#include <stdio.h>

#include <gsl/gsl_multifit.h>

int

main (int argc, char **argv)

{

  int i, n;

  double xi, yi, ei, chisq;

  gsl_matrix *X, *cov;

  gsl_vector *y, *w, *c;

  if (argc != 2)

    {

      fprintf (stderr,"usage: fit n < data\n");

      exit (-1);

    }

  n = atoi (argv[1]);

  X = gsl_matrix_alloc (n, 3);

  y = gsl_vector_alloc (n);

  w = gsl_vector_alloc (n);

  c = gsl_vector_alloc (3);

  cov = gsl_matrix_alloc (3, 3);

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

    {

      int count = fscanf (stdin, "%lg %lg %lg",

                          &xi, &yi, &ei;;

      if (count != 3)

        {

          fprintf (stderr, "error reading file\n");

          exit (-1);

        }

      printf ("%g %g +/- %g\n", xi, yi, ei);

      gsl_matrix_set (X, i, 0, 1.0);

      gsl_matrix_set (X, i, 1, xi);

      gsl_matrix_set (X, i, 2, xi*xi);

      gsl_vector_set (y, i, yi);

      gsl_vector_set (w, i, 1.0/(ei*ei));

    }

  {

    gsl_multifit_linear_workspace * work 

      = gsl_multifit_linear_alloc (n, 3);

    gsl_multifit_wlinear (X, w, y, c, cov,

                          &chisq, work);

    gsl_multifit_linear_free (work);

  }

#define C(i) (gsl_vector_get(c,(i)))

#define COV(i,j) (gsl_matrix_get(cov,(i),(j)))

  {

    printf ("# best fit: Y = %g + %g X + %g X^2\n", 

            C(0), C(1), C(2));

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

    printf ("[ %+.5e, %+.5e, %+.5e  \n",

               COV(0,0), COV(0,1), COV(0,2));

    printf ("  %+.5e, %+.5e, %+.5e  \n", 

               COV(1,0), COV(1,1), COV(1,2));

    printf ("  %+.5e, %+.5e, %+.5e ]\n", 

               COV(2,0), COV(2,1), COV(2,2));

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

  }

  gsl_matrix_free (X);

  gsl_vector_free (y);

  gsl_vector_free (w);

  gsl_vector_free (c);

  gsl_matrix_free (cov);

  return 0;

}