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_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_index_init():
with pytest.raises(ValueError):
Index("x0")
with pytest.raises(ValueError):
Index("ax1")
with pytest.raises(ValueError):
Index("a1.25")
with pytest.raises(TypeError):
Index(123)
def test_indices_init():
with pytest.raises(ValueError):
Indices("a0 c1, P2, V8")
with pytest.raises(ValueError):
Indices(["a0"] * 3)
a = Indices("a0, P2")
assert a.indices == [Index("a0"), Index("P2")]
assert a.size == 2
assert a.indices_set == {Index("a0"), Index("P2")}
a = Indices([])
assert a == Indices("")
assert a.size == 0
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_indices_si_latex_permute_format():
a = IndicesSpinIntegrated(["P0", "P1", "P2", "A3"])
part = [["P2"], ["P0", "P1"], ["A3"]]
with pytest.raises(TypeError):
a.latex_permute_format(part)
part = [[Index("P2")], [Index("P0"), Index("P1")], [Index("A3")]]
n_perm, perm_str = a.latex_permute_format(part)
assert (n_perm, perm_str) == (12,
'{\\cal P} ( P_{2} / P_{0} P_{1} / A_{3} )')
a = IndicesSpinIntegrated(["p0", "P1", "V2", "A3"])
with pytest.raises(ValueError):
list(a.ambit_permute_format(part))
def test_indices_si_ambit_perm():
a = IndicesSpinIntegrated(["P0", "P1", "V2", "A3"])
part = [[Index("V2")], [Index("P0"), Index("P1")], [Index("A3")]]
ref = {
"P0,P1,V2,A3", "P0,P1,A3,V2", "P0,A3,P1,V2", "A3,P0,P1,V2",
"P0,V2,P1,A3", "V2,P0,P1,A3", "P0,A3,V2,P1", "P0,V2,A3,P1",
"V2,P0,A3,P1", "A3,P0,V2,P1", "A3,V2,P0,P1", "V2,A3,P0,P1"
}
for sign, indices_str in a.ambit_permute_format(part):
assert sign == (-1)**a.count_permutations(Indices(indices_str))
assert indices_str in ref
ref.remove(indices_str)
assert len(ref) == 0
a = IndicesSpinIntegrated(["P0", "P1", "c2", "A3"])
with pytest.raises(ValueError):
list(a.ambit_permute_format(part))
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_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_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_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_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_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_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_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 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_index_ne_2():
assert Index("a0") != Index("a20")
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_index_gt():
assert Index("H0") > Index("a4")
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_indices_so_ambit_perm():
a = IndicesSpinOrbital(["p0", "p1", "v2", "a3"])
part = [[Index("p0"), Index("p1")], [Index("v2")], [Index("a3")]]
for sign, indices_str in a.ambit_permute_format(part):
assert sign == (-1)**a.count_permutations(Indices(indices_str))
def test_index_ge():
assert Index("P1") >= Index("P1")
def test_index_le():
assert Index("p0") <= Index("p1")
def test_indices_get():
with pytest.raises(IndexError):
assert Indices([])[0]
assert Indices("p0, p1, a0, h0, g4, g1, c1, v2")[2] == Index("a0")
def test_index_ne_1():
assert Index("a0") != Index("P0")
def test_index_spin():
assert Index("G1").is_beta()
assert not Index("g1").is_beta()
assert Index("a0").to_beta() == Index("A0")
assert Index("p0").to_alpha() == Index("p0")
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_index_lt():
assert Index("h0") < Index("G2")
def test_indices_so_latex_perm():
part = [[Index("g2")], [Index("p0"), Index("p1")], [Index("a4")]]
n_perm, perm = IndicesSpinOrbital("p0, p1, g2, a4").latex_permute_format(
part)
assert n_perm == 12
assert perm == "{\\cal P} ( g_{2} / p_{0} p_{1} / a_{4} )"