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 normalOrder(inTerm):
"Returns a list of terms resulting from normal ordering the operators in inTerm."
# if options.verbose:
# print "converting to normal order: %s" %(str(inTerm))
# check that inTerm is a term
if not isinstance(inTerm, term):
raise TypeError, "inTerm must be of class term"
# determine what types of operators the term contains
has_creDesOps = False
has_sfExOps = False
for t in inTerm.tensors:
if isinstance(t, creOp) or isinstance(t, desOp):
has_creDesOps = True
elif isinstance(t, sfExOp):
has_sfExOps = True
# If term has both creation/destruction operators and spin free excitation operators,
# raise an error
if has_creDesOps and has_sfExOps:
raise RuntimeError, "Normal ordering not implemented when both creOp/desOp and sfExOp " + \
"tensors are present"
# if the term is already normal ordered, return it unchanged
elif inTerm.isNormalOrdered():
outTerms = [inTerm.copy()]
# Normal ordering for creOp/desOp
elif has_creDesOps:
# Separate the cre/des operators from other tensors
ops = []
nonOps = []
for t in inTerm.tensors:
if isinstance(t, creOp) or isinstance(t, desOp):
ops.append(t.copy())
else:
nonOps.append(t.copy())
# Generate all contraction pairs
contractionPairs = []
for i in range(len(ops)):
iTerm = ops[i]
for j in range(i+1,len(ops)):
jTerm = ops[j]
if isinstance(iTerm, desOp) and isinstance(jTerm, creOp):
contractionPairs.append((i,j));
#print "contractionPairs\n", contractionPairs
# Determine maximum contraction order
creCount = 0
maxConOrder = 0
for i in range(len(ops)-1,-1,-1):
iTerm = ops[i]
if isinstance(iTerm, creOp):
creCount +=1
elif isinstance(iTerm, desOp) and creCount > 0:
maxConOrder += 1
creCount -= 1
del(creCount,iTerm)
# Generate all contractions
contractions = []
for i in range(maxConOrder+1):
subCons = makeTuples(i,contractionPairs)
j = 0
while j < len(subCons):
creOpTags = []
desOpTags = []
for k in range(i):
creOpTags.append(subCons[j][k][1])
desOpTags.append(subCons[j][k][0])
if allDifferent(creOpTags) and allDifferent(desOpTags):
j += 1
else:
del(subCons[j])
for j in range(len(subCons)):
contractions.append(subCons[j])
del(subCons,creOpTags,desOpTags,contractionPairs)
#print "contractions:\n", contractions
# For each contraction, generate the resulting term
outTerms = []
for contraction in contractions:
conSign = 1
deltaFuncs = []
conIndeces = []
subOpString = []
subOpString.extend(ops)
for conPair in contraction:
index1 = ops[conPair[0]].indices[0]
index2 = ops[conPair[1]].indices[0]
deltaFuncs.append(kroneckerDelta([index1,index2]))
subOpString[conPair[0]] = 'contracted'
subOpString[conPair[1]] = 'contracted'
for q in subOpString[conPair[0]+1:conPair[1]]:
if not (q is 'contracted'):
conSign *= -1
i = 0
while i < len(subOpString):
if subOpString[i] is 'contracted':
del(subOpString[i])
else:
i += 1
(sortSign,sortedOps) = sortOps(subOpString)
totalSign = conSign * sortSign
outTensors = []
outTensors.extend(nonOps)
outTensors.extend(deltaFuncs)
outTensors.extend(sortedOps)
outTerms.append( term(totalSign * inTerm.numConstant, inTerm.constants, outTensors) )
# Normal ordering for sfExOps
elif has_sfExOps:
# 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
n = len(sfExOp_list)
# Set the original term, with all excitation operators moved to the end, as the
# first iteration's input term
iter_input_terms = [term(inTerm.numConstant, inTerm.constants, other_list + sfExOp_list)]
# Successively normal order the last two excitation operators until each term
# has only one exitation operator left (at which point the term is normal ordered)
while n > 1:
# Initialize the list to hold this iteration's output terms
iter_output_terms = []
# For each of this iteration's input terms, produce all terms resulting from normal ordering
# the last two excitation operators
for t in iter_input_terms:
# Make a list of the term's tensors that excludes the last two excitation operators
tensors_except_last_two = []
tensors_except_last_two.extend(t.tensors[0:-2])
# Give short names for the last two excitation operators and their orders
e1 = t.tensors[-2]
e2 = t.tensors[-1]
o1 = e1.order
o2 = e2.order
# Loop over the number of contractions
for nc in range(min(o1,o2)+1):
# Compute the order of excitation operator for the current number of contractions
newOrder = o1 + o2 - nc
# Compute all nc-tuples of index numbers from e1 and e2, as well as all permutations of
# the order in which the tuples may be combined to form a contraction
perms = [0]
if nc > 0:
perms = makePermutations(nc)
tups1 = makeTuples(nc, range(o1))
tups2 = makeTuples(nc, range(o2))
# For each contraction, compute the resulting term
for perm in perms:
for tup1 in tups1:
for tup2 in tups2:
# Initialize the term's tensor list
tensorList = []
tensorList.extend(tensors_except_last_two)
# 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(tup1[perm[i]])
conPairs[1].append(tup2[i])
# 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
for i in range(o1):
indexList[i] = e1.indices[i] # The usual one
if i in conPairs[0]:
i1 = i+o1
i2 = conPairs[1][conPairs[0].index(i)]
ind1 = e1.indices[i1]
ind2 = e2.indices[i2]
tensorList.insert(0, kroneckerDelta([ind1,ind2]))
indexList[i+newOrder] = e2.indices[o2+i2]
else:
indexList[i+newOrder] = e1.indices[i+o1] # Put the usual counterpart into indexList
count = 0 # in case of that e1.indices[i] is not contracted
for i in range(o2):
if not (i in conPairs[1]):
indexList[o1+count] = e2.indices[i]
indexList[o1+count+newOrder] = e2.indices[i+o2]
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
tensorList.append(sfExOp(indexList))
# Add the resulting term to this iteration's list of output terms
iter_output_terms.append(term(inTerm.numConstant, inTerm.constants, tensorList))
# Set this iteration's list of output terms as the next iteration's input terms
iter_input_terms = iter_output_terms
# Decrement the counter for the number of excitation operators
n -= 1; #print "MADE OK!!!"
# Set the return value as the final iteration's output terms
outTerms = iter_output_terms
else:
raise RuntimeError, "Normal ordering function failed to choose what to do."
# print "Terms after normal ordering:"
# for t in outTerms:
# print t
return outTerms
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 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 normalOrder(inTerm):
"Returns a list of terms resulting from normal ordering the operators in inTerm."
# if options.verbose:
# print "converting to normal order: %s" %(str(inTerm))
# check that inTerm is a term
if not isinstance(inTerm, term):
raise TypeError, "inTerm must be of class term"
# determine what types of operators the term contains
has_creDesOps = False
has_sfExOps = False
for t in inTerm.tensors:
if isinstance(t, creOp) or isinstance(t, desOp):
has_creDesOps = True
elif isinstance(t, sfExOp):
has_sfExOps = True
# If term has both creation/destruction operators and spin free excitation operators,
# raise an error
if has_creDesOps and has_sfExOps:
raise RuntimeError, "Normal ordering not implemented when both creOp/desOp and sfExOp " + \
"tensors are present"
# if the term is already normal ordered, return it unchanged
elif inTerm.isNormalOrdered():
outTerms = [inTerm.copy()]
# Normal ordering for creOp/desOp
elif has_creDesOps:
# Separate the cre/des operators from other tensors
ops = []
nonOps = []
for t in inTerm.tensors:
if isinstance(t, creOp) or isinstance(t, desOp):
ops.append(t.copy())
else:
nonOps.append(t.copy())
# Generate all contraction pairs
contractionPairs = []
for i in range(len(ops)):
iTerm = ops[i]
for j in range(i + 1, len(ops)):
jTerm = ops[j]
if isinstance(iTerm, desOp) and isinstance(jTerm, creOp):
contractionPairs.append((i, j))
#print "contractionPairs\n", contractionPairs
# Determine maximum contraction order
creCount = 0
maxConOrder = 0
for i in range(len(ops) - 1, -1, -1):
iTerm = ops[i]
if isinstance(iTerm, creOp):
creCount += 1
elif isinstance(iTerm, desOp) and creCount > 0:
maxConOrder += 1
creCount -= 1
del (creCount, iTerm)
# Generate all contractions
contractions = []
for i in range(maxConOrder + 1):
subCons = makeTuples(i, contractionPairs)
j = 0
while j < len(subCons):
creOpTags = []
desOpTags = []
for k in range(i):
creOpTags.append(subCons[j][k][1])
desOpTags.append(subCons[j][k][0])
if allDifferent(creOpTags) and allDifferent(desOpTags):
j += 1
else:
del (subCons[j])
for j in range(len(subCons)):
contractions.append(subCons[j])
del (subCons, creOpTags, desOpTags, contractionPairs)
#print "contractions:\n", contractions
# For each contraction, generate the resulting term
outTerms = []
for contraction in contractions:
conSign = 1
deltaFuncs = []
conIndeces = []
subOpString = []
subOpString.extend(ops)
for conPair in contraction:
index1 = ops[conPair[0]].indices[0]
index2 = ops[conPair[1]].indices[0]
deltaFuncs.append(kroneckerDelta([index1, index2]))
subOpString[conPair[0]] = 'contracted'
subOpString[conPair[1]] = 'contracted'
for q in subOpString[conPair[0] + 1:conPair[1]]:
if not (q is 'contracted'):
conSign *= -1
i = 0
while i < len(subOpString):
if subOpString[i] is 'contracted':
del (subOpString[i])
else:
i += 1
(sortSign, sortedOps) = sortOps(subOpString)
totalSign = conSign * sortSign
outTensors = []
outTensors.extend(nonOps)
outTensors.extend(deltaFuncs)
outTensors.extend(sortedOps)
outTerms.append(
term(totalSign * inTerm.numConstant, inTerm.constants,
outTensors))
# Normal ordering for sfExOps
elif has_sfExOps:
# 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
n = len(sfExOp_list)
# Set the original term, with all excitation operators moved to the end, as the
# first iteration's input term
iter_input_terms = [
term(inTerm.numConstant, inTerm.constants,
other_list + sfExOp_list)
]
# Successively normal order the last two excitation operators until each term
# has only one exitation operator left (at which point the term is normal ordered)
while n > 1:
# Initialize the list to hold this iteration's output terms
iter_output_terms = []
# For each of this iteration's input terms, produce all terms resulting from normal ordering
# the last two excitation operators
for t in iter_input_terms:
# Make a list of the term's tensors that excludes the last two excitation operators
tensors_except_last_two = []
tensors_except_last_two.extend(t.tensors[0:-2])
# Give short names for the last two excitation operators and their orders
e1 = t.tensors[-2]
e2 = t.tensors[-1]
o1 = e1.order
o2 = e2.order
#lsh spin
s1 = e1.spin
s2 = e2.spin
spin1f = s1[0][:]
spin1e = s1[1][:]
spin2f = s2[0][:]
spin2e = s2[1][:]
shift = max(max(spin1f), max(spin1e))
# Loop over the number of contractions
for nc in range(min(o1, o2) + 1):
# Compute the order of excitation operator for the current number of contractions
newOrder = o1 + o2 - nc
# Compute all nc-tuples of index numbers from e1 and e2, as well as all permutations of
# the order in which the tuples may be combined to form a contraction
perms = [0]
if nc > 0:
perms = makePermutations(nc)
tups1 = makeTuples(nc, range(o1))
tups2 = makeTuples(nc, range(o2))
#print('perms=',perms)
#print('tups1=',tups1)
#print('tups2=',tups2)
# For each contraction, compute the resulting term
for perm in perms:
for tup1 in tups1:
for tup2 in tups2:
# Initialize the term's tensor list
tensorList = []
tensorList.extend(tensors_except_last_two)
# 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(tup1[perm[i]])
conPairs[1].append(tup2[i])
# 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
for i in range(o1):
indexList[i] = e1.indices[
i] # The usual one
if i in conPairs[0]:
i1 = i + o1
i2 = conPairs[1][conPairs[0].index(i)]
ind1 = e1.indices[i1]
ind2 = e2.indices[i2]
tensorList.insert(
0, kroneckerDelta([ind1, ind2]))
indexList[i +
newOrder] = e2.indices[o2 +
i2]
else:
indexList[i + newOrder] = e1.indices[
i +
o1] # Put the usual counterpart into indexList
count = 0 # in case of that e1.indices[i] is not contracted
for i in range(o2):
if not (i in conPairs[1]):
indexList[o1 + count] = e2.indices[i]
indexList[o1 + count +
newOrder] = e2.indices[i +
o2]
count += 1
#lsh parity test
#print 'conPairs=', conPairs
parity_n = 0
o1_l = [i for i in range(o1)]
o2_l = [i for i in range(o2)]
for i in range(len(conPairs[0])):
p1 = conPairs[0][i]
p2 = conPairs[1][i]
parity_n += o1_l.index(p1)
#print 'parity = ', p1, p2, o1_l, o2_l, parity_n
parity_n += o2_l.index(p2)
#print 'parity = ', p1, p2, o1_l, o2_l, parity_n
o1_l.remove(p1)
o2_l.remove(p2)
parity = (-1)**(parity_n)
#parity *= 2**(len(conPairs[0]))
#lsh spin test
spin_dict = {}
for i in range(len(conPairs[0])):
p1 = conPairs[0][i]
p2 = conPairs[1][i]
spin_dict[spin2f[p2]] = spin1e[p1]
spin_new_f = spin1f[:]
#print 'spin 1 = ', spin_new_f
for i in range(len(spin2f)):
if i not in conPairs[1]:
spin_new_f.append(spin2f[i] + shift +
1)
#print 'spin 2 = ', spin_new_f
spin_new_e = []
for i in range(len(spin1e)):
if i not in conPairs[0]:
spin_new_e.append(spin1e[i])
#print 'spin 3 = ', spin_new_e
for i in spin2e:
if i not in spin_dict:
spin_new_e.append(i + shift + 1)
else:
spin_new_e.append(spin_dict[i])
#print 'spin 4 = ', spin_new_e
# 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."
#print 'spin= ', spin_new_f, spin_new_e
# Add the new excitation operator to the tensor list
tensorList.append(
sfExOp(indexList,
spin=[spin_new_f, spin_new_e]))
# Add the resulting term to this iteration's list of output terms
iter_output_terms.append(
term(parity * inTerm.numConstant,
inTerm.constants, tensorList))
# Set this iteration's list of output terms as the next iteration's input terms
iter_input_terms = iter_output_terms
# Decrement the counter for the number of excitation operators
n -= 1
#print "MADE OK!!!"
# Set the return value as the final iteration's output terms
outTerms = iter_output_terms
else:
raise RuntimeError, "Normal ordering function failed to choose what to do."
# print "Terms after normal ordering:"
# for t in outTerms:
# print t
return outTerms