def test_vector_gradient_field():
"""test the vector gradient operator"""
grid = CartesianGrid([[0, 2 * np.pi], [0, 2 * np.pi]], [16, 16],
periodic=True)
x, y = grid.cell_coords[..., 0], grid.cell_coords[..., 1]
data = [np.cos(x) + y, np.sin(y) - x]
v = VectorField(grid, data)
t1 = v.gradient("periodic")
assert t1.data.shape == (2, 2, 16, 16)
d00 = -np.sin(x)
d10 = -np.ones(grid.shape)
d01 = np.ones(grid.shape)
d11 = np.cos(y)
t2 = Tensor2Field(grid, np.array([[d00, d01], [d10, d11]]))
np.testing.assert_allclose(t1.data[1:-1, 1:-1],
t2.data[1:-1, 1:-1],
rtol=0.1,
atol=0.1)
v.gradient("auto_periodic_neumann", out=t1)
assert t1.data.shape == (2, 2, 16, 16)
np.testing.assert_allclose(t1.data[1:-1, 1:-1],
t2.data[1:-1, 1:-1],
rtol=0.1,
atol=0.1)
def test_vector_boundary_conditions():
""" test some boundary conditions of operators of vector fields """
grid = CartesianGrid([[0, 2 * np.pi], [0, 1]], 32, periodic=False)
v_x = np.sin(grid.cell_coords[..., 0])
v_y = grid.cell_coords[..., 1]
vf = VectorField(grid, np.array([v_x, v_y]))
bc_x = [
{
"type": "derivative",
"value": [0, -1]
},
{
"type": "derivative",
"value": [0, 1]
},
]
bc_y = [{
"type": "value",
"value": [0, 0]
}, {
"type": "value",
"value": [1, 1]
}]
tf = vf.gradient(bc=[bc_x, bc_y])
np.testing.assert_allclose(tf[0, 1].data[1:-1, :], 0)
np.testing.assert_allclose(tf[1, 1].data, 1)
def test_vector_gradient_divergence_field_cyl():
"""test the divergence operator"""
grid = CylindricalSymGrid(2 * np.pi, [0, 2 * np.pi], [8, 16], periodic_z=True)
r, z = grid.cell_coords[..., 0], grid.cell_coords[..., 1]
data = [np.cos(r) + np.sin(z) ** 2, np.cos(r) ** 2 + np.sin(z), np.zeros_like(r)]
v = VectorField(grid, data=data)
t = v.gradient(bc="natural")
assert t.data.shape == (3, 3, 8, 16)
v = t.divergence(bc="natural")
assert v.data.shape == (3, 8, 16)
def test_vector_gradient():
""" test the vector gradient operator """
grid = CartesianGrid([[0, 2 * np.pi], [0, 2 * np.pi]], [16, 16],
periodic=True)
x, y = grid.cell_coords[..., 0], grid.cell_coords[..., 1]
data = [np.cos(x) + y, np.sin(y) - x]
v = VectorField(grid, data)
t1 = v.gradient("periodic")
assert t1.data.shape == (2, 2, 16, 16)
d00 = -np.sin(x)
d10 = np.ones(grid.shape)
d01 = -d10.copy()
d10[:, 0] = d10[:, -1] = -7
d01[0, :] = d01[-1, :] = 7
d11 = np.cos(y)
t2 = Tensor2Field(grid, np.array([[d00, d01], [d10, d11]]))
np.testing.assert_allclose(t1.data, t2.data, rtol=0.1, atol=0.1)
v.gradient("natural", out=t1)
assert t1.data.shape == (2, 2, 16, 16)
np.testing.assert_allclose(t1.data, t2.data, rtol=0.1, atol=0.1)
