General eigenvalue problem proposal

[Rafael Gonzalez]

I saw the project ideas list for octave for GSoC 2013 and I'm interested in the implementation of the eig function. I'm guessing that the goal is to achieve the different forms for calling the "eig" function in Matlab in order to ensure full portability. I've made a comparation and I'm listing the differences I found here:

Matlab:

d = eig(A)          Ax=λx

d = eig(A,B)       Ax=λBx

[V,D] = eig(A)

[V,D] = eig(A,'nobalance')*

[V,D] = eig(A,B)

[V,D] = eig(A,B,flag)*

Octave:

 -- Loadable Function: LAMBDA = eig (A)

 -- Loadable Function: LAMBDA = eig (A, B)

 -- Loadable Function: [V, LAMBDA] = eig (A)

 -- Loadable Function: [V, LAMBDA] = eig (A, B)

I was told that the generalized eigenvalue problem is not implemented yet, but isn't it the "eig(A, B)" call form? Anyways, Other difference I found was the possiblity to avoid the balance process for the eigenvalue problem and choosing wheter to use the cholesky factorization or the QZ method when B is singular, and maybe that's what is not implemented yet. Am I correct with the current overview on this?