GNU Scientific Library – Reference Manual: Interpolation Example programs

Next: Interpolation References and Further Reading, Previous: Higher-level Interface, Up: Interpolation [Index]

### 27.7 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.

Next: Interpolation References and Further Reading, Previous: Higher-level Interface, Up: Interpolation [Index]