def decomp_4rdm_to_3rdm_sf(d4, d1, d2, d2_hom, d2_het, d3):
"""
Returns the list of terms composing the decomposition of the 4 body spin free rdm d4
in terms of one, two, and three body rdms"
"""
# This decomposition assumes the density matrices correspond to a spin averaged ensemble state.
# d4 -- Spin free 4rdm to be decomposed
# d1 -- One body spin free rdm
# d2 -- Two body spin free rdm
# d2_hom -- Sum of all alpha and all beta two body rdms. The "homogeneous spin" 2rdm.
# d2_het -- Sum of abab and baba two body rdms. The "heterogeneous spin" 2rdm.
# d3 -- Three body spin free rdm
# Note that d2 = d2_hom + d2_het
# Check input
if ( not isinstance(d4, tensor) ) or (len(d4.indices) != 8):
raise TypeError, "d4 must be a tensor with 8 indices"
if ( not isinstance(d1, tensor) ) or (len(d1.indices) != 2):
raise TypeError, "d1 must be a tensor with 2 indices"
if ( not isinstance(d2, tensor) ) or (len(d2.indices) != 4):
raise TypeError, "d2 must be a tensor with 4 indices"
if ( not isinstance(d2_hom, tensor) ) or (len(d2_hom.indices) != 4):
raise TypeError, "d2_hom must be a tensor with 4 indices"
if ( not isinstance(d2_het, tensor) ) or (len(d2_het.indices) != 4):
raise TypeError, "d2_het must be a tensor with 4 indices"
if ( not isinstance(d3, tensor) ) or (len(d3.indices) != 6):
raise TypeError, "d3 must be a tensor with 6 indices"
# Initialize the return value
decomp = []
# Compute terms from the sum involving the 3-body cumulant
for p in range(4):
ti = range(4)
del(ti[p])
ti.insert(0,p)
for q in range(4):
bi = range(4)
del(bi[q])
bi.insert(0,q)
for i in range(1,4):
for j in range(1,4):
if i != j and ti[i] == bi[j]:
temp = bi[i]
bi[i] = bi[j]
bi[j] = temp
# Determine the number of index permutations
n_perm = get_num_perms(ti,bi)
# Determine the sign
sign = (-1)**n_perm
# Create the 1RDM 3RDM term
bj = [i+4 for i in bi]
coeff = sign * (0.5)**n_perm
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d4.indices[i] for i in (ti[0:1] + bj[0:1])]
d3_copy_0 = d3.copy()
d3_copy_0.indices = [d4.indices[i] for i in (ti[1:4] + bj[1:4])]
decomp.append(term(coeff, [], [d1_copy_0, d3_copy_0]))
# Create terms not involving the 3RDM
d3_decomp = decomp_3rdm_to_2rdm_sf(d3_copy_0, d1, d2)
for t in d3_decomp:
coeff = (-1) * sign * (0.5)**n_perm * t.numConstant
decomp.append(term(coeff, [], [d1_copy_0] + t.tensors))
# Compute terms from the sum involving two 2-body cumulants
for p in range(1):
for q in range(p+1,4):
ti = [p,q]
for i in range(4):
if not (i in ti):
ti.append(i)
for r in range(4):
for s in range(r+1,4):
if s == p or r == q:
bi = [s,r]
else:
bi = [r,s]
temp = range(4)
del temp[s]
del temp[r]
if temp[0] == ti[3] or temp[1] == ti[2]:
temp = [temp[1], temp[0]]
bi += temp
# Determine the number of index permutations
n_perm = get_num_perms(ti,bi)
# Determine the sign
sign = (-1)**n_perm
# Create 2RDM 2RDM term
bj = [i+4 for i in bi]
if n_perm < 2:
coeff = sign * (0.5)**n_perm
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d4.indices[i] for i in (ti[0:2] + bj[0:2])]
d2_copy_1 = d2.copy()
d2_copy_1.indices = [d4.indices[i] for i in (ti[2:4] + bj[2:4])]
decomp.append(term(coeff, [], [d2_copy_0, d2_copy_1]))
elif n_perm == 2:
coeff = sign * 0.5
d2_hom_copy_0 = d2_hom.copy()
d2_hom_copy_0.indices = [d4.indices[i] for i in (ti[0:2] + bj[0:2])]
d2_hom_copy_1 = d2_hom.copy()
d2_hom_copy_1.indices = [d4.indices[i] for i in (ti[2:4] + bj[2:4])]
decomp.append(term(coeff, [], [d2_hom_copy_0, d2_hom_copy_1]))
d2_het_copy_0 = d2_het.copy()
d2_het_copy_0.indices = [d4.indices[i] for i in (ti[0:2] + bj[0:2])]
d2_het_copy_1 = d2_het.copy()
d2_het_copy_1.indices = [d4.indices[i] for i in (ti[2:4] + bj[2:4])]
decomp.append(term(coeff, [], [d2_het_copy_0, d2_het_copy_1]))
d2_het_copy_0 = d2_het.copy()
d2_het_copy_0.indices = [d4.indices[i] for i in (ti[0:2] + [bj[1], bj[0]])]
d2_het_copy_1 = d2_het.copy()
d2_het_copy_1.indices = [d4.indices[i] for i in (ti[2:4] + [bj[3], bj[2]])]
decomp.append(term(coeff, [], [d2_het_copy_0, d2_het_copy_1]))
else:
raise RuntimeError, "Did not expect a term with %i permutations" %n_perm
# Create 'un-permuted' 2RDM 1RDM 1RDM terms
coeff = sign * (-1) * (0.5)**n_perm
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d4.indices[i] for i in (ti[0:2] + bj[0:2])]
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d4.indices[i] for i in (ti[2:3] + bj[2:3])]
d1_copy_1 = d1.copy()
d1_copy_1.indices = [d4.indices[i] for i in (ti[3:4] + bj[3:4])]
decomp.append(term(coeff, [], [d2_copy_0, d1_copy_0, d1_copy_1]))
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d4.indices[i] for i in (ti[2:4] + bj[2:4])]
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d4.indices[i] for i in (ti[0:1] + bj[0:1])]
d1_copy_1 = d1.copy()
d1_copy_1.indices = [d4.indices[i] for i in (ti[1:2] + bj[1:2])]
decomp.append(term(coeff, [], [d2_copy_0, d1_copy_0, d1_copy_1]))
# Create 'permuted' 2RDM 1RDM 1RDM terms
if n_perm < 2:
bj = bi[0:2] + bi[3:4] + bi[2:3]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (0.5)**n_perm
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d4.indices[i] for i in (ti[0:2] + bj[0:2])]
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d4.indices[i] for i in (ti[2:3] + bj[2:3])]
d1_copy_1 = d1.copy()
d1_copy_1.indices = [d4.indices[i] for i in (ti[3:4] + bj[3:4])]
decomp.append(term(coeff, [], [d2_copy_0, d1_copy_0, d1_copy_1]))
bj = bi[1:2] + bi[0:1] + bi[2:4]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (0.5)**n_perm
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d4.indices[i] for i in (ti[2:4] + bj[2:4])]
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d4.indices[i] for i in (ti[0:1] + bj[0:1])]
d1_copy_1 = d1.copy()
d1_copy_1.indices = [d4.indices[i] for i in (ti[1:2] + bj[1:2])]
decomp.append(term(coeff, [], [d2_copy_0, d1_copy_0, d1_copy_1]))
elif n_perm == 2:
bj = bi[1:2] + bi[0:1] + bi[3:4] + bi[2:3]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (-1) * (0.5)**n_perm
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d4.indices[i] for i in (ti[0:2] + bj[0:2])]
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d4.indices[i] for i in (ti[2:3] + bj[2:3])]
d1_copy_1 = d1.copy()
d1_copy_1.indices = [d4.indices[i] for i in (ti[3:4] + bj[3:4])]
decomp.append(term(coeff, [], [d2_copy_0, d1_copy_0, d1_copy_1]))
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d4.indices[i] for i in (ti[2:4] + bj[2:4])]
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d4.indices[i] for i in (ti[0:1] + bj[0:1])]
d1_copy_1 = d1.copy()
d1_copy_1.indices = [d4.indices[i] for i in (ti[1:2] + bj[1:2])]
decomp.append(term(coeff, [], [d2_copy_0, d1_copy_0, d1_copy_1]))
else:
raise RuntimeError, "Did not expect a term with %i permutations" %n_perm
# Create 1RDM 1RDM 1RDM 1RDM terms
bj = [i for i in bi]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (0.5)**n_perm
d1_copies = []
for j in range(4):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d4.indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
bj = bi[0:2] + bi[3:4] + bi[2:3]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (-1) * (0.5)**n_perm
d1_copies = []
for j in range(4):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d4.indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
bj = bi[1:2] + bi[0:1] + bi[2:4]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (-1) * (0.5)**n_perm
d1_copies = []
for j in range(4):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d4.indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
bj = bi[1:2] + bi[0:1] + bi[3:4] + bi[2:3]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (0.5)**n_perm
d1_copies = []
for j in range(4):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d4.indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
# Compute terms from the sum involving one 2-body cumulant
for p in range(4):
for q in range(p+1,4):
ti = [p,q]
for i in range(4):
if not (i in ti):
ti.append(i)
for r in range(4):
for s in range(4):
if r == s:
continue
bi = [r,s]
temp = range(4)
del temp[max(r,s)]
del temp[min(r,s)]
if temp[0] == ti[3] or temp[1] == ti[2]:
temp = [temp[1], temp[0]]
bi += temp
# Determine the number of index permutations
n_perm = get_num_perms(ti,bi)
# Determine the sign
sign = (-1)**n_perm
# Compute 1RDM 1RDM 2RDM term
coeff = 1
bj = [i for i in bi]
pairs_rdm1 = [ [ti[i],bj[i]] for i in range(2)]
pairs_rdm2 = [ [bj[i],ti[i]] for i in range(2,4)]
for pair in pairs_rdm2:
if pair[0] == pair[1]:
pairs_rdm2 = []
break
for pair in pairs_rdm2:
if not (pair in pairs_rdm1):
#print "swapping bj[2] and bj[3]"
(bj[3],bj[2]) = (bj[2],bj[3])
coeff *= -1
break
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff *= sign * (0.5)**n_perm
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d4.indices[i] for i in (ti[0:1] + bj[0:1])]
d1_copy_1 = d1.copy()
d1_copy_1.indices = [d4.indices[i] for i in (ti[1:2] + bj[1:2])]
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d4.indices[i] for i in (ti[2:4] + bj[2:4])]
decomp.append(term(coeff, [], [d1_copy_0, d1_copy_1, d2_copy_0]))
# Compute 'un-permuted' 1RDM 1RDM 1RDM 1RDM term
bj = [i for i in bi]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (-1) * (0.5)**n_perm
d1_copies = []
for j in range(4):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d4.indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
# Compute 'permuted' 1RDM 1RDM 1RDM 1RDM term
bj = bi[0:2] + bi[3:4] + bi[2:3]
n_perm = get_num_perms(ti,bj)
bj = [i+4 for i in bj]
coeff = sign * (0.5)**n_perm
d1_copies = []
for j in range(4):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d4.indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
# Compute terms from the sum involving only one particle density matrices
ti = range(4)
for bi in makePermutations(4):
# Determine the number of permutations
n_perm = get_num_perms(ti,bi)
# Determine the sign
sign = (-1)**n_perm
# Compute 1RDM 1RDM 1RDM 1RDM term
bj = [i+4 for i in bi]
coeff = sign * (0.5)**n_perm
d1_copies = []
for j in range(4):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d4.indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
# Combine like terms
for t in decomp:
t.tensors.sort()
decomp.sort()
i = 0
while i < len(decomp)-1:
if decomp[i].tensors == decomp[i+1].tensors:
decomp[i+1].numConstant += decomp[i].numConstant
del(decomp[i])
else:
i += 1
termChop(decomp)
# Return the decomposition
return decomp
def decomp_3rdm_to_2rdm_sf(d3, d1, d2, indexOrder = '1212'):
"""
Returns the list of terms composing the decomposition of the 3 body spin free rdm d3
in terms of one and two body rdms"
"""
if ( not isinstance(d1, tensor) ) or (len(d1.indices) != 2):
raise TypeError, "d1 must be a tensor with 2 indices"
if ( not isinstance(d2, tensor) ) or (len(d2.indices) != 4):
raise TypeError, "d2 must be a tensor with 4 indices"
if ( not isinstance(d3, tensor) ) or (len(d3.indices) != 6):
raise TypeError, "d3 must be a tensor with 6 indices"
# sort the 3-body RDM's indices into 1212 ordering
d3_indices = []
if indexOrder == '1212':
d3_indices.extend(d3.indices)
elif indexOrder == '1122':
for i in range(3):
d3_indices.append(d3.indices[2*i])
for i in range(3):
d3_indices.append(d3.indices[2*i+1])
else:
raise ValueError, "unexpected indexOrder parameter: %s" %(indexOrder)
decomp = []
# Prepare terms from sum (-1)^p %gamma^{i_1}_{i_4} %lambda^{i_2`i_3}_{i_5`i_6}
for p0 in range(3):
temp = range(3)
del temp[p0]
p1 = temp[0]
p2 = temp[1]
ti = [p0, p1, p2]
for q0 in range(3):
temp = range(3)
del temp[q0]
q1 = temp[0]
q2 = temp[1]
if q1 == p2 or q2 == p1:
bi = [q0, q2, q1]
else:
bi = [q0, q1, q2]
# determine the sign of the term based on the number of index permutations
n_perm = get_num_perms(ti,bi)
if n_perm > 1:
raise ValueError, "n_perm = %i which is > 1. This was unexpected." %n_perm
sign = (-1)**n_perm
# create the 1RDM 2RDM term
bj = [i for i in bi]
n_perm = get_num_perms(ti,bj)
coeff = sign * (0.5)**n_perm
bj = [i+3 for i in bj]
d1_copy_0 = d1.copy()
d1_copy_0.indices = [d3_indices[i] for i in (ti[0:1] + bj[0:1])]
d2_copy_0 = d2.copy()
d2_copy_0.indices = [d3_indices[i] for i in (ti[1:3] + bj[1:3])]
decomp.append(term(coeff, [], [d1_copy_0, d2_copy_0]))
# create the 1RDM 1RDM 1RDM terms
bj = [i for i in bi]
n_perm = get_num_perms(ti,bj)
coeff = sign * (-1) * (0.5)**n_perm
bj = [i+3 for i in bj]
d1_copies = []
for j in range(3):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d3_indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
bj = bi[0:1] + bi[2:3] + bi[1:2]
n_perm = get_num_perms(ti,bj)
coeff = sign * (0.5)**n_perm
bj = [i+3 for i in bj]
d1_copies = []
for j in range(3):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d3_indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
# Compute terms from the sum involving only one particle density matrices
ti = range(3)
for bi in makePermutations(3):
# Determine the number of permutations
n_perm = get_num_perms(ti,bi)
# Determine the sign
sign = (-1)**n_perm
# Compute 1RDM 1RDM 1RDM 1RDM term
bj = [i+3 for i in bi]
coeff = sign * (0.5)**n_perm
d1_copies = []
for j in range(3):
d1_copies.append(d1.copy())
d1_copies[-1].indices = [d3_indices[i] for i in (ti[j:j+1] + bj[j:j+1])]
decomp.append(term(coeff, [], d1_copies))
# Combine like terms
for t in decomp:
t.tensors.sort()
decomp.sort()
i = 0
while i < len(decomp)-1:
if decomp[i].tensors == decomp[i+1].tensors:
decomp[i+1].numConstant += decomp[i].numConstant
del(decomp[i])
else:
i += 1
termChop(decomp)
# if original ordering was 1122, convert back to it
if indexOrder == '1122':
for t in decomp:
for ten in t.tensors:
if ten.name == d2.name:
ten.indices = [ten.indices[0], ten.indices[2], ten.indices[1], ten.indices[3]]
# Return the decomposition
return decomp
def contractCoreOps_sf(inTerm):
"Returns a list of terms resulting from normal ordering the operators in inTerm."
# check that inTerm is a term
if not isinstance(inTerm, term):
raise TypeError, "inTerm must be of class term"
# Make separate lists of the spin free excitation operators and other tensors
sfExOp_list = []
other_list = []
for t in inTerm.tensors:
if isinstance(t, sfExOp):
sfExOp_list.append(t.copy())
else:
other_list.append(t.copy())
# Initialize n, the number of remaining spin free excitation operators
if len(sfExOp_list) != 1:
raise RuntimeError, "terms should have single sfExOp"
# Give short names for the excitation operator and their order
e1 = sfExOp_list[0]
o1 = e1.order
# list of offset of "core" type indices
cIndsCre = []
cIndsDes = []
for i in range(o1):
if e1.indices[i].indType == (options.core_type,):
cIndsCre.append(i)
if e1.indices[i+o1].indType == (options.core_type,):
cIndsDes.append(i+o1)
# all the "core" type indices should be contracted
nc = len(cIndsCre)
outTerms = []
if nc != len(cIndsDes):
outTerms.append(term(0.0, [], []))
return outTerms
if nc == 0:
outTerms = [inTerm.copy()]
return outTerms
newOrder = o1 - nc
# For each contraction, compute the resulting term
perms = makePermutations(nc)
for perm in perms:
# Compute the pairs of indices to be contracted
# Example: (conPairs[0][p], conPairs[1][p]) is the pth contraction pair.
conPairs = [[],[]]
for i in range(nc):
conPairs[0].append(cIndsCre[perm[i]])
conPairs[1].append(cIndsDes[i])
# evaluate constant prefactor
prefactor = 1
inds = []
for i in range(nc):
if i not in inds:
inds.append(i)
i0 = conPairs[0][i]
i1 = conPairs[1][i] - o1
if i1 == i0:
prefactor *= 2
continue
#old if i1 in conPairs[0]:
#old inds.append(conPairs[0].index(i1))
#old i2 = conPairs[1][conPairs[0].index(i1)] - o1
#old if i2 == i0:
#old prefactor *= 2
#old continue
#old if i2 in conPairs[0]:
#old inds.append(conPairs[0].index(i2))
#old i3 = conPairs[1][conPairs[0].index(i2)] - o1
#old if i3 == i0:
#old prefactor *= 2
#old continue
#old if i3 in conPairs[0]:
#old inds.append(conPairs[0].index(i3))
#old i4 = conPairs[1][conPairs[0].index(i3)] - o1
#old if i4 == i0:
#old prefactor *= 2
#old continue
#old else:
#old raise RuntimeError, "NYI:recursive algorithm1"
while i1 in conPairs[0]:
inds.append(conPairs[0].index(i1))
i1 = conPairs[1][conPairs[0].index(i1)] - o1
if i1 == i0:
prefactor *= 2
break
#
# Initialize the term's tensor list
tensorList = other_list[:]
# Initialize the index list for the new excitation operator
indexList = [False] * (2*newOrder)
# Populate the index list for the new excitation operator
# Also, create a kronecker delta function for each contraction pair
count = 0
for i1 in range(o1):
if i1 in conPairs[0]:#create a kronecker delta
i2 = conPairs[1][conPairs[0].index(i1)]
ind1 = e1.indices[i1]
ind2 = e1.indices[i2]
tensorList.insert(0, kroneckerDelta([ind1,ind2]))
else: #insert a pair of indices
indexList[count] = e1.indices[i1]
i2 = i1+o1
#old if i2 in conPairs[1]:
#old i2 = conPairs[0][conPairs[1].index(i2)] + o1
#old if i2 in conPairs[1]:
#old i2 = conPairs[0][conPairs[1].index(i2)] + o1
#old if i2 in conPairs[1]:
#old i2 = conPairs[0][conPairs[1].index(i2)] + o1
#old if i2 in conPairs[1]:
#old i2 = conPairs[0][conPairs[1].index(i2)] + o1
#old if i2 in conPairs[1]:
#old raise RuntimeError, "NYI:recursive algorithm2"
#old else:
#old indexList[count+newOrder] = e1.indices[i2]
#old else:
#old indexList[count+newOrder] = e1.indices[i2]
#old else:
#old indexList[count+newOrder] = e1.indices[i2]
#old else:
#old indexList[count+newOrder] = e1.indices[i2]
while i2 in conPairs[1]:
i2 = conPairs[0][conPairs[1].index(i2)] + o1
else: indexList[count+newOrder] = e1.indices[i2]
#
count += 1
# Ensure that all slots in the index list have been filled
for ind in indexList:
if ind is False:
raise RuntimeError, "There is at least one unassigned index in the new spin free operator."
# Add the new excitation operator to the tensor list
if len(indexList) != 0:
tensorList.append(sfExOp(indexList))
# Determine the sign
indPairs = [[],[]]
for i in range(o1):
indPairs[0].append(i)
if i in conPairs[0]:
indPairs[1].append(conPairs[1][conPairs[0].index(i)]-o1)
else:
a = e1.indices[i]
b = indexList[indexList.index(a)+newOrder]
#indPairs[1].append(e1.indices.index(b)-o1)#is not correct when there are duplicate indices
indPairs[1].append(e1.indices[o1:2*o1].index(b))
#for i in range(o1): indPairs[1].index(i)
n_perm = get_num_perms(indPairs[0], indPairs[1])
sign = (-1)**n_perm
# Add the resulting term to this iteration's list of output terms
#print term(sign*prefactor*inTerm.numConstant, inTerm.constants, tensorList)
#print "-------------------------------------------------------------------"
outTerms.append(term(sign*prefactor*inTerm.numConstant, inTerm.constants, tensorList))
return outTerms
def decomp_3op_to_2op_2rdm_sf(op, d1, d2, indexOrder = '1212'):
"""
Returns the list of terms composing the decomposition of the 3 body sfExOp op
in terms of one and two body operators"
"""
# Check input
if ( not isinstance(op, sfExOp) ) or (op.order != 3):
raise TypeError, "op must be a 3-particle sfExOp"
if ( not isinstance(d1, tensor) ) or (len(d1.indices) != 2):
raise TypeError, "d1 must be a tensor with 2 indices"
if ( not isinstance(d2, tensor) ) or (len(d2.indices) != 4):
raise TypeError, "d2 must be a tensor with 4 indices"
if indexOrder != '1212' and indexOrder != '1122':
raise ValueError, "indexOrder must be '1212' or '1122'"
# Initialize the return value
decomp = []
# Loop over the nine index permutations used in the decomposition
for p0 in range(3):
# Compute the top indices
temp = range(3)
del temp[p0]
p1 = temp[0]
p2 = temp[1]
ti = [p0, p1, p2]
for q0 in range(3):
# Compute the bottom indices, remembering that the second and third index pairs
# should retain original pairing as much as possible.
temp = range(3)
del temp[q0]
q1 = temp[0]
q2 = temp[1]
if q1 == p2 or q2 == p1:
bi = [q0, q2, q1]
else:
bi = [q0, q1, q2]
# Determine the number of permutations from original pairing
n_perms = get_num_perms(ti,bi)
# Shift bi to match the bottom indices of op
bi = [i+op.order for i in bi]
# Create 1RDM 2op term
d1_copy = d1.copy()
d1_copy.indices = [op.indices[ti[0]], op.indices[bi[0]]]
indexList = [op.indices[i] for i in ti[1:]] + [op.indices[i] for i in bi[1:]]
decomp.append( term( (-0.5)**n_perms, [], [d1_copy, sfExOp(indexList)] ) )
# Create 2RDM 1op term
d2_copy = d2.copy()
d2_copy.indices = [op.indices[i] for i in ti[1:]] + [op.indices[i] for i in bi[1:]]
if indexOrder == '1122':
d2_copy.indices = [d2_copy.indices[0], d2_copy.indices[2], d2_copy.indices[1], d2_copy.indices[3]]
indexList = [op.indices[ti[0]], op.indices[bi[0]]]
decomp.append( term( (-0.5)**n_perms, [], [d2_copy, sfExOp(indexList)] ) )
# Create 1RDM 1RDM 1op terms
d1_copy = d1.copy()
d1_copy.indices = [op.indices[ti[1]], op.indices[bi[1]]]
d1_copy_2 = d1.copy()
d1_copy_2.indices = [op.indices[ti[2]], op.indices[bi[2]]]
indexList = [op.indices[ti[0]], op.indices[bi[0]]]
decomp.append( term( -2 * (-0.5)**n_perms, [], [d1_copy, d1_copy_2, sfExOp(indexList)] ) )
d1_copy = d1.copy()
d1_copy.indices = [op.indices[ti[2]], op.indices[bi[1]]]
d1_copy_2 = d1.copy()
d1_copy_2.indices = [op.indices[ti[1]], op.indices[bi[2]]]
indexList = [op.indices[ti[0]], op.indices[bi[0]]]
decomp.append( term( (-0.5)**n_perms, [], [d1_copy, d1_copy_2, sfExOp(indexList)] ) )
# Create 1RDM 2RDM term
d1_copy = d1.copy()
d1_copy.indices = [op.indices[ti[0]], op.indices[bi[0]]]
d2_copy = d2.copy()
d2_copy.indices = [op.indices[i] for i in ti[1:]] + [op.indices[i] for i in bi[1:]]
if indexOrder == '1122':
d2_copy.indices = [d2_copy.indices[0], d2_copy.indices[2], d2_copy.indices[1], d2_copy.indices[3]]
decomp.append( term( - (-0.5)**n_perms, [], [d1_copy, d2_copy] ) )
# Create 1RDM 1RDM 1RDM terms
d1_copy = d1.copy()
d1_copy.indices = [op.indices[ti[0]], op.indices[bi[0]]]
d1_copy_2 = d1.copy()
d1_copy_2.indices = [op.indices[ti[1]], op.indices[bi[1]]]
d1_copy_3 = d1.copy()
d1_copy_3.indices = [op.indices[ti[2]], op.indices[bi[2]]]
decomp.append( term( (4.0 / 3.0) * (-0.5)**n_perms, [], [d1_copy, d1_copy_2, d1_copy_3] ) )
d1_copy = d1.copy()
d1_copy.indices = [op.indices[ti[0]], op.indices[bi[0]]]
d1_copy_2 = d1.copy()
d1_copy_2.indices = [op.indices[ti[2]], op.indices[bi[1]]]
d1_copy_3 = d1.copy()
d1_copy_3.indices = [op.indices[ti[1]], op.indices[bi[2]]]
decomp.append( term( (-2.0 / 3.0) * (-0.5)**n_perms, [], [d1_copy, d1_copy_2, d1_copy_3] ) )
# Return the decomposition
return decomp
def contractCoreOps_sf(inTerm):
"Returns a list of terms resulting from normal ordering the operators in inTerm."
# check that inTerm is a term
if not isinstance(inTerm, term):
raise TypeError, "inTerm must be of class term"
# Make separate lists of the spin free excitation operators and other tensors
sfExOp_list = []
other_list = []
for t in inTerm.tensors:
if isinstance(t, sfExOp):
sfExOp_list.append(t.copy())
else:
other_list.append(t.copy())
# Initialize n, the number of remaining spin free excitation operators
if len(sfExOp_list) != 1:
raise RuntimeError, "terms should have single sfExOp"
# Give short names for the excitation operator and their order
e1 = sfExOp_list[0]
o1 = e1.order
# list of offset of "core" type indices
cIndsCre = []
cIndsDes = []
for i in range(o1):
if e1.indices[i].indType == (options.core_type, ):
cIndsCre.append(i)
if e1.indices[i + o1].indType == (options.core_type, ):
cIndsDes.append(i + o1)
# all the "core" type indices should be contracted
nc = len(cIndsCre)
outTerms = []
if nc != len(cIndsDes):
outTerms.append(term(0.0, [], []))
return outTerms
if nc == 0:
outTerms = [inTerm.copy()]
return outTerms
newOrder = o1 - nc
# For each contraction, compute the resulting term
perms = makePermutations(nc)
for perm in perms:
# Compute the pairs of indices to be contracted
# Example: (conPairs[0][p], conPairs[1][p]) is the pth contraction pair.
conPairs = [[], []]
for i in range(nc):
conPairs[0].append(cIndsCre[perm[i]])
conPairs[1].append(cIndsDes[i])
# evaluate constant prefactor
prefactor = 1
inds = []
for i in range(nc):
if i not in inds:
inds.append(i)
i0 = conPairs[0][i]
i1 = conPairs[1][i] - o1
if i1 == i0:
prefactor *= 2
continue
#old if i1 in conPairs[0]:
#old inds.append(conPairs[0].index(i1))
#old i2 = conPairs[1][conPairs[0].index(i1)] - o1
#old if i2 == i0:
#old prefactor *= 2
#old continue
#old if i2 in conPairs[0]:
#old inds.append(conPairs[0].index(i2))
#old i3 = conPairs[1][conPairs[0].index(i2)] - o1
#old if i3 == i0:
#old prefactor *= 2
#old continue
#old if i3 in conPairs[0]:
#old inds.append(conPairs[0].index(i3))
#old i4 = conPairs[1][conPairs[0].index(i3)] - o1
#old if i4 == i0:
#old prefactor *= 2
#old continue
#old else:
#old raise RuntimeError, "NYI:recursive algorithm1"
while i1 in conPairs[0]:
inds.append(conPairs[0].index(i1))
i1 = conPairs[1][conPairs[0].index(i1)] - o1
if i1 == i0:
prefactor *= 2
break
#
# Initialize the term's tensor list
tensorList = other_list[:]
# Initialize the index list for the new excitation operator
indexList = [False] * (2 * newOrder)
# Populate the index list for the new excitation operator
# Also, create a kronecker delta function for each contraction pair
count = 0
for i1 in range(o1):
if i1 in conPairs[0]: #create a kronecker delta
i2 = conPairs[1][conPairs[0].index(i1)]
ind1 = e1.indices[i1]
ind2 = e1.indices[i2]
tensorList.insert(0, kroneckerDelta([ind1, ind2]))
else: #insert a pair of indices
indexList[count] = e1.indices[i1]
i2 = i1 + o1
#old if i2 in conPairs[1]:
#old i2 = conPairs[0][conPairs[1].index(i2)] + o1
#old if i2 in conPairs[1]:
#old i2 = conPairs[0][conPairs[1].index(i2)] + o1
#old if i2 in conPairs[1]:
#old i2 = conPairs[0][conPairs[1].index(i2)] + o1
#old if i2 in conPairs[1]:
#old i2 = conPairs[0][conPairs[1].index(i2)] + o1
#old if i2 in conPairs[1]:
#old raise RuntimeError, "NYI:recursive algorithm2"
#old else:
#old indexList[count+newOrder] = e1.indices[i2]
#old else:
#old indexList[count+newOrder] = e1.indices[i2]
#old else:
#old indexList[count+newOrder] = e1.indices[i2]
#old else:
#old indexList[count+newOrder] = e1.indices[i2]
while i2 in conPairs[1]:
i2 = conPairs[0][conPairs[1].index(i2)] + o1
else:
indexList[count + newOrder] = e1.indices[i2]
#
count += 1
# Ensure that all slots in the index list have been filled
for ind in indexList:
if ind is False:
raise RuntimeError, "There is at least one unassigned index in the new spin free operator."
# Add the new excitation operator to the tensor list
if len(indexList) != 0:
tensorList.append(sfExOp(indexList))
# Determine the sign
indPairs = [[], []]
for i in range(o1):
indPairs[0].append(i)
if i in conPairs[0]:
indPairs[1].append(conPairs[1][conPairs[0].index(i)] - o1)
else:
a = e1.indices[i]
b = indexList[indexList.index(a) + newOrder]
#indPairs[1].append(e1.indices.index(b)-o1)#is not correct when there are duplicate indices
indPairs[1].append(e1.indices[o1:2 * o1].index(b))
#for i in range(o1): indPairs[1].index(i)
n_perm = get_num_perms(indPairs[0], indPairs[1])
sign = (-1)**n_perm
# Add the resulting term to this iteration's list of output terms
#print term(sign*prefactor*inTerm.numConstant, inTerm.constants, tensorList)
#print "-------------------------------------------------------------------"
outTerms.append(
term(sign * prefactor * inTerm.numConstant, inTerm.constants,
tensorList))
return outTerms