[SciPy-user] generalized eigenvalue problem for sparse matrices

[Neilen Marais]

Abinav,

On Tue, 15 Apr 2008 01:50:20 +0530, abhinav sarkar wrote:

> Hi
>  n = 3
>  h = 1.0/(n+1)
> 
>  a = 1
>  Pr = 7.0
>  Ra = 1000
> 
>  A = get_A_mat(n, h, a, Pr, Ra)
>  M = get_M_mat(n, h, a, Pr, Ra)
> 
>  sigma = 10.0
^^^
I think you're looking for -10.

>  B = A - sigma*M
>  s = dsolve.splu(B)
>  e, v = ARPACK_gen_eigs(M.matvec, s.solve, 2*n, sigma, 2, 'LR') 
                                                             ^^
You may try futzing around with this parameter.

Anyway, I did play around a bit with your example and never really got a 
good answer. But my experience has been that ARPACK doesn't really work 
well with small matrices. Try a bigger problem and see if things turn out 
better, I mean, obviously you don't need a sparse solver to solve a 6x6 
matrix system ;). You may also find that if you force Matlab to do this 
problem using a sparse solver you'll run into the same issues. 
Unfortunately I don't know enough about the ARPACK routines to give more 
insight. They do work quite well on my problems, where the eigenvalues 
are always positive.

>  which also seems to be correct to me. Please tell if the method I am
>  using is correct or not and why am I not getting correct solutions. Is
>  the ARPACK_gen_eigs broken? Or is there a problem in my code?

Seems OK, but I'm no expert ;)

Regards
Neilen

> 
>  Regards
>  --
>  Abhinav Sarkar
>  4th year Undergraduate Student
>  Deptt. of Mechanical Engg.
>  Indian Institute of Technology, Kharagpur India
> 
>  Web: http://claimid.com/abhin4v
>  Twitter: http://twitter.com/abhin4v
>  ---------
>  The world is a book, those who do not travel read only one page.
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