Solve for eigenvalues for small matrix in serial

[Pai Liu]

Hi all,

In my parallel code, I want to solve the eigenvalues of a small matrix (e.g. 3 by 3) in serial on each processor.

I know Step-36 depends on MPI communication to create the eigenfunctions and to solve the problem, BUT I only need to compute the eigenvalues of a small matrix in serial on each processor.

So, is there a easy way to do this, perferly with matrix type FullMatrix<double>?

Actually I also have a look at the function "EigenInverse (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData())", which may be a good choice.

But I do not understand the description of the second parameter "VectorMemory< VectorType > &mem", and thus I dont know how to use this solve function. Maybe someone can show me an example of this function.

Many thanks in advance.

[Jean-Paul Pelteret]

Hi Pai,

If you’ve got LAPACK installed then the LAPACKFullMatrix class is able to do the job for you. It has several methods implemented to compute eigenvalues, and you’d then use the eigenvalue() method to retrieve each eigenvalue.

I hope this helps.

Best,

Jean-Paul

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[Wolfgang Bangerth]

On 12/19/19 8:23 PM, Pai Liu wrote:
> In my parallel code, I want to solve the eigenvalues of a small matrix (e.g. 3
> by 3) in serial on each processor.

In addition to Jean-Paul's answer, if your 3x3 matrix is symmetric, you can
also put the entries into an object of type SymmetriTensor<2,3> for which
there is an eigenvalues() function.

Best
W.

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Wolfgang Bangerth email: bang...@colostate.edu
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[Pai Liu]

Thanks very much!