def test_poisson_solver_polar():
""" test the poisson solver on Polar grids """
grid = PolarGrid(4, 8)
for bc_val in ["natural", {"value": 1}]:
bcs = grid.get_boundary_conditions(bc_val)
poisson = grid.get_operator("poisson_solver", bcs)
laplace = grid.get_operator("laplace", bcs)
d = np.random.random(grid.shape)
d -= ScalarField(grid, d).average # balance the right hand side
np.testing.assert_allclose(laplace(poisson(d)),
d,
err_msg=f"bcs = {bc_val}")
grid = PolarGrid([2, 4], 8)
for bc_val in ["natural", {"value": 1}]:
bcs = grid.get_boundary_conditions(bc_val)
poisson = grid.get_operator("poisson_solver", bcs)
laplace = grid.get_operator("laplace", bcs)
d = np.random.random(grid.shape)
d -= ScalarField(grid, d).average # balance the right hand side
np.testing.assert_allclose(laplace(poisson(d)),
d,
err_msg=f"bcs = {bc_val}")
def test_polar_annulus():
""" test simple polar grid with a hole """
grid = PolarGrid((2, 4), 8)
assert grid.dim == 2
assert grid.numba_type == "f8[:]"
assert grid.shape == (8, )
assert grid.has_hole
assert grid.discretization[0] == pytest.approx(0.25)
assert not grid.uniform_cell_volumes
np.testing.assert_array_equal(grid.discretization, np.array([0.25]))
assert grid.volume == pytest.approx(np.pi * (4**2 - 2**2))
assert grid.volume == pytest.approx(grid.integrate(1))
assert grid.radius == (2, 4)
np.testing.assert_allclose(grid.axes_coords[0],
np.linspace(2.125, 3.875, 8))
a = grid.get_operator("laplace", "natural")(np.random.random(8))
assert a.shape == (8, )
assert np.all(np.isfinite(a))
# random points
c = np.random.randint(8, size=(6, 1))
p = grid.cell_to_point(c)
np.testing.assert_array_equal(c, grid.point_to_cell(p))
assert grid.contains_point(grid.get_random_point())
assert grid.contains_point(grid.get_random_point(1.99))
# test boundary points
np.testing.assert_equal(grid._boundary_coordinates(0, False),
np.array([2]))
np.testing.assert_equal(grid._boundary_coordinates(0, True), np.array([4]))
def test_grid_div_grad():
""" compare div grad to laplacian for polar grids """
grid = PolarGrid(2 * np.pi, 16)
r = grid.axes_coords[0]
arr = np.cos(r)
laplace = grid.get_operator("laplace", "derivative")
grad = grid.get_operator("gradient", "derivative")
div = grid.get_operator("divergence", "value")
a = laplace(arr)
b = div(grad(arr))
res = -np.sin(r) / r - np.cos(r)
# do not test the radial boundary points
np.testing.assert_allclose(a[1:-1], res[1:-1], rtol=0.1, atol=0.1)
np.testing.assert_allclose(b[1:-1], res[1:-1], rtol=0.1, atol=0.1)
def test_polar_grid():
""" test simple polar grid """
grid = PolarGrid(4, 8)
assert grid.dim == 2
assert grid.numba_type == "f8[:]"
assert grid.shape == (8, )
assert not grid.has_hole
assert grid.discretization[0] == pytest.approx(0.5)
assert not grid.uniform_cell_volumes
np.testing.assert_array_equal(grid.discretization, np.array([0.5]))
assert grid.volume == pytest.approx(np.pi * 4**2)
assert grid.volume == pytest.approx(grid.integrate(1))
np.testing.assert_allclose(grid.axes_coords[0], np.linspace(0.25, 3.75, 8))
a = grid.get_operator("laplace", "natural")(np.random.random(8))
assert a.shape == (8, )
assert np.all(np.isfinite(a))
# random points
c = np.random.randint(8, size=(6, 1))
p = grid.cell_to_point(c)
np.testing.assert_array_equal(c, grid.point_to_cell(p))
assert grid.contains_point(grid.get_random_point())
assert grid.contains_point(grid.get_random_point(3.99))
assert "laplace" in grid.operators