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 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 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 test_delta(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
a = Idx(0, "vir")
b = Idx(1, "vir")
D1 = Delta(i, j)
D2 = Delta(i, j)
D3 = Delta(j, i)
D4 = Delta(a, b)
self.assertTrue(D1 == D2)
self.assertTrue(D1 == D3)
self.assertTrue(D1 != D4)
def testEdea1(self):
bra = braEdea1("vir", "vir")
ket = ketEdea1("vir", "vir")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
a = Idx(0, "vir")
b = Idx(1, "vir")
c = Idx(2, "vir")
d = Idx(3, "vir")
tensors = [Tensor([a, b], ""), Tensor([c, d], "")]
tr1 = Term(1, [], tensors, [], [Delta(a, c), Delta(b, d)])
tr2 = Term(-1, [], tensors, [], [Delta(a, d), Delta(b, c)])
ref = Expression([tr1, tr2])
aref = AExpression(Ex=ref)
self.assertTrue(aout.pmatch(aref))
def testEdip1(self):
bra = braEdip1("occ", "occ")
ket = ketEdip1("occ", "occ")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
i = Idx(0, "occ")
j = Idx(1, "occ")
k = Idx(2, "occ")
l = Idx(3, "occ")
tensors = [Tensor([i, j], ""), Tensor([k, l], "")]
tr1 = Term(1, [], tensors, [], [Delta(i, k), Delta(j, l)])
tr2 = Term(-1, [], tensors, [], [Delta(i, l), Delta(j, k)])
ref = Expression([tr1, tr2])
aref = AExpression(Ex=ref)
self.assertTrue(aout.pmatch(aref))
def test_resolve0(self):
I1 = Idx(0, "o1")
I2 = Idx(1, "o1")
I3 = Idx(0, "o2")
operators = [FOperator(I1, True), FOperator(I3, False)]
out = Term(
1, [Sigma(I3)],
[Tensor([I1, I3], "T")],
operators, [Delta(I1, I2)])
out.resolve()
ref = Term(
1, [Sigma(I3)],
[Tensor([I1, I3], "T")],
operators, [Delta(I1, I2)])
self.assertTrue(ref == 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 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_resolve_chain(self):
I1 = Idx(0, "v1")
I2 = Idx(0, "o1")
I3 = Idx(1, "v1")
I4 = Idx(1, "o1")
operators = [
FOperator(I1, True), FOperator(I2, True),
FOperator(I4, False), FOperator(I3, False)]
out = Term(
1, [Sigma(I2), Sigma(I3), Sigma(I4)],
[Tensor([I1, I2, I3, I4], "T")],
operators, [Delta(I1, I3), Delta(I2, I4)])
out.resolve()
roperators = [
FOperator(I1, True), FOperator(I2, True),
FOperator(I2, False), FOperator(I1, False)]
ref = Term(
1, [Sigma(I2)],
[Tensor([I1, I2, I1, I2], "T")],
roperators, [])
self.assertTrue(ref == out)
def test_str(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
sums = [Sigma(i)]
tensors = [Tensor([i, j], "X")]
operators = [FOperator(i, False)]
e1 = Term(1, sums, tensors, operators, [Delta(i, j)])
ex = Expression([e1])
out = str(ex)
ref = "1\\sum_{0}\\delta_{0,1}X_{01}a_0(occ)"
self.assertTrue(ref == out)
out = ex._print_str()
ref = " + 1\\sum_{i}\\delta_{ij}X_{ij}a_i"
self.assertTrue(ref == out)
def test_resolve3(self):
I1 = Idx(0, "o1")
I2 = Idx(1, "o1")
operators = [FOperator(I1, True), FOperator(I2, False)]
out = Term(
1, [Sigma(I1), Sigma(I2)],
[Tensor([I1, I2], "T")],
operators, [Delta(I1, I2)])
out.resolve()
roperators = [FOperator(I1, True), FOperator(I1, False)]
ref = Term(
1, [Sigma(I1)],
[Tensor([I1, I1], "T")],
roperators, [])
self.assertTrue(ref == out)
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_string(self):
P1 = Projector()
self.assertTrue(str(P1) == "P")
i = Idx(0, "occ")
a = Idx(0, "vir")
O1 = FOperator(i, False)
O2 = FOperator(i, True)
O3 = FOperator(a, False)
O4 = FOperator(a, True)
so1 = "a_0(occ)"
so2 = "a^{\\dagger}_0(occ)"
so3 = "a_0(vir)"
so4 = "a^{\\dagger}_0(vir)"
self.assertTrue(str(O1) == so1)
self.assertTrue(str(O2) == so2)
self.assertTrue(str(O3) == so3)
self.assertTrue(str(O4) == so4)
x = Idx(0, "nm", fermion=False)
Ob1 = BOperator(x, False)
Ob2 = BOperator(x, True)
sob1 = "b_0(nm)"
sob2 = "b^{\\dagger}_0(nm)"
self.assertTrue(str(Ob1) == sob1)
self.assertTrue(str(Ob2) == sob2)
T1 = Tensor([i, a], "g")
st1 = "g_{00}"
self.assertTrue(str(T1) == st1)
S1 = Sigma(i)
ss1 = "\\sum_{0}"
self.assertTrue(str(S1) == ss1)
j = Idx(1, "occ")
D1 = Delta(i, j)
sd1 = "\\delta_{0,1}"
self.assertTrue(str(D1) == sd1)
def test_inc(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
a = Idx(0, "vir")
I = Idx(0, "nm", fermion=False)
J = Idx(1, "nm", fermion=False)
iii = 3
# Fermion operator
O1 = FOperator(i, False)._inc(iii)
self.assertTrue(O1.idx.index == iii)
# Boson operator
O2 = BOperator(I, False)._inc(iii)
O3 = BOperator(J, True)._inc(iii)
self.assertTrue(O2.idx.index == iii)
self.assertTrue(O3.idx.index == iii + 1)
# Projector
P1 = Projector()
P2 = P1._inc(iii)
self.assertTrue(P1 == P2)
# tensor
T1 = Tensor([i, a], "g")._inc(iii)
self.assertTrue(T1.indices[0].index == iii)
self.assertTrue(T1.indices[1].index == iii)
# sigma
S3 = Sigma(j)._inc(iii)
self.assertTrue(S3.idx.index == iii + 1)
# delta
D1 = Delta(i, j)._inc(iii)
self.assertTrue(D1.i1.index == iii)
self.assertTrue(D1.i2.index == iii + 1)
