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_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