[SciPy-user] generalized eigenvalue problem for sparse matrices
abhinav sarkar
abhinav.sarkar@gmail....
Tue Apr 15 09:43:38 CDT 2008
On Tue, Apr 15, 2008 at 6:24 PM, Neilen Marais <nmarais@sun.ac.za> wrote:
> 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.
i am looking for the largest eigenvalue
>
>
> > 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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>
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>
>
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I have formulated the problem in a slightly different way and now I
am able to obtain the correct eigenvalues. Here is the new code:
class Solver:
def __init__(self, A, M, sigma):
self.A = A
self.M = M
self.sigma = sigma
def solve(self, b):
#(M-sigma*A)*x=A*b
#return x
return dsolve.spsolve((self.M-self.sigma*self.A), self.A*b)
A = get_A_mat(n, h, a, Pr, Ra)
M = get_M_mat(n, h, a, Pr, Ra)
I = sparse.eye(2*n,2*n)
sigma = 0.0
sigma_solve = Solver(A, M, sigma).solve
e = 1.0/ARPACK_gen_eigs(I.matvec, sigma_solve, I.shape[0], sigma, 5, 'LR')[0]
Here I have converted the A*x = sigma*M*x to inv(A)*M*x = nu*I*x where
nu = 1/sigma. And replaced s.solve by my own Solver class. Now
solutions obtained are correct.
--
Abhinav Sarkar
4th year Undergraduate Student
Deptt. of Mechanical Engg.
Indian Institute of Technology, Kharagpur
India
Mobile:+91-99327-41517
Residence:+91-631-2429887
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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