def test_product_of_scalars():
f1 = SingleVarFunctionScalar("f", "x")
f2 = SingleVarFunctionScalar("f", "y")
d = DeltaFunction("x", "y")
expr = f1 * f2.conjugate() * d
print(expr)
assert set(expr) == set([f1, f2.conjugate(), d])
def test_integrate_single_function():
f = SingleVarFunctionScalar("f", "x")
d = DeltaFunction("x", "y")
expr = f * d
res = integrate(expr, "x")
print(res)
assert res == SingleVarFunctionScalar("f", "y")
def test_integrate_same_function():
fx = SingleVarFunctionScalar("f", "x")
fy = SingleVarFunctionScalar("f", "y").conjugate()
d = DeltaFunction("x", "y")
expr = fx * fy * d
res = integrate(expr)
print(res)
assert res == 1
def test_has_variable():
fx = SingleVarFunctionScalar("f", "x")
fy = SingleVarFunctionScalar("f", "y").conjugate()
expr = fx * fy
res = integrate(expr, "x")
print(res)
assert not has_variable(res, "x")
assert has_variable(res, "y")
def test_integrate_all_vars():
f = SingleVarFunctionScalar("f", "x")
g = SingleVarFunctionScalar("g", "y").conjugate()
d = DeltaFunction("x", "y")
expr = f * g * d
res = integrate(expr)
print(res)
assert res == InnerProductFunction("f", "g")
def test_atoms_product():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
prod = 2 * a * b
print(prod)
atoms = prod.atoms()
assert set([2, a, b]) == set(atoms)
def test_atoms_sum():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
sm = 2 + a + b
print(sm)
atoms = sm.atoms()
assert set([2, a, b]) == set(atoms)
def test_atoms_nested():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
c = SingleVarFunctionScalar('c', 'x')
sm = 2 + a + (b * c)
print(sm)
atoms = sm.atoms()
assert set([2, a, b, c]) == set(atoms)
def test_sum_vars():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
c = SingleVarFunctionScalar('c', 'y')
sm = a + b + c
assert get_variables(sm) == set(['x', 'y'])
sm = replace_var(sm, 'y', 'x')
assert get_variables(sm) == set(['x'])
assert not has_variable(sm, 'y')
def test_combine_factors():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
c = SingleVarFunctionScalar('c', 'x')
prod = a * b * c
prod[0] = 2
prod[2] = 5
prod = simplify(prod)
assert prod == 10 * b
def test_sum_commutative():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
c = SingleVarFunctionScalar('c', 'x')
d = SingleVarFunctionScalar('d', 'x')
sm1 = a * b + c * d
sm2 = d * c + b * a
assert sm1 == sm2
def test_iszero_prod():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
prod = a * b
prod[1] = 1e-17
prod = simplify(prod)
assert prod == 0
assert is_zero(prod)
def test_integrate_sum():
f1 = SingleVarFunctionScalar("f", "x")
f2 = SingleVarFunctionScalar("g", "x")
d = DeltaFunction("x", "y")
expr = (f1 + f2) * d
res = integrate(expr, "x")
print(res)
assert isinstance(res, SumOfScalars)
assert set(res) == set([
SingleVarFunctionScalar("f", "y"),
SingleVarFunctionScalar("g", "y"),
])
def test_simplify():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
c = SingleVarFunctionScalar('c', 'x')
expr = (a + b) * (c + 0)
expr = expr.simplify()
print(expr)
assert isinstance(expr, SumOfScalars)
assert len(expr) == 2
print(expr[0])
assert len(expr[0]) == 2
def test_expand():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
c = SingleVarFunctionScalar('c', 'x')
d = SingleVarFunctionScalar('d', 'x')
expr = (a + b) * (c + d)
expr = simplify(expr.expand())
print(expr)
assert isinstance(expr, SumOfScalars)
assert len(expr) == 4
print(expr[0])
assert len(expr[0]) == 2
def test_sum_scalar():
a = SingleVarFunctionScalar('a', 'x')
b = SingleVarFunctionScalar('b', 'x')
c = SingleVarFunctionScalar('c', 'x')
d = SingleVarFunctionScalar('d', 'x')
sm1 = a + b
sm2 = c + d
tot = sm1 + sm2
assert len(tot) == 4
assert set(tot) == set([a, b, c, d])
tot += 2
assert len(tot) == 5
assert set(tot) == set([2, a, b, c, d])
def test_setitem():
a = SingleVarFunctionScalar('a', 'x')
sm = 2 + a
sm[1] = 1
print(sm)
sm = simplify(sm)
assert sm == 3
def get_fock_states():
"""Construct the fock states (eq. (42)-(45) in https://arxiv.org/abs/1903.09778)"""
bs0 = BaseFockState()
bsc = BaseFockState([FockOp("c", "w1")])
bsd = BaseFockState([FockOp("d", "w1")])
phi = SingleVarFunctionScalar("phi", "w1")
psi = SingleVarFunctionScalar("psi", "w1")
s0 = bs0.to_state()
f = 1 / np.sqrt(2)
sphi = f * phi * (bsc.to_state() + bsd.to_state())
spsi = f * psi * (bsc.to_state() - bsd.to_state())
bscc = BaseFockState([FockOp("c", "w1"), FockOp("c", "w2")])
bscd = BaseFockState([FockOp("c", "w1"), FockOp("d", "w2")])
bsdc = BaseFockState([FockOp("d", "w1"), FockOp("c", "w2")])
bsdd = BaseFockState([FockOp("d", "w1"), FockOp("d", "w2")])
phipsi = SingleVarFunctionScalar("phi", "w1") * SingleVarFunctionScalar(
"psi", "w2")
sphipsi = (1 / 2) * phipsi * (bscc.to_state() + bsdc.to_state() -
bscd.to_state() - bsdd.to_state())
return s0, sphi, spsi, sphipsi
def test_integrate():
f1 = SingleVarFunctionScalar("f", "x")
f2 = SingleVarFunctionScalar("f", "y")
d = DeltaFunction("x", "y")
expr = f1 * f2.conjugate() * d
res = integrate(expr, "x")
print(res)
assert set(res) == set([
SingleVarFunctionScalar("f", "y", False),
SingleVarFunctionScalar("f", "y", True),
])
def test_integrate_equal_terms():
f1 = SingleVarFunctionScalar("f", "x")
f2 = SingleVarFunctionScalar("f", "y")
f3 = f1 * f2.conjugate()
d = DeltaFunction("x", "y")
expr = (f3 + f3) * d
res = integrate(expr, "x")
print(res)
assert isinstance(res, ProductOfScalars)
assert set(res) == set([
2,
SingleVarFunctionScalar("f", "y", False),
SingleVarFunctionScalar("f", "y", True),
])