def test_smooth_flat_1d(self):
arr = self._flat_arr
a = 1.2
d = .2
arr = np.arange(5) * a + d
surf = UniformLineScan(arr, (1,)).detrend(detrend_mode='center')
self.assertTrue(surf.is_uniform)
self.assertAlmostEqual(surf.mean(), 0)
surf = UniformLineScan(arr, (1.5,)).detrend(detrend_mode='slope')
self.assertEqual(surf.dim, 1)
self.assertTrue(surf.is_uniform)
self.assertAlmostEqual(surf.mean(), 0)
self.assertAlmostEqual(surf.rms_slope_from_profile(), 0)
surf = UniformLineScan(arr, arr.shape).detrend(detrend_mode='height')
self.assertEqual(surf.dim, 1)
self.assertTrue(surf.is_uniform)
self.assertAlmostEqual(surf.mean(), 0)
self.assertAlmostEqual(surf.rms_slope_from_profile(), 0)
self.assertTrue(
surf.rms_height_from_profile() < UniformLineScan(arr, arr.shape).rms_height_from_profile())
surf2 = UniformLineScan(arr, (1,)).detrend(detrend_mode='height')
self.assertEqual(surf.dim, 1)
self.assertTrue(surf2.is_uniform)
self.assertAlmostEqual(surf2.rms_slope_from_profile(), 0)
self.assertTrue(
surf2.rms_height_from_profile() < UniformLineScan(arr, arr.shape).rms_height_from_profile())
self.assertAlmostEqual(surf.rms_height_from_profile(), surf2.rms_height_from_profile())
x, z = surf2.positions_and_heights()
self.assertAlmostEqual(np.mean(np.diff(x)),
surf2.physical_sizes[0] / surf2.nb_grid_pts[0])
def test_detrend_reduces(self):
""" tests if detrending really reduces the heights (or slope) as claimed
"""
n = 10
dx = 0.5
h = [0.82355941, -1.32205074, 0.77084813, 0.49928252, 0.57872149,
2.80200331, 0.09551251, -1.11616977,
2.07630937, -0.65408072]
t = UniformLineScan(h, dx * n)
for mode in ['height', 'curvature', 'slope']:
detrended = t.detrend(detrend_mode=mode)
self.assertAlmostEqual(detrended.mean(), 0)
if mode == 'slope':
self.assertGreater(t.rms_slope_from_profile(),
detrended.rms_slope_from_profile(),
msg=mode)
else:
self.assertGreater(t.rms_height_from_profile(),
detrended.rms_height_from_profile(),
msg=mode)
def test_lbfgsb_1D(dx, n):
# test the 1D periodic objective is working
s = n * dx
Es = 1.
substrate = PeriodicFFTElasticHalfSpace((n,), young=Es,
physical_sizes=(s,), fft='serial')
surface = UniformLineScan(np.cos(2 * np.pi * np.arange(n) / n), (s,))
system = make_system(substrate, surface)
offset = 0.005
lbounds = np.zeros(n)
bnds = system._reshape_bounds(lbounds, )
init_gap = np.zeros(n, ) # .flatten()
disp = init_gap + surface.heights() + offset
res = optim.minimize(system.primal_objective(offset, gradient=True),
disp,
method='L-BFGS-B', jac=True,
bounds=bnds,
options=dict(gtol=1e-5 * Es * surface.rms_slope_from_profile()
* surface.area_per_pt,
ftol=0))
forces = res.jac
gap = res.x
converged = res.success
assert converged
if hasattr(res.message, "decode"):
decoded_message = res.message.decode()
else:
decoded_message = res.message
assert decoded_message == \
'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL'
x = np.arange(n) * s / n
mean_pressure = np.mean(forces) / substrate.area_per_pt
assert mean_pressure > 0
pth = mean_pressure * _pressure(
x / s,
mean_pressure=s * mean_pressure / Es)
if False:
import matplotlib.pyplot as plt
plt.figure()
# plt.plot(np.arange(n)*s/n, surface.heights())
plt.plot(x, gap + (surface.heights()[:] + offset), 'r-')
plt.plot(x, (surface.heights()[:] + offset), 'k-')
plt.figure()
plt.plot(x, forces / substrate.area_per_pt, 'k-')
plt.plot(x, pth, 'r-')
plt.show()
assert (np.allclose(
forces /
substrate.area_per_pt, pth, atol=1e-2))