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tamaas/tests/test_surface.py
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test_surface.py
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# -*- coding: utf-8 -*-
#
# Copyright (©) 2016-2021 EPFL (École Polytechnique Fédérale de Lausanne),
# Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from __future__ import print_function, division
import numpy as np
import tamaas as tm
import pytest
import scipy.integrate as integrate
from scipy.special import jv
from numpy import pi
from scipy.interpolate import interp2d
def spectrum(r, isopowerlaw):
kl, kr, ks = isopowerlaw.q0, isopowerlaw.q1, isopowerlaw.q2
H = isopowerlaw.hurst
C = 1.
if r > ks:
return 0
elif r > kr:
return C * (r/float(kr))**(-2.*(H+1))
elif r > kl:
return C
else:
return 0
def integrate_bessel(x, spectrum, n):
return 2 * pi * integrate.quad(lambda y: y*jv(0, y*x) * spectrum(n*y),
0, np.inf, limit=200)[0]
def radial_average(field):
x = np.linspace(-1, 1, field.shape[0])
y = np.linspace(-1, 1, field.shape[1])
interpolation = interp2d(x, y, field)
n = field.shape[0] // 2
radii = np.linspace(0, 1, n)
thetas = np.linspace(0, 2 * pi, endpoint=False)
sum = np.zeros_like(radii)
for Θ in thetas:
for i, r in enumerate(radii):
sum[i] += interpolation(r * np.cos(Θ), r * np.sin(Θ))
return sum / thetas.size
integrate_bessel = np.vectorize(integrate_bessel, otypes=[tm.dtype])
@pytest.fixture(scope="module",
params=[tm.SurfaceGeneratorFilter2D,
tm.SurfaceGeneratorRandomPhase2D])
def stats(request):
iso = tm.Isopowerlaw2D()
iso.q0 = 16
iso.q1 = 32
iso.q2 = 64
iso.hurst = 0.8
N = 243
sg = request.param()
sg.spectrum = iso
sg.shape = [N, N]
analytical_stats = {
"rms_heights": iso.rmsHeights(),
"rms_slopes_spectral": iso.rmsSlopes(),
"moments": iso.moments(),
"alpha": iso.alpha()
}
stats = {k: [] for k in analytical_stats}
acf = np.zeros(sg.shape, dtype=tm.dtype)
realizations = 1000
for i in range(realizations):
sg.random_seed = i
s = sg.buildSurface()
stats['rms_heights'].append(
tm.Statistics2D.computeRMSHeights(s))
stats['rms_slopes_spectral'].append(
tm.Statistics2D.computeSpectralRMSSlope(s))
stats['moments'].append(tm.Statistics2D.computeMoments(s))
acf += tm.Statistics2D.computeAutocorrelation(s) / realizations
L = 1 * sg.spectrum.q0
n = sg.shape[0] // 2
x = np.linspace(0, L/2, n)
true_acf = (L / (2 * pi))**2 \
* integrate_bessel(x, lambda x: spectrum(x, sg.spectrum), L / (2 * pi))
return analytical_stats, stats, acf, true_acf
@pytest.mark.parametrize('key', ['rms_heights', 'rms_slopes_spectral'])
def test_statistics(stats, key):
analytical_stats, stats, _, _ = stats
mu = np.mean(stats[key])
error = np.abs(mu - analytical_stats[key]) / analytical_stats[key]
assert error < 3e-3
def test_autocorrelation(stats):
_, _, acf, true_acf = stats
acf = radial_average(np.fft.fftshift(acf))
acf_error = np.sum((acf-true_acf)**2) / np.sum(true_acf**2)
assert acf_error < 2e-3
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