[Bug-gsl] [bug #39713] roots/secant.c "derivative value is not finite" for a good guess

[Max]

URL:
  <http://savannah.gnu.org/bugs/?39713>

                 Summary: roots/secant.c "derivative value is not finite" for
a good guess
                 Project: GNU Scientific Library
            Submitted by: nikulin
            Submitted on: Срд 07 Авг 2013 03:52:26
                Category: Runtime error
                Severity: 3 - Normal
        Operating System: Linux
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: bzr
         Discussion Lock: Any

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Details:

Implementation of the secant method for root finding fails
for an (almost) linear function. If at a certain iteration
the root approximation is within DBL_EPSILON, then
the next iteration fails with "derivative value is not finite"
error. Actually it means that a good approximation has been found.

It may be tested with the following function
(full program source is attached as well)

double test_f (double x, void *params)
{
   return -M_PI*x + M_E;
}
double test_df (double x, void *params)
{
   return -M_PI;
}

# i   x_i-r      x_i - x_p status
  0  0.000e+00 -2.347e-01 -2
gsl: secant.c:104: ERROR: derivative value is not finite
Default GSL error handler invoked.

I think that an addition test should be added and
derivative should be updated only if the step is
significantly greater then DBL_EPSILON. Otherwise
rounding error or even zero division may be the issue.

The proposed patch is attached. When it is applied
the programs works correctly.
# i   x_i-r      x_i - x_p status
  0  0.000e+00 -2.347e-01 -2
  1  0.000e+00  0.000e+00 0
# Converged
# f(x_i) =  2.9707e-17

It seems that all 82 tests supplied in roots directory
are passed correctly with this patch.





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File Attachments:


-------------------------------------------------------
Date: Срд 07 Авг 2013 03:52:26  Name: gsl-secant.c  Size: 2kB   By:
nikulin
A program to demonstrate the issue and the patch
<http://savannah.gnu.org/bugs/download.php?file_id=28779>
-------------------------------------------------------
Date: Срд 07 Авг 2013 03:52:26  Name: gsl-roots-secant.patch  Size: 795B
  By: nikulin
A program to demonstrate the issue and the patch
<http://savannah.gnu.org/bugs/download.php?file_id=28780>

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