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tamaas/tests/test_surface.py
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test_surface.py
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# -*- coding: utf-8 -*-
#
# Copyright (©) 2016-2022 EPFL (École Polytechnique Fédérale de Lausanne),
# Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
# Copyright (©) 2020-2022 Lucas Frérot
#
# 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 pytest
import numpy as np
import tamaas as tm
from numpy import pi
integrate = pytest.importorskip('scipy.integrate')
special = pytest.importorskip('scipy.special')
jv = special.jv
E = special.ellipe
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]
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):
from tamaas.utils import radial_average
_, _, acf, true_acf = stats
x, y = (np.linspace(-1, 1, acf.shape[i]) for i in range(2))
r = np.linspace(0, 1, true_acf.shape[0])
theta = np.linspace(0, 2 * np.pi, endpoint=False)
r_acf = radial_average(x, y, np.fft.fftshift(acf),
r, theta, endpoint=False)
acf_error = np.sum((r_acf - true_acf)**2) / np.sum(true_acf**2)
assert acf_error < 2e-3
def test_graph_area():
N = 100
x = np.linspace(0, 1, N, endpoint=False)
f = np.sin(2 * np.pi * x)
df = 2 * np.pi * np.cos(2 * np.pi * x)
num_area = np.sqrt(1 + df**2).mean()
area = 2 * np.sqrt(1 + 4 * np.pi**2) / np.pi * E(4 * np.pi**2 /
(1 + 4 * np.pi**2))
fourier_area = tm.Statistics1D.graphArea(f)
assert np.abs(num_area - fourier_area) / num_area < 1e-10
assert np.abs(area - fourier_area) / area < 2e-10
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