28.2 Examples

The following code estimates the derivative of the function f(x) = x^{3/2} at x=2 and at x=0. The function f(x) is undefined for x<0 so the derivative at x=0 is computed using gsl_deriv_forward.

     #include <stdio.h>
     #include <gsl/gsl_math.h>
     #include <gsl/gsl_deriv.h>
     
     double f (double x, void * params)
     {
       return pow (x, 1.5);
     }
     
     int
     main (void)
     {
       gsl_function F;
       double result, abserr;
     
       F.function = &f;
       F.params = 0;
     
       printf ("f(x) = x^(3/2)\n");
     
       gsl_deriv_central (&F, 2.0, 1e-8, &result, &abserr);
       printf ("x = 2.0\n");
       printf ("f'(x) = %.10f +/- %.10f\n", result, abserr);
       printf ("exact = %.10f\n\n", 1.5 * sqrt(2.0));
     
       gsl_deriv_forward (&F, 0.0, 1e-8, &result, &abserr);
       printf ("x = 0.0\n");
       printf ("f'(x) = %.10f +/- %.10f\n", result, abserr);
       printf ("exact = %.10f\n", 0.0);
     
       return 0;
     }

Here is the output of the program,

     $ ./a.out
     f(x) = x^(3/2)
     x = 2.0
     f'(x) = 2.1213203120 +/- 0.0000004064
     exact = 2.1213203436
     
     x = 0.0
     f'(x) = 0.0000000160 +/- 0.0000000339
     exact = 0.0000000000