def test_local_stencil_operator_multiplication(self):
x = np.linspace(0, 10, 101)
y = np.linspace(0, 10, 101)
X, Y = np.meshgrid(x, y, indexing='ij')
u = X * Y
dx = x[1] - x[0]
dy = y[1] - y[0]
d1x = FinDiff(0, dx) * FinDiff(1, dy)
stencil1 = d1x.stencil(u.shape)
du_dx = stencil1.apply_all(u)
np.testing.assert_array_almost_equal(np.ones_like(X), du_dx)
def test_local_stencil_single_axis_center_2d_compared_with_findiff(self):
n = 70
(X, Y), _, (dx, dy) = grid(2, n, -1, 1)
u = X**3 * Y**3
d4_dx2dy2 = FinDiff(1, dx, 2)
expected = d4_dx2dy2(u)
stl = d4_dx2dy2.stencil(u.shape)
actual = stl.apply_all(u)
np.testing.assert_array_almost_equal(expected, actual)
def test_local_stencil_operator_addition(self):
n = 100
(X, Y), _, (dx, dy) = grid(2, n, -1, 1)
u = X**3 + Y**3
d = FinDiff(0, dx, 2) + FinDiff(1, dy, 2)
expected = d(u)
stl = d.stencil(u.shape)
actual = stl.apply_all(u)
np.testing.assert_array_almost_equal(expected, actual)
def test_local_stencil_single_axis_center_1d(self):
x = np.linspace(0, 1, 50)
dx = x[1] - x[0]
u = x**3
d2_dx2 = FinDiff((0, dx, 2))
stl = d2_dx2.stencil(u.shape)
idx = 5
actual = stl.apply(u, idx)
d2u_dx2 = d2_dx2(u)
expected = d2u_dx2[idx]
self.assertAlmostEqual(expected, actual)
actual = stl.apply_all(u)
expected = d2u_dx2
np.testing.assert_array_almost_equal(expected, actual)