def test_rms_curvature_paraboloid_uniform_2D():
n = 16
X, Y = np.mgrid[slice(0, n), slice(0, n)]
curvature = 0.1
heights = 0.5 * curvature * (X**2 + Y**2)
surf = Topography(heights, physical_sizes=(n, n), periodic=False)
# central finite differences are second order and so exact for the
# paraboloid
assert abs(
(surf.rms_curvature_from_area() - curvature) / curvature) < 1e-15
def test_rms_curvature_sinewave_2D(periodic):
precision = 5
n = 256
X, Y = np.mgrid[slice(0, n), slice(0, n)]
hm = 0.3
L = float(n)
size = (L, L)
surf = Topography(np.sin(2 * np.pi / L * X) * hm,
physical_sizes=size,
periodic=periodic)
numerical_lapl = surf.rms_laplacian()
analytical_lapl = np.sqrt((2 * np.pi / L)**4 * hm**2 / 2)
# print(numerical-analytical)
np.testing.assert_almost_equal(numerical_lapl, analytical_lapl, precision)
np.testing.assert_almost_equal(surf.rms_curvature_from_area(),
analytical_lapl / 2, precision)
def test_smooth_curved(self):
a = 1.2
b = 2.5
c = 0.1
d = 0.2
e = 0.3
f = 5.5
x = np.arange(5).reshape((1, -1))
y = np.arange(6).reshape((-1, 1))
arr = f + x * a + y * b + x * x * c + y * y * d + x * y * e
sx, sy = 3, 2.5
nx, ny = arr.shape
surf = Topography(arr, physical_sizes=(sx, sy))
surf = surf.detrend(detrend_mode='curvature')
self.assertTrue(surf.is_uniform)
self.assertAlmostEqual(surf.coeffs[0], b * nx)
self.assertAlmostEqual(surf.coeffs[1], a * ny)
self.assertAlmostEqual(surf.coeffs[2], d * (nx * nx))
self.assertAlmostEqual(surf.coeffs[3], c * (ny * ny))
self.assertAlmostEqual(surf.coeffs[4], e * (nx * ny))
self.assertAlmostEqual(surf.coeffs[5], f)
self.assertAlmostEqual(surf.rms_height_from_area(), 0.0)
self.assertAlmostEqual(surf.rms_gradient(), 0.0)
self.assertAlmostEqual(surf.rms_curvature_from_area(), 0.0)