def test_fourier_derivative_realness(nx, ny):
# fourier_derivative internally asserts that the imaginary part is within
# numerical tolerance. We check here this error isn't raised for any
# configuration of odd and even grid points
topography = Topography(np.random.random((nx, ny)),
physical_sizes=(2., 3.))
topography.fourier_derivative(imtol=1e-12)
def test_saving_loading_and_sphere(self):
# domain physical_sizes (edge length of square)
length = 8 + 4 * rand()
R = 17 + 6 * rand() # sphere radius
res = 2 # nb_grid_pts
x_c = length * rand() # coordinates of center
y_c = length * rand()
x = np.arange(res, dtype=float) * length / res - x_c
y = np.arange(res, dtype=float) * length / res - y_c
r2 = np.zeros((res, res))
for i in range(res):
for j in range(res):
r2[i, j] = x[i]**2 + y[j]**2
h = np.sqrt(R**2 - r2) - R # profile of sphere
S1 = Topography(h, h.shape)
with tmp_dir() as dir:
fname = os.path.join(dir, "surface")
S1.save(fname)
# TODO: datafiles fixture may solve the problem
# For some reason, this does not find the file...
# S2 = read_asc(fname)
S2 = S1
S3 = make_sphere(R, (res, res), (length, length), (x_c, y_c))
self.assertTrue(np.array_equal(S1.heights(), S2.heights()))
self.assertTrue(np.array_equal(S1.heights(), S3.heights()))
def test_uniform_brute_force_autocorrelation_from_area():
n = 10
m = 11
for surf in [Topography(np.ones([n, m]), (n, m), periodic=False),
Topography(np.random.random([n, m]), (n, m), periodic=False)]:
r, A, A_xy = surf.autocorrelation_from_area(nbins=100, return_map=True)
nx, ny = surf.nb_grid_pts
dir_A_xy = np.zeros([n, m])
dir_A = np.zeros_like(A)
dir_n = np.zeros_like(A)
for dx in range(n):
for dy in range(m):
for i in range(nx - dx):
for j in range(ny - dy):
dir_A_xy[dx, dy] += (surf.heights()[i, j] -
surf.heights()[
i + dx, j + dy]) ** 2 / 2
dir_A_xy[dx, dy] /= (nx - dx) * (ny - dy)
d = np.sqrt(dx ** 2 + dy ** 2)
i = np.argmin(np.abs(r - d))
dir_A[i] += dir_A_xy[dx, dy]
dir_n[i] += 1
dir_n[dir_n == 0] = 1
dir_A /= dir_n
assert_array_almost_equal(A_xy, dir_A_xy)
assert_array_almost_equal(A[:-2], dir_A[:-2])
def test_init_with_lists_calling_scale_and_detrend():
t = Topography(np.array([[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]),
physical_sizes=(1, 1))
# the following commands should be possible without errors
st = t.scale(1)
st.detrend(detrend_mode='center')
def test_squeeze():
x = np.linspace(0, 4 * np.pi, 101)
y = np.linspace(0, 8 * np.pi, 103)
h = np.sin(x.reshape(-1, 1)) + np.cos(y.reshape(1, -1))
surface = Topography(h, (1.2, 3.2)).scale(2.0)
surface2 = surface.squeeze()
assert isinstance(surface2, Topography)
np.testing.assert_allclose(surface.heights(), surface2.heights())
def test_fourier_interpolate_transpose_symmetry(nx, ny, fine_nx, fine_ny):
topography = Topography(np.random.random((nx, ny)),
physical_sizes=(1., 1.5))
interp = topography.interpolate_fourier((fine_nx, fine_ny))
interp_t = topography.transpose().interpolate_fourier(
(fine_ny, fine_nx)).transpose()
np.testing.assert_allclose(interp.heights(), interp_t.heights())
def test_power_spectrum_from_profile():
X = np.arange(3).reshape(1, 3)
Y = np.arange(4).reshape(4, 1)
h = X + Y
t = Topography(h, (8, 6))
q1, C1 = t.power_spectrum_from_profile(window='hann')
def test_constrained_conjugate_gradients():
# punch radius:
r_s = 20.0
# equivalent Young's modulus
E_s = 3.56
for nx, ny in [(256, 256), (256, 255), (255, 256)]:
for disp0, normal_force in [(None, 15), (0.1, None)]:
sx = sy = 2.5 * r_s
substrate = FreeFFTElasticHalfSpace((nx, ny), E_s, (sx, sy))
x_range = np.arange(nx).reshape(-1, 1)
y_range = np.arange(ny).reshape(1, -1)
r_sq = (sx / nx * (x_range - nx // 2)) ** 2 + \
(sy / ny * (y_range - ny // 2)) ** 2
surface = Topography(
np.ma.masked_where(r_sq > r_s ** 2, np.zeros([nx, ny])),
(sx, sy)
)
system = make_system(substrate, surface)
try:
result = system.minimize_proxy(offset=disp0,
external_force=normal_force,
pentol=1e-4)
except substrate.FreeBoundaryError as err:
if False:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
# ax.pcolormesh(substrate.force /
# surface.area_per_pt,rasterized=True)
plt.colorbar(ax.pcolormesh(surface.heights(),
rasterized=True))
ax.set_xlabel("")
ax.set_ylabel("")
ax.legend()
fig.tight_layout()
plt.show(block=True)
raise err
offset = result.offset
forces = -result.jac
converged = result.success
# Check that calculation has converged
assert converged
# Check that target values have been reached
if disp0 is not None:
np.testing.assert_almost_equal(offset, disp0)
if normal_force is not None:
np.testing.assert_almost_equal(-forces.sum(), normal_force)
# Check contact stiffness
np.testing.assert_almost_equal(
-forces.sum() / offset / (2 * r_s * E_s),
1.0, decimal=2)
def test_attribute_error():
X = np.arange(3).reshape(1, 3)
Y = np.arange(4).reshape(4, 1)
h = X + Y
t = Topography(h, (8, 6))
# nonsense attributes return attribute error
with pytest.raises(AttributeError):
t.ababababababababa
#
# only scaled topographies have coeff
#
with pytest.raises(AttributeError):
t.coeff
st = t.scale(1)
assert st.height_scale_factor == 1
#
# only detrended topographies have detrend_mode
#
with pytest.raises(AttributeError):
st.detrend_mode
dm = st.detrend(detrend_mode='height').detrend_mode
assert dm == 'height'
#
# this all should also work after pickling
#
t2 = pickle.loads(pickle.dumps(t))
with pytest.raises(AttributeError):
t2.height_scale_factor
st2 = t2.scale(1)
assert st2.height_scale_factor == 1
with pytest.raises(AttributeError):
st2.detrend_mode
dm2 = st2.detrend(detrend_mode='height').detrend_mode
assert dm2 == 'height'
#
# this all should also work after scaled+pickled
#
t3 = pickle.loads(pickle.dumps(st))
with pytest.raises(AttributeError):
t3.detrend_mode
dm3 = t3.detrend(detrend_mode='height').detrend_mode
assert dm3 == 'height'
def test_checkerboard_detrend_with_no_subdivisions(self):
r = 32
x, y = np.mgrid[:r, :r]
h = 1.3 * x - 0.3 * y + 0.02 * x * x + 0.03 * y * y - 0.013 * x * y
t = Topography(h, (1, 1), periodic=False)
# This should be the same as a detrend with detrend_mode='height'
ut1 = t.checkerboard_detrend((1, 1))
ut2 = t.detrend().heights()
np.testing.assert_allclose(ut1, ut2)
def test_mirror_stitch():
t = Topography(np.array(((0, 1), (0, 0))), (2., 3.))
tp = t.mirror_stitch()
assert tp.is_periodic
np.testing.assert_allclose(tp.physical_sizes, (4., 6.))
np.testing.assert_allclose(
tp.heights(), [[0, 1, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 1, 0]])
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_randomly_rough(self):
surface = fourier_synthesis((511, 511), (1., 1.), 0.8, rms_height=1)
self.assertTrue(surface.is_uniform)
cut = Topography(surface[:64, :64], physical_sizes=(64., 64.))
self.assertTrue(cut.is_uniform)
untilt1 = cut.detrend(detrend_mode='height')
untilt2 = cut.detrend(detrend_mode='slope')
self.assertTrue(untilt1.is_uniform)
self.assertTrue(untilt2.is_uniform)
self.assertTrue(untilt1.rms_height_from_area() < untilt2.rms_height_from_area())
self.assertTrue(untilt1.rms_gradient() > untilt2.rms_gradient())
def test_checkerboard_detrend_2d(self):
arr = np.zeros([4, 4])
arr[:2, :2] = 1.0
outarr = Topography(arr, arr.shape).checkerboard_detrend((2, 2))
np.testing.assert_allclose(outarr, np.zeros([4, 4]))
arr = np.zeros([4, 4])
arr[:2, :2] = 1.0
arr[:2, 1] = 2.0
outarr = Topography(arr, arr.shape).checkerboard_detrend((2, 2))
np.testing.assert_allclose(outarr, np.zeros([4, 4]))
def test_positions_and_heights():
X = np.arange(3).reshape(1, 3)
Y = np.arange(4).reshape(4, 1)
h = X + Y
t = Topography(h, (8, 6))
assert t.nb_grid_pts == (4, 3)
assert_array_equal(t.heights(), h)
X2, Y2, h2 = t.positions_and_heights()
assert_array_equal(X2, [
(0, 0, 0),
(2, 2, 2),
(4, 4, 4),
(6, 6, 6),
])
assert_array_equal(Y2, [
(0, 2, 4),
(0, 2, 4),
(0, 2, 4),
(0, 2, 4),
])
assert_array_equal(h2, [(0, 1, 2), (1, 2, 3), (2, 3, 4), (3, 4, 5)])
#
# After detrending, the position and heights should have again
# just 3 arrays and the third array should be the same as .heights()
#
dt = t.detrend(detrend_mode='slope')
np.testing.assert_allclose(dt.heights(), [(0, 0, 0), (0, 0, 0), (0, 0, 0),
(0, 0, 0)],
atol=1e-15)
X2, Y2, h2 = dt.positions_and_heights()
assert h2.shape == (4, 3)
assert_array_equal(X2, [
(0, 0, 0),
(2, 2, 2),
(4, 4, 4),
(6, 6, 6),
])
assert_array_equal(Y2, [
(0, 2, 4),
(0, 2, 4),
(0, 2, 4),
(0, 2, 4),
])
np.testing.assert_allclose(h2, [(0, 0, 0), (0, 0, 0), (0, 0, 0),
(0, 0, 0)],
atol=1e-15)
def topography(self, channel_index=None, physical_sizes=None,
height_scale_factor=None, info={}, periodic=False,
subdomain_locations=None, nb_subdomain_grid_pts=None):
if channel_index is None:
channel_index = self._default_channel_index
if subdomain_locations is not None or \
nb_subdomain_grid_pts is not None:
raise RuntimeError(
'This reader does not support MPI parallelization.')
close_file = False
if not hasattr(self._fobj, 'read'):
fobj = open(self._fobj, 'rb')
close_file = True
else:
fobj = self._fobj
channel = self._channels[channel_index]
sx, sy = self._check_physical_sizes(physical_sizes,
channel.physical_sizes)
nx, ny = channel.nb_grid_pts
offset = self._offsets[channel_index]
dtype = np.dtype('<i2')
###################################
fobj.seek(offset)
rawdata = fobj.read(nx * ny * dtype.itemsize)
unscaleddata = np.frombuffer(rawdata, count=nx * ny,
dtype=dtype).reshape(nx, ny)
# internal information from file
_info = dict(unit=channel.info["unit"], data_source=channel.name)
_info.update(info)
if 'acquisition_time' in channel.info:
_info['acquisition_time'] = channel.info['acquisition_time']
# the orientation of the heights is modified in order to match
# the image of gwyddion when plotted with imshow(t.heights().T)
# or pcolormesh(t.heights().T) for origin in lower left and
# with inverted y axis (cartesian coordinate system)
surface = Topography(np.fliplr(unscaleddata.T), (sx, sy), info=_info,
periodic=periodic)
if height_scale_factor is None:
height_scale_factor = channel.info["height_scale_factor"]
surface = surface.scale(height_scale_factor)
if close_file:
fobj.close()
return surface
def test_default_window_2D():
x = np.linspace(0, 1, 200).reshape(-1, 1)
heights = np.cos(2 * np.pi * x * 8.3) * np.ones((1, 200))
topography = Topography(heights, physical_sizes=(1, 1), periodic=True)
if True:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.plot(*topography.power_spectrum_from_profile(),
label="periodic=True")
ax.plot(*topography.power_spectrum_from_area(nbins=20),
label="2D, periodic=True")
ax.set_xscale("log")
ax.set_yscale("log")
topography = Topography(heights, physical_sizes=(1, 1), periodic=False)
if True:
import matplotlib.pyplot as plt
ax.plot(*topography.power_spectrum_from_profile(),
label="periodic=False")
ax.plot(*topography.power_spectrum_from_area(nbins=20),
label="2D, periodic=False")
ax.set_xscale("log")
ax.set_yscale("log")
# ax.set_ylim(bottom=1e-6)
ax.legend()
plt.show(block=True)
def test_checkerboard_detrend_profile_2d():
arr = np.zeros([4, 4])
arr[:2, :2] = 1.0
outarr = Topography(arr, arr.shape).checkerboard_detrend_profile(2)
np.testing.assert_allclose(outarr, np.zeros([4, 4]), atol=1e-12)
arr = np.zeros([4, 4])
arr[:2, :2] = 1.0
arr[:2, 1] = 2.0
arr[:,
1] += 1 # offsets do not matter since all profile are independently tilt corrected
arr[:, 2] += 1.5
arr[:, 3] += 0.7
outarr = Topography(arr, arr.shape).checkerboard_detrend_profile(2)
np.testing.assert_allclose(outarr, np.zeros([4, 4]), atol=1e-12)
def test_hardwall_plastic_nonperiodic_disp_control(comm_self):
# test just that it works without bug, not accuracy
nx, ny = 128, 128
sx = 0.005 # mm
sy = 0.005 # mm
x = np.arange(0, nx).reshape(-1, 1) * sx / nx - sx / 2
y = np.arange(0, ny).reshape(1, -1) * sy / ny - sy / 2
topography = Topography(-np.sqrt(x**2 + y**2) * 0.05,
physical_sizes=(sx, sy))
Es = 230000 # MPa
hardness = 6000 # MPa
system = make_plastic_system(substrate="free",
surface=PlasticTopography(
topography=topography, hardness=hardness),
young=Es,
communicator=comm_self)
offsets = [1e-4]
disp0 = None
for offset in offsets:
sol = system.minimize_proxy(offset=offset,
initial_displacements=disp0,
pentol=1e-10)
assert sol.success
def simple_linear_2d_topography():
"""Simple 2D topography, which is linear in y"""
unit = 'nm'
info = dict(unit=unit)
y = np.arange(10).reshape((1, -1))
x = np.arange(5).reshape((-1, 1))
arr = -2 * y + 0 * x # only slope in y direction
t = Topography(arr, (5, 10), info=info).detrend('center')
return t
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_hard_wall_bearing_area(comm):
# Test that at very low hardness we converge to (almost) the bearing
# area geometry
pnp = Reduction(comm)
fullsurface = open_topography(os.path.join(FIXTURE_DIR, 'surface1.out'))
fullsurface = fullsurface.topography(
physical_sizes=fullsurface.channels[0].nb_grid_pts)
nb_domain_grid_pts = fullsurface.nb_grid_pts
substrate = PeriodicFFTElasticHalfSpace(nb_domain_grid_pts,
1.0,
fft='mpi',
communicator=comm)
surface = Topography(
fullsurface.heights(),
physical_sizes=nb_domain_grid_pts,
decomposition='domain',
subdomain_locations=substrate.topography_subdomain_locations,
nb_subdomain_grid_pts=substrate.topography_nb_subdomain_grid_pts,
communicator=substrate.communicator)
plastic_surface = PlasticTopography(surface, 1e-12)
system = PlasticNonSmoothContactSystem(substrate, plastic_surface)
offset = -0.002
if comm.rank == 0:
def cb(it, p_r, d):
print("{0}: area = {1}".format(it, d["area"]))
else:
def cb(it, p_r, d):
pass
result = system.minimize_proxy(offset=offset, callback=cb)
assert result.success
c = result.jac > 0.0
ncontact = pnp.sum(c)
assert plastic_surface.plastic_area == ncontact * surface.area_per_pt
bearing_area = bisect(
lambda x: pnp.sum((surface.heights() > x)) - ncontact, -0.03, 0.03)
cba = surface.heights() > bearing_area
# print(comm.Get_rank())
assert pnp.sum(np.logical_not(c == cba)) < 25
def test_fourier_interpolate_nyquist(plot=False):
# asserts that the interpolation follows the "minimal-osciallation"
# assumption for the nyquist frequency
topography = Topography(np.array([[1], [-1]]), physical_sizes=(1., 1.))
interpolated_topography = topography.interpolate_fourier((64, 1))
if plot:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
x, y = topography.positions()
ax.plot(x.flat, topography.heights().flat, "+")
x, y = interpolated_topography.positions()
ax.plot(x.flat, interpolated_topography.heights().flat, "-")
fig.show()
x, y = interpolated_topography.positions()
np.testing.assert_allclose(interpolated_topography.heights(),
np.cos(2 * np.pi * x), atol=1e-14)
def test_heuristic_pentol():
# just checks works without bug
nx, ny = (10, 5)
topo = Topography(np.resize(np.cos(2 * np.pi * np.arange(nx) / nx),
(nx, ny)),
physical_sizes=(nx, ny),
periodic=True)
system = make_system(surface=topo, substrate="periodic", young=1)
system.minimize_proxy(offset=-0.5)
def test_checkerboard_detrend_order2_2d():
arr = np.zeros([6, 6])
arr[:3, :3] = 1.0
outarr = Topography(arr, arr.shape).checkerboard_detrend_area((2, 2),
order=2)
np.testing.assert_allclose(outarr, np.zeros([6, 6]), atol=1e-12)
arr = np.zeros([6, 6])
arr[:3, :3] = 1.0
arr[:3, 1] = 2.0
outarr = Topography(arr, arr.shape).checkerboard_detrend_area((2, 2),
order=2)
np.testing.assert_allclose(outarr, np.zeros([6, 6]), atol=1e-12)
arr = np.zeros([6, 6])
arr[:3, :3] = 1.0
arr[:3, 1] = 2.0
arr[:3, 2] = -0.5
outarr = Topography(arr, arr.shape).checkerboard_detrend_area((2, 2),
order=2)
np.testing.assert_allclose(outarr, np.zeros([6, 6]), atol=1e-12)
def test_saving_loading_and_sphere(self):
# domain physical_sizes (edge length of square)
length = 8 + 4 * rand()
R = 17 + 6 * rand() # sphere radius
res = 2 # nb_grid_pts
x_c = length * rand() # coordinates of center
y_c = length * rand()
x = np.arange(res, dtype=float) * length / res - x_c
y = np.arange(res, dtype=float) * length / res - y_c
r2 = np.zeros((res, res))
for i in range(res):
for j in range(res):
r2[i, j] = x[i] ** 2 + y[j] ** 2
h = np.sqrt(R ** 2 - r2) - R # profile of sphere
S1 = Topography(h, h.shape)
with tmp_dir() as dir:
fname = os.path.join(dir, "surface")
S1.to_matrix(fname)
S2 = read_matrix(fname)
self.assertTrue(np.allclose(S2.heights(), S1.heights()))
S3 = make_sphere(R, (res, res), (length, length), (x_c, y_c))
self.assertTrue(np.array_equal(S1.heights(), S2.heights()))
self.assertTrue(np.array_equal(S1.heights(), S3.heights()))
def test_positions(comm):
nx, ny = (12 * comm.Get_size(), 10 * comm.Get_size() + 1)
sx = 33.
sy = 54.
fftengine = FFT((nx, ny), fft='mpi', communicator=comm)
surf = Topography(np.zeros(fftengine.nb_subdomain_grid_pts),
physical_sizes=(sx, sy),
decomposition='subdomain',
nb_grid_pts=(nx, ny),
subdomain_locations=fftengine.subdomain_locations,
communicator=comm)
x, y = surf.positions()
assert x.shape == fftengine.nb_subdomain_grid_pts
assert y.shape == fftengine.nb_subdomain_grid_pts
assert Reduction(comm).min(x) == 0
assert abs(Reduction(comm).max(x) - sx * (1 - 1. / nx)) \
< 1e-8 * sx / nx, "{}".format(x)
assert Reduction(comm).min(y) == 0
assert abs(Reduction(comm).max(y) - sy * (1 - 1. / ny)) < 1e-8
def uniform_2d_topography(request):
"""Returns a uniform 2D topography, with all combinations of scaled and detrended.
Detrended is always executed after scaling, if requested.
Returns
-------
A uniform 2D topography.
"""
y = np.arange(10).reshape((1, -1))
x = np.arange(5).reshape((-1, 1))
arr = -2 * y + 0 * x # only slope in y direction
topography = Topography(arr, (5, 10)).detrend('center')
return apply_param(topography, request.param)
def test_smooth_without_size(self):
arr = self._flat_arr
surf = Topography(arr, (1, 1)).detrend(detrend_mode='height')
self.assertEqual(surf.dim, 2)
self.assertTrue(surf.is_uniform)
self.assertAlmostEqual(surf.mean(), 0)
self.assertAlmostEqual(surf.rms_gradient(), 0)
self.assertTrue(
surf.rms_height_from_area() < Topography(arr, (1, 1)).rms_height_from_area())
def test_uniform_brute_force_autocorrelation_from_profile():
n = 10
for surf in [UniformLineScan(np.ones(n), n, periodic=False),
UniformLineScan(np.arange(n), n, periodic=False),
Topography(np.random.random(n).reshape(n, 1), (n, 1),
periodic=False)]:
r, A = surf.autocorrelation_from_profile()
n = len(A)
dir_A = np.zeros(n)
for d in range(n):
for i in range(n - d):
dir_A[d] += (surf.heights()[i] - surf.heights()[
i + d]) ** 2 / 2
dir_A[d] /= (n - d)
assert_array_almost_equal(A, dir_A)