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fractal_surface.py
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Sat, Nov 2, 14:14

fractal_surface.py
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#!/usr/bin/python
# -*- coding: utf-8 -*-
##*
#
# @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
#
# @section LICENSE
#
# Copyright (©) 2016 EPFL (Ecole Polytechnique Fédérale de
# Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
# Solides)
#
# Tamaas is free software: you can redistribute it and/or modify it under the
# terms of the GNU Lesser General Public License as published by the Free
# Software Foundation, either version 3 of the License, or (at your option) any
# later version.
#
# Tamaas 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 Lesser General Public License for more
# details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with Tamaas. If not, see <http://www.gnu.org/licenses/>.
#
#
################################################################
from tamaas import *
import argparse
parser = argparse.ArgumentParser()
parser.add_argument("--rescale", help="Rescale surface for RMS(slopes) = 1", action='store_true')
parser.add_argument("--N", help="Number of points", type=int, default=512)
parser.add_argument("--k0", help="Roll-off wave number", type=int, default=4)
parser.add_argument("--k1", help="Low cutoff wave number", type=int, default=4)
parser.add_argument("--k2", help="High cutoff wave number", type=int, default=32)
parser.add_argument("--rms", help="RMS(heights)", default=1.)
parser.add_argument("--H", help="Hurst exponent", default=0.8)
args = parser.parse_args()
#generate surface
SG = SurfaceGeneratorFilterFFT()
SG.getGridSize().assign(args.N)
SG.getHurst().assign(args.H)
SG.getRMS().assign(args.rms);
SG.getQ0().assign(args.k0);
SG.getQ1().assign(args.k1);
SG.getQ2().assign(args.k2);
SG.getRandomSeed().assign(156);
SG.Init()
a = SG.buildSurface()
if args.rescale:
rms_slopes = SurfaceStatistics.computeSpectralRMSSlope(a)
a /= rms_slopes
#compute and print surface statistics
class Stats:
def __getitem__(self,key):
return self.__dict__[key]
stats = Stats()
stats.size = SG.getGridSize()
stats.hurst = SG.getHurst().value()
stats.rms = SG.getRMS()
stats.k0 = SG.getQ0()
stats.k1 = SG.getQ1().value()
stats.k2 = SG.getQ2().value()
stats.seed = SG.getRandomSeed()
stats.rms_spectral = SurfaceStatistics.computeSpectralStdev(a);
stats.rms_slopes_spectral = SurfaceStatistics.computeSpectralRMSSlope(a);
stats.rms_geometric = a.std(ddof=1)
stats.rms_slopes_geometric = SurfaceStatistics.computeRMSSlope(a);
stats.moments = SurfaceStatistics.computeMoments(a);
stats.m0 = stats['rms_spectral']**2
stats.m2 = stats.moments[0]
stats.m4 = stats.moments[1]
stats.alpha = stats['m0']*stats['m4']/(stats['m2']**2)
stats.L = 1.
stats.m0prime = SurfaceStatistics.computeAnalyticFractalMoment(0,stats.k1,stats.k2,stats.hurst,1. , stats.L)
stats.moment_A = stats.m0/stats.m0prime
stats.analytic_m0 = SurfaceStatistics.computeAnalyticFractalMoment(0,stats.k1,stats.k2,stats.hurst,stats.moment_A,stats.L);
stats.analytic_m2 = SurfaceStatistics.computeAnalyticFractalMoment(2,stats.k1,stats.k2,stats.hurst,stats.moment_A,stats.L);
stats.analytic_m4 = SurfaceStatistics.computeAnalyticFractalMoment(4,stats.k1,stats.k2,stats.hurst,stats.moment_A,stats.L);
stats.analytic_alpha = stats.analytic_m0*stats.analytic_m4/(stats.analytic_m2*stats.analytic_m2);
print """
[N] {size}
[rms] {rms}
[rmsSpectral] {rms_spectral}
[rmsSlopeSpectral] {rms_slopes_spectral}
[rmsSlopeGeometric] {rms_slopes_geometric}
[Hurst] {hurst}
[k1] {k1}
[k2] {k2}
[moment A] {moment_A}
[m0] {m0}
[analytic m0] {analytic_m0}
[m2] {m2}
[analytic m2] {analytic_m2}
[m4] {m4}
[analytic m4] {analytic_m4}
[alpha] {alpha}
[analytic_alpha] {analytic_alpha}
[seed] {seed}
""".format(**stats.__dict__)
#plot the surface
b = a.real
import matplotlib.pyplot as plt
plt.imshow(b)
plt.show()

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