def cre_des_linkstr(strs, norb, nelec):
addrs = dict(zip(strs, range(len(strs))))
nvir = norb - nelec
link_index = numpy.zeros((len(addrs), nelec + nelec * nvir, 4), dtype=int)
link_index[:, :, 0] = -1
for i0, str1 in enumerate(strs):
occ = []
vir = []
for i in range(norb):
if str1 & (1 << i):
occ.append(i)
else:
vir.append(i)
k = 0
for i in occ:
link_index[i0, k] = (i, i, i0, 1)
k += 1
for a in vir:
for i in occ:
str0 = str1 ^ (1 << i) | (1 << a)
if str0 in addrs:
# [cre, des, targetddress, parity]
link_index[i0, k] = (a, i, addrs[str0], cistring.cre_des_sign(a, i, str1))
k += 1
return link_index
def cre_des_linkstr(strs, norb, nelec):
addrs = dict(zip(strs, range(len(strs))))
nvir = norb - nelec
link_index = numpy.zeros((len(addrs), nelec + nelec * nvir, 4),
dtype=numpy.int32)
for i0, str1 in enumerate(strs):
occ = []
vir = []
for i in range(norb):
if str1 & (1 << i):
occ.append(i)
else:
vir.append(i)
k = 0
for i in occ:
link_index[i0, k] = (i, i, i0, 1)
k += 1
for a in vir:
for i in occ:
str0 = str1 ^ (1 << i) | (1 << a)
if str0 in addrs:
# [cre, des, targetddress, parity]
link_index[i0, k] = (a, i, addrs[str0],
cistring.cre_des_sign(a, i, str1))
k += 1
return link_index
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 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 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 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 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 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
