question about root finding example

[Faheem Mitha <faheem at email dot unc dot edu>]

Dear People,

I have a question about the example in the GSl documentation

One dimensional Root-Finding:
* Root Finding Examples::

which appears at the bottom of this message.

In the main do loop, status is assigned to twice. Namely,

   status = gsl_root_fsolver_iterate (s);

and then

   status = gsl_root_test_interval (x_lo, x_hi,
                                            0, 0.001);

I'm unclear on what the first assignment does. Surely, regardless of the
value, it is overwritten by the second line?

Also, I am not really clear on what is going on with
gsl_root_fsolver_iterate. However, I took the lazy way out and ran through
it with a debugger. The first line returns 0 on every loop, the second
returns -2 (GSL_CONTINUE) for the first few loops, which is correct.

I realise that gsl_root_fsolver_iterate needs to be called, since it is
preforming the actual algorithm (if I'm following this correctly) but why
does it need to write to status, and why is returning 0 for status anyway,
when -2 would be correct?

Can anyone clarify? Thanks.

                                              Faheem.

*******************************************************************

     #include <stdio.h>
     #include <gsl/gsl_errno.h>
     #include <gsl/gsl_math.h>
     #include <gsl/gsl_roots.h>

     #include "demo_fn.h"
     #include "demo_fn.c"

     int
     main (void)
     {
       int status;
       int iter = 0, max_iter = 100;
       const gsl_root_fsolver_type *T;
       gsl_root_fsolver *s;
       double r = 0, r_expected = sqrt (5.0);
       double x_lo = 0.0, x_hi = 5.0;
       gsl_function F;
       struct quadratic_params params = {1.0, 0.0, -5.0};

       F.function = &quadratic;
       F.params = &params;

       T = gsl_root_fsolver_brent;
       s = gsl_root_fsolver_alloc (T);
       gsl_root_fsolver_set (s, &F, x_lo, x_hi);

       printf ("using %s method\n",
               gsl_root_fsolver_name (s));

       printf ("%5s [%9s, %9s] %9s %10s %9s\n",
               "iter", "lower", "upper", "root",
               "err", "err(est)");

       do
         {
           iter++;
           status = gsl_root_fsolver_iterate (s);
           r = gsl_root_fsolver_root (s);
           x_lo = gsl_root_fsolver_x_lower (s);
           x_hi = gsl_root_fsolver_x_upper (s);
           status = gsl_root_test_interval (x_lo, x_hi,
                                            0, 0.001);

           if (status == GSL_SUCCESS)
             printf ("Converged:\n");

           printf ("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n",
                   iter, x_lo, x_hi,
                   r, r - r_expected,
                   x_hi - x_lo);
         }
       while (status == GSL_CONTINUE && iter < max_iter);
       return status;
     }