RE: inverse symmetric matrix

Hi,
My code is related to optimization and I used a code was available for
testing suite.

typedef matrix<double, 
               symmetric<lower>, 
               array< compressed<> >, 
               column_major>::type SDMATRIX;

int max_iter = 256;
itl::cholesky<SDMATRIX> precond(mfSymmMatrix);
itl::noisy_iteration<double> iter(vfGradient, max_iter, 1e-6);
itl::cg(mfSymmMatrix, vfDelta, vfGradient, precond(), iter);

I am not sure about the result (I do not mean to) as I have test
environment with 5*5 matrix. I am planning to use to for matrix from
(500 up to 1000 dimension matrices). I guess the difference may be clear
for large matrices.

So, you recommend using CG for the fastest results. One more question if
I change array< compressed<> > to dense<>, the templates are not able to
generate a valid code and the compilation stops. 


Thanks and best regards,
Yasser
-----Original Message-----
From: [email protected] [mailto:[email protected]] 
Sent: Monday, June 09, 2003 1:13 AM
To: General Matrix Template Library (MTL) list
Subject: RE: MTL: inverse symmetric matrix


Hi -- the standard method for iterative solution of sparse SPD is to
use preconditioned CG.  How well this will work depends strongly on
your preconditioner.  If your problem is elliptic, then an incomplete
Cholesky preconditioner is probably a pretty good bet.

It is surprising that lu_inv would be faster since lu is an N^3
algorithm.  Preconditioned CG should be much faster than that.  How
large is your problem?  What kind of matrix are you using for the CG
algorithm?


In our last exciting episode "Yasser H. Abdel-Haleem" wrote:
> Importance: Normal

> Hi,

> Thanks for your reply. Your comment was helpful. I was able to make my
> problem work as A*x=b. Hence, I was able to use ITL to get the X
vector
> directly. However, I have some comments.
> 1- If I use lu_inv(A) * b, the consumed time was less than for cg
> method.
> 2- The method cgs required the same amount of time of cg. I use
Cholesky
> pre-conditioner in both cg, cgs methods. 

> I wonder why I got slower performance with cg, cgs for the symmetric
> matrix relative to lu_inverse or this is normal.

> Can any one suggest an iterative method that is fast for PD symmetric
> matrix? I use VC++ version 6.0.

> Thanks in advance,
> Yasser
>  


> -----Original Message-----
> From: Gunter Winkler [mailto:[email protected]] 
> Sent: Thursday, June 05, 2003 8:05 AM
> To: General Matrix Template Library (MTL) list
> Subject: Re: MTL: inverse symmetric matrix

> Yasser H. Abdel-Haleem wrote:
> > Hi,
> 
> > I would like to get the inverse of a symmetric matrix. Currently, I
> copy 
> > it to a dense matrix and get the inverse using LU inverse.  However,
I

> > search a very fast method to do that directly without this
> intermediate 
> > step. Can any one suggest a solution?

> For symmetric matrices you should use the Cholesky-Factorization 
> (similar to LU: A = L L^T) I don't know if someone implemented it 
> already for MTL, but google gives lots if information about that.

> mfg
> Gunter


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Kind Regards,
Andrew Lumsdaine

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