Fwd: inverselliptic2.m

[Igor Moiseev]

---------- Forwarded message ----------
From: Nen Huynh
Date: 2014/1/5
Subject: inverselliptic2.m
To: moisee...@gmail.com

Hi,

I have a project that requires the use of your elliptic functions project. Thanks for that. I do have a suggestion:

- 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

- Also, have you considered using the Matlab function "integral" to evaluate the elliptic functions? It has the benefit of not needing a tolerance parameter.

Thanks, again.

[Igor Moiseev]

Hi Neh Huynh!

Thank you for a valuable suggestions and I glad it was useful for your research! 

The four iterations approach is the more stable option, if something goes wrong and it may go wrong in singularities and special values ;)

To embrace precision and stability we may apply both approaches 

1. while for precision 

2. and iteration control, let say step<10

I've opened the issue 12 for this request

https://code.google.com/p/elliptic/issues/detail?id=12

Igor Moiseev

 

---------- Forwarded message ----------
From: Nen Huynh
Date: 2014/1/5
Subject: inverselliptic2.m