time-to-botec/C/samples/samples.c

#include <gsl/gsl_randist.h>
#include <gsl/gsl_rng.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

#define N 1000000
/* 
 * For very high values of N, you will want to increase the maximum stack trace, otherwise you will suffer a segmentation fault
 * In Ubuntu/bash you can do this with $ ulimit -Ss 256000 ## ~256Mbs
 * And confirm it with $ ulimit -a
*/

/* Helpers */
void print(double* ys)
{
    for (int i = 0; i < N; i++) {
        printf("%f\n", ys[i]);
    }
    printf("\n");
}

void fill(double* ys, float f)
{
    for (int i = 0; i < N; i++) {
        ys[i] = f;
    }
}

double sum(double* ps, int n)
{
    double result = 0;
    for (int i = 0; i < n; i++) {
        result += ps[i];
    }
    return (result);
}

void cumsum(double* ps, double* rs, int n)
{
    double counter = 0;
    for (int i = 0; i < n; i++) {
        counter += ps[i];
        rs[i] = counter;
    }
}

/* Distributions*/
void normal(gsl_rng* r, double* ys, double mean, double std)
{
    for (int i = 0; i < N; i++) {
        ys[i] = mean + gsl_ran_gaussian(r, std);
    }
}

void lognormal(gsl_rng* r, double* ys, double zeta, double sigma)
{
    for (int i = 0; i < N; i++) {
        ys[i] = gsl_ran_lognormal(r, zeta, sigma);
    }
}

void to(gsl_rng* r, double* ys, double low, double high)
{
    double normal95confidencePoint = 1.6448536269514722;
    double log_low = log(low);
    double log_high = log(high);
    double zeta = (log_low + log_high) / 2;
    double sigma = (log_high - log_low) / (2.0 * normal95confidencePoint);
    lognormal(r, ys, zeta, sigma);
}

/* Mixture of distributions */
void mixture(gsl_rng* r, double* dists[], double* weights, int n, double* results)
{
    /* Get cummulative, normalized weights */
    double sum_weights = sum(weights, n);
    double normalized_weights[n];
    for (int i = 0; i < n; i++) {
        normalized_weights[i] = weights[i] / sum_weights;
    }
    double cummulative_weights[n];
    cumsum(normalized_weights, cummulative_weights, n);

    /* Get N samples, drawn from the different distributions in proportion to their weights. */
    for (int i = 0; i < N; i++) {
        double p_1 = gsl_rng_uniform(r);
        double p_2 = gsl_rng_uniform(r);

        int index_found = 0;
        int index_counter = 0;
        while ((index_found == 0) && (index_counter < n)) {
            if (p_1 < cummulative_weights[index_counter]) {
                index_found = 1;
            } else {
                index_counter++;
            }
        }
        if (index_found == 0) {
            printf("\nThis shouldn't be able to happen");
            // gsl_rng_free (r);
            // abort(); // this shouldn't have happened.

        } else {
            int sample_index = (int)floor(p_2 * N);
            results[i] = dists[index_counter][sample_index];
        }
    }
}

/* Main */
int main(void)
{
    /* Initialize GNU Statistical Library (GSL) stuff */
    const gsl_rng_type* T;
    gsl_rng* r;
    // gsl_rng_env_setup();
    T = gsl_rng_default;
    r = gsl_rng_alloc(T);

    /* Toy example */
    /* Declare variables in play */
    double p_a, p_b, p_c;
    double dist_none[N], dist_one[N], dist_few[N], dist_many[N], dist_mixture[N];

    /* Initialize variables */
    p_a = 0.8;
    p_b = 0.5;
    p_c = p_a * p_b;

    fill(dist_none, 0);
    fill(dist_one, 1);
    to(r, dist_few, 1, 3);
    to(r, dist_many, 2, 10);

    /* Generate mixture */
    int n = 4;
    double weights[] = { 1 - p_c, p_c / 2, p_c / 4, p_c / 4 };
    double* dists[] = { dist_none, dist_one, dist_few, dist_many };

    mixture(r, dists, weights, n, dist_mixture);
    printf("%f\n", sum(dist_mixture, N) / N);

    /* Clean up GSL */
    gsl_rng_free(r);

    /* Return success*/
    return EXIT_SUCCESS;
}