1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
|
# 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 math import isclose
from numpy import linspace, zeros
import matplotlib.pyplot as plt
rtol = 0.1
eccentricity = 2
dimension = linspace(10, 100, 10, dtype=int)
oracle = lambda n: nsmc.make_spheroid_extent_oracle(n, eccentricity)
true_volume = lambda n: nsmc.spheroid_true_volume(n, eccentricity)
samples_per_cone = 1000
solid_angle_factor = 4
solid_angle_threshold_exponent_factor = 0.25
def samples_for_dimension(oracle, samples_per_cone, solid_angle_factor, solid_angle_threshold_exponent_factor, dimension):
for n in dimension:
print(n, end=' ', flush=True)
mean = zeros(n)
mean[0] = 1
vol, samples = nsmc.volume_importance(oracle(n), mean, samples_per_cone,
solid_angle_factor, solid_angle_threshold_exponent_factor)
vol = 2 * vol
print(f'{vol} {true_volume(n)} {samples}')
if not isclose(vol, true_volume(n), rel_tol=rtol):
print(f'Volume computation failed to reach tolerance {rtol} for dimension {n}')
yield samples
samples = list(samples_for_dimension(oracle, samples_per_cone, solid_angle_factor, solid_angle_threshold_exponent_factor, dimension))
plt.plot(dimension, samples, '-x')
plt.yscale('log')
plt.xlabel('Dimension')
plt.ylabel('Number of samples')
plt.savefig('spheroid.png')
plt.close()
|
