[Bug-gsl] gsl_multiroot_test_delta

[franky . backeljauw]

Hello,

when looking for a real root to a complex function using gsl_multiroot,
I discovered a bug in the gsl_multiroot_test_delta routine.  This test
does the following:

      double xi = gsl_vector_get(x,i);
      double dxi = gsl_vector_get(dx,i);
      double tolerance = epsabs + epsrel * fabs(xi)  ;

      if (fabs(dxi) < tolerance)
        {
          ok = 1;
        }

However, in the case of a real root, the imaginary part is zero, and 
also dxi = 0, so that tolerance = epsabs.  If we now set epsabs = 0, then 
fabs(dxi) = 0 < tolerance = epsabs = 0 will always fail, even though it is 
the correct answer.

When checking the one-dimensional case, the gsl_root_test_delta code 
contains the test

      if (fabs(x1 - x0) < tolerance || x1 == x0)

The problem above can be eliminated by replacing the test with

      if (fabs(dxi) < tolerance || dxi == 0)

which is the generalization of the one-dimensional test to the 
multidimensional case.

Could you inform me about the status of this bug report?

Thank you very much for this nice library!

-- Regards,

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Franky Backeljauw                  (e-mail) address@hidden
Universiteit Antwerpen                   (jabber) address@hidden
Departement Wiskunde en Informatica          (tel) (0032|0)3/265.38.55
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