def test_index_contraction2():
_type = (2, 1)
basis = [t, x, y, z]
dim = len(basis)
c_indices = gr.get_all_multiindices(2, 4)
ct_indices = gr.get_all_multiindices(1, 4)
dict_of_values = {(a, b): 2**a[0] * 3**a[1] * 5**b[0]
for a in c_indices for b in ct_indices}
tensor = gr.Tensor(basis, _type, dict_of_values)
contracted_tensor_1 = gr.contract_indices(tensor, 1, 0)
dict_of_values2 = {((a, ), ()):
sum([2**a * 3**r * 5**r for r in range(dim)])
for a in range(dim)}
contracted_tensor_2 = gr.Tensor(basis, (1, 0), dict_of_values2)
assert contracted_tensor_1 == contracted_tensor_2
def test_index_contraction1():
_type = (2, 2)
indices = gr.get_all_multiindices(2, 4)
dict_of_values = {(a, b): sum(a) / (sum(b) + 1)
for a in indices for b in indices}
basis = [t, x, y, z]
tensor = gr.Tensor(basis, _type, dict_of_values)
new_tensor = gr.contract_indices(tensor, 1, 0)
other_indices = gr.get_all_multiindices(1, 4)
other_dict_of_values = {(a, b): sum([(sum(a) + r) / (sum(b) + r + 1)
for r in range(4)])
for a in other_indices for b in other_indices}
other_tensor = gr.Tensor(basis, (1, 1), other_dict_of_values)
assert other_tensor == new_tensor
def test_subs_in_tensor1():
_type = (1, 1)
s = sympy.Symbol('s')
dict_of_values = {
((1, ), (0, )): s**2,
((1, ), (1, )): s**3,
((0, ), (1, )): 4
}
basis = [t, x, y, z]
tensor_1 = gr.Tensor(basis, _type, dict_of_values)
dict_of_values2 = {
((1, ), (0, )): 9,
((1, ), (1, )): 27,
((0, ), (1, )): 4
}
tensor_2 = gr.Tensor(basis, _type, dict_of_values2)
assert tensor_2 == tensor_1.subs([(s, 3)])
def test_dict_completer_for_tensor_2():
dict_of_values = {
((0, 1), 2): 1,
((2, 1), (0, )): 2,
}
basis = [t, x, y, z]
T = gr.Tensor(basis, (2, 1), dict_of_values)
assert T[(0, 1), 2] == 1 and T[(2, 1), 3] == 0
def test_wrong_dict_in_creation2():
_type = (2, 2)
basis = [t, x, y, z]
dict_of_values = {((0, 0), (1, 1)): 3, ((0, 0), (1, 4)): -1}
try:
tensor = gr.Tensor(basis, _type, dict_of_values)
except ValueError:
assert True
def test_return_value_one_multiindex():
dict_of_values = {
((0, 0, 0), ()): 1,
((0, 0, 1), ()): 2,
((0, 1, 0), ()): 3
}
basis = [t, x, y, z]
T = gr.Tensor(basis, (3, 0), dict_of_values)
assert T[0, 0, 1] == 2
def test_return_value_tensor2():
dict_of_values = {
((1, 1), (0, )): 5,
((0, 1), (0, )): -3,
((1, 0), (2, )): 8,
}
basis = [t, x, y, z]
_type = (2, 1)
tensor = gr.Tensor(basis, _type, dict_of_values)
assert tensor[(1, 1), 0] == 5
def test_change_basis1():
basis1 = [e0, e1, e2, e3]
v0, v1, v2, v3 = sympy.symbols('v_0 v_1 v_2 v_3')
basis2 = [v0, v1, v2, v3]
values = {(0, ): 2, (1, ): 3, (2, ): 1}
v = gr.Tensor(basis1, (1, 0), values)
basis_change = {e0: v0 + v1, e1: v1, e2: v1 + v3, e3: v2}
v_new_basis = v.change_basis(basis2, basis_change)
print(v_new_basis)
assert v_new_basis[(0, )] == 2
def test_different_tensors():
dict_of_values_1 = {
((1, 1), (0, )): 5,
((0, 1), (0, )): -3,
((1, 0), (2, )): 8,
}
dict_of_values_2 = {
((1, 1), (0, )): -5,
((0, 1), (0, )): -3,
((1, 0), (2, )): 8,
}
basis = [t, x, y, z]
_type = (2, 1)
tensor_1 = gr.Tensor(basis, _type, dict_of_values_1)
tensor_2 = gr.Tensor(basis, _type, dict_of_values_2)
assert tensor_1 != tensor_2
def test_dict_completer_for_tensor_1():
dict_of_values = {
(1, (0, 1)): 1,
((2, ), (0, 1)): 2,
(0, (1, 1)): 3,
(3, (0, 0)): 4
}
basis = [t, x, y, z]
T = gr.Tensor(basis, (1, 2), dict_of_values)
assert T[3, (0, 0)] == 4 and T[(2, ), (0, 1)] == 2 and T[3, (0, 1)] == 0
def test_change_coordinates1():
basis1 = [x, y]
r, theta = sympy.symbols('r \\theta')
basis2 = [r, theta]
values = {(0, 0): 1, (1, 1): 1}
v = gr.Tensor(basis1, (0, 2), values)
basis_change = {x: r * sympy.cos(theta), y: r * sympy.sin(theta)}
v_new_basis = v.change_coordinates(basis2, basis_change).simplify()
print(v_new_basis)
assert v_new_basis[(1, 1)] == r**2
def test_lower_index1():
_type = (2, 1)
basis = [t, x, y, z]
dim = len(basis)
c_indices = gr.get_all_multiindices(2, 4)
ct_indices = gr.get_all_multiindices(1, 4)
dict_of_values = {(a, b): 2**a[0] * 3**a[1] * 5**b[0]
for a in c_indices for b in ct_indices}
tensor = gr.Tensor(basis, _type, dict_of_values)
metric = gr.get_tensor_from_matrix(sympy.diag(-1, 1, 1, 1), basis)
lowered_tensor_1 = gr.lower_index(tensor, metric, 1)
_type2 = (1, 2)
ct_indices_2 = gr.get_all_multiindices(1, 4)
c_indices_2 = gr.get_all_multiindices(2, 4)
dict_of_values_2 = {(a, b): sum(
[metric[(), (r, b[0])] * tensor[(a[0], r), b[1]] for r in range(dim)])
for a in ct_indices_2 for b in c_indices_2}
lowered_tensor_2 = gr.Tensor(basis, _type2, dict_of_values_2)
assert lowered_tensor_1 == lowered_tensor_2
def test_raise_index1():
_type = (2, 1)
basis = [t, x, y, z]
dim = len(basis)
c_indices = gr.get_all_multiindices(2, 4)
ct_indices = gr.get_all_multiindices(1, 4)
dict_of_values = {(a, b): 2**a[0] * 3**a[1] * 5**b[0]
for a in c_indices for b in ct_indices}
tensor = gr.Tensor(basis, _type, dict_of_values)
metric = gr.get_tensor_from_matrix(sympy.diag(-1, 1, 1, 1), basis)
raised_tensor_1 = gr.raise_index(tensor, metric, 0)
inv_metric = gr.get_matrix_from_tensor(metric).inv()
_type2 = (3, 0)
c_indices_2 = gr.get_all_multiindices(3, 4)
ct_indices_2 = gr.get_all_multiindices(0, 4)
dict_of_values_2 = {(a, b): sum(
[inv_metric[r, a[2]] * tensor[(a[0], a[1]), r] for r in range(dim)])
for a in c_indices_2 for b in ct_indices_2}
raised_tensor_2 = gr.Tensor(basis, _type2, dict_of_values_2)
assert raised_tensor_1 == raised_tensor_2
def test_return_value_tensor():
dict_of_values = {
((), (0, 0)): -1,
((), (1, 1)): 1,
((), (2, 2)): 1,
((), (3, 3)): 1
}
basis = [t, x, y, z]
_type = (0, 2)
metric = gr.Tensor(basis, _type, dict_of_values)
assert metric[(),
(0, 0)] == -1 and metric[(),
(1, 2)] == 0 and metric[2, 2] == 1
def test_error_with_wrong_key():
dict_of_values = {
((1, 1), (0, )): 5,
((0, 1), (0, )): -3,
((1, 0), (2, )): 8,
}
basis = [t, x, y, z]
_type = (2, 1)
tensor = gr.Tensor(basis, _type, dict_of_values)
try:
assert tensor[(1, 1), (1, 1)] == 5
except KeyError:
assert True
def test_scalar_curvature_Schwarzschild():
t, r, theta, phi = sympy.symbols('t r \\theta \\phi')
Rs = sympy.Symbol('R_s')
basis = [t, r, theta, phi]
values = {
(0, 0): -(1 - Rs / r),
(1, 1): 1 / (1 - Rs / r),
(2, 2): r**2,
(3, 3): r**2 * sympy.sin(theta)**2
}
g = gr.Tensor(basis, (0, 2), values)
cs = gr.get_chrisoffel_symbols_from_metric(g)
R = gr.get_scalar_curvature(cs, g)
assert R[(), ()] == 0
def test_return_value_one_one_tensor():
dict_of_values = {((1, ), (0, )): 1, ((0, ), (1, )): 2, ((1, ), (1, )): 3}
basis = [t, x, y, z]
T = gr.Tensor(basis, (1, 1), dict_of_values)
assert T[1, 0] == 1 and T[2, 2] == 0
def test_dict_completer_for_tensor_3():
dict_of_values = {(0, 0): -1, (1, 1): 1, (2, 2): 1, (3, 3): 1}
basis = [t, x, y, z]
T = gr.Tensor(basis, (0, 2), dict_of_values)
assert T[(0, 0)] == -1 and T[(1, 2)] == 0
