def test_pde_vector():
"""test PDE with a single vector field"""
eq = PDE({"u": "vector_laplace(u) + exp(-t)"})
assert eq.explicit_time_dependence
assert not eq.complex_valued
grid = grids.UnitGrid([8, 8])
field = VectorField.random_normal(grid)
res_a = eq.solve(field, t_range=1, dt=0.01, backend="numpy", tracker=None)
res_b = eq.solve(field, t_range=1, dt=0.01, backend="numba", tracker=None)
res_a.assert_field_compatible(res_b)
np.testing.assert_allclose(res_a.data, res_b.data)
def test_random_normal_types():
"""test whether random normal fields behave correctly for different types"""
grid = UnitGrid([8])
for dtype in [bool, int, float, complex]:
field = VectorField.random_normal(grid, dtype=dtype)
assert field.dtype == np.dtype(dtype)
assert isinstance(field.data.flat[0].item(), dtype)
assert ScalarField.random_normal(grid, 0, 1).dtype == np.dtype(float)
assert ScalarField.random_normal(grid, mean=0 + 0j).dtype == np.dtype(complex)
assert ScalarField.random_normal(grid, std=1 + 0j).dtype == np.dtype(complex)
assert ScalarField.random_normal(grid, 0 + 0j, 1 + 0j).dtype == np.dtype(complex)
m = complex(np.random.random(), np.random.random())
s = complex(1 + np.random.random(), 1 + np.random.random())
grid = UnitGrid([256, 256])
field = field.random_normal(grid, m, s)
assert np.mean(field.average) == pytest.approx(m, rel=0.1, abs=0.1)
assert np.std(field.data.real) == pytest.approx(s.real, rel=0.1, abs=0.1)
assert np.std(field.data.imag) == pytest.approx(s.imag, rel=0.1, abs=0.1)
def test_dot_product():
"""test dot products between vectors and tensors"""
g = UnitGrid([3, 2])
vf = VectorField.random_normal(g)
tf = Tensor2Field.random_normal(g)
v_dot = vf.make_dot_operator()
t_dot = tf.make_dot_operator()
expected = np.einsum("i...,i...->...", vf.data, vf.data)
np.testing.assert_allclose((vf @ vf).data, expected)
np.testing.assert_allclose(v_dot(vf.data, vf.data), expected)
expected = np.einsum("i...,i...->...", vf.data, tf.data)
np.testing.assert_allclose((vf @ tf).data, expected)
np.testing.assert_allclose(v_dot(vf.data, tf.data), expected)
expected = np.einsum("ji...,i...->j...", tf.data, vf.data)
np.testing.assert_allclose((tf @ vf).data, expected)
np.testing.assert_allclose(t_dot(tf.data, vf.data), expected)
expected = np.einsum("ij...,jk...->ik...", tf.data, tf.data)
np.testing.assert_allclose((tf @ tf).data, expected)
np.testing.assert_allclose(t_dot(tf.data, tf.data), expected)
