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Mathieu functions toolbox

some functions to solve Mathieu equations and calculate some Mathieu functions
(125 downloads for this version - 13785 downloads for all versions)
Details
Version
1.0
A more recent valid version with binaries for Scilab 5.2 exists: 3.0
Author
R. Coisson, G. Vernizzi, XK. Yang, N. Strelkov
Owner Organization
Parma University
Maintainers
Nikolay Strelkov
Robert Coisson
Michael Baudin
License
Creation Date
April 8, 2011
Source created on
Scilab 5.2.x
Binaries available on
The maintainer of this module has not provided binaries.
Description
            A set of functions to solve Mathieu equations and to calculate the main Mathieu
functions.
The toolbox now has 8 demos. All demos can be acessed from "?->Scilab
Demonstrations"
The program is described in: R. Coïsson, G. Vernizzi and X.K. Yang,
"Mathieu functions and numerical solutions of the Mathieu equation",
IEEE Proceedings of OSSC2009, online at http://www.fis.unipr.it/~coisson/Mathieu.pdf

Other references:
N.W. McLachlan, Theory and Application of Mathieu Functions, Oxford Univ. Press,
1947 (historical reference)
 J. C. Gutiérrez-Vega, R. M. Rodríguez-Dagnino, M. A. Meneses-Nava, and S.
Chávez-Cerda, "Mathieu functions, a visual approach" // American
Journal of Physics, 71 (233), 233-242. An introduction to applications, online
at http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/modern/matheiu0.pdf            
Files (1)
[30.77 kB]
Source code archive

News (0)
Comments (6)     Leave a comment 
Comment from Michael Baudin -- May 14, 2011, 12:18:03 PM    
Hi,

Your module seems interesting. It builds and loads without problems: it is based only on 
macros.
I found a small problem in the example of the mathieuf function:

h=0;
  for j=-10:.1:10;
    h=h+1; 
    q(h)=j;
    a(:,h)=mathieuf(j,10);
  end 
  plot(q,a);

produces

!--error 15 
Sous-matrice incorrectement définie.

Most functions are documented which is excellent, but the ellipse function has 
undocumented input arguments. There are many examples in the help pages (except the 
ell2cart and mathieuS functions, which have no example).
The demos are impressive and seems to make use of the latest LaTeX features.

Very nice addition indeed !

Regards,

Michaël Baudin

Comment from Robert Coisson -- May 15, 2011, 12:19:09 PM    
Thank you for your remarks!

I tried the example you mention about mathieuf function, and it worked, but gave this
warning: Function sort is obsolete, please use gsort instead; this function will be
permanently removed in Scilab 5.3 
The version I used was 5.2.1, and you probably used 5.3, so "sort" did not exist
any more.
So it will be necessary to change "sort" into "gsort" in mathieuf.sci:
can you do this
change or should I send the file again? 

I shall look into the input arguments of the ellipse.sci function, and see if I can think
of an example of MathieuS function.
ell2cart.sci is an auxiliary function (and it is used in examples of modes with elliptical
boundary conditions), and in fact could be used also outside this context, when one has to
plot functions given in elliptical coordinates. Maybe I should send it also to "file
exchange"?

regards
roberto coisson
Comment from Nikolay Strelkov -- May 15, 2011, 12:58:31 PM    
Michael, thank you for feedback.

I also tried the example about mathieuf function. It's OK. But I get no warning. I tested 
it under Scilab 5.2.2, 5.3.0, 5.3.1 on Ubuntu 11.04 and Windows XP. What version and OS do

you use?

Hello, Roberto!
In mathieuf.sci we already have 'gsort' instead of 'sort' (see line 31). The comment in 
this line is incorrect ('sort' is deprecated, 'gsort' is alive). I.e. 5.3.0 there is no 
'sort', but there is 'gsort' instead.
Answer from Robert Coisson -- May 15, 2011, 03:04:51 PM    
Thank you Nikolay, 
I see that you already corrected the "sort" problem. Apparently I used the
previous version. 
Comment from Robert Coisson -- May 15, 2011, 02:59:29 PM    
Thank you for your remarks!

I tried the example you mention about mathieuf function, and it worked, but gave this
warning: Function sort is obsolete, please use gsort instead; this function will be
permanently removed in Scilab 5.3 
The version I used was 5.2.1, and you probably used 5.3, so "sort" did not exist
any more.
So it will be necessary to change "sort" into "gsort" in mathieuf.sci:
can you do this
change or should I send the file again? 

I shall look into the input arguments of the ellipse.sci function, and see if I can think
of an example of MathieuS function.
ell2cart.sci is an auxiliary function (and it is used in examples of modes with elliptical
boundary conditions), and in fact could be used also outside this context, when one has to
plot functions given in elliptical coordinates. Maybe I should send it also to "file
exchange"?

regards
roberto coisson
Comment from Nikolay Strelkov -- May 15, 2011, 06:27:03 PM    
Also tested under Scilab 5.3.2 on Ubuntu 11.04 and Windows XP with no error.

It seems that your use version of Scilab, which affected by Scilab bug 8669 (see http://bugzilla.scilab.org/show_bug.cgi?id=8669
for details) or something other.
Comment from Nikolay Strelkov -- May 16, 2011, 09:44:59 PM    
@Michael

After many trials a get the same error 15 on mathieuf example. It occurs if one runs 
examples from Mathieu Functions Toolbox help in a sequence: mathieuexp, mathieuf. These 
examples use the same variables 'a' and 'q'. 
Fixed in 1.0-2.

Thank you for discovering!
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