bugGNU Scientific Library - Bugs: bug #46678, Bug in gsl_sf_coulomb_wave_F_array


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bug #46678: Bug in gsl_sf_coulomb_wave_F_array

Submitter:  Patrick Alken <psa>
Submitted:  Sat 12 Dec 2015 09:09:10 PM UTC
Category:  None Severity:  3 - Normal
Operating System:  Status:  None
Assigned to:  None Open/Closed:  Open

Sat 12 Dec 2015 09:09:10 PM UTC, original submission:  

from nih =at= pks =dot= mpg =dot= de

Dear GSL developers,

I found a bug in the function gsl_sf_coulomb_wave_F_array which uses the recurrence relation to obtain F for different l's.
To be short, when eta is large, and l is at least moderately large, inaccuracy occurs in the implementation of the recurrence such that F has unphysical spikes at certain x for smaller l's.
My observation is that F is determined directly for the largest l, and F for smaller l's are determined from the recurrence relation.
When l is large, the number of recurrence is large to obtain F for small l's.
Therefore, errors in F's get accumulated as we proceed to get F for small l's.

Attached please find a test program.
The program uses two methods to obtain F for different l's and x's.
The first method obtains F directly, and the second method obtains F from recurrence relation.

Please compile it using "g++ testCoulomb.cpp -lgsl -lgslcblas".
Now run the program using "./a.out > resultCoulomb".
We can now take a look at the output of the program using gnuplot.
After launching gnuplot, just type      plot "resultCoulomb" using 1:2 every ::2::2000      to see the output for l=0 at different x's using the first method.
And type      plot "resultCoulomb" using 1:2 every ::2002::4000 to see the output for l=0 at different x's using the second method.

Now you can find, F is fine using the first method, but F has unphysical spikes.
You can see similar behaviors for other l's by "using 1:3", "using 1:4" etc in gnuplot.

I can of course always stick to the first method, but the second method is much faster.
So it would be great if you could fix this problem.

Patrick Alken <psa>
Group administrator


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Attached Files
file #35718:  testCoulomb.cpp added by psa (914B - text/x-c++src)


Depends on the following items: None found

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    Date Changed by Updated Field Previous Value => Replaced by
    2015-12-12 psa Attached File- Added testCoulomb.cpp, #35718

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