def test_multiset_permutation_5():
# n_multiset_permutation for spin-adapted operators is always one
a = SecondQuantizedOperator("g0,v1,p2", "p0,a1,c2", 'spin-adapted')
p_cre = [[Index('g0'), Index('v1'), Index('p2')]]
p_ann = [[Index('p0')], [Index('a1')], [Index('c2')]]
assert not a.exist_permute_format(p_cre, p_ann)
assert a.n_multiset_permutation(p_cre, p_ann) == 1
def test_possible_excitation():
assert SecondQuantizedOperator("g0, g1", "g2, p0").is_possible_excitation()
assert SecondQuantizedOperator("p0, p1", "c0, h0").is_possible_excitation()
assert not SecondQuantizedOperator("c0, h0",
"p0, p1").is_possible_excitation()
assert not SecondQuantizedOperator("a0, A0", "a1, A1",
'si').is_possible_excitation()
def process_composite_contractions(contraction, elementary_contractions,
n_indices, expand_hole, base_order_map,
upper_indices_set, lower_indices_set):
"""
Process a single composite contraction expressed in terms of indices of elementary contractions.
:param contraction: a composite contraction
:param elementary_contractions: a list of density cumulants / hole densities
:param n_indices: the total number of indices
:param expand_hole: expand hole densities to Kronecker delta minus one density if True
:param base_order_map: the index map to ordering index, e.g., {"ug0": 0, "lg0": 1, ...}, u/l for upper/lower
:param upper_indices_set: the set of all creation operators
:param lower_indices_set: the set of all annihilation operators
:return: a list of contractions in terms of (sign, list_of_densities, sq_op)
"""
list_of_densities = []
current_order = []
n_open = 0
for con in contraction:
ele_con = elementary_contractions[con]
list_of_densities.append(ele_con)
n_open += ele_con.n_upper
if isinstance(ele_con, HoleDensity):
current_order += [
f"l{ele_con.lower_indices[0].name}",
f"u{ele_con.upper_indices[0].name}"
]
else:
current_order += [f"u{i.name}" for i in ele_con.upper_indices]
current_order += [
f"l{i.name}" for i in ele_con.lower_indices[::-1]
]
n_open = n_indices - 2 * n_open
# sort the open indices
if n_open != 0:
contracted = set(current_order)
open_upper_indices = IndicesSpinOrbital(
sorted(Index(i[1:]) for i in upper_indices_set - contracted))
open_lower_indices = IndicesSpinOrbital(
sorted(Index(i[1:]) for i in lower_indices_set - contracted))
current_order += [f"u{i.name}" for i in open_upper_indices]
current_order += [f"l{i.name}" for i in open_lower_indices[::-1]]
sq_op = SecondQuantizedOperator(open_upper_indices, open_lower_indices)
else:
sq_op = SecondQuantizedOperator.make_empty()
# expand hole densities to delta - lambda_1
sign_densities_pairs = expand_hole_densities(
list_of_densities) if expand_hole else [(1, list_of_densities)]
# determine sign
sign = (-1)**Permutation([base_order_map[i]
for i in current_order]).inversions()
return [(sign * _s, list_of_densities, sq_op)
for _s, list_of_densities in sign_densities_pairs]
def test_latex_permute_format_2():
a = SecondQuantizedOperator("g0,v1,p3", "p0,a1,p2", 'spin-integrated')
p_cre = [[Index('g0')], [Index('p3')], [Index('v1')]]
p_ann = [[Index('p0'), Index('p2')], [Index('a1')]]
n_perm, perm, latex_str = a.latex_permute_format(p_cre, p_ann)
assert n_perm == 18
assert perm == '{\\cal P} ( g_{0} / p_{3} / v_{1} ) {\\cal P} ( p_{0} p_{2} / a_{1} )'
assert latex_str == 'a^{ g_{0} v_{1} p_{3} }_{ p_{0} a_{1} p_{2} }'
def test_init():
id_type = 'spin-orbital'
assert SecondQuantizedOperator([], []).is_empty()
a = SecondQuantizedOperator("g0,g1,g2", "p0,p1,p2", id_type)
assert a.cre_ops == Indices.make_indices("g0,g1,g2", id_type)
assert a.ann_ops == Indices.make_indices("p0,p1,p2", id_type)
assert a.n_ann == 3
assert a.n_cre == 3
def test_latex_permute_format_1():
a = SecondQuantizedOperator("g0,g1,g2", "p0,p1,p2", 'spin-orbital')
p_cre = [[Index(i) for i in "g0,g1,g2".split(',')]]
p_ann = [[Index(i) for i in "p0,p1,p2".split(',')]]
n_perm, perm, latex_str = a.latex_permute_format(p_cre, p_ann)
assert n_perm == 1
assert perm == ''
assert latex_str == 'a^{ g_{0} g_{1} g_{2} }_{ p_{0} p_{1} p_{2} }'
def test_multiset_permutation_2():
a = SecondQuantizedOperator("g0,g1,g2", "p0,p1,p2", 'spin-integrated')
p_cre = [[Index(i) for i in "g0,g1,g2".split(',')]]
p_ann = [[Index('p0')], [Index('p1')], [Index('p2')]]
assert a.exist_permute_format(p_cre, p_ann)
assert a.n_multiset_permutation(p_cre, p_ann) == 6
p_ann = [[Index('p0'), Index('p1')], [Index('p2')]]
assert a.n_multiset_permutation(p_cre, p_ann) == 3
def test_ambit_permute_format_2():
a = SecondQuantizedOperator("g0,g1,c2", "p0,p1,p2", 'spin-integrated')
p_cre = [[Index('g0'), Index('g1')], [Index('c2')]]
p_ann = [[Index('p0'), Index('p1'), Index('p2')]]
ref = {(1, '["p0,p1,p2,g0,g1,c2"]'), (-1, '["p0,p1,p2,g0,c2,g1"]'),
(1, '["p0,p1,p2,c2,g0,g1"]')}
for pair in a.ambit_permute_format(p_cre, p_ann, cre_first=False):
assert pair in ref
ref.remove(pair)
assert len(ref) == 0
def test_latex_permute_format_3():
# TODO: is this necessary?
# ignore multiset permutations for mixed spin indices
a = SecondQuantizedOperator("g0,v1,p2", "p0,a1,P2", 'spin-integrated')
p_cre = [[Index('g0')], [Index('p2')], [Index('v1')]]
p_ann = [[Index('p0'), Index('P2')], [Index('a1')]]
n_perm, perm, latex_str = a.latex_permute_format(p_cre, p_ann)
assert n_perm == 6
assert perm == '{\\cal P} ( g_{0} / p_{2} / v_{1} )'
assert latex_str == 'a^{ g_{0} v_{1} p_{2} }_{ p_{0} a_{1} P_{2} }'
def test_eq():
a = SecondQuantizedOperator("g0,g1,g2", "p0,p1,p2", 'spin-orbital')
b = SecondQuantizedOperator("g0,g1,g2", "p0,p1,p2", 'so')
assert a is not b
assert a == b
with pytest.raises(TypeError):
assert a == IndicesPair("g0,g1,g2", "p0,p1,p2", 'spin-orbital')
with pytest.raises(TypeError):
assert a == SecondQuantizedOperator("g0,g1,g2", "p0,p1,p2",
'spin-integrated')
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_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_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_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 process_composite_categorized(com_cat, ele_con, compatible,
upper_indices_set, lower_indices_set,
base_order_map, n_indices, expand_hole):
"""
Process one composite categorized contraction.
:param com_cat: a list of connected operator indices
:param ele_con: an ElementaryContractionCategorized object
:param compatible: compatible elementary contractions
:param upper_indices_set: the set of all creation operators
:param lower_indices_set: the set of all annihilation operators
:param base_order_map: the Index map to ordering index
:param n_indices: the total number of cre and ann operators
:param expand_hole: expand hole densities to Kronecker delta minus one density if True
:return: a list of contractions in terms of (sign, list_of_densities, sq_op)
"""
n_open = n_indices - sum(len(i) for i in com_cat)
out = []
for coded_cons in ele_con.composite_contractions(Counter(com_cat),
compatible):
contractions = [ele_con.decode(i) for i in coded_cons]
# cre/ann ordering of the current composite contraction
current_order = []
for con in contractions:
if isinstance(con, HoleDensity):
current_order += [
f"l{con.lower_indices[0].name}",
f"u{con.upper_indices[0].name}"
]
else:
current_order += [f"u{i.name}" for i in con.upper_indices]
current_order += [
f"l{i.name}" for i in con.lower_indices[::-1]
]
# sort open indices
if n_open != 0:
contracted = set(current_order)
open_upper = IndicesSpinOrbital(
sorted(Index(i[1:]) for i in upper_indices_set - contracted))
open_lower = IndicesSpinOrbital(
sorted(Index(i[1:]) for i in lower_indices_set - contracted))
current_order += [f"u{i.name}" for i in open_upper]
current_order += [f"l{i.name}" for i in open_lower[::-1]]
sq_op = SecondQuantizedOperator(open_upper, open_lower)
else:
sq_op = SecondQuantizedOperator.make_empty()
# determine sign of current ordering
sign = (-1)**Permutation([base_order_map[i]
for i in current_order]).inversions()
# expand hole density to delta - 1-cumulant
sign_densities = expand_hole_densities(
contractions) if expand_hole else [(1, contractions)]
# append results
out += [(sign * _s, cons, sq_op) for _s, cons in sign_densities]
return out
def test_multiset_permutation_4():
a = SecondQuantizedOperator("g0,v1,p2", "p0,a1,c2", 'spin-orbital')
p_cre = [[Index('g0'), Index('v1'), Index('p2')]]
p_ann = [[Index('p0'), Index('a1'), Index('c2')]]
assert not a.exist_permute_format(p_cre, p_ann)
assert a.n_multiset_permutation(p_cre, p_ann) == 1
def test_multiset_permutation_3():
a = SecondQuantizedOperator("g0,v1,p2", "p0,a1,p2", 'spin-integrated')
p_cre = [[Index('g0')], [Index('v1')], [Index('p2')]]
p_ann = [[Index('p0'), Index('p2')], [Index('a1')]]
assert a.exist_permute_format(p_cre, p_ann)
assert a.n_multiset_permutation(p_cre, p_ann) == 18
def test_ambit_permute_format_3():
# TODO: is this necessary?
# ignore all input partitions for mixed spin indices
a = SecondQuantizedOperator("g0,G1,c2", "p0,p1,P2", 'spin-integrated')
for pair in a.ambit_permute_format([], [], cre_first=True):
assert pair == (1, '["g0,G1,c2,p0,p1,P2"]')
def test_canonicalize():
a = SecondQuantizedOperator("G2, p0, p1", "g0, A0, h2, A2", 'si')
c, sign = a.canonicalize()
assert c == SecondQuantizedOperator("p0, p1, G2", "g0, h2, A0, A2", 'si')
assert sign == -1
def test_base_strong_generating_set():
with pytest.raises(ValueError):
SecondQuantizedOperator("", "", 'si').base_strong_generating_set()
def test_is_spin_conserving():
assert SecondQuantizedOperator("p0", "p0", 'si').is_spin_conserving()
assert not SecondQuantizedOperator("p0", "H0", 'si').is_spin_conserving()
with pytest.raises(ValueError):
assert SecondQuantizedOperator("p0", "p0, p1",
'so').is_spin_conserving()
def test_is_particle_conserving():
assert SecondQuantizedOperator("G0,G1,g2", "p0,P1,P2",
'spin-integrated').is_particle_conserving()
assert SecondQuantizedOperator("p0", "p0", 'so').is_particle_conserving()
assert not SecondQuantizedOperator("p0", "p0, p1",
'so').is_particle_conserving()
def test_ge():
a = SecondQuantizedOperator("G0,G1,g2", "p0,P1,P2", 'spin-integrated')
assert a >= SecondQuantizedOperator("g0,g1,g2", "p0,P1,p2,p3", 'si')
with pytest.raises(TypeError):
assert a >= 1
def test_lt():
a = SecondQuantizedOperator("g0,g1,g2", "p0,P1,p2", 'spin-integrated')
assert a < SecondQuantizedOperator("g0,g1,g2", "p0,P1,p2,p3", 'si')
assert a < SecondQuantizedOperator("g0,g1,g2", "p0,P2,p2", 'si')
def compute_operator_contractions_general(ops_list,
max_cu=3,
max_n_open=6,
min_n_open=0,
expand_hole=True,
n_process=1,
batch_size=1):
"""
Generate operator contractions for a list of SQOperator (disconnected contractions are included).
:param ops_list: a list of SecondQuantizedOperator to be contracted
:param max_cu: max level of cumulant
:param max_n_open: max number of open indices for contractions kept for return
:param min_n_open: min number of open indices for contractions kept for return
:param expand_hole: expand hole density to Kronecker delta and 1-cumulant if True
:param n_process: the number of processes launched by multiprocessing
:param batch_size: the chunk size for multiprocessing
:return: a list of contractions in terms of (sign, list_of_densities, sq_op)
"""
max_cu_allowed = check_max_cu(ops_list, max_cu)
# original ordering of the second-quantized operators
base_order_map, upper_indices_set, lower_indices_set = generate_base_order_map(
ops_list)
n_indices = len(base_order_map)
# un-contracted term
if min_n_open <= n_indices <= max_n_open:
sq_op = SecondQuantizedOperator(
sorted(Index(i[1:]) for i in upper_indices_set),
sorted(Index(i[1:]) for i in lower_indices_set))
current_order = [base_order_map[f"u{i.name}"] for i in sq_op.cre_ops]
current_order += [
base_order_map[f"l{i.name}"] for i in sq_op.ann_ops[::-1]
]
sign = (-1)**Permutation(current_order).inversions()
yield [(sign, [], sq_op)]
# max/min numbers of contracted indices
max_n_con, min_n_con = n_indices - min_n_open, n_indices - max_n_open
elementary_contractions = compute_elementary_contractions_list(
ops_list, max_cu_allowed)
compatible = compute_compatible_elementary_contractions_list(
elementary_contractions)
n_ele_con = len(elementary_contractions)
if n_ele_con > 1000:
sys.setrecursionlimit(n_ele_con)
if n_process == 1:
for con in composite_contractions_backtrack(set(range(n_ele_con)),
set(), compatible, 0,
elementary_contractions,
(min_n_con, max_n_con)):
yield process_composite_contractions(con, elementary_contractions,
n_indices, expand_hole,
base_order_map,
upper_indices_set,
lower_indices_set)
else:
composite = [
list(i)
for i in composite_contractions_backtrack(set(range(
n_ele_con)), set(), compatible, 0, elementary_contractions, (
min_n_con, max_n_con))
]
n_process = min(n_process, multiprocessing.cpu_count())
if batch_size == 0:
n_upper, n_lower = len(upper_indices_set), len(lower_indices_set)
batch_size = estimate_batch_size(n_upper, n_lower, max_n_con,
min_n_con, n_process)
with multiprocessing.Pool(n_process, maxtasksperchild=1000) as pool:
tasks = [(process_composite_contractions,
(con, elementary_contractions, n_indices, expand_hole,
base_order_map, upper_indices_set, lower_indices_set))
for con in composite]
imap_unordered_it = pool.imap_unordered(calculate_star,
tasks,
chunksize=batch_size)
for results in imap_unordered_it:
yield results
def test_multiset_permutation_1():
a = SecondQuantizedOperator("g0,g1,g2", "p0,p1,p2", 'spin-orbital')
p_cre = [[Index(i) for i in "g0,g1,g2".split(',')]]
p_ann = [[Index(i) for i in "p0,p1,p2".split(',')]]
assert not a.exist_permute_format(p_cre, p_ann)
assert a.n_multiset_permutation(p_cre, p_ann) == 1
def test_ne():
a = SecondQuantizedOperator("g0,g1,g2", "p0,p1,p2", 'so')
assert a != SecondQuantizedOperator(["g0", "v1", "p2"], ["p0", "a1", "p2"])
def test_void():
a = SecondQuantizedOperator("G2, p0, p1", "g0, A0, h2", 'si')
b = a.void()
assert a.indices_type == b.indices_type
assert b.size == 0
assert b is not SecondQuantizedOperator.make_empty('si')