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[Bug-gsl] Re: GSL Mathieu Function Bug

From: Lowell Johnson
Subject: [Bug-gsl] Re: GSL Mathieu Function Bug
Date: Tue, 9 Dec 2008 22:04:35 -0600
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On Tuesday 09 December 2008 8:42:25 pm Lowell Johnson wrote:

> So I suggest trying the array functions.  Hopefully, they'll work for your
> needs.  But I do plan to use your report to improve the root-finding
> procedure. I'm fairly confident that I can patch the "blips" you've
> reported (hopefully fixing others in the process).  But the equations are
> pretty fickle -- even very minor perturbations can throw them off the
> desired convergence.

Following up on my earlier response, I just tried recreating your problem case 
of order=29, 0 < q < 1000.  The array functions do indeed avoid the "blips" at 
q~480, 630, and 850.

But the array is truncated too short for accurate results beyond q=50 or so.  
So I rebuilt, adding another 20 rows to the recurrence matrix.  That appears 
to give accurate results all the way to q=1000 (as far as I computed).  If you 
want to give it a shot, apply the following patch to your build:

diff --git a/specfunc/mathieu_workspace.c b/specfunc/mathieu_workspace.c
index 782c7dd..e6a4615 100644
--- a/specfunc/mathieu_workspace.c
+++ b/specfunc/mathieu_workspace.c
@@ -36,6 +36,7 @@ gsl_sf_mathieu_workspace *gsl_sf_mathieu_alloc(const size_t 
   /* Compute the maximum number of extra terms required for 10^-18 root
      accuracy for a given value of q (contributed by Brian Gladman). */
   extra_values = (int)(2.1*pow(fabs(qq), 0.37)) + 9;
+  extra_values += 20;  /* additional fudge */

   if (nn + 1 == 0)



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