Kristjan Onu wrote:
Hi Raymond et al.,

Before proceeding much further, one question I'd like to clarify is
what form this documentation will take eventually.

Will it become part of the documentation for ellint_Kcomp,
ellint_Ecomp and ellipke (what one would see when typing "help
function_name" at the octave prompt)? If so, then should the
documentation effort underway take the form of patches to ellpke.m and
buildgsl_sf.sh? Working on a LaTeX based document is fine for me, but
if the goal is to eventually improve the functions' documentation,
perhaps switching to the structure described in the "Octave
Documentation Strings Tips" [1] soon should be considered. I bring
this up since I think this may impact the structure of the
documentation. For example, the current document has all forms of the
elliptic integrals defined in the GSL section whereas for online
documentation, I think something will be needed in the ellipke.m
section.

Two technical points:

I would remove the general Legendre form definitions from the
documentation. I think the important point to document is that the
definitions used by ellipke and ellint_[KE]comp are different.

ellipke accepts n x 1 arrays as you wrote, but also n x m arrays, if m
= 2.

Kristjan

[1] 
http://www.gnu.org/software/octave/doc/interpreter/Documentation-Tips.html#Documentation-Tips

Hi,
I 've been going over the thread. Your original comment about modifying the ellipke documentation is a lot more modest than what I did. OTOH: my description was aiming to be more explanatory; for myself if nothing else. Perhaps of little use since it is basically paraphrasing information presented elsewhere. Either you or I could add a ellint_[KE]comp comment to the ellipke code. I could enter the k^2/m directions in the ellint_[KE]comp documents; or perhaps that would go in both cases? It is documented in the gsl documentation. I think your suggestions are sound. I will take out the Legendre equation; it serves no purpose in this context unless somebody sets up a gsl interface. I will probably add the Jacobian elliptic interface when I get back to it. I believe it can be interpreted as a solution to the diffusion equation on a confined strip; such as are used for biochemical testing. As I remember, I managed to formulate that several years ago but never actually wrote down the example or explanation. I went back and looked at the ellipke code and your changes. For some reason the changes don't jibe with my source-forge copy. It's like they are already half done even though my source copy was svn on 4/28 like your diff header. Perhaps somebody inserted the fixes? In any case they don't seem to work; although the only failure seems to be [x,y,z]. I am obviously out of sync somewhere. Here are my test cases:
[a,b]=ellipke([[.3, .5,.6];[.4,.6,.6];[.4,.5,.6]])
[a,b]=ellipke([[.3, .5,.6];[.4,.6,.6]])
[a,b]=ellipke([[.3, .5];[.4,.6];[.4,.5]])
  [a,b]=ellipke([.3;.5])
  disp("last line")
 [a,b]=ellipke([.3,.5])

RayR



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