gsl_sf_coupling_3j

gsl_sf_coupling_3j

[jdwright]

Dear gsl users,

Does anyone out there have experience using the "gsl_sf_coupling_3j" routine of
the "gsl_sf_coupling" package?  I wonder if the call: 

gsl_sf_coupling_3j (two_ja,two_jb,two_jc,two_ma,two_mb,two_mc)

yields accurate results for large values of two_ja, two_jb, and two_jc around 30
with two_ma=0,two_mb=0,two_mc=0.

Thanks,

J. David Wright
Physics Department
Wesleyan University
jdwright@wesleyan.edu

gsl_sf_coupling_3j

[jdwright]

Dear gsl users,

Does anyone out there have experience using the "gsl_sf_coupling_3j" routine of
the "gsl_sf_coupling" package?  I wonder if the call: 

gsl_sf_coupling_3j (two_ja,two_jb,two_jc,two_ma,two_mb,two_mc)

yields accurate results for large values of two_ja, two_jb, and two_jc around 30
with two_ma=0,two_mb=0,two_mc=0.

Thanks,

J. David Wright
Physics Department
Wesleyan University
jdwright@wesleyan.edu

Re: gsl_sf_coupling_3j

[Brian Gough]

jdwright@wesleyan.edu writes:
 > Dear gsl users,
 >  Does anyone out there have experience using the
 > "gsl_sf_coupling_3j" routine of the "gsl_sf_coupling" package?  I
 > wonder if the call:
 >  gsl_sf_coupling_3j (two_ja,two_jb,two_jc,two_ma,two_mb,two_mc)
 >  yields accurate results for large values of two_ja, two_jb, and
 > two_jc around 30 with two_ma=0,two_mb=0,two_mc=0.
 >  Thanks,
 >  J. David Wright Physics Department Wesleyan University
 > jdwright@wesleyan.edu

The result->error term from the full version of the function
gsl_sf_coupling_3j_e() should give an estimate of the error.  

If it's not accurate please send a bug report, thanks.  The exact
value could be computed to high precision using GP-PARI, which is free
software.

regards
Brian Gough

Re: gsl_sf_coupling_3j

[Brian Gough]

jdwright@wesleyan.edu writes:
 > Dear gsl users,
 >  Does anyone out there have experience using the
 > "gsl_sf_coupling_3j" routine of the "gsl_sf_coupling" package?  I
 > wonder if the call:
 >  gsl_sf_coupling_3j (two_ja,two_jb,two_jc,two_ma,two_mb,two_mc)
 >  yields accurate results for large values of two_ja, two_jb, and
 > two_jc around 30 with two_ma=0,two_mb=0,two_mc=0.
 >  Thanks,
 >  J. David Wright Physics Department Wesleyan University
 > jdwright@wesleyan.edu

The result->error term from the full version of the function
gsl_sf_coupling_3j_e() should give an estimate of the error.  

If it's not accurate please send a bug report, thanks.  The exact
value could be computed to high precision using GP-PARI, which is free
software.

regards
Brian Gough

Re: Abramowitz and Stegun (1964) online

[Brian Gough]

Serge Winitzki writes:
 > Hi,
 >  Thanks for a great library! I use it in my research.

Thanks.  If you'd like to cite GSL in any papers a suitable reference
is:

  GNU Scientific Library Reference Manual, M. Galassi et al, 
  ISBN 095416170X 

 >  In the TODO file, I noticed a wish to distribute Abramowitz and
 > Stegun with GSL. It seems that the old edition Abramowitz and
 > Stegun is now available online
 > (http://members.fortunecity.com/aadns/) as page images, total about
 > 50 MB.  (Just to let you know.)

Wow that's good news. I didn't know about it, thanks for posting the
information.

(corrected url for the list: http://members.fortunecity.com/aands/)

Do you have any idea how to contact the person behind it?  I could not
find any information on the site itself.

Brian

Re: gsl_sf_coupling_3j

[Serge Winitzki]

Filip Floegel writes:
 > hello gsl community,
 >  gsl_sf_coupling_3j doesn't work properly for large angular mementa

The package "matpack" (www.matpack.de) includes many special functions, 
also the 3j symbols. They refer to some quite complicated numerical 
methods using recursion relations to get the right answers for large 
momenta, and to 1975-1976 papers by Schulten and Gordon for the 
description of the algorithms. The papers can be downloaded for free at
http://www.ks.uiuc.edu/Publications/Papers/ 

-- 
	Serge

gsl_sf_coupling_3j

[Filip Floegel]

hello gsl community,

gsl_sf_coupling_3j doesn't work properly for large
angular mementa like j1=j2=j3=40 m1=m2=m3=0 !!!

gsl_sf_coupling_3j_e(80,80,80,0,0,0,&result)

which correspond to j1=j2=j3=40 m1=m2=m3=0

gives me:

      result.val = 0.0625
      result.err = 0.172766

mathematica gives me:

      N[ThreeJSymbol[{40,0},{40,0},{40,0}]] = 0.0149685

my guess is that gamma.c which is used for calculating fractional
numbers probably diverges for large integers. 

cheers,
        ff
 
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| ITP/Universitaet Hannover  phone: 0511/762-3381               |               
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Re: gsl_sf_coupling_3j

[Brian Gough]

Filip Floegel writes:
 > hello gsl community,
 >  gsl_sf_coupling_3j doesn't work properly for large angular mementa
 > like j1=j2=j3=40 m1=m2=m3=0 !!!
 >  gsl_sf_coupling_3j_e(80,80,80,0,0,0,&result)
 >  which correspond to j1=j2=j3=40 m1=m2=m3=0
 >  gives me:
 >       result.val = 0.0625 result.err = 0.172766
 >  mathematica gives me:
 >       N[ThreeJSymbol[{40,0},{40,0},{40,0}]] = 0.0149685
 >  my guess is that gamma.c which is used for calculating fractional
 > numbers probably diverges for large integers.

Thanks for the bug report.

If you can take a look at the source maybe a different expansion can
be used for large values to improve the accuracy?

Brian