# 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')