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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