moiseevigor / elliptic Goto Github PK

Infinite precision evaluation functions for elliptic integrals and others

  NaN +    NaNi

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Transform Matlab functions into c++.

To perform the Octave script tests and make it compatible when possible

These two equivalent calculations:

    elliptic12i(asin(sqrt(5)*sin(pi/4)),1/5)
    elliptic12i(1.5708 - 1.0317i,1/5)

Produce the following answers:

       1.6596
       1.6596 -     1.2298i

Only the second is correct. The problem occurs because 

    mu(I)     = atan( sqrt(1./m(I).*(tan(phi(I)).^2.*cot(lambda(I)).^2 - 1)) );

has a singularity for phi = pi/2.

(Note that having cot(lambda) in there is also a problem for similar numerical 
reasons (since lambda=acot(...) but that's an issue for another day.)

Unfortunately I don't know how to fix this problem.

How can I compute the inverse Jacobi elliptic function using MATLAB 7.4 
(R2007a)?
http://www.mathworks.com/support/solutions/en/data/1-8DZ7LZ/?solution=1-
8DZ7LZ

Weierstrass's elliptic functions implementation request in terms of elliptic 
integrals and jacobi's elliptic functions

http://en.wikipedia.org/wiki/Weierstrass's_elliptic_functions
http://www.mai.liu.se/~halun/complex/elliptic/
http://mathworld.wolfram.com/WeierstrassEllipticFunction.html

To implement with the elliptic package the inverse Complete Elliptic Integrals 
of First K(k) and Second Type E(e).

Various hints from: Louis V. King On The Direct Numerical Calculation Of 
Elliptic Functions And Integrals, 
http://www.archive.org/details/onthenumerical032686mbp

When computing the complete third elliptic integral, the algorithm listed here 
will be much more efficient: http://dlmf.nist.gov/19.8

- Consider using atan2 instead of atan for the inverselliptic2.m because it's 
more stable and you won't need the eps for the denominator.
- My project required plugging in large numbers in the inverselliptic2.m 
function, which won't work because there's only 4 iterations. So I'd recommend 
using a while loop:
        [~, E] = elliptic12(invE(:),m,tol);
        dinvE = (E - z)./sqrt( 1-m.*sin(invE(:)).^2 );
        while max(abs(dinvE)) > tol
            invE(:) = invE(:)-dinvE;
            [~, E] = elliptic12(invE(:),m,tol);
            dinvE = (E - z)./sqrt( 1-m.*sin(invE(:)).^2 );
        end
        invE(:) = invE(:)-dinvE;

    instead of:
        for iter=1:4
            [~, E] = elliptic12(invE(:),m,tol);
            invE(:) = invE(:)-(E - z)./sqrt( 1-m.*sin(invE(:)).^2 );
        end

Carlson symmetric form realization request

http://en.wikipedia.org/wiki/Carlson_symmetric_form

I am sorry to report the following bug in your Matlab package for Elliptic 
Integrals and Functions. I use Matlab2013b and I find that the error message 
jumps out:

Error using .*
Matrix dimensions must agree.

Error in ellipj (line 95)
phin(:) = (2 .^ double(n(K))).*a(i,K).*u(I);

Error in ellipji (line 76)
[s,c,d] = ellipj(phi,m,tol);

Elliptic functions and integrals with complex modulus and complex arguments

Add examples for every function of the package.

error: =: nonconformant arguments (op1 is 2x1, op2 is 2x2)
error: called from
    ellipj at line 95 column 10