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# nsmc --- n-sphere Monte Carlo method
# Copyright © 2022 Arun I <arunisaac@systemreboot.net>
# Copyright © 2022 Murugesan Venkatapathi <murugesh@iisc.ac.in>
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU 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
# General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see
# <https://www.gnu.org/licenses/>.
import nsmc
from numpy import linspace
from statistics import mean
import matplotlib.pyplot as plt
def mean_thunk(f, trials):
return mean([f() for i in range(trials)])
def samples_for_dimension_rtol(integrand, oracle, true_integral, n, rtol):
print(n, end=' ', flush=True)
integral, samples = nsmc.integral(integrand, oracle, true_integral(n), n, rtol)
return samples
def average_samples_for_rtol(integrand, oracle, true_integral, rtol, trials, dimension):
for n in dimension:
yield mean_thunk(lambda: samples_for_dimension_rtol(integrand, oracle, true_integral, n, rtol), trials)
def experiment(integrand, oracle, true_integral, rtols, trials, dimension, filename):
print(filename)
for rtol in rtols:
print(f'rtol = {rtol}:', end=' ', flush=True)
samples = list(average_samples_for_rtol(integrand, oracle, true_integral, rtol, trials, dimension))
plt.plot(dimension, samples, '-x', label=f'rtol = {rtol}')
print()
plt.yscale('log')
plt.xlabel('Dimension')
plt.ylabel('Average number of samples')
plt.legend()
plt.savefig(filename)
plt.close()
# Number of trials to average each dimension, rtol point over
trials = 2
# Dimensions and relative error tolerances to plot
dimension = linspace(10, 100, 10, dtype=int)
rtols = [0.2, 0.1, 0.05]
# uniform(0,1) domain
max_extent = 1.0
oracle = nsmc.make_uniform_extent_oracle(0, max_extent)
# Gaussian integrand
integrand = nsmc.gaussian_integrand()
true_integral = lambda n: nsmc.gaussian_true_integral(n, max_extent)
experiment(integrand, oracle, true_integral, rtols, trials, dimension, 'gaussian.png')
# Polynomial integrand
coefficients = [1, -1.5, 0.6875, -0.09375]
integrand = nsmc.polynomial_integrand(coefficients)
true_integral = lambda n: nsmc.polynomial_true_integral(n, max_extent, coefficients)
experiment(integrand, oracle, true_integral, rtols, trials, dimension, 'polynomial.png')
# x-coordinate integrand
integrand = nsmc.x_coordinate_integrand()
true_integral = lambda n: nsmc.x_coordinate_true_integral(n, max_extent)
experiment(integrand, oracle, true_integral, rtols, trials, dimension, 'x-coordinate.png')
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