26.7 Examples

The following program demonstrates the use of the interpolation and spline functions. It computes a cubic spline interpolation of the 10-point dataset (x_i, y_i) where x_i = i + \sin(i)/2 and y_i = i + \cos(i^2) for i = 0 \dots 9.

     #include <stdlib.h>
     #include <stdio.h>
     #include <math.h>
     #include <gsl/gsl_errno.h>
     #include <gsl/gsl_spline.h>
     
     int
     main (void)
     {
       int i;
       double xi, yi, x[10], y[10];
     
       printf ("#m=0,S=2\n");
     
       for (i = 0; i < 10; i++)
         {
           x[i] = i + 0.5 * sin (i);
           y[i] = i + cos (i * i);
           printf ("%g %g\n", x[i], y[i]);
         }
     
       printf ("#m=1,S=0\n");
     
       {
         gsl_interp_accel *acc 
           = gsl_interp_accel_alloc ();
         gsl_spline *spline 
           = gsl_spline_alloc (gsl_interp_cspline, 10);
     
         gsl_spline_init (spline, x, y, 10);
     
         for (xi = x[0]; xi < x[9]; xi += 0.01)
           {
             yi = gsl_spline_eval (spline, xi, acc);
             printf ("%g %g\n", xi, yi);
           }
         gsl_spline_free (spline);
         gsl_interp_accel_free (acc);
       }
       return 0;
     }

The output is designed to be used with the gnu plotutils graph program,

     $ ./a.out > interp.dat
     $ graph -T ps < interp.dat > interp.ps

The result shows a smooth interpolation of the original points. The interpolation method can be changed simply by varying the first argument of gsl_spline_alloc.

The next program demonstrates a periodic cubic spline with 4 data points. Note that the first and last points must be supplied with the same y-value for a periodic spline.

     #include <stdlib.h>
     #include <stdio.h>
     #include <math.h>
     #include <gsl/gsl_errno.h>
     #include <gsl/gsl_spline.h>
     
     int
     main (void)
     {
       int N = 4;
       double x[4] = {0.00, 0.10,  0.27,  0.30};
       double y[4] = {0.15, 0.70, -0.10,  0.15}; 
                  /* Note: y[0] == y[3] for periodic data */
     
       gsl_interp_accel *acc = gsl_interp_accel_alloc ();
       const gsl_interp_type *t = gsl_interp_cspline_periodic; 
       gsl_spline *spline = gsl_spline_alloc (t, N);
     
       int i; double xi, yi;
     
       printf ("#m=0,S=5\n");
       for (i = 0; i < N; i++)
         {
           printf ("%g %g\n", x[i], y[i]);
         }
     
       printf ("#m=1,S=0\n");
       gsl_spline_init (spline, x, y, N);
     
       for (i = 0; i <= 100; i++)
         {
           xi = (1 - i / 100.0) * x[0] + (i / 100.0) * x[N-1];
           yi = gsl_spline_eval (spline, xi, acc);
           printf ("%g %g\n", xi, yi);
         }
       
       gsl_spline_free (spline);
       gsl_interp_accel_free (acc);
       return 0;
     }

The output can be plotted with gnu graph.

     $ ./a.out > interp.dat
     $ graph -T ps < interp.dat > interp.ps

The result shows a periodic interpolation of the original points. The slope of the fitted curve is the same at the beginning and end of the data, and the second derivative is also.