def testEP11op(self):
op = ep11("Hp", ["occ", "vir"], ["nm"], name2="Hq")
bra = braP1E1("nm", "occ", "vir")
ex = apply_wick(bra * op)
ex.resolve()
out = AExpression(Ex=ex)
x = Idx(0, "nm", fermion=False)
a = Idx(0, "vir")
i = Idx(0, "occ")
tr1 = ATerm(scalar=1,
sums=[],
tensors=[Tensor([x, a, i], ""),
Tensor([x, a, i], "Hq")])
ref = AExpression(terms=[tr1])
self.assertTrue(ref.pmatch(out))
ket = ketP1E1("nm", "occ", "vir")
ex = apply_wick(op * ket)
ex.resolve()
out = AExpression(Ex=ex)
tr1 = ATerm(scalar=1,
sums=[],
tensors=[Tensor([x, i, a], "Hp"),
Tensor([x, i, a], "")])
ref = AExpression(terms=[tr1])
self.assertTrue(ref.pmatch(out))
def testP1op(self):
op = one_p("Hp", name2="Hq")
bra = braP1("nm")
ex = apply_wick(bra * op)
ex.resolve()
out = AExpression(Ex=ex)
x = Idx(0, "nm", fermion=False)
tr1 = ATerm(scalar=1,
sums=[],
tensors=[Tensor([x], "Hq"),
Tensor([x], "")])
ref = AExpression(terms=[tr1])
self.assertTrue(ref.pmatch(out))
ket = ketP1("nm")
ex = apply_wick(op * ket)
ex.resolve()
out = AExpression(Ex=ex)
tr1 = ATerm(scalar=1,
sums=[],
tensors=[Tensor([x], "Hp"),
Tensor([x], "")])
ref = AExpression(terms=[tr1])
self.assertTrue(ref.pmatch(out))
def testEea2(self):
bra = braEea2("occ", "vir", "vir")
ket = ketEea2("occ", "vir", "vir")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
i = Idx(0, "occ")
a = Idx(0, "vir")
b = Idx(1, "vir")
k = Idx(2, "occ")
c = Idx(2, "vir")
d = Idx(3, "vir")
tensors = [Tensor([i, a, b], ""), Tensor([c, d, k], "")]
tr1 = Term(1, [], tensors, [], [Delta(i, k), Delta(a, c), Delta(b, d)])
tr2 = Term(
-1, [], tensors, [],
[Delta(i, k), Delta(a, d), Delta(b, c)])
ref = Expression([tr1, tr2])
aref = AExpression(Ex=ref)
self.assertTrue(aout.pmatch(aref))
op = Eea2("A", ["occ"], ["vir"])
out = apply_wick(bra * op)
out.resolve()
aout = AExpression(Ex=out)
ext = Tensor([a, b, i], "")
ten = Tensor([a, b, i], "A", sym=get_sym_ea2())
at1 = ATerm(scalar=1, sums=[], tensors=[ext, ten])
self.assertTrue(len(aout.terms) == 1)
self.assertTrue(at1.pmatch(aout.terms[0]))
def test_term_map3(self):
s = 1
i = Idx(0, "occ")
a = Idx(0, "vir")
sums = [Sigma(i), Sigma(a)]
tensors = [Tensor([i, a], 'f'), Tensor([a, i], 't')]
t1 = ATerm(s, sums, tensors)
sums = [Sigma(i)]
t2 = ATerm(s, sums, tensors)
self.assertFalse(t1.match(t2))
def test_term_map2(self):
s = 1
i = Idx(0, "occ")
j = Idx(1, "occ")
sums = [Sigma(i), Sigma(j)]
tensors = [Tensor([i, j], 'f')]
t1 = ATerm(s, sums, tensors)
sums = [Sigma(i)]
tensors = [Tensor([j, i], 'f')]
t2 = ATerm(s, sums, tensors)
self.assertFalse(t1.match(t2))
def test_tensor_sort(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
a = Idx(0, "vir")
tensors = [
Tensor([j, i], 'f'),
Tensor([a, i], ''),
Tensor([a, j], "t")
]
st = [tensors[1], tensors[0], tensors[2]]
sigmas = [Sigma(j)]
tt = ATerm(scalar=1.0, sums=sigmas, tensors=tensors)
tt.sort_tensors()
for ref, out in zip(st, tt.tensors):
self.assertTrue(ref == out)
def testP1E1(self):
bra = braP1E1("nm", "occ", "vir")
ket = ketP1E1("nm", "occ", "vir")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
x = Idx(0, "nm", fermion=False)
y = Idx(1, "nm", fermion=False)
i = Idx(0, "occ")
a = Idx(0, "vir")
j = Idx(1, "occ")
b = Idx(1, "vir")
tensors = [Tensor([x, i, a], ""), Tensor([y, b, j], "")]
tr1 = Term(1, [], tensors, [], [Delta(x, y), Delta(i, j), Delta(a, b)])
ref = Expression([tr1])
aref = AExpression(Ex=ref)
self.assertTrue(aout.pmatch(aref))
op = EPS1("A", ["nm"], ["occ"], ["vir"])
out = apply_wick(bra * op)
out.resolve()
aout = AExpression(Ex=out)
ext = Tensor([x, a, i], "")
t1 = Tensor([x, a, i], "A")
at1 = ATerm(scalar=1, sums=[], tensors=[ext, t1])
self.assertTrue(at1 == aout.terms[0])
def testP2(self):
bra = braP2("nm")
ket = ketP2("nm")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
x = Idx(0, "nm", fermion=False)
y = Idx(1, "nm", fermion=False)
u = Idx(2, "nm", fermion=False)
v = Idx(3, "nm", fermion=False)
tensors = [Tensor([x, y], ""), Tensor([u, v], "")]
tr1 = Term(1, [], tensors, [], [Delta(x, u), Delta(y, v)])
tr2 = Term(1, [], tensors, [], [Delta(x, v), Delta(y, u)])
ref = Expression([tr1, tr2])
aref = AExpression(Ex=ref)
self.assertTrue(aout.pmatch(aref))
op = P2("A", ["nm"])
out = apply_wick(bra * op)
out.resolve()
aout = AExpression(Ex=out)
sym = TensorSym([(0, 1), (1, 0)], [1, 1])
ext = Tensor([x, y], "")
t1 = Tensor([x, y], "A", sym=sym)
at1 = ATerm(scalar=1, sums=[], tensors=[ext, t1])
self.assertTrue(at1 == aout.terms[0])
def testE1(self):
bra = braE1("occ", "vir")
ket = ketE1("occ", "vir")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
i = Idx(0, "occ")
a = Idx(0, "vir")
j = Idx(1, "occ")
b = Idx(1, "vir")
tr1 = Term(1, [],
[Tensor([a, i], ""), Tensor([j, b], "")], [],
[Delta(i, j), Delta(a, b)])
ref = Expression([tr1])
aref = AExpression(Ex=ref)
self.assertTrue(aout.pmatch(aref))
op = E1("A", ["occ"], ["vir"])
out = apply_wick(bra * op)
out.resolve()
aout = AExpression(Ex=out)
ext = Tensor([a, i], "")
ten = Tensor([a, i], "A")
at1 = ATerm(scalar=1, sums=[], tensors=[ext, ten])
self.assertTrue(len(aout.terms) == 1)
self.assertTrue(at1 == aout.terms[0])
def test_string(self):
a = Idx(0, "vir")
b = Idx(1, "vir")
sums = [Sigma(a), Sigma(b)]
tensors = [Tensor([a, b], 'f')]
t1 = ATerm(sums=sums, tensors=tensors)
out = str(t1)
ref = "1\\sum_{0}\\sum_{1}f_{01}"
self.assertTrue(out == ref)
out = t1._print_str()
ref = "1.0\\sum_{ab}f_{ab}"
self.assertTrue(out == ref)
out = t1._einsum_str()
ref = "1.0*einsum('ab->', f)"
self.assertTrue(out == ref)
a = Idx(0, "vir")
b = Idx(1, "vir")
sums = [Sigma(b)]
tensors = [Tensor([a], ''), Tensor([a, b], 'f')]
t2 = ATerm(sums=sums, tensors=tensors)
out = t2._einsum_str()
ref = "1.0*einsum('ab->a', f)"
self.assertTrue(out == ref)
def test_eq(self):
s = 1.0
i = Idx(0, "occ")
j = Idx(1, "occ")
sums = [Sigma(i), Sigma(j)]
tensors = [Tensor([i, j], 'f')]
t1 = ATerm(s, sums, tensors)
t0 = t1.copy()
sums = [Sigma(i), Sigma(j)]
tensors = [Tensor([j, i], 'f'), Tensor([i, j], 'g')]
t2 = ATerm(s, sums, tensors)
sums = [Sigma(i)]
tensors = [Tensor([i, j], 'f')]
t3 = ATerm(s, sums, tensors)
sums = [Sigma(i)]
tensors = [Tensor([i, j], 'g')]
t4 = ATerm(s, sums, tensors)
self.assertTrue(t1 < t2)
self.assertTrue(t1 != t2)
self.assertFalse(t0 < t1)
self.assertTrue(t0 <= t1)
self.assertTrue(t0 >= t1)
self.assertTrue(t1 > t3)
self.assertTrue(t3 < t4)
def testP2E1(self):
bra = braP2E1("nm", "nm", "occ", "vir")
op = EPS2("A", ["nm"], ["occ"], ["vir"])
out = apply_wick(bra * op)
out.resolve()
x = Idx(0, "nm", fermion=False)
y = Idx(1, "nm", fermion=False)
a = Idx(0, "vir")
i = Idx(0, "occ")
sym = TensorSym([(0, 1, 2, 3), (1, 0, 2, 3)], [1, 1])
aout = AExpression(Ex=out)
ext = Tensor([x, y, a, i], "")
t1 = Tensor([x, y, a, i], "A", sym=sym)
at1 = ATerm(scalar=1, sums=[], tensors=[ext, t1])
self.assertTrue(at1 == aout.terms[0])
def test_null(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
a = Idx(0, "vir")
b = Idx(1, "vir")
L1 = Tensor([i, j, a, b], "L")
J1 = Tensor([j, b], "J")
S1j = Sigma(j)
S1b = Sigma(b)
T1 = ATerm(scalar=1, sums=[S1j, S1b], tensors=[L1, J1])
T2 = ATerm(scalar=1, sums=[S1j, S1b], tensors=[L1, J1])
self.assertTrue(T1.match(T2))
self.assertTrue(T2.match(T1))
def testP2op(self):
op = two_p("H")
bra = braP1("nm")
ket = ketP1("nm")
ex = apply_wick(bra * op * ket)
ex.resolve()
out = AExpression(Ex=ex)
x = Idx(0, "nm", fermion=False)
y = Idx(1, "nm", fermion=False)
sym = TensorSym([(0, 1), (1, 0)], [1, 1])
tensors = [
Tensor([x], ""),
Tensor([x, y], "H", sym=sym),
Tensor([y], "")
]
tr1 = ATerm(scalar=1, sums=[], tensors=tensors)
ref = AExpression(terms=[tr1])
self.assertTrue(ref.pmatch(out))
def test_merge_external(self):
bra = braE1("occ", "vir")
ket = ketE1("occ", "vir")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
aterm = aout.terms[0]
aterm.merge_external()
i = Idx(0, "occ")
a = Idx(0, "vir")
j = Idx(1, "occ")
b = Idx(1, "vir")
tensors = [
Tensor([a, i, j, b], ""),
tensor_from_delta(Delta(i, j)),
tensor_from_delta(Delta(a, b))
]
aref = ATerm(scalar=1, sums=[], tensors=tensors)
self.assertTrue(aterm == aref)
def testP1(self):
bra = braP1("nm")
ket = ketP1("nm")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
x = Idx(0, "nm", fermion=False)
y = Idx(1, "nm", fermion=False)
tensors = [Tensor([x], ""), Tensor([y], "")]
tr1 = Term(1, [], tensors, [], [Delta(x, y)])
ref = Expression([tr1])
aref = AExpression(Ex=ref)
self.assertTrue(aout.pmatch(aref))
op = P1("A", ["nm"])
out = apply_wick(bra * op)
out.resolve()
aout = AExpression(Ex=out)
ext = Tensor([x], "")
ten = Tensor([x], "A")
at1 = ATerm(scalar=1, sums=[], tensors=[ext, ten])
self.assertTrue(at1 == aout.terms[0])
def test_mul(self):
s = 1
i = Idx(0, "occ")
j = Idx(1, "occ")
sums = [Sigma(i), Sigma(j)]
tensors = [Tensor([i, j], 'f')]
t1 = ATerm(s, sums, tensors)
t2 = t1.copy()
out = t1 * t2
k = Idx(2, "occ")
l = Idx(3, "occ")
sumsx = [Sigma(i), Sigma(j), Sigma(k), Sigma(l)]
tensorsx = [Tensor([i, j], 'f'), Tensor([k, l], 'f')]
tx = ATerm(s, sumsx, tensorsx)
self.assertTrue(tx == out)
tx.scalar = 2
out = 2 * out
self.assertTrue(tx == out)
self.assertTrue(4 * tx == out * 4)