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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(oracle, true_volume, n, rtol):
print(n, end=' ', flush=True)
volume, samples = nsmc.volume(oracle(n), true_volume(n), n, rtol)
return samples
def average_samples_for_rtol(oracle, true_volume, rtol, trials, dimension):
for n in dimension:
yield mean_thunk(lambda: samples_for_dimension_rtol(oracle, true_volume, n, rtol), trials)
def experiment(oracle, true_volume, rtols, trials, dimension, filename):
print(filename)
for rtol in rtols:
print(f'rtol = {rtol}:', end=' ', flush=True)
samples = list(average_samples_for_rtol(oracle, true_volume, 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)
oracle = lambda n: nsmc.make_uniform_extent_oracle(0, 1)
true_volume = lambda n: nsmc.uniform_true_volume(0, 1, n)
experiment(oracle, true_volume, rtols, trials, dimension, 'uniform.png')
# beta(2,2)
oracle = lambda n: nsmc.make_beta_extent_oracle(2, 2)
true_volume = lambda n: nsmc.beta_true_volume(2, 2, n)
experiment(oracle, true_volume, rtols, trials, dimension, 'beta.png')
# arcsine
oracle = lambda n: nsmc.make_beta_extent_oracle(0.5, 0.5)
true_volume = lambda n: nsmc.beta_true_volume(0.5, 0.5, n)
experiment(oracle, true_volume, rtols, trials, dimension, 'arcsine.png')
# cube (pretty slow for large dimensions and tight tolerances)
oracle = lambda n: nsmc.make_cube_extent_oracle(n, 1.0)
true_volume = lambda n: nsmc.cube_true_volume(n, 1.0)
dimension = linspace(10, 40, 4, dtype=int)
rtols = [0.2, 0.1]
experiment(oracle, true_volume, rtols, trials, dimension, 'cube.png')
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