#include <stdio.h>

#include <gsl/gsl_fit.h>

int

main (void)

{

  int i, n = 4;

  double x[4] = { 1970, 1980, 1990, 2000 };

  double y[4] = {   12,   11,   14,   13 };

  double w[4] = {  0.1,  0.2,  0.3,  0.4 };

  double c0, c1, cov00, cov01, cov11, chisq;

  gsl_fit_wlinear (x, 1, w, 1, y, 1, n, 

                   &c0, &c1, &cov00, &cov01, &cov11, 

                   &chisq);

  printf ("# best fit: Y = %g + %g X\n", c0, c1);

  printf ("# covariance matrix:\n");

  printf ("# [ %g, %g\n#   %g, %g]\n", 

          cov00, cov01, cov01, cov11);

  printf ("# chisq = %g\n", chisq);

  for (i = 0; i < n; i++)

    printf ("data: %g %g %g\n", 

                   x[i], y[i], 1/sqrt(w[i]));

  printf ("\n");

  for (i = -30; i < 130; i++)

    {

      double xf = x[0] + (i/100.0) * (x[n-1] - x[0]);

      double yf, yf_err;

      gsl_fit_linear_est (xf, 

                          c0, c1, 

                          cov00, cov01, cov11, 

                          &yf, &yf_err);

      printf ("fit: %g %g\n", xf, yf);

      printf ("hi : %g %g\n", xf, yf + yf_err);

      printf ("lo : %g %g\n", xf, yf - yf_err);

    }

  return 0;

}