void sample_gauss_poly(poly x)
{
unsigned int j;
double gauss;
for(j=0; j<PARAM_N; j++)
{
gauss = fmodq(sample_gauss());
x[j] = gauss;
}
}
/*******************************************************************************
* gaussian_test
* This function creates a fits table, then populates it with the mean, sigma,
* and error on the mean from experiments sampling from a gaussian num_samples
* number of times.
* Input:
* fptr: Fits file to write the table to
* num_iter: Number of experiments to run
* num_samples: Number of samples for each experiment
* mean: Mean for the distibution in the experiments
* sigma: Sigma for the distribution in the experiments
* Output:
* status: Fits error status
******************************************************************************/
void gaussian_test(fitsfile *fptr, long num_iter, long num_samples, double mean,
double sigma, int *status){
long nrows, i, num_sigma;
double *stats, ratio_sigma, ave_mean, mean_sd, *all_means;
/* Fits file columns */
char *ttype[] = {"mean", "sigma", "error"};
char *tform[] = {"D", "D", "D"};
char *tunit[] = {NULL, NULL, NULL};
char *key[] = {"NSAMPLES", "MEAN", "SIGMA", "MEANAVE", "MEANSD"};
char *comment[] = {"Number of samples per iteration",
"True mean of the gaussian",
"True standard deviation of the gaussian",
"Average mean",
"Standard deviation of all means"};
/* Create the fits table */
fits_create_tbl(fptr, BINARY_TBL, 0, 3, ttype, tform, tunit, NULL, status);
if (*status){
printf("Error creating fits table in guassian_test.\n");
exit(*status);
}
/* Get mean, sigma, and error, then save to a fits file */
all_means = (double *) malloc(num_iter * sizeof(double));
ave_mean = 0;
for (nrows = 0; nrows < num_iter; nrows++){
stats = sample_gauss(num_samples, mean, sigma);
ave_mean += stats[0];
all_means[nrows] = stats[0];
/* Write to file */
for (i=0; i < 3; i++){
fits_write_col(fptr, TDOUBLE, i+1, nrows+1, 1L,1L, stats+i, status);
if (*status){
printf("Error writing to fits table in gaussian_test.\n");
exit(1);
}
}
free(stats); /* free memory for next iteration */
}
ave_mean /= num_iter;
/* Get standard deviation of all means */
mean_sd = 0;
for (i=0; i<num_iter; i++)
mean_sd += pow(ave_mean - all_means[i], 2);
mean_sd /= num_iter - 1;
mean_sd = sqrt(mean_sd);
/* Get percentage of experiments within 2 sigma */
num_sigma = 0;
for (i=0; i<num_iter; i++){
if (fabs(all_means[i] - ave_mean) < 2 * mean_sd)
num_sigma++;
}
ratio_sigma = (double) num_sigma / num_iter;
free(all_means);
/* print some results */
printf("Average mean: %g\n", ave_mean);
printf("Sigma of all means: %g\n", mean_sd);
printf("Percentage of experiments within 2 sigma: ");
printf("%g%c\n", 100 * ratio_sigma, (char) 37);
/* Write the number of samples to the fits table */
fits_write_key(fptr, TLONG, key[0], &num_samples, comment[0], status);
fits_write_key(fptr, TDOUBLE, key[1], &mean, comment[1], status);
fits_write_key(fptr, TDOUBLE, key[2], &num_sigma, comment[2], status);
fits_write_key(fptr, TDOUBLE, key[3], &ave_mean, comment[3], status);
fits_write_key(fptr, TDOUBLE, key[4], &mean_sd, comment[4], status);
if (*status){
printf("Error writing to fits header.\n");
exit(*status);
}
}
/*******************************************************************************
* gauss_stats
* This function ggenerates sampling experiments with gaussians and collects the
* statistics on them.
******************************************************************************/
int main(int argc, char **argv){
double *stats;
double mean = 0, sigma = 1;
int i, status = 0;
long num_iter;
long num_samples[5] = {5, 10, 50, 100, 1000};
/* Variables for reading in options */
int opt;
fitsfile *outfile;
char *filename;
/***************************************************************************
* Initialize random number generator using time for the seed. The RNG
* algorithm is Mersenne Twister.
**************************************************************************/
randnumgen = gsl_rng_alloc(gsl_rng_mt19937);
gsl_rng_set(randnumgen, time(NULL));
/* Parse options */
filename = NULL;
while ((opt = getopt(argc, argv, "o:")) != -1){
switch (opt){
case 'o':
filename = (char *) malloc((strlen(optarg)+2)*sizeof(char));
/* Prepend ! to filename to force overwriting it. */
filename[0] = '!';
strcat(filename, optarg);
printf("Writing output to %s.\n\n", filename + 1);
break;
case '?':
if (optopt == 'o'){
printf("Error: No output file specified.\n");
exit(1);
} else {
printf("Unknown option -%c. Exiting.\n", optopt);
exit(1);
}
break;
default:
exit(1);
}
}
if (filename == NULL){
printf("Error: No output file specified.\n");
exit(1);
}
/* Create file and generate results for it. */
fits_create_file(&outfile, filename, &status);
if (status){
printf("Error creating file %s.\n", filename + 1);
exit(status);
}
fits_open_file(&outfile, filename+1, READWRITE, &status);
if (status){
printf("Error opening file %s.\n", filename + 1);
exit(status);
}
/* Loop over number of samples */
num_iter = 1000;
for (i = 0; i < 5; i++){
stats = sample_gauss(num_samples[i], mean, sigma);
/* Print example list. */
printf("Example list for %ld number of samples.\n", num_samples[i]);
printf("Mean: %g\n", stats[0]);
printf("Standard deviation: %g\n", stats[1]);
printf("Error on the mean: %g\n", stats[2]);
printf("Expected error on the mean: %g\n", 1 / sqrt(num_samples[i]));
printf("\n");
free(stats);
/* Sample guassian and save to file */
printf("Sampling from %ld gaussians %ld times each.\n",
num_iter, num_samples[i]);
gaussian_test(outfile, num_iter, num_samples[i], mean, sigma, &status);
if (status){
printf("Error: unable to write to file.\n");
exit(status);
}
printf("\nWritten to file %s.\n\n", filename + 1);
}
printf("Closing file %s.\n\n", filename + 1);
fits_close_file(outfile, &status);
if (status){
printf("Error closing file %s.\n", filename + 1);
exit(status);
}
free(stats);
free(filename);
return 0;
}