Question

I want to use the GSL for integration
http://www.gnu.org/software/gsl/manual/html_node/Numerical-Integration.html
However, I find no convenient way how the integrated function

(the function f in the example http://www.gnu.org/software/gsl/manual/html_node/Numerical-integration-examples.html)

can report an error to the integrator. I want to integrate a function which itself results from an integration that could fail. This is my sample program

#include <stdio.h>
#include <math.h>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_errno.h>

double f (double x, void * params) {
    GSL_ERROR("test error",GSL_FAILURE);
    return 0.0;
}



int main (void)
{
gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000);

double result, error;

gsl_function F;
F.function = &f;

gsl_set_error_handler_off();
int status = gsl_integration_qags (&F, 0, 1, 0, 1e-7, 1000,
                     w, &result, &error); 

printf ("status          = %d\n", status);
status  = GSL_FAILURE;
printf ("status          = %d\n", status);


gsl_integration_workspace_free (w);

return 0;
}

resulting in the output
status = 0
status = -1

I think the integrator should rather stop and return my error code. How can I achieve this?

Thank you very much for your help!!!

2011-04-27: I also tried this variant, after Brian Gough told me,

#include <stdio.h>
#include <math.h>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_errno.h>

double f (double x, void * params) {
    GSL_ERROR("test error",GSL_FAILURE);
    return GSL_NAN;
}



int main (void)
{
gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000);

double result, error;

gsl_function F;
F.function = &f;

gsl_set_error_handler_off();
int status = gsl_integration_qags (&F, 0, 1, 0, 1e-7, 1000,
                     w, &result, &error); 

printf ("status          = %d\n", status);
status  = GSL_FAILURE;
printf ("status          = %d\n", status);


gsl_integration_workspace_free (w);

return 0;
}

it did not help either. I will now fill out a bug report.

Answer 1

Thanks to Xuebin Wu from the GSL Mailing list the problem is solved:

Hi,

GSL_ERROR itself is a macro, it looks like

      gsl_error (reason, __FILE__, __LINE__, gsl_errno);
      return gsl_errno;

The function already returns before you return NAN, because GSL_ERROR
has been called. Turning the handler off just let the first line do
nothing. The default error handler abort the program after printing
error message.

I do not think it is a bug. Maybe you can write your own error handler
to solve your problem. For example, you can use “goto” to jump out of
gsl_integration_qags, or set some global variable to indicate the
integration result is incorrect.

PS: I believe this macro is what you need,

Macro: GSL_ERROR_VAL (reason, gsl_errno, value)
This macro is the same as GSL_ERROR but returns a user-defined value
of value instead of an error code. It can be used for mathematical
functions that return a floating point value.

The following example shows how to return a NaN at a mathematical
singularity using the GSL_ERROR_VAL macro,

 if (x == 0)
   {
     GSL_ERROR_VAL("argument lies on singularity",
                   GSL_ERANGE, GSL_NAN);
   }

So I adjusted the code according to

#include <stdio.h>
#include <math.h>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_errno.h>

double f (double x, void * params) {
//  return GSL_NAN;
    GSL_ERROR_VAL ("argument lies on singularity", GSL_ERANGE, GSL_NAN);
}



int main (void)
{
gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000);

double result, error;

gsl_function F;
F.function = &f;

gsl_set_error_handler_off();
int status = gsl_integration_qags (&F, 0, 1, 0, 1e-7, 1000,
                     w, &result, &error); 

printf ("status          = %d\n", status);
status  = GSL_FAILURE;
printf ("status          = %d\n", status);


gsl_integration_workspace_free (w);

return 0;
}

and everything works as expected…