def test_almost_eq():
a = Term([make_tensor('H', 'g0, h1', 'g1, p1')],
make_sq('g1, p1', 'g0, h1'))
b = Term.from_term(a, flip_sign=True)
assert a != b
assert a.almost_equal(b)
assert a.coeff + b.coeff == 0
def test_copy_1():
# OK to have diagonal indices, but attributes not fully functional
a = Term([make_tensor('H', 'g0', 'g0')], make_sq("g0", "g0"))
b = Term.from_term(a, flip_sign=True)
assert a.coeff == -b.coeff
b.coeff = 1
assert a == b
def test_perm_part_1():
list_of_tensors = [
make_tensor('H', 'g0, g1', 'g2, p0'),
make_tensor('T', 'h0, h1', 'p0, p1')
]
sq_op = make_sq('g0, g1, p1', 'g2, h0, h1')
a = Term(list_of_tensors, sq_op)
cre_part, ann_part = a.perm_partition_open()
assert cre_part == [[Index('g0'), Index('g1')], [Index('p1')]]
assert ann_part == [[Index('g2')], [Index('h0'), Index('h1')]]
def test_ambit_2():
a = Term([make_tensor('H', 'g0, h1', 'g0, p1')],
make_sq('g0, p1', 'g0, h1'))
ref = '// Error: diagonal indices are not supported by ambit.\n' \
'temp = ambit::BlockedTensor::build(ambit::CoreTensor, "temp", {"ghgp"});\n' \
'temp["g0,h1,g0,p1"] += 1.0 * H2["g0,h1,g0,p1"];\n' \
'C2["g0,h1,g0,p1"] += temp["g0,h1,g0,p1"];\n' \
'C2["g0,h1,p1,g0"] -= temp["g0,h1,g0,p1"];\n' \
'C2["h1,g0,g0,p1"] -= temp["g0,h1,g0,p1"];\n' \
'C2["h1,g0,p1,g0"] += temp["g0,h1,g0,p1"];\n'
assert a.ambit() == ref
def test_canonicalize_1():
list_of_tensors = [
make_tensor('H', "g0", "g0"),
make_tensor('t', "h0", "p0"),
make_tensor('t', "p1", "c1"),
make_tensor('L', 'g0', 'c1'),
make_tensor('K', 'p0', 'p1')
]
a = Term(list_of_tensors, SecondQuantizedOperator('h0', 'g0'))
with pytest.raises(NotImplementedError):
assert a.canonicalize()
def test_latex_1():
list_of_tensors = [
make_tensor('H', 'v0, v1', 'c0, c1'),
make_tensor('t', 'c0, c1', 'v0, v1')
]
sq_op = SecondQuantizedOperator.make_empty()
a = Term(list_of_tensors, sq_op, 0.25)
assert a.latex(
) == "1/4 H^{ v_{0} v_{1} }_{ c_{0} c_{1} } T^{ c_{0} c_{1} }_{ v_{0} v_{1} }"
assert a.latex(
dollar=True
) == "$1/4 H^{ v_{0} v_{1} }_{ c_{0} c_{1} } T^{ c_{0} c_{1} }_{ v_{0} v_{1} }$"
def test_ambit_3():
a = Term([make_tensor('H', 'g0, h1', 'g1, p1')],
make_sq('g1, p1', 'g0, h1'))
ref = 'temp = ambit::BlockedTensor::build(ambit::CoreTensor, "temp", {"ghgp"});\n' \
'temp["g0,h1,g1,p1"] += 1.0 * H2["g0,h1,g1,p1"];'
assert a.ambit(ignore_permutations=True) == ref
assert a.ambit(
ignore_permutations=True,
init_temp=False) == 'temp["g0,h1,g1,p1"] += 1.0 * H2["g0,h1,g1,p1"];'
assert a.ambit(init_temp=False, declared_temp=False
) == 'C2["g0,h1,g1,p1"] += 1.0 * H2["g0,h1,g1,p1"];\n'
def test_generate_spin_cases_4():
# a = Term([make_tensor('H', 'v2,c0', 'v0,c2'), make_tensor('t', 'c1,c2', 'v1,v2')],
# make_sq('v0,v1', 'c0,c1'))
# print(a)
# print(a.latex())
# print(a.ambit(), '\n')
#
# for i in a.generate_spin_cases_naive():
# print(i.latex())
# print()
a = Term([
make_tensor('H', 'v2,v3', 'v0,v1'),
make_tensor('t', 'c0,c1', 'v2,v3')
], make_sq('v0,v1', 'c0,c1'), 0.125)
print(a)
print(a.latex(), '\n')
for i in a.generate_spin_cases_naive():
print(i.latex())
print(i.ambit())
a = Term([
make_tensor('H', 'p0,g0', 'c0,g1'),
make_tensor('t', 'c0,h0', 'p0,p1')
], make_sq('g0,h0', 'g1,p1'))
print(a)
print(a.latex(), '\n')
for i in a.generate_spin_cases_naive():
print(i.latex())
print(i.ambit())
def test_contract_terms_1():
h = hamiltonian_operator(2)
t2e = cluster_operator(2, hole_label='c', particle_label='v')
t2ee = cluster_operator(2, start=4, hole_label='c', particle_label='v')
a = contract_terms([h, t2e, t2ee], max_cu=1, scale_factor=0.5, for_commutator=True, n_process=2)
ref = {Term([make_tensor('H', 'c2,c3', 'v2,v3'),
make_tensor('t', 'c0,c1', 'v0,v2'), make_tensor('t', 'c2,c3', 'v1,v3')],
make_sq('v0,v1', 'c0,c1'), -0.25),
Term([make_tensor('H', 'c2,c3', 'v2,v3'),
make_tensor('t', 'c0,c1', 'v2,v3'), make_tensor('t', 'c2,c3', 'v0,v1')],
make_sq('v0,v1', 'c0,c1'), 1.0/16.0),
Term([make_tensor('H', 'c2,c3', 'v2,v3'),
make_tensor('t', 'c0,c2', 'v0,v1'), make_tensor('t', 'c1,c3', 'v2,v3')],
make_sq('v0,v1', 'c0,c1'), -0.25),
Term([make_tensor('H', 'c2,c3', 'v2,v3'),
make_tensor('t', 'c0,c2', 'v0,v2'), make_tensor('t', 'c1,c3', 'v1,v3')],
make_sq('v0,v1', 'c0,c1'), 0.5),
Term([make_tensor('H', 'v2,v3', 'g0,c3'),
make_tensor('t', 'c0,c1', 'v0,v2'), make_tensor('t', 'c2,c3', 'v1,v3')],
make_sq('g0,v0,v1', 'c0,c1,c2'), -0.5),
Term([make_tensor('H', 'v2,v3', 'g0,c3'),
make_tensor('t', 'c0,c3', 'v0,v1'), make_tensor('t', 'c1,c2', 'v2,v3')],
make_sq('g0,v0,v1', 'c0,c1,c2'), 0.125),
Term([make_tensor('H', 'c2,c3', 'g0,v3'),
make_tensor('t', 'c0,c1', 'v2,v3'), make_tensor('t', 'c2,c3', 'v0,v1')],
make_sq('v0,v1,v2', 'g0,c0,c1'), -0.125),
Term([make_tensor('H', 'c2,c3', 'g0,v3'),
make_tensor('t', 'c0,c2', 'v0,v1'), make_tensor('t', 'c1,c3', 'v2,v3')],
make_sq('v0,v1,v2', 'g0,c0,c1'), 0.5)
}
for i in a:
assert i in ref
def test_singlet_adaptation():
"""
C0 += (1.0 / 4.0) * H2["c0,c1,v0,v1"] * T2["c0,c1,v0,v1"];
C0 += 1.0 * H2["c0,C0,v0,V0"] * T2["c0,C0,v0,V0"];
C0 += (1.0 / 4.0) * H2["C0,C1,V0,V1"] * T2["C0,C1,V0,V1"];
"""
a = [Term([make_tensor('H', 'c0,c1', 'v0,v1', 'si'), make_tensor('t', 'c0,c1', 'v0,v1', 'si')],
make_sq('', '', 'si'), 0.25),
Term([make_tensor('H', 'C0,C1', 'V0,V1', 'si'), make_tensor('t', 'C0,C1', 'V0,V1', 'si')],
make_sq('', '', 'si'), 0.25),
Term([make_tensor('H', 'c0,C1', 'v0,V1', 'si'), make_tensor('t', 'c0,C1', 'v0,V1', 'si')],
make_sq('', '', 'si'), 1.0)
]
b = combine_terms([i for term in a for i in term.generate_singlet_adaptation()])
print_terms_ambit(b)
def test_canonicalize_2():
# H^{ v_{0} }_{ v_{1} } T^{ v_{1} }_{ c_{1} } T^{ v_{2} }_{ c_{0} } T^{ c_{0} c_{1} }_{ v_{0} v_{2} }
indices_type = 'so'
list_of_tensors = [
make_tensor('Hamiltonian', "v0", "v1", indices_type),
make_tensor('cluster_amplitude', "v1", "c1", indices_type),
make_tensor('cluster_amplitude', "v2", "c0", indices_type),
make_tensor('cluster_amplitude', "c0,c1", "v0,v2", indices_type)
]
sq_op = SecondQuantizedOperator.make_empty(indices_type)
a = Term(list_of_tensors, sq_op)
# H^{ v_{0} }_{ v_{1} } T^{ c_{0} }_{ v_{2} } T^{ c_{1} }_{ v_{0} } T^{ v_{1} v_{2} }_{ c_{0} c_{1} }
list_of_tensors = [
make_tensor('Hamiltonian', "v0", "v1", indices_type),
make_tensor('cluster_amplitude', "c0", "v2", indices_type),
make_tensor('cluster_amplitude', "c1", "v0", indices_type),
make_tensor('cluster_amplitude', "v1,v2", "c0,c1", indices_type)
]
b = Term(list_of_tensors, sq_op)
ref = Term([
make_tensor('Hamiltonian', "v1", "v0", indices_type),
make_tensor('cluster_amplitude', "c0", "v0", indices_type),
make_tensor('cluster_amplitude', "c1", "v2", indices_type),
make_tensor('cluster_amplitude', "c0,c1", "v1,v2", indices_type)
], sq_op, -1)
assert ref == a.canonicalize() == b.canonicalize()
def test_canonicalize_4():
list_of_tensors = [
make_tensor('Hamiltonian', "g0,g1,c0", "g2,p0,v0"),
make_tensor('cluster_amplitude', "p0,p1,g3", "a0,h1,a1"),
make_tensor('Kronecker', "v0", "p1"),
make_tensor('cumulant', "h1", "c0"),
make_tensor('cumulant', "a1", "g3"),
make_tensor('cumulant', "g2,a0", "g0,g1")
]
a = Term(list_of_tensors, SecondQuantizedOperator.make_empty())
ref = Term([
make_tensor('H', "c0,a1,a2", "p0,v0,a0"),
make_tensor('t', "c0,a4,a5", "p0,v0,a3"),
make_tensor('L', "a4", "a3"),
make_tensor('L', "a1,a2", "a0,a5")
], SecondQuantizedOperator.make_empty())
assert a.canonicalize() == ref
def test_latex_3():
list_of_tensors = [
make_tensor('H', 'v3, v4', 'v0, c3'),
make_tensor('T', 'c0, c1', 'v1, v3'),
make_tensor('T', 'c2, c3', 'v2, v4')
]
sq_op = make_sq('v0, v1, v2', 'c0, c1, c2')
a = Term(list_of_tensors, sq_op, -1)
ref = "-1/18 & {\\cal P} ( v_{0} / v_{1} / v_{2} ) {\\cal P} ( c_{0} c_{1} / c_{2} ) " \
"H^{ v_{3} v_{4} }_{ v_{0} c_{3} } " \
"T^{ c_{0} c_{1} }_{ v_{1} v_{3} } " \
"T^{ c_{2} c_{3} }_{ v_{2} v_{4} } " \
"a^{ v_{0} v_{1} v_{2} }_{ c_{0} c_{1} c_{2} } \\\\"
assert a.latex(delimiter=True, backslash=True) == ref
ref = "-1 H^{ v_{3} v_{4} }_{ v_{0} c_{3} } T^{ c_{0} c_{1} }_{ v_{1} v_{3} } " \
"T^{ c_{2} c_{3} }_{ v_{2} v_{4} } a^{ v_{0} v_{1} v_{2} }_{ c_{0} c_{1} c_{2} }"
assert a.latex(permute_format=False) == str(a) == ref
def test_comparision():
# sequence: sq_op, number of tensors, tensors, absolute value of coeff, coeff
a = Term([make_tensor('H', 'g0,h1', 'g1,p1')], make_sq('g1,p1', 'g0,h1'))
b = Term(
[make_tensor('H', 'g0,h1', 'g1,p1'),
make_tensor('t', 'h1', 'p1')], make_sq('g1', 'g0'))
assert a > b
b = Term([
make_tensor('H', 'g0,h1,c0', 'g1,p1,v0'),
make_tensor('t', 'c0', 'v0')
], make_sq('g1,p1', 'g0,h1'))
assert a < b
c = Term([
make_tensor('H', 'g0,v0,c0', 'g1,p1,c0'),
make_tensor('t', 'h1', 'v0')
], make_sq('g1,p1', 'g0,h1'))
assert c > b
assert c.list_of_tensors > b.list_of_tensors
b = Term.from_term(a, flip_sign=True)
c = Term.from_term(a)
d = sorted([a, b, c])
assert d[0] == b
assert d[1] == d[2] == a == c
def test_void():
a = Term([make_tensor('H', 'g0, h1', 'g0, p1')],
make_sq('g0, p1', 'g0, h1'), 0.0)
assert a.is_void()
b = a.void()
assert b.is_void()
assert b is not a
assert b != a
c = Term.make_empty('so')
assert b == c
a.void_self()
assert a == b
def test_generate_spin_cases_1():
a = Term([make_tensor('H', 'g0,g1', 'g2,g3')], make_sq('g2,g3', 'g0,g1'))
ref = {
Term([make_tensor('H', 'g2,g3', 'g0,g1', 'si')],
make_sq('g2,g3', 'g0,g1', 'si')),
Term([make_tensor('H', 'g1,G1', 'g0,G0', 'si')],
make_sq('g1,G1', 'g0,G0', 'si')),
Term([make_tensor('H', 'G2,G3', 'G0,G1', 'si')],
make_sq('G2,G3', 'G0,G1', 'si'))
}
for i in a.generate_spin_cases_naive():
assert i in ref
def canonicalize_contractions_batch(n_process,
contractions,
tensors,
coeff,
simplify,
chunk_size,
hermitian_tensor=True):
"""
Canonicalize a batch of contractions
:param n_process: number of processes launched for tensor canonicalization
:param contractions: a list of contractions [(sign, densities, sq_op)]
:param tensors: a list of tensors
:param coeff: a scale factor for all contractions
:param simplify: combine similar terms if True
:param chunk_size: the chunk size for multiprocessing
:param hermitian_tensor: assume tensors being Hermitian if True
:return: a list of simplified canonicalized terms
"""
if len(contractions) == 0:
return []
print("in func", len(contractions))
if n_process == 1:
temp = [
Term(tensors + densities, sq_op, sign *
coeff).canonicalize_sympy(hermitian_tensor=hermitian_tensor)
for sign, densities, sq_op in contractions
]
else:
with multiprocessing.Pool(n_process, maxtasksperchild=1000) as pool:
tasks = [(multiprocessing_canonicalize_contractions,
(tensors + densities, sq_op, sign * coeff,
hermitian_tensor))
for sign, densities, sq_op in contractions]
imap_unordered_it = pool.imap_unordered(calculate_star,
tasks,
chunksize=chunk_size)
temp = [x for x in imap_unordered_it]
return combine_terms(temp) if simplify else temp
def test_perm_part_3():
list_of_tensors = [make_tensor('H', 'g0, h1', 'p1, g0')]
sq_op = make_sq('g0, p1', 'g0, h1')
a = Term(list_of_tensors, sq_op, -1)
cre_part, ann_part = a.perm_partition_open()
assert cre_part == [[Index('g0')], [Index('p1')]]
assert ann_part == [[Index('g0')], [Index('h1')]]
list_of_tensors = [
make_tensor('H', 'g0, h0, a0', 'g1, p0, p1'),
make_tensor('t', 'p0, p1', 'a0,a1')
]
sq_op = make_sq('g1, a1', 'g0, h0')
a = Term(list_of_tensors, sq_op, -1)
cre_part, ann_part = a.perm_partition_open()
assert cre_part == [[Index('g1')], [Index('a1')]]
assert ann_part == [[Index('g0')], [Index('h0')]]
def test_ambit_1():
list_of_tensors = [
make_tensor('H', 'v0, v1', 'c0, c1'),
make_tensor('t', 'c0, c1', 'v0, v1')
]
sq_op = SecondQuantizedOperator.make_empty()
a = Term(list_of_tensors, sq_op, 0.25)
assert a.ambit(
name='X'
) == 'X0 += (1.0 / 4.0) * H2["v0,v1,c0,c1"] * T2["c0,c1,v0,v1"];'
list_of_tensors = [
make_tensor('H', 'v0, v1', 'g0, c1'),
make_tensor('t', 'c0, c1', 'v0, v1')
]
sq_op = make_sq('g0', 'c0')
a = Term(list_of_tensors, sq_op, 0.5)
assert a.ambit(
) == 'C1["c0,g0"] += (1.0 / 2.0) * H2["v0,v1,g0,c1"] * T2["c0,c1,v0,v1"];'
def test_perm_part_4():
list_of_tensors = [
make_tensor('H', 'c1', 'c0'),
make_tensor('t', 'c1,a0', 'v0,v1')
]
sq_op = make_sq('v0,v1', 'c0,a0')
a = Term(list_of_tensors, sq_op)
cre_part_1, ann_part_1 = a.perm_partition_open()
list_of_tensors = [
make_tensor('H', 'a1', 'a0'),
make_tensor('t', 'c0,a1', 'v0,v1')
]
sq_op = make_sq('v0,v1', 'c0,a0')
a = Term(list_of_tensors, sq_op)
cre_part_2, ann_part_2 = a.perm_partition_open()
assert cre_part_1 == cre_part_2
assert ann_part_1 == ann_part_2
def test_perm_part_2():
list_of_tensors = [
make_tensor('H', 'v4, c2', 'v3, c1'),
make_tensor('T', 'c1', 'v0'),
make_tensor('T', 'c0, c3', 'v1, v4'),
make_tensor('T', 'c2, c3', 'v2, v3')
]
sq_op = make_sq('v2, c0', 'v0, v1')
a = Term(list_of_tensors, sq_op)
cre_part, ann_part = a.perm_partition_open()
assert cre_part == [[Index('v2')], [Index('c0')]]
assert ann_part == [[Index('v0')], [Index('v1')]]
list_of_tensors = [
make_tensor('H', 'v3, v4', 'v0, c3'),
make_tensor('T', 'c0, c1', 'v1, v3'),
make_tensor('T', 'c2, c3', 'v2, v4')
]
sq_op = make_sq('v0, v1, v2', 'c0, c1, c2')
a = Term(list_of_tensors, sq_op)
cre_part, ann_part = a.perm_partition_open()
assert cre_part == [[Index('v0')], [Index('v1')], [Index('v2')]]
assert ann_part == [[Index('c0'), Index('c1')], [Index('c2')]]
def test_bch_cc_rsc_1():
# single-reference CCSD with recursive single commutator approximation
a = bch_cc_rsc(4, [1, 2], 1, [(0, 6), (0, 8), (0, 8), (0, 4)],
single_reference=True, unitary=False)
r = sorted(i for n, terms in a.items() for i in terms
if n != 0 and i.n_body < 3 and i.sq_op.is_possible_excitation())
assert len(r) == 46
samples = [Term([make_tensor('H', 'v2,v3', 'v0,c2'), make_tensor('t', 'c2', 'v2'),
make_tensor('t', 'c0,c1', 'v1,v3')], make_sq('v0,v1', 'c0,c1'), 0.5),
Term([make_tensor('H', 'c2,c3', 'v2,c0'), make_tensor('t', 'c2', 'v2'),
make_tensor('t', 'c1,c3', 'v0,v1')], make_sq('v0,v1', 'c0,c1'), 0.5),
Term([make_tensor('H', 'c2,c3', 'v2,v3'), make_tensor('t', 'c0,c1', 'v0,v2'),
make_tensor('t', 'c2,c3', 'v1,v3')], make_sq('v0,v1', 'c0,c1'), -0.25),
Term([make_tensor('H', 'c2,c3', 'v2,v3'), make_tensor('t', 'c0,c2', 'v0,v1'),
make_tensor('t', 'c1,c3', 'v2,v3')], make_sq('v0,v1', 'c0,c1'), -0.25),
Term([make_tensor('H', 'c2,c3', 'v2,v3'), make_tensor('t', 'c0', 'v2'),
make_tensor('t', 'c2', 'v3'), make_tensor('t', 'c1,c3', 'v0,v1')],
make_sq('v0,v1', 'c0,c1'), -0.5),
Term([make_tensor('H', 'c2,c3', 'v2,v3'), make_tensor('t', 'c2', 'v0'),
make_tensor('t', 'c3', 'v2'), make_tensor('t', 'c0,c1', 'v1,v3')],
make_sq('v0,v1', 'c0,c1'), -0.5)]
for i in samples:
assert i in r
def test_canonicalize_3():
# -1 * H^{g0,g1}_{g2,g3} * T^{h0,h1}_{p0,p1} * L^{p1}_{g2} * L^{p0}_{g3} * a^{g0,g1}_{h0, h1}
list_of_tensors = [
make_tensor('H', 'g0, g1', 'g2, g3'),
make_tensor('t', 'p0, p1', 'h0, h1'),
make_tensor('L', 'p1', 'g2'),
make_tensor('L', 'p0', 'g3')
]
sq_op = make_sq('g0, g1', 'h0, h1')
a = Term(list_of_tensors, sq_op, -1)
ref = Term([
make_tensor('H', 'a0, a1', 'g0, g1'),
make_tensor('t', 'a2, a3', 'h0, h1'),
make_tensor('L', 'a2', 'a0'),
make_tensor('L', 'a3', 'a1')
], sq_op, 1)
assert a.canonicalize() == ref
list_of_tensors = [
make_tensor('H', 'g0, G1', 'g2, G3', 'si'),
make_tensor('t', 'P0, p1', 'H0, h1', 'si'),
make_tensor('L', 'p1', 'g2', 'si'),
make_tensor('L', 'P0', 'G3', 'si')
]
a = Term(list_of_tensors, make_sq('g0, G1', 'H0, h1', 'si'))
ref = Term([
make_tensor('H', 'a0, A0', 'g0, G0', 'si'),
make_tensor('t', 'a1, A1', 'h0, H0', 'si'),
make_tensor('L', 'a1', 'a0', 'si'),
make_tensor('L', 'A1', 'A0', 'si')
], make_sq('g0, G0', 'h0, H0', 'si'), -1)
assert ref == a.canonicalize()
list_of_tensors = [
make_tensor('H', 'g0, G1', 'g2, G3', 'sa'),
make_tensor('t', 'P0, p1', 'H0, h1', 'sa'),
make_tensor('L', 'p1', 'g2', 'sa'),
make_tensor('L', 'P0', 'G3', 'sa')
]
a = Term(list_of_tensors, make_sq('g0, G1', 'h1, H0', 'sa'))
ref = Term([
make_tensor('H', 'a0, A0', 'g0, G0', 'sa'),
make_tensor('t', 'a1, A1', 'h0, H0', 'sa'),
make_tensor('L', 'a1', 'a0', 'sa'),
make_tensor('L', 'A1', 'A0', 'sa')
], make_sq('g0, G0', 'h0, H0', 'sa'))
assert ref == a.canonicalize()
def test_contraction_paths():
t = Term([
make_tensor('H', 'c0,v0', 'v1,v2', 'so'),
make_tensor('t', 'c1,c2', 'v2,v3', 'so'),
make_tensor('t', 'c3,c1,c2', 'v1,v4,v5', 'so'),
make_tensor('t', 'c3,c5,c6', 'v6,v4,v5', 'so')
], make_sq("v0,v3,v6", "c0,c5,c6", 'so')).canonicalize()
for i in t.contraction_paths():
print(i)
# print(t.optimal_contraction_cost())
#
# t = Term([make_tensor('H', 'v3,v4', 'v0,c3', 'so'),
# make_tensor('t', 'c4,c5', 'v5,v6', 'so'),
# make_tensor('t', 'c0,c1,c2', 'v4,v5,v6', 'so'),
# make_tensor('t', 'c3,c4,c5', 'v1,v2,v3', 'so')],
# make_sq("v0,v1,v2", "c0,c1,c2", 'so')).canonicalize()
# print(t.optimal_contraction_cost())
t = Term([
make_tensor('H', 'v4,v5', 'v2,v3', 'so'),
make_tensor('t', 'c1,c2', 'v0,v3', 'so'),
make_tensor('t', 'c0,c3', 'v1,v6', 'so'),
make_tensor('t', 'c1,c2,c3', 'v4,v5,v6', 'so')
], make_sq("v0,v1", "c0,v2", 'so'))
print()
for i in t.contraction_paths():
print(i)
t = Term([
make_tensor('H', 'c4,c5', 'v3,c3', 'so'),
make_tensor('t', 'c1,c2', 'v3,v5', 'so'),
make_tensor('t', 'c0,c6', 'v0,v4', 'so'),
make_tensor('t', 'c4,c5,c7', 'v1,v2,v6', 'so'),
make_tensor('t', 'c3,c6,c7', 'v4,v5,v6', 'so')
], make_sq("v0,v1,v2", "c0,c1,c2", 'so'))
print()
print(t.optimal_contraction_cost())
# for i in t.contraction_paths():
# print(i)
# simply reverse the h-h line to v-v line
t = Term([
make_tensor('H', 'c4,v9', 'v3,v8', 'so'),
make_tensor('t', 'c1,c8', 'v3,v2', 'so'),
make_tensor('t', 'c0,c6', 'v0,v4', 'so'),
make_tensor('t', 'c4,c2,c7', 'v1,v9,v6', 'so'),
make_tensor('t', 'c8,c6,c7', 'v4,v8,v6', 'so')
], make_sq("v0,v1,v2", "c0,c1,c2", 'so'))
print()
print(t.optimal_contraction_cost())
t = Term([make_tensor('H', 'c4,c5', 'v3,c3', 'so')],
make_sq('c4,c5', 'v3,c3', 'so'))
print()
print(t.optimal_contraction_cost())
def test_latex_2():
a = Term([make_tensor('H', 'g0, h1', 'g0, p1')],
make_sq('g0, p1', 'g0, h1'))
ref = "1/4 & {\\cal P} ( g_{0} / p_{1} ) {\\cal P} ( g_{0} / h_{1} ) " \
"H^{ g_{0} h_{1} }_{ g_{0} p_{1} } a^{ g_{0} p_{1} }_{ g_{0} h_{1} }"
assert a.latex(delimiter=True) == ref
def test_simplify():
list_of_tensors = [
make_tensor('H', "g0", "g0"),
make_tensor('t', "h0", "p0"),
make_tensor('t', "p1", "h1"),
make_tensor('L', 'h0', 'g0'),
make_tensor('L', 'g0, p1', 'p0, h1')
]
a = Term(list_of_tensors, SecondQuantizedOperator.make_empty(), -1)
a.simplify()
assert a.is_void()
list_of_tensors = [
make_tensor('H', "g0", "g0"),
make_tensor('t', "h0", "p0"),
make_tensor('t', "p1", "h1"),
make_tensor('L', 'g0', 'h1'),
make_tensor('L', 'h0', 'g0'),
make_tensor('K', 'p0', 'p1')
]
a = Term(list_of_tensors, SecondQuantizedOperator.make_empty())
a.simplify()
assert a.list_of_tensors == [
make_tensor('H', 'h6', 'h6'),
make_tensor('t', 'p1', 'h3'),
make_tensor('t', 'h4', 'p1'),
make_tensor('L', 'h6', 'h3'),
make_tensor('L', 'h4', 'h6')
]
assert a.sq_op == SecondQuantizedOperator.make_empty()
assert a.indices_set == {Index(i) for i in ['h6', 'p1', 'h3', 'h4']}
assert a.diagonal_indices == {Index('h6'): 4}
list_of_tensors = [
make_tensor('H', "g0", "g0"),
make_tensor('t', "h0", "p0"),
make_tensor('t', "p1", "c1"),
make_tensor('L', 'g0', 'c1'),
make_tensor('K', 'p0', 'p1')
]
a = Term(list_of_tensors, SecondQuantizedOperator('h0', 'g0'))
a.simplify()
assert a.list_of_tensors == [
make_tensor('H', "c2", "c2"),
make_tensor('t', "p1", "c2"),
make_tensor('t', "h0", "p1")
]
assert a.sq_op == SecondQuantizedOperator('h0', 'c2')
assert a.indices_set == {Index(i) for i in ['c2', 'p1', 'h0']}
assert a.diagonal_indices == {Index('c2'): 4}
def test_generate_spin_cases_3():
list_of_tensors = [
make_tensor('H', "v0,c0", "v1,c1"),
make_tensor('t', "v1", "c2"),
make_tensor('t', "v2,v3", "c0,c3"),
make_tensor('t', "c2,c3", "v0,v3")
]
a = Term(list_of_tensors, make_sq("c1", "v2"))
ac = Term([
make_tensor('H', 'v2,c1', 'v1,c0'),
make_tensor('t', 'c2', 'v1'),
make_tensor('t', 'c1,c3', 'v0,v3'),
make_tensor('t', 'c2,c3', 'v2,v3')
], make_sq("c0", "v0"))
assert a.canonicalize() == ac
i_type = 'si'
ref = [
Term([
make_tensor('H', 'v2,c1', 'v1,c0', i_type),
make_tensor('t', 'c2', 'v1', i_type),
make_tensor('t', 'c1,c3', 'v0,v3', i_type),
make_tensor('t', 'c2,c3', 'v2,v3', i_type)
], make_sq("c0", "v0", i_type)),
Term([
make_tensor('H', 'v2,c1', 'v1,c0', i_type),
make_tensor('t', 'c2', 'v1', i_type),
make_tensor('t', 'c1,C3', 'v0,V3', i_type),
make_tensor('t', 'c2,C3', 'v2,V3', i_type)
], make_sq("c0", "v0", i_type)).canonicalize(),
Term([
make_tensor('H', 'v2,C1', 'V1,c0', i_type),
make_tensor('t', 'C2', 'V1', i_type),
make_tensor('t', 'C1,c3', 'v0,V3', i_type),
make_tensor('t', 'C2,c3', 'v2,V3', i_type)
], make_sq("c0", "v0", i_type)).canonicalize(),
Term([
make_tensor('H', 'V2,c1', 'V1,c0', i_type),
make_tensor('t', 'C2', 'V1', i_type),
make_tensor('t', 'c1,c3', 'v0,v3', i_type),
make_tensor('t', 'C2,c3', 'V2,v3', i_type)
], make_sq("c0", "v0", i_type)).canonicalize(),
Term([
make_tensor('H', 'V2,c1', 'V1,c0', i_type),
make_tensor('t', 'C2', 'V1', i_type),
make_tensor('t', 'c1,C3', 'v0,V3', i_type),
make_tensor('t', 'C2,C3', 'V2,V3', i_type)
], make_sq("c0", "v0", i_type)).canonicalize(),
Term([
make_tensor('H', 'V2,C1', 'V1,C0', i_type),
make_tensor('t', 'C2', 'V1', i_type),
make_tensor('t', 'C1,C3', 'V0,V3', i_type),
make_tensor('t', 'C2,C3', 'V2,V3', i_type)
], make_sq("C0", "V0", i_type)),
Term([
make_tensor('H', 'V2,C1', 'V1,C0', i_type),
make_tensor('t', 'C2', 'V1', i_type),
make_tensor('t', 'C1,c3', 'V0,v3', i_type),
make_tensor('t', 'C2,c3', 'V2,v3', i_type)
], make_sq("C0", "V0", i_type)).canonicalize(),
Term([
make_tensor('H', 'V2,c1', 'v1,C0', i_type),
make_tensor('t', 'c2', 'v1', i_type),
make_tensor('t', 'c1,C3', 'V0,v3', i_type),
make_tensor('t', 'c2,C3', 'V2,v3', i_type)
], make_sq("C0", "V0", i_type)).canonicalize(),
Term([
make_tensor('H', 'v2,C1', 'v1,C0', i_type),
make_tensor('t', 'c2', 'v1', i_type),
make_tensor('t', 'C1,c3', 'V0,v3', i_type),
make_tensor('t', 'c2,c3', 'v2,v3', i_type)
], make_sq("C0", "V0", i_type)).canonicalize(),
Term([
make_tensor('H', 'v2,C1', 'v1,C0', i_type),
make_tensor('t', 'c2', 'v1', i_type),
make_tensor('t', 'C1,C3', 'V0,V3', i_type),
make_tensor('t', 'c2,C3', 'v2,V3', i_type)
], make_sq("C0", "V0", i_type)).canonicalize()
]
count = 0
for i in ac.generate_spin_cases_naive():
assert i in ref
count += 1
assert count == len(ref)
def test_generate_spin_cases_2():
from collections import defaultdict
# -0.25 * H^{aw}_{xy} * T^{uv}_{az} * L^{xyz}_{uvw}
a = Term([
make_tensor('H', 'a1,a2', 'p0,a0'),
make_tensor('t', 'a4,a5', 'p0,a3'),
make_tensor('L', 'a1,a2,a3', 'a0,a4,a5')
], SecondQuantizedOperator.make_empty(), -0.25)
spin_combined = {}
spin_coeff = defaultdict(list)
for term in a.generate_spin_cases_naive():
name = term.hash_term()
spin_coeff[name].append(term.coeff)
spin_combined[name] = term
for name, term in spin_combined.items():
term.coeff = sum(spin_coeff[name])
if abs(term.coeff) < 1.0e-15:
spin_combined.pop(name)
ref = {
Term([
make_tensor('H', 'a1,a2', 'p0,a0', 'si'),
make_tensor('t', 'a4,a5', 'p0,a3', 'si'),
make_tensor('L', 'a1,a2,a3', 'a0,a4,a5', 'si')
], SecondQuantizedOperator.make_empty('si'), -0.25),
Term([
make_tensor('H', 'A1,A2', 'P0,A0', 'si'),
make_tensor('t', 'A4,A5', 'P0,A3', 'si'),
make_tensor('L', 'A1,A2,A3', 'A0,A4,A5', 'si')
], SecondQuantizedOperator.make_empty('si'), -0.25),
Term([
make_tensor('H', 'a1,A2', 'p0,A0', 'si'),
make_tensor('t', 'a4,a5', 'p0,a3', 'si'),
make_tensor('L', 'a1,A2,a3', 'A0,a4,a5', 'si')
], SecondQuantizedOperator.make_empty('si'), -0.5).canonicalize(),
Term([
make_tensor('H', 'a1,a2', 'p0,a0', 'si'),
make_tensor('t', 'a4,A5', 'p0,A3', 'si'),
make_tensor('L', 'a1,a2,A3', 'a0,a4,A5', 'si')
], SecondQuantizedOperator.make_empty('si'), -0.5).canonicalize(),
Term([
make_tensor('H', 'A1,a2', 'P0,a0', 'si'),
make_tensor('t', 'A4,a5', 'P0,a3', 'si'),
make_tensor('L', 'A1,a2,a3', 'a0,A4,a5', 'si')
], SecondQuantizedOperator.make_empty('si'), -1).canonicalize(),
Term([
make_tensor('H', 'a1,A2', 'P0,a0', 'si'),
make_tensor('t', 'A4,A5', 'P0,A3', 'si'),
make_tensor('L', 'a1,A2,A3', 'a0,A4,A5', 'si')
], SecondQuantizedOperator.make_empty('si'), -0.5).canonicalize(),
Term([
make_tensor('H', 'A1,A2', 'P0,A0', 'si'),
make_tensor('t', 'A4,a5', 'P0,a3', 'si'),
make_tensor('L', 'A1,A2,a3', 'A0,A4,a5', 'si')
], SecondQuantizedOperator.make_empty('si'), -0.5).canonicalize(),
Term([
make_tensor('H', 'a1,A2', 'p0,A0', 'si'),
make_tensor('t', 'a4,A5', 'p0,A3', 'si'),
make_tensor('L', 'a1,A2,A3', 'A0,a4,A5', 'si')
], SecondQuantizedOperator.make_empty('si'), -1).canonicalize()
}
for i in spin_combined.values():
assert i in ref
assert len(spin_combined) == len(ref)
def test_copy_2():
# OK to have diagonal indices, but attributes not fully functional
a = Term([make_tensor('H', 'g0', 'g1')], make_sq("g1", "g0"))
b = Term.from_term(a, flip_sign=True, hc=True)
assert b.sq_op == make_sq("g0", "g1")
assert b.list_of_tensors == a.list_of_tensors
def test_init_4():
# indices not appear in pairs
with pytest.raises(ValueError):
assert Term(
[make_tensor('H', 'c0', 'g1'),
make_tensor('t', 'c0', 't0')], make_sq('t0', 't1'))