
hdiag = numpy.empty(na * nb)
jdiag = numpy.asarray(numpy.einsum('iijj->ij', eri), order='C')
kdiag = numpy.asarray(numpy.einsum('ijji->ij', eri), order='C')
c_h1e = h1e.ctypes.data_as(ctypes.c_void_p)
c_jdiag = jdiag.ctypes.data_as(ctypes.c_void_p)
c_kdiag = kdiag.ctypes.data_as(ctypes.c_void_p)
libfci.FCImake_hdiag_uhf(hdiag.ctypes.data_as(ctypes.c_void_p), c_h1e,
c_h1e, c_jdiag, c_jdiag, c_jdiag, c_kdiag,
c_kdiag, ctypes.c_int(norb), ctypes.c_int(na),
ctypes.c_int(nb), ctypes.c_int(neleca),
ctypes.c_int(nelecb),
occslsta.ctypes.data_as(ctypes.c_void_p),
occslstb.ctypes.data_as(ctypes.c_void_p))
return hdiag
def make_hdiag(h1e, eri, norb, nelec):
neleca, nelecb = direct_spin1._unpack_nelec(nelec)
h1e_a = numpy.ascontiguousarray(h1e[0])
h1e_b = numpy.ascontiguousarray(h1e[1])
g2e_aa = ao2mo.restore(1, eri[0], norb)
g2e_ab = ao2mo.restore(1, eri[1], norb)
g2e_bb = ao2mo.restore(1, eri[2], norb)
occslsta = occslstb = cistring._gen_occslst(range(norb), neleca)
if neleca != nelecb:
occslstb = cistring._gen_occslst(range(norb), nelecb)
na = len(occslsta)
nb = len(occslstb)
hdiag = numpy.empty(na*nb)
jdiag_aa = numpy.asarray(numpy.einsum('iijj->ij',g2e_aa), order='C')
jdiag_ab = numpy.asarray(numpy.einsum('iijj->ij',g2e_ab), order='C')
jdiag_bb = numpy.asarray(numpy.einsum('iijj->ij',g2e_bb), order='C')
kdiag_aa = numpy.asarray(numpy.einsum('ijji->ij',g2e_aa), order='C')
kdiag_bb = numpy.asarray(numpy.einsum('ijji->ij',g2e_bb), order='C')
libfci.FCImake_hdiag_uhf(hdiag.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
jdiag_aa.ctypes.data_as(ctypes.c_void_p),
jdiag_ab.ctypes.data_as(ctypes.c_void_p),
jdiag_bb.ctypes.data_as(ctypes.c_void_p),
kdiag_aa.ctypes.data_as(ctypes.c_void_p),
kdiag_bb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(neleca), ctypes.c_int(nelecb),
occslsta.ctypes.data_as(ctypes.c_void_p),
occslstb.ctypes.data_as(ctypes.c_void_p))
return numpy.asarray(hdiag)
def make_hdiag(h1e, eri, norb, nelec):
'''Diagonal Hamiltonian for Davidson preconditioner
'''
neleca, nelecb = _unpack_nelec(nelec)
h1e = numpy.asarray(h1e, order='C')
eri = ao2mo.restore(1, eri, norb)
occslsta = occslstb = cistring._gen_occslst(range(norb), neleca)
if neleca != nelecb:
occslstb = cistring._gen_occslst(range(norb), nelecb)
na = len(occslsta)
nb = len(occslstb)
hdiag = numpy.empty(na*nb)
jdiag = numpy.asarray(numpy.einsum('iijj->ij',eri), order='C')
kdiag = numpy.asarray(numpy.einsum('ijji->ij',eri), order='C')
c_h1e = h1e.ctypes.data_as(ctypes.c_void_p)
c_jdiag = jdiag.ctypes.data_as(ctypes.c_void_p)
c_kdiag = kdiag.ctypes.data_as(ctypes.c_void_p)
libfci.FCImake_hdiag_uhf(hdiag.ctypes.data_as(ctypes.c_void_p),
c_h1e, c_h1e, c_jdiag, c_jdiag, c_jdiag, c_kdiag, c_kdiag,
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(neleca), ctypes.c_int(nelecb),
occslsta.ctypes.data_as(ctypes.c_void_p),
occslstb.ctypes.data_as(ctypes.c_void_p))
return hdiag
def make_hdiag(h1e, g2e, norb, nelec, opt=None):
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
occslista = cistring._gen_occslst(range(norb), neleca)
occslistb = cistring._gen_occslst(range(norb), nelecb)
g2e = ao2mo.restore(1, g2e, norb)
diagj = numpy.einsum('iijj->ij',g2e)
diagk = numpy.einsum('ijji->ij',g2e)
hdiag = []
for aocc in occslista:
for bocc in occslistb:
e1 = h1e[aocc,aocc].sum() + h1e[bocc,bocc].sum()
e2 = diagj[aocc][:,aocc].sum() + diagj[aocc][:,bocc].sum() \
+ diagj[bocc][:,aocc].sum() + diagj[bocc][:,bocc].sum() \
- diagk[aocc][:,aocc].sum() - diagk[bocc][:,bocc].sum()
hdiag.append(e1 + e2*.5)
return numpy.array(hdiag)
def make_hdiag(h1e, eri, norb, nelec, opt=None):
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
occslista = cistring._gen_occslst(range(norb), neleca)
occslistb = cistring._gen_occslst(range(norb), nelecb)
eri = ao2mo.restore(1, eri, norb)
diagj = numpy.einsum('iijj->ij', eri)
diagk = numpy.einsum('ijji->ij', eri)
hdiag = []
for aocc in occslista:
for bocc in occslistb:
e1 = h1e[aocc, aocc].sum() + h1e[bocc, bocc].sum()
e2 = diagj[aocc][:,aocc].sum() + diagj[aocc][:,bocc].sum() \
+ diagj[bocc][:,aocc].sum() + diagj[bocc][:,bocc].sum() \
- diagk[aocc][:,aocc].sum() - diagk[bocc][:,bocc].sum()
hdiag.append(e1 + e2 * .5)
return numpy.array(hdiag)
def test_strings4orblist(self):
ref = ['0b1010', '0b100010', '0b101000', '0b10000010', '0b10001000',
'0b10100000']
for i, x in enumerate(cistring.gen_strings4orblist([1,3,5,7], 2)):
self.assertEqual(bin(x), ref[i])
ref = ['0b11', '0b101', '0b110', '0b1001', '0b1010', '0b1100',
'0b10001', '0b10010', '0b10100', '0b11000']
for i, x in enumerate(cistring.gen_strings4orblist(range(5), 2)):
self.assertEqual(bin(x), ref[i])
strs = cistring.gen_strings4orblist(range(8), 4)
occlst = cistring._gen_occslst(range(8), 4)
self.assertAlmostEqual(abs(occlst - cistring._strs2occslst(strs, 8)).sum(), 0, 12)
self.assertAlmostEqual(abs(strs - cistring._occslst2strs(occlst)).sum(), 0, 12)
def test_strings4orblist(self):
ref = [
'0b1010', '0b100010', '0b101000', '0b10000010', '0b10001000',
'0b10100000'
]
for i, x in enumerate(cistring.gen_strings4orblist([1, 3, 5, 7], 2)):
self.assertEqual(bin(x), ref[i])
ref = [
'0b11', '0b101', '0b110', '0b1001', '0b1010', '0b1100', '0b10001',
'0b10010', '0b10100', '0b11000'
]
for i, x in enumerate(cistring.gen_strings4orblist(range(5), 2)):
self.assertEqual(bin(x), ref[i])
strs = cistring.gen_strings4orblist(range(8), 4)
occlst = cistring._gen_occslst(range(8), 4)
self.assertAlmostEqual(
abs(occlst - cistring._strs2occslst(strs, 8)).sum(), 0, 12)
self.assertAlmostEqual(
abs(strs - cistring._occslst2strs(occlst)).sum(), 0, 12)
def cylindrical_init_guess(mol,
norb,
nelec,
orbsym,
wfnsym=0,
singlet=True,
nroots=1):
'''
FCI initial guess for system of cylindrical symmetry.
(In testing)
Examples:
>>> mol = gto.M(atom='O; O 1 1.2', spin=2, symmetry=True)
>>> orbsym = [6,7,2,3]
>>> ci0 = fci.addons.cylindrical_init_guess(mol, 4, (3,3), orbsym, wfnsym=10)[0]
>>> print(ci0.reshape(4,4))
>>> ci0 = fci.addons.cylindrical_init_guess(mol, 4, (3,3), orbsym, wfnsym=10, singlet=False)[0]
>>> print(ci0.reshape(4,4))
'''
neleca, nelecb = _unpack_nelec(nelec)
if isinstance(orbsym[0], str):
orbsym = [symm.irrep_name2id(mol.groupname, x) for x in orbsym]
orbsym = numpy.asarray(orbsym)
if isinstance(wfnsym, str):
wfnsym = symm.irrep_name2id(mol.groupname, wfnsym)
if mol.groupname in ('Dooh', 'Coov'):
def irrep_id2lz(irrep_id):
# See also symm.basis.DOOH_IRREP_ID_TABLE
level = irrep_id // 10
d2h_id = irrep_id % 10
# irrep_id 0,1,4,5 corresponds to lz = 0,2,4,...
# irrep_id 2,3,6,7 corresponds to lz = 1,3,5,...
lz = level * 2 + ((d2h_id == 2) | (d2h_id == 3) | (d2h_id == 6) |
(d2h_id == 7))
if isinstance(irrep_id, (int, numpy.number)):
# irrep_id 1,3,4,6 corresponds to E_y (E_{(-)})
# irrep_id 0,2,5,7 corresponds to E_x (E_{(+)})
if (d2h_id == 1) | (d2h_id == 3) | (d2h_id == 4) | (d2h_id
== 6):
lz = -lz
else:
lz[(d2h_id == 1) | (d2h_id == 3) | (d2h_id == 4) |
(d2h_id == 6)] *= -1
return lz
orb_lz = irrep_id2lz(orbsym)
wfn_lz = irrep_id2lz(wfnsym)
d2h_wfnsym_id = wfnsym % 10
else:
raise NotImplementedError
orb_lz = wfn_lz = d2h_wfnsym_id = None
occslsta = occslstb = cistring._gen_occslst(range(norb), neleca)
if neleca != nelecb:
occslstb = cistring._gen_occslst(range(norb), nelecb)
na = len(occslsta)
nb = len(occslsta)
gx_mask = orbsym == 2
gy_mask = orbsym == 3
ux_mask = orbsym == 7
uy_mask = orbsym == 6
all_lz = set(abs(orb_lz))
def search_open_shell_det(occ_lst):
occ_mask = numpy.zeros(norb, dtype=bool)
occ_mask[occ_lst] = True
# First search Lz of the open-shell orbital
for lz_open in all_lz:
if numpy.count_nonzero(orb_lz == lz_open) % 2 == 1:
break
n_gx = numpy.count_nonzero(gx_mask & occ_mask & (orb_lz == lz_open))
n_gy = numpy.count_nonzero(gy_mask & occ_mask & (orb_lz == -lz_open))
n_ux = numpy.count_nonzero(ux_mask & occ_mask & (orb_lz == lz_open))
n_uy = numpy.count_nonzero(uy_mask & occ_mask & (orb_lz == -lz_open))
if n_gx > n_gy:
idx = numpy.where(occ_mask & (orb_lz == lz_open) & gx_mask)[0][0]
idy = numpy.where((~occ_mask) & (orb_lz == -lz_open)
& gy_mask)[0][0]
elif n_gx < n_gy:
idx = numpy.where((~occ_mask) & (orb_lz == lz_open)
& gx_mask)[0][0]
idy = numpy.where(occ_mask & (orb_lz == -lz_open) & gy_mask)[0][0]
elif n_ux > n_uy:
idx = numpy.where(occ_mask & (orb_lz == lz_open) & ux_mask)[0][0]
idy = numpy.where((~occ_mask) & (orb_lz == -lz_open)
& uy_mask)[0][0]
elif n_ux < n_uy:
idx = numpy.where((~occ_mask) & (orb_lz == lz_open)
& ux_mask)[0][0]
idy = numpy.where(occ_mask & (orb_lz == -lz_open) & uy_mask)[0][0]
else:
raise RuntimeError
nelec = len(occ_lst)
det_x = occ_mask.copy()
det_x[idx] = True
det_x[idy] = False
str_x = ''.join(['1' if i else '0' for i in det_x[::-1]])
addr_x = cistring.str2addr(norb, nelec, str_x)
det_y = occ_mask.copy()
det_y[idx] = False
det_y[idy] = True
str_y = ''.join(['1' if i else '0' for i in det_y[::-1]])
addr_y = cistring.str2addr(norb, nelec, str_y)
return addr_x, addr_y
ci0 = []
iroot = 0
for addr in range(na * nb):
ci_1 = numpy.zeros((na, nb))
addra = addr // nb
addrb = addr % nb
occa = occslsta[addra]
occb = occslstb[addrb]
tot_sym = 0
for i in occa:
tot_sym ^= orbsym[i]
for i in occb:
tot_sym ^= orbsym[i]
if tot_sym == d2h_wfnsym_id:
n_Ex_a = (gx_mask[occa]).sum() + (ux_mask[occa]).sum()
n_Ey_a = (gy_mask[occa]).sum() + (uy_mask[occa]).sum()
n_Ex_b = (gx_mask[occb]).sum() + (ux_mask[occb]).sum()
n_Ey_b = (gy_mask[occb]).sum() + (uy_mask[occb]).sum()
if abs(n_Ex_a - n_Ey_a) == 1 and abs(n_Ex_b - n_Ey_b) == 1:
# open-shell for both alpha det and beta det e.g. the
# valence part of O2 molecule
addr_x_a, addr_y_a = search_open_shell_det(occa)
addr_x_b, addr_y_b = search_open_shell_det(occb)
if singlet:
if wfn_lz == 0:
ci_1[addr_x_a,addr_x_b] = \
ci_1[addr_y_a,addr_y_b] = numpy.sqrt(.5)
else:
ci_1[addr_x_a, addr_x_b] = numpy.sqrt(.5)
ci_1[addr_y_a, addr_y_b] = -numpy.sqrt(.5)
else:
ci_1[addr_x_a, addr_y_b] = numpy.sqrt(.5)
ci_1[addr_y_a, addr_x_b] = -numpy.sqrt(.5)
else:
# TODO: Other direct-product to direct-sum transofromation
# which involves CG coefficients.
ci_1[addra, addrb] = 1
ci0.append(ci_1.ravel())
iroot += 1
if iroot >= nroots:
break
return ci0
def cylindrical_init_guess(mol, norb, nelec, orbsym, wfnsym=0, singlet=True,
nroots=1):
'''
FCI initial guess for system of cylindrical symmetry.
(In testing)
Examples:
>>> mol = gto.M(atom='O; O 1 1.2', spin=2, symmetry=True)
>>> orbsym = [6,7,2,3]
>>> ci0 = fci.addons.cylindrical_init_guess(mol, 4, (3,3), orbsym, wfnsym=10)[0]
>>> print(ci0.reshape(4,4))
>>> ci0 = fci.addons.cylindrical_init_guess(mol, 4, (3,3), orbsym, wfnsym=10, singlet=False)[0]
>>> print(ci0.reshape(4,4))
'''
neleca, nelecb = _unpack_nelec(nelec)
if isinstance(orbsym[0], str):
orbsym = [symm.irrep_name2id(mol.groupname, x) for x in orbsym]
orbsym = numpy.asarray(orbsym)
if isinstance(wfnsym, str):
wfnsym = symm.irrep_name2id(mol.groupname, wfnsym)
if mol.groupname in ('Dooh', 'Coov'):
def irrep_id2lz(irrep_id):
# See also symm.basis.DOOH_IRREP_ID_TABLE
level = irrep_id // 10
d2h_id = irrep_id % 10
# irrep_id 0,1,4,5 corresponds to lz = 0,2,4,...
# irrep_id 2,3,6,7 corresponds to lz = 1,3,5,...
lz = level * 2 + ((d2h_id==2) | (d2h_id==3) | (d2h_id==6) | (d2h_id==7))
if isinstance(irrep_id, (int, numpy.number)):
# irrep_id 1,3,4,6 corresponds to E_y (E_{(-)})
# irrep_id 0,2,5,7 corresponds to E_x (E_{(+)})
if (d2h_id==1) | (d2h_id==3) | (d2h_id==4) | (d2h_id==6):
lz = -lz
else:
lz[(d2h_id==1) | (d2h_id==3) | (d2h_id==4) | (d2h_id==6)] *= -1
return lz
orb_lz = irrep_id2lz(orbsym)
wfn_lz = irrep_id2lz(wfnsym)
d2h_wfnsym_id = wfnsym % 10
else:
raise NotImplementedError
orb_lz = wfn_lz = d2h_wfnsym_id = None
occslsta = occslstb = cistring._gen_occslst(range(norb), neleca)
if neleca != nelecb:
occslstb = cistring._gen_occslst(range(norb), nelecb)
na = len(occslsta)
nb = len(occslsta)
gx_mask = orbsym == 2
gy_mask = orbsym == 3
ux_mask = orbsym == 7
uy_mask = orbsym == 6
all_lz = set(abs(orb_lz))
def search_open_shell_det(occ_lst):
occ_mask = numpy.zeros(norb, dtype=bool)
occ_mask[occ_lst] = True
# First search Lz of the open-shell orbital
for lz_open in all_lz:
if numpy.count_nonzero(orb_lz == lz_open) % 2 == 1:
break
n_gx = numpy.count_nonzero(gx_mask & occ_mask & (orb_lz == lz_open))
n_gy = numpy.count_nonzero(gy_mask & occ_mask & (orb_lz ==-lz_open))
n_ux = numpy.count_nonzero(ux_mask & occ_mask & (orb_lz == lz_open))
n_uy = numpy.count_nonzero(uy_mask & occ_mask & (orb_lz ==-lz_open))
if n_gx > n_gy:
idx = numpy.where(occ_mask & (orb_lz == lz_open) & gx_mask)[0][0]
idy = numpy.where((~occ_mask) & (orb_lz ==-lz_open) & gy_mask)[0][0]
elif n_gx < n_gy:
idx = numpy.where((~occ_mask) & (orb_lz == lz_open) & gx_mask)[0][0]
idy = numpy.where(occ_mask & (orb_lz ==-lz_open) & gy_mask)[0][0]
elif n_ux > n_uy:
idx = numpy.where(occ_mask & (orb_lz == lz_open) & ux_mask)[0][0]
idy = numpy.where((~occ_mask) & (orb_lz ==-lz_open) & uy_mask)[0][0]
elif n_ux < n_uy:
idx = numpy.where((~occ_mask) & (orb_lz == lz_open) & ux_mask)[0][0]
idy = numpy.where(occ_mask & (orb_lz ==-lz_open) & uy_mask)[0][0]
else:
raise RuntimeError
nelec = len(occ_lst)
det_x = occ_mask.copy()
det_x[idx] = True
det_x[idy] = False
str_x = ''.join(['1' if i else '0' for i in det_x[::-1]])
addr_x = cistring.str2addr(norb, nelec, str_x)
det_y = occ_mask.copy()
det_y[idx] = False
det_y[idy] = True
str_y = ''.join(['1' if i else '0' for i in det_y[::-1]])
addr_y = cistring.str2addr(norb, nelec, str_y)
return addr_x, addr_y
ci0 = []
iroot = 0
for addr in range(na*nb):
ci_1 = numpy.zeros((na,nb))
addra = addr // nb
addrb = addr % nb
occa = occslsta[addra]
occb = occslstb[addrb]
tot_sym = 0
for i in occa:
tot_sym ^= orbsym[i]
for i in occb:
tot_sym ^= orbsym[i]
if tot_sym == d2h_wfnsym_id:
n_Ex_a = (gx_mask[occa]).sum() + (ux_mask[occa]).sum()
n_Ey_a = (gy_mask[occa]).sum() + (uy_mask[occa]).sum()
n_Ex_b = (gx_mask[occb]).sum() + (ux_mask[occb]).sum()
n_Ey_b = (gy_mask[occb]).sum() + (uy_mask[occb]).sum()
if abs(n_Ex_a - n_Ey_a) == 1 and abs(n_Ex_b - n_Ey_b) == 1:
# open-shell for both alpha det and beta det e.g. the
# valence part of O2 molecule
addr_x_a, addr_y_a = search_open_shell_det(occa)
addr_x_b, addr_y_b = search_open_shell_det(occb)
if singlet:
if wfn_lz == 0:
ci_1[addr_x_a,addr_x_b] = \
ci_1[addr_y_a,addr_y_b] = numpy.sqrt(.5)
else:
ci_1[addr_x_a,addr_x_b] = numpy.sqrt(.5)
ci_1[addr_y_a,addr_y_b] =-numpy.sqrt(.5)
else:
ci_1[addr_x_a,addr_y_b] = numpy.sqrt(.5)
ci_1[addr_y_a,addr_x_b] =-numpy.sqrt(.5)
else:
# TODO: Other direct-product to direct-sum transofromation
# which involves CG coefficients.
ci_1[addra,addrb] = 1
ci0.append(ci_1.ravel())
iroot += 1
if iroot >= nroots:
break
return ci0
