## Example programs for 2D histograms

This program demonstrates two features of two-dimensional histograms. First a 10 by 10 2d-histogram is created with x and y running from 0 to 1. Then a few sample points are added to the histogram, at (0.3,0.3) with a height of 1, at (0.8,0.1) with a height of 5 and at (0.7,0.9) with a height of 0.5. This histogram with three events is used to generate a random sample of 1000 simulated events, which are printed out.

    #include <stdio.h>
    #include <gsl/gsl_rng.h>
    #include <gsl/gsl_histogram2d.h>

    int
    main (void)
    {
      const gsl_rng_type * T;
      gsl_rng * r;

      gsl_histogram2d * h = gsl_histogram2d_alloc (10, 10);

      gsl_histogram2d_set_ranges_uniform (h,
                                          0.0, 1.0,
                                          0.0, 1.0);

      gsl_histogram2d_accumulate (h, 0.3, 0.3, 1);
      gsl_histogram2d_accumulate (h, 0.8, 0.1, 5);
      gsl_histogram2d_accumulate (h, 0.7, 0.9, 0.5);

      gsl_rng_env_setup();

      T = gsl_rng_default;
      r = gsl_rng_alloc(T);

      {
        int i;
        gsl_histogram2d_pdf * p
          = gsl_histogram2d_pdf_alloc (h->nx, h->ny);

        gsl_histogram2d_pdf_init (p, h);

        for (i = 0; i < 1000; i++) {
          double x, y;
          double u = gsl_rng_uniform (r);
          double v = gsl_rng_uniform (r);

          int status
           = gsl_histogram2d_pdf_sample (p, u, v, &x, &y);

          printf("%g %g\n", x, y);
        }
      }

     return 0;
    }

The following plot shows the distribution of the simulated events. Using a higher resolution grid we can see the original underlying histogram and also the statistical fluctuations caused by the events being uniformly distributed over the area of the original bins.