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/*
* Copyright ©️ 2024 Mario Forzanini <mf@marioforzanini.com>
*
* This file is part of my exercises for LSN.
*
* My exercises for LSN are free software: you can redistribute them
* and/or modify them 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.
*
* My exercises for LSN are distributed in the hope that they 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 my exercises for LSN. If not, see
* <https://www.gnu.org/licenses/>.
*
*/
#include <errno.h>
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <string.h>
#include "random.h"
#include "std.h"
/* Total number of "throws" of the MonteCarlo algorithm. */
#define TOTAL 10000
/* Argument to select uniform sampling */
#define UNIFORM_NAME "UNIFORM"
/* Argument to select importance sampling */
#define IMPORTANCE_NAME "IMPORTANCE"
enum method {
METHOD_UNKNOWN,
METHOD_UNIFORM,
METHOD_IMPORTANCE,
};
const double M_PI_SQUARE = M_PI * M_PI;
#define M_PI_2 (M_PI / 2.0)
double
integrand(double x)
{
return M_PI_2 * cos(M_PI_2 * x);
}
double
d(double x)
{
return 3. / 2. * (1 - x * x);
}
double
sample(Random rnd[static 1])
{
double x, r;
do {
x = random_rannyu(rnd);
r = random_rannyu(rnd);
} while (r >= 1 - x * x);
return r;
}
void
usage(char *argv0)
{
fprintf(stderr, "USAGE: %s [UNIFORM|IMPORTANCE]\n", argv0);
exit(1);
}
/* Numbers of blocks to be tested. */
static int Ns[] = { 5, 10, 20, 50, 100, 200 };
int
main(int argc, char *argv[])
{
FILE *primes, *input;
Random rnd = { 0 };
if (!(primes = fopen("Primes", "r"))) {
STD_ERROR("Error opening Primes: %s\n", strerror(errno));
return 1;
} else if (!(input = fopen("seed.in", "r"))) {
STD_ERROR("Error opening seed.in: %s\n", strerror(errno));
return 1;
}
if (!random_init(&rnd, primes, input)) {
return 1;
}
enum method method = METHOD_UNKNOWN;
if (argc < 2) {
usage(argv[0]);
} else {
if (strcmp(argv[1], UNIFORM_NAME) == 0) {
method = METHOD_UNIFORM;
} else if (strcmp(argv[1], IMPORTANCE_NAME) == 0) {
method = METHOD_IMPORTANCE;
}
}
for (size_t i = 0; i < LEN(Ns); i++) {
int nblock = Ns[i];
int block_steps = TOTAL / nblock;
double avg = 0.0, avg2 = 0.0, sum = 0.0;
if (method == METHOD_IMPORTANCE) {
for (int block = 0; block < nblock; block++) {
for (int step = 0; step < block_steps;
step++) {
double x = sample(&rnd);
sum += integrand(x) / d(x);
}
sum /= (double)(block_steps);
avg += sum;
avg2 += sum * sum;
}
} else if (method == METHOD_UNIFORM) {
for (int block = 0; block < nblock; block++) {
for (int step = 0; step < block_steps;
step++) {
sum += integrand(random_rannyu(&rnd));
}
sum /= (double)(block_steps);
avg += sum;
avg2 += sum * sum;
}
}
avg /= (double)(nblock);
printf("%d %lf %lf\n", nblock, avg,
sqrt(avg2 / (double)(nblock)-avg * avg));
}
random_save_seed(&rnd, "seed.out");
return 0;
}
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