def from_fci(fcivec, ci_strs, norb, nelec):
fcivec, nelec, ci_strs = _unpack(fcivec, nelec, ci_strs)
addrsa = [cistring.str2addr(norb, nelec[0], x) for x in ci_strs[0]]
addrsb = [cistring.str2addr(norb, nelec[1], x) for x in ci_strs[1]]
na = cistring.num_strings(norb, nelec[0])
nb = cistring.num_strings(norb, nelec[1])
fcivec = fcivec.reshape(na, nb)
civec = lib.take_2d(fcivec, addrsa, addrsb)
return _as_SCIvector(civec, ci_strs)
def from_fci(fcivec, ci_strs, norb, nelec):
fcivec, nelec, ci_strs = _unpack(fcivec, nelec, ci_strs)
addrsa = [cistring.str2addr(norb, nelec[0], x) for x in ci_strs[0]]
addrsb = [cistring.str2addr(norb, nelec[1], x) for x in ci_strs[1]]
na = cistring.num_strings(norb, nelec[0])
nb = cistring.num_strings(norb, nelec[1])
fcivec = fcivec.reshape(na,nb)
civec = lib.take_2d(fcivec, addrsa, addrsb)
return _as_SCIvector(civec, ci_strs)
def to_fci(civec_strs, norb, nelec):
ci_coeff, nelec, ci_strs = _unpack(civec_strs, nelec)
addrsa = [cistring.str2addr(norb, nelec[0], x) for x in ci_strs[0]]
addrsb = [cistring.str2addr(norb, nelec[1], x) for x in ci_strs[1]]
na = cistring.num_strings(norb, nelec[0])
nb = cistring.num_strings(norb, nelec[1])
ci0 = numpy.zeros((na, nb))
lib.takebak_2d(ci0, ci_coeff, addrsa, addrsb)
return ci0
def to_fci(civec_strs, norb, nelec):
ci_coeff, nelec, ci_strs = _unpack(civec_strs, nelec)
addrsa = [cistring.str2addr(norb, nelec[0], x) for x in ci_strs[0]]
addrsb = [cistring.str2addr(norb, nelec[1], x) for x in ci_strs[1]]
na = cistring.num_strings(norb, nelec[0])
nb = cistring.num_strings(norb, nelec[1])
ci0 = numpy.zeros((na,nb))
lib.takebak_2d(ci0, ci_coeff, addrsa, addrsb)
return ci0
def to_fci(cisdvec, norb, nelec):
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
nocc = neleca
nvir = norb - nocc
c0, c1, c2 = cisdvec_to_amplitudes(cisdvec, norb, nocc)
t1addr, t1sign = t1strs(norb, nocc)
na = cistring.num_strings(norb, nocc)
fcivec = numpy.zeros((na, na))
fcivec[0, 0] = c0
c1 = c1[::-1].T.ravel()
fcivec[0, t1addr] = fcivec[t1addr, 0] = c1 * t1sign
c2ab = c2[::-1, ::-1].transpose(2, 0, 3, 1).reshape(nocc * nvir, -1)
c2ab = numpy.einsum('i,j,ij->ij', t1sign, t1sign, c2ab)
lib.takebak_2d(fcivec, c2ab, t1addr, t1addr)
if nocc > 1 and nvir > 1:
hf_str = int('1' * nocc, 2)
for a in range(nocc, norb):
for b in range(nocc, a):
for i in reversed(range(1, nocc)):
for j in reversed(range(i)):
c2aa = c2[i, j, a - nocc,
b - nocc] - c2[j, i, a - nocc, b - nocc]
str1 = hf_str ^ (1 << j) | (1 << b)
c2aa *= cistring.cre_des_sign(b, j, hf_str)
c2aa *= cistring.cre_des_sign(a, i, str1)
str1 ^= (1 << i) | (1 << a)
addr = cistring.str2addr(norb, nocc, str1)
fcivec[0, addr] = fcivec[addr, 0] = c2aa
return fcivec
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
def initguess_triplet(norb, nelec, binstring):
'''Generate a triplet initial guess for FCI solver
'''
neleca, nelecb = _unpack(nelec)
na = cistring.num_strings(norb, neleca)
nb = cistring.num_strings(norb, nelecb)
addr = cistring.str2addr(norb, neleca, int(binstring, 2))
ci0 = numpy.zeros((na, nb))
ci0[addr, 0] = numpy.sqrt(.5)
ci0[0, addr] = -numpy.sqrt(.5)
return ci0
def t1strs(norb, nelec):
nocc = nelec
hf_str = int('1'*nocc, 2)
addrs = []
signs = []
for a in range(nocc, norb):
for i in reversed(range(nocc)):
str1 = hf_str ^ (1 << i) | (1 << a)
addrs.append(cistring.str2addr(norb, nelec, str1))
signs.append(cistring.cre_des_sign(a, i, hf_str))
return numpy.asarray(addrs), numpy.asarray(signs)
def t1strs(norb, nelec):
nocc = nelec
hf_str = int('1' * nocc, 2)
addrs = []
signs = []
for a in range(nocc, norb):
for i in reversed(range(nocc)):
str1 = hf_str ^ (1 << i) | (1 << a)
addrs.append(cistring.str2addr(norb, nelec, str1))
signs.append(cistring.cre_des_sign(a, i, hf_str))
return numpy.asarray(addrs), numpy.asarray(signs)
def initguess_triplet(norb, nelec, binstring):
'''Generate a triplet initial guess for FCI solver
'''
neleca, nelecb = _unpack(nelec)
na = cistring.num_strings(norb, neleca)
nb = cistring.num_strings(norb, nelecb)
addr = cistring.str2addr(norb, neleca, int(binstring,2))
ci0 = numpy.zeros((na,nb))
ci0[addr,0] = numpy.sqrt(.5)
ci0[0,addr] =-numpy.sqrt(.5)
return ci0
def initguess_triplet(norb, nelec, binstring):
if isinstance(nelec, (int, numpy.integer)):
neleca = nelecb = nelec//2
else:
neleca, nelecb = nelec
na = cistring.num_strings(norb, neleca)
nb = cistring.num_strings(norb, nelecb)
addr = cistring.str2addr(norb, neleca, int(binstring,2))
ci0 = numpy.zeros((na,nb))
ci0[addr,0] = numpy.sqrt(.5)
ci0[0,addr] =-numpy.sqrt(.5)
return ci0
def t1strs(norb, nelec):
'''FCI strings (address) for CIS single-excitation amplitues'''
nocc = nelec
hf_str = int('1' * nocc, 2)
addrs = []
signs = []
for a in range(nocc, norb):
for i in reversed(range(nocc)):
str1 = hf_str ^ (1 << i) | (1 << a)
addrs.append(cistring.str2addr(norb, nelec, str1))
signs.append(cistring.cre_des_sign(a, i, hf_str))
return numpy.asarray(addrs), numpy.asarray(signs)
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
def test_str2addr(self):
self.assertEqual(cistring.str2addr(6, 3, int('0b11001' ,2)), 7)
self.assertEqual(cistring.str2addr(6, 3, int('0b11010' ,2)), 8)
self.assertEqual(cistring.str2addr(7, 4, int('0b110011',2)), 9)
self.assertEqual(cistring.str2addr(6, 3, cistring.addr2str(6, 3, 7)), 7)
self.assertEqual(cistring.str2addr(6, 3, cistring.addr2str(6, 3, 8)), 8)
self.assertEqual(cistring.str2addr(7, 4, cistring.addr2str(7, 4, 9)), 9)
self.assertTrue(all(numpy.arange(20) ==
cistring.strs2addr(6, 3, cistring.addrs2str(6, 3, range(20)))))
def t2strs(norb, nelec):
nocc = nelec
hf_str = int('1'*nocc, 2)
addrs = []
signs = []
for a in range(nocc+1, norb):
for b in range(nocc, a):
for i in reversed(range(1,nocc)):
for j in reversed(range(i)):
str1 = hf_str ^ (1 << j) | (1 << b)
sign = cistring.cre_des_sign(b, j, hf_str)
sign*= cistring.cre_des_sign(a, i, str1)
str1^= (1 << i) | (1 << a)
addrs.append(cistring.str2addr(norb, nelec, str1))
signs.append(sign)
return numpy.asarray(addrs), numpy.asarray(signs)
def t2strs(norb, nelec):
nocc = nelec
hf_str = int('1'*nocc, 2)
addrs = []
signs = []
for a in range(nocc+1, norb):
for b in range(nocc, a):
for i in reversed(range(1,nocc)):
for j in reversed(range(i)):
str1 = hf_str ^ (1 << j) | (1 << b)
sign = cistring.cre_des_sign(b, j, hf_str)
sign*= cistring.cre_des_sign(a, i, str1)
str1^= (1 << i) | (1 << a)
addrs.append(cistring.str2addr(norb, nelec, str1))
signs.append(sign)
return numpy.asarray(addrs), numpy.asarray(signs)
def test_str2addr(self):
self.assertEqual(cistring.str2addr(6, 3, int('0b11001', 2)), 7)
self.assertEqual(cistring.str2addr(6, 3, int('0b11010', 2)), 8)
self.assertEqual(cistring.str2addr(7, 4, int('0b110011', 2)), 9)
self.assertEqual(cistring.str2addr(6, 3, cistring.addr2str(6, 3, 7)),
7)
self.assertEqual(cistring.str2addr(6, 3, cistring.addr2str(6, 3, 8)),
8)
self.assertEqual(cistring.str2addr(7, 4, cistring.addr2str(7, 4, 9)),
9)
self.assertTrue(
all(
numpy.arange(20) == cistring.strs2addr(
6, 3, cistring.addrs2str(6, 3, range(20)))))
def to_fci(cisdvec, norb, nelec):
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
nocc = neleca
nvir = norb - nocc
c0 = cisdvec[0]
c1 = cisdvec[1:nocc*nvir+1].reshape(nocc,nvir)
c2 = cisdvec[nocc*nvir+1:].reshape(nocc,nocc,nvir,nvir)
t1addr, t1sign = t1strs(norb, nocc)
na = cistring.num_strings(norb, nocc)
fcivec = numpy.zeros((na,na))
fcivec[0,0] = c0
c1 = c1[::-1].T.ravel()
fcivec[0,t1addr] = fcivec[t1addr,0] = c1 * t1sign
c2ab = c2[::-1,::-1].transpose(2,0,3,1).reshape(nocc*nvir,-1)
c2ab = numpy.einsum('i,j,ij->ij', t1sign, t1sign, c2ab)
lib.takebak_2d(fcivec, c2ab, t1addr, t1addr)
if nocc > 1 and nvir > 1:
hf_str = int('1'*nocc, 2)
for a in range(nocc, norb):
for b in range(nocc, a):
for i in reversed(range(1, nocc)):
for j in reversed(range(i)):
c2aa = c2[i,j,a-nocc,b-nocc] - c2[j,i,a-nocc,b-nocc]
str1 = hf_str ^ (1 << j) | (1 << b)
c2aa*= cistring.cre_des_sign(b, j, hf_str)
c2aa*= cistring.cre_des_sign(a, i, str1)
str1^= (1 << i) | (1 << a)
addr = cistring.str2addr(norb, nocc, str1)
fcivec[0,addr] = fcivec[addr,0] = c2aa
return fcivec
def find_addr_(stra, aonly, nelec):
stra[orbleft[aonly]] = True
return cistring.str2addr(norb, nelec, ('%i'*norb)%tuple(stra)[::-1])
def test_str2addr(self):
self.assertEqual(cistring.str2addr(6, 3, int('0b11001' ,2)), 7)
self.assertEqual(cistring.str2addr(6, 3, int('0b11010' ,2)), 8)
self.assertEqual(cistring.str2addr(7, 4, int('0b110011',2)), 9)
def find_addr_(stra, aonly, nelec):
stra[orbleft[aonly]] = True
return cistring.str2addr(norb, nelec,
('%i' * norb) % tuple(stra)[::-1])
def test_str2addr(self):
self.assertEqual(cistring.str2addr(6, 3, int('0b11001' ,2)), 7)
self.assertEqual(cistring.str2addr(6, 3, int('0b11010' ,2)), 8)
self.assertEqual(cistring.str2addr(7, 4, int('0b110011',2)), 9)
def to_fcivec(cisdvec, norb, nelec, frozen=0):
'''Convert CISD coefficients to FCI coefficients'''
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
assert (neleca == nelecb)
frozen_mask = numpy.zeros(norb, dtype=bool)
if isinstance(frozen, (int, numpy.integer)):
nfroz = frozen
frozen_mask[:frozen] = True
else:
nfroz = len(frozen)
frozen_mask[frozen] = True
nocc = numpy.count_nonzero(~frozen_mask[:neleca])
nmo = norb - nfroz
nvir = nmo - nocc
c0, c1, c2 = cisdvec_to_amplitudes(cisdvec, nmo, nocc)
t1addr, t1sign = t1strs(nmo, nocc)
na = cistring.num_strings(nmo, nocc)
fcivec = numpy.zeros((na, na))
fcivec[0, 0] = c0
c1 = c1[::-1].T.ravel()
fcivec[0, t1addr] = fcivec[t1addr, 0] = c1 * t1sign
c2ab = c2[::-1, ::-1].transpose(2, 0, 3, 1).reshape(nocc * nvir, -1)
c2ab = numpy.einsum('i,j,ij->ij', t1sign, t1sign, c2ab)
lib.takebak_2d(fcivec, c2ab, t1addr, t1addr)
if nocc > 1 and nvir > 1:
hf_str = int('1' * nocc, 2)
for a in range(nocc, nmo):
for b in range(nocc, a):
for i in reversed(range(1, nocc)):
for j in reversed(range(i)):
c2aa = c2[i, j, a - nocc,
b - nocc] - c2[j, i, a - nocc, b - nocc]
str1 = hf_str ^ (1 << j) | (1 << b)
c2aa *= cistring.cre_des_sign(b, j, hf_str)
c2aa *= cistring.cre_des_sign(a, i, str1)
str1 ^= (1 << i) | (1 << a)
addr = cistring.str2addr(nmo, nocc, str1)
fcivec[0, addr] = fcivec[addr, 0] = c2aa
if nfroz == 0:
return fcivec
assert (norb < 63)
strs = cistring.gen_strings4orblist(range(norb), neleca)
na = len(strs)
count = numpy.zeros(na, dtype=int)
parity = numpy.zeros(na, dtype=bool)
core_mask = numpy.ones(na, dtype=bool)
# During the loop, count saves the number of occupied orbitals that
# lower (with small orbital ID) than the present orbital i.
# Moving all the frozen orbitals to the beginning of the orbital list
# (before the occupied orbitals) leads to parity odd (= True, with
# negative sign) or even (= False, with positive sign).
for i in range(norb):
if frozen_mask[i]:
if i < neleca:
# frozen occupied orbital should be occupied
core_mask &= (strs & (1 << i)) != 0
parity ^= (count & 1) == 1
else:
# frozen virtual orbital should not be occupied.
# parity is not needed since it's unoccupied
core_mask &= (strs & (1 << i)) == 0
else:
count += (strs & (1 << i)) != 0
sub_strs = strs[core_mask & (count == nocc)]
addrs = cistring.strs2addr(norb, neleca, sub_strs)
fcivec1 = numpy.zeros((na, na))
fcivec1[addrs[:, None], addrs] = fcivec
fcivec1[parity, :] *= -1
fcivec1[:, parity] *= -1
return fcivec1
