def test_scalar_mul(self):
s = 1.0
i = Idx(0, "occ")
j = Idx(1, "occ")
sums = [Sigma(i), Sigma(j)]
tensors = [Tensor([i, j], 'f')]
operators = [FOperator(i, True), FOperator(j, False)]
t = Term(s, sums, tensors, operators, [])
t1 = 3.14 * t
t2 = t * 3.14
self.assertTrue(t1 == t2)
def test_ilist(self):
s = 1.0
i = Idx("i", "occ")
j = Idx("j", "occ")
sums = [Sigma(i), Sigma(j)]
tensors = [Tensor([i, j], 'f')]
operators = [FOperator(i, True), FOperator(j, False)]
t1 = Term(s, sums, tensors, operators, [])
ilist = t1.ilist()
iref = [i, j]
self.assertTrue(set(iref) == set(ilist))
def test_split_operators(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
k = Idx(3, "occ")
l = Idx(4, "occ")
O1 = FOperator(i, False)
O2 = FOperator(j, False)
O3 = FOperator(k, False)
O4 = FOperator(l, True)
P = Projector()
ops = [O1, O2, P, O3, P, O4]
olists = split_operators(ops)
self.assertTrue(len(olists) == 3)
self.assertTrue(olists[0] == [O1, O2])
self.assertTrue(olists[1] == [O3])
self.assertTrue(olists[2] == [O4])
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 test_pair_list(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
k = Idx(2, "occ")
l = Idx(3, "occ")
O1 = FOperator(i, False)
O2 = FOperator(j, True)
O3 = FOperator(k, False)
O4 = FOperator(l, True)
os = [O2, O4, O1, O3]
pl = pair_list(os)
self.assertTrue(len(pl) == 2)
os = [O2, O1, O4, O3]
pl = pair_list(os)
self.assertTrue(len(pl) == 1)
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_foperator(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
O1 = FOperator(i, False)
O2 = FOperator(i, False)
O3 = FOperator(j, False)
O4 = FOperator(j, True)
self.assertTrue(O1 == O2)
self.assertTrue(O1 != O3)
self.assertTrue(O1 != O4)
self.assertTrue(O2 != O4)
self.assertTrue(O1.qp_creation())
self.assertTrue(O4.qp_annihilation())
def test_mul(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
a = Idx(0, "vir")
b = Idx(1, "vir")
sum1 = [Sigma(i), Sigma(j)]
ten1 = [Tensor([i, j], 'f')]
ops1 = [FOperator(i, True), FOperator(j, False)]
t1 = Term(1.0, sum1, ten1, ops1, [])
sum2 = [Sigma(a), Sigma(b)]
ten2 = [Tensor([a, b], 'f')]
ops2 = [FOperator(a, True), FOperator(b, False)]
t2 = Term(1.0, sum2, ten2, ops2, [])
sum3 = sum2 + sum1
ten3 = ten1 + ten2
ops3 = ops1 + ops2
ref = Term(1.0, sum3, ten3, ops3, [])
out = t1 * t2
self.assertTrue(ref == out)
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_valid_contraction(self):
i = Idx(0, "occ")
j = Idx(1, "occ")
a = Idx(0, "vir")
b = Idx(1, "vir")
O1 = FOperator(i, False)
O2 = FOperator(j, True)
O3 = FOperator(a, False)
O4 = FOperator(b, True)
self.assertTrue(valid_contraction(O2, O1))
self.assertTrue(not valid_contraction(O1, O2))
self.assertTrue(valid_contraction(O3, O4))
self.assertTrue(not valid_contraction(O4, O3))
self.assertTrue(not valid_contraction(O1, O3))
x = Idx(0, "nm", fermion=False)
y = Idx(1, "nm", fermion=False)
Ob1 = BOperator(x, False)
Ob2 = BOperator(y, True)
self.assertTrue(not valid_contraction(Ob2, Ob1))
self.assertTrue(valid_contraction(Ob1, Ob2))
self.assertTrue(not valid_contraction(Ob2, O1))
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_dagger(self):
i = Idx(0, "occ")
O1 = FOperator(i, False)
O2 = FOperator(i, True)
self.assertTrue(O1.dagger() == O2)
self.assertTrue(O2.dagger() == O1)
x = Idx(0, "nm", fermion=False)
Ob1 = BOperator(x, False)
Ob2 = BOperator(x, True)
self.assertTrue(Ob1.dagger() == Ob2)
self.assertTrue(Ob2.dagger() == Ob1)
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_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)
def test_mul2(self):
s = 1.0
i = Idx(0, "occ")
j = Idx(1, "occ")
sums = [Sigma(i), Sigma(j)]
tensors = [Tensor([i, j], 'f')]
operators = [FOperator(i, True), FOperator(j, False)]
t1 = Term(s, sums, tensors, operators, [])
t3 = t1 * t1
k = Idx(2, "occ")
l = Idx(3, "occ")
sums = [Sigma(i), Sigma(j), Sigma(k), Sigma(l)]
tensors = [Tensor([i, j], 'f'), Tensor([k, l], 'f')]
operators = [
FOperator(i, True),
FOperator(j, False),
FOperator(k, True),
FOperator(l, False)
]
ttest = Term(s, sums, tensors, operators, [])
self.assertTrue(t3 == ttest)
i = Idx(0, "occ")
a = Idx(0, "vir")
j = Idx(1, "occ")
b = Idx(1, "vir")
T1 = E1("t", ["occ"], ["vir"])
T2 = E2("t", ["occ"], ["vir"])
T = T1 + T2
L1 = E1("L", ["vir"], ["occ"])
L2 = E2("L", ["vir"], ["occ"])
L = L1 + L2
# ov block
operators = [FOperator(a, True), FOperator(i, False)]
pvo = Expression([Term(1, [], [Tensor([i, a], "")], operators, [])])
PT = commute(pvo, T)
PTT = commute(PT, T)
mid = pvo + PT + Fraction('1/2') * PTT
full = L * mid
out = apply_wick(full)
out.resolve()
final = AExpression(Ex=out)
print("P_{ov} = ")
print(final)
# vv block
operators = [FOperator(a, True), FOperator(b, False)]
pvv = Expression([Term(1, [], [Tensor([b, a], "")], operators, [])])