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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
Paperback (6"x9"), 592 pages, 60 figures
ISBN 0954612078
RRP £24.95 ($39.95)

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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.

ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition