Node:Example programs for 2D histograms, Previous:Resampling from 2D histograms, Up:Histograms



Example programs for 2D histograms

This program demonstrates two features of two-dimensional histograms. First a 10-by-10 two-dimensional 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);
            
           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.