26.2 Example

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_diff_forward.

#include <stdio.h> #include <gsl/gsl_math.h> #include <gsl/gsl_diff.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_diff_central (&F, 2.0, &result, &abserr); printf("x = 2.0\n"); printf("f'(x) = %.10f +/- %.5f\n", result, abserr); printf("exact = %.10f\n\n", 1.5 * sqrt(2.0)); gsl_diff_forward (&F, 0.0, &result, &abserr); printf("x = 0.0\n"); printf("f'(x) = %.10f +/- %.5f\n", result, abserr); printf("exact = %.10f\n", 0.0); return 0; }

Here is the output of the program,

$ ./demo f(x) = x^(3/2) x = 2.0 f'(x) = 2.1213203435 +/- 0.01490 exact = 2.1213203436 x = 0.0 f'(x) = 0.0012172897 +/- 0.05028 exact = 0.0000000000