Condition number and Eigen Values of a Matrix

[Mohammad Sabawi]

Hello every one,

 

How to compute the condition number and eigen values of a matrix I use it in my code in deal.II not in Trillions or PETSc? Is there any difference if  is it a block or non block matrix?

 

Best

 

Mohammad

[Wolfgang Bangerth]

On 01/31/2016 12:18 PM, Mohammad Sabawi wrote:
> **
>
> *How to compute the condition number and eigen values of a matrix I use it in

> my code in deal.II not in Trillions or PETSc? Is there any difference if is

> it a block or non block matrix?*

deal.II doesn't currently provide a way to compute eigenvalues of sparse
matrices other than through Trilinos and PETSc/Slepc (unless you're only
interested in the largest/smallest eigenvector, for which you can use the
EigenPower/EigenInverse classes).

But you could output the matrix in text format and input it into matlab, for
example, if you just want to experiment a bit.

Best
W.


--
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Wolfgang Bangerth email: bang...@math.tamu.edu
www: http://www.math.tamu.edu/~bangerth/

[Reza Rastak]

Dear Wolfgang,

I am trying to calculate the condition number of a Trilinos Block Sparse matrix. Is there an example of that in the documentation that you can point me to?

Thank you,

Reza

[Wolfgang Bangerth]

On 12/2/20 9:30 PM, Reza Rastak wrote:
>
> I am trying to calculate the condition number of a Trilinos Block Sparse
> matrix. Is there an example of that in the documentation that you can point me to?

No, and that's actually a quite difficult task because you have to estimate
eigenvalues. The easiest way is probably to use the power iteration and
inverse power iteration to estimate largest and smallest eigenvalues -- see
the EigenPower and EigenInverse classes.

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Jean-Paul Pelteret]

If it's of any help, our CG and GMRES solvers (and maybe some of the
others?) can return the estimated condition number during / after a call
to solve().
https://dealii.org/developer/doxygen/deal.II/classSolverCG.html#a52f1fd3d41765ec06d2d0add1a74a37c
<https://dealii.org/developer/doxygen/deal.II/classSolverCG.html#a52f1fd3d41765ec06d2d0add1a74a37c>
https://dealii.org/developer/doxygen/deal.II/classSolverGMRES.html#a3025d81c3d7db3e1a1b0114bef794202
<https://dealii.org/developer/doxygen/deal.II/classSolverGMRES.html#a3025d81c3d7db3e1a1b0114bef794202>

Jean-Paul

[Reza Rastak]

Thank you so much Jean-Paul. I was able to use SolverCG::connect_condition_number_slot() successfully in my code.

Best,

Reza