[Insight-users] solving large linear equations

[Wes Turner]

Habib,
Check the condition number of your matrix.  If the condition number of the
matrix is too high, iterative methods have a difficult time converging.
 Also, it is likely that the iterative algorithm requires your matrix to be
symmetric, positive definite.

- Wes

On Wed, Jun 17, 2009 at 11:19 AM, Habib Baluwala <habibbaluwala at gmail.com>wrote:

>
> Arnaud ,
>          It takes around 10 min to solve the linear system of equations. I
> also tried the vnl_sparse_matrix_linear_system but that too takes a long
> time for solving these equations.
>
>
>
>
> Arnaud Gelas wrote:
> >
> > Habib,
> >
> > Right, your matrix is not that large and is really sparse...
> > I am curious to know how long it takes to solve your system?
> >
> > I am not so sure about the efficiency of vnl direct solver (LU
> > solver)... (Until recently, sparse iterative solver were really
> > efficient in comparison to direct ones, and this is still a very active
> > field of research!)
> > If you need to solve several times linear systems which involve the same
> > matrix, I would recommend to use a direct solver like LU, LLT, LDLT;
> > else an iterative solution like vnl_sparse_matrix_linear_system.
> >
> >
> > Arnaud
> >
> >
> >
> > Habib Baluwala wrote:
> >> Hi Arnaud,
> >>                The size of the matrix is around 40,000 rows and columns
> >> but
> >> the density is around 5 percent which is very small. I am using the
> >> vnl_sparse_matrix for reading the sparse matrix and then using the
> >> vnl_sparse_lu and for solving the equations. I thought that the blas and
> >> lapack libraries are linked with the linear solver but that does not
> seem
> >> to
> >> be the case or I am currently not using any pointers for the sparse
> >> matrix.
> >> Can this be a reason for the failure????? I look forward to yor reply
> >>
> >>
> >>
> >>
> >>
> >> Arnaud Gelas wrote:
> >>
> >>> Hi habbib,
> >>>
> >>> How large is your matrix?
> >>> How sparse is your matrix? Do you know the number of non null elements
> >>> in your matrix? Or can you tell me the number of non null elements per
> >>> row (in average)?
> >>>
> >>> Solving sparse linear system highly depends on the sparsity of your
> >>> matrix.
> >>> When you say I am "using VNL sparse system solver", what do you mean?
> >>> which class are you using?
> >>>
> >>> Note that it is not because you use BLAS and LAPACK that the code will
> >>> be fast, it depends how they are used in in the library. For example
> >>> mumps, taucs are also based on blas and lapack and performances are
> >>> really different...
> >>>
> >>> Arnaud
> >>>
> >>> Habib Baluwala wrote:
> >>>
> >>>> Hi everyone ,
> >>>>                  I am currently using a large sparse system of linear
> >>>> equation which is non-symmetric. I tried using VNL sparse system
> >>>> solvers
> >>>> but
> >>>> they are very slow , I can't still understand why they are slow
> because
> >>>> they
> >>>> are supposed to utilise the BLAS and Lapack libraries to speed up. Can
> >>>> anyone tell me how can I speed up the procedure???? I also tried the
> >>>> release
> >>>> instead of debug. It was able to reduce the time taken but not to a
> >>>> significant effect. Would including the Utilities folder in the
> >>>> CMakeFile.txt help ???
> >>>>
> >>>> I look forward to your reply and sorry for any inconvenience.
> >>>>
> >>>>
> >>>>
> >>>>
> >>>>
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> >>
> >>
> >
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-- 
Wesley D. Turner, Ph.D.
Kitware, Inc.
R&D Engineer
28 Corporate Drive
Clifton Park, NY 12065-8662
Phone: 518-371-3971 x120
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