[SciPy-user] generalized eigenvalue problem for sparse matrices
Abhinav Sarkar
abhinav.sarkar@gmail....
Tue Apr 15 01:48:50 CDT 2008
abhinav sarkar <abhinav.sarkar <at> gmail.com> writes:
>
> Hi
> I am trying to solve a generalized eigenvalue problem for sparse
> matrices. The problem is in form
> A*x = 𝜎*M*x
> where A and M are sparse matrices and x is a vector and sigma is a
> scalar whose value is to be found.
>
> For this I am using the Arpack function ARPACK_gen_eigs provided in
> the module scipy.sparse.linalg.eigen.arpack.speigs . However the
> solution which I am getting does not match with the solution obtained
> from the eig function in MATLAB. For example:
>
> A = [1 0 0 -33 16 0; 0 1 0 16 -33 16; 0 0 1 0 16 -33; 1601 -96 256
> -1800 0 0; -96 1601 -96 0 -1800 0; 256 -96 1601 0 0 -1800]
> M = [0 0 0 1 0 0; 0 0 0 0 1 0; 0 0 0 0 0 1; -33 16 0 0 0 0; 16 -33 16
> 0 0 0; 0 16 -33 0 0 0]
>
> The matrices are written in MATLAB format, spaces separating the row
> elements and ";" separating the rows.
> When I solve this problem in MATLAB using the function eig, I get the
> following eigenvalues:
> -155.0345, -56.9898, -45.2209, -31.9376, -28.5367, -9.1611
>
> However when I solve it using ARPACK_gen_eigs to find the two
> eigenvalues near 10, I get the following solution:
> 13.83675153-1.71439075j, 13.83675153+1.71439075j
> which is certainly not correct.
> --
> Abhinav Sarkar
I tried the eigenvalue problem solver provided for the dense matrices at
scipy.linalg.eig and it gives the same result as the MATLAB functin eig. Then
why is scipy.sparse.linalg.eigen.arpack.speigs.ARPACK_gen_eigs giving different
result? Please help me out.
Regards
---
Abhinav Sarkar
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