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