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 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_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_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_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')
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)