[Trilinos-Users] problems with transpose, inverse and products with Epetra_CRSMatrix

[Erik Boman]

Antonella,

Is your system overdetermined (more rows than columns)?
Your approach is to form the pseudoinverse B of A. Computationally, this 
is very expensive.
Rather, you should use an iterative method directly on the rectangular 
system.
Do you know the LSQR method by Paige and Saunders? There is an 
implementation in Belos.

Erik

Antonella Longo wrote:
> Thank you for your prompt answer.
> In this email we try to explain the complete problem that we must solve.
>
> We have a non-square system of equation for which we found a preconditioner
> to make it square so that it can be solved with GMRES.
>
> Our initial non-square system is Ax=b.
> The preconditioner requires the computation of the matrix B
> that is $B=(diag(A^T A))^{-1}A^T$. 
> A is an Epetra_CRSMatrix and we have its map. 
> The final system to be solved will be BAx=Bb.
>
> We were not successful to make this B matrix defined above.
>
> Another problem that we have is that even though the EpetraExt package
> is installed, and the proper ".h" files are included, the compiler does not 
> recognize the functions that you suggested us. 
>
> We are wondering if you could suggest us the right functions
> to solve the above problem.
>
> -----------------------------------------------
> Antonella Longo
> Istituto Nazionale di Geofisica e Vulcanologia
> Sezione di Pisa
> Via Uguccione della Faggiola, 32
> Pisa, Italy
> Tel. office: 050 8311939
> Cell.: 339 7532089
>
> ----- Original Message -----
> From: "Mike Heroux" <MHeroux at CSBSJU.EDU>
> To: "Antonella Longo" <longo at pi.ingv.it>, "Deepak Garg" <deepak.garg at pi.ingv.it>
> Cc: trilinos-users at software.sandia.gov, "Alicia Marie Klinvex" <aklinvex at purdue.edu>
> Sent: Wednesday, September 10, 2014 11:17:47 PM
> Subject: Re: [Trilinos-Users] problems with transpose, inverse and products with Epetra_CRSMatrix
>
> In addition to the pointers that Alicia provided, you can compute the
> matrix-transpose times vector product using the specific Epetra_CrsMatrix
> method called Multiply().  This method has a bool input argument that
> indicates whether or not to apply the matrix-transpose operation:
>
> http://trilinos.org/docs/dev/packages/epetra/doc/html/classEpetra__CrsMatri
> x.html#ae97a6c65b11aa29b3bb25d9788c56b3a
>
> In general, it is unusual (but not necessarily wrong) to explicitly form
> the transpose of a matrix.  In many situations, just being able to apply
> the action of the matrix transpose is sufficient.
>
> Following up on Alicia¹s comments on inverses, it is almost never best to
> explicitly compute the inverse of a sparse matrix, unless it is small or
> has very special structure.
>
> Perhaps if you describe the algorithms you are trying to implement we can
> suggest some other options.
>
> Mike
>
> On 9/10/14, 8:10 AM, "Alicia Marie Klinvex" <aklinvex at purdue.edu> wrote:
>
>   
>> Hello Antonella and Deepak,
>>
>> The matrix multiplication is in the EpetraExt package:
>> http://trilinos.org/docs/dev/packages/epetraext/doc/html/classEpetraExt_1_
>> 1MatrixMatrix.html
>>
>> I believe the transpose function you seek is also in EpetraExt:
>> http://trilinos.org/docs/dev/packages/epetraext/doc/html/classEpetraExt_1_
>> 1RowMatrix__Transpose.html
>> (I could be wrong about that one; I've never used that particular
>> function before.)
>>
>> The matrix vector multiplication is in Epetra (called Apply):
>> http://trilinos.org/docs/dev/packages/epetra/doc/html/classEpetra__CrsMatr
>> ix.html#a77c4232f1b3d32ff76504ed314df5f76
>>
>> Do you absolutely need to compute the inverse of your matrix, or do you
>> just want to apply the inverse to a vector?  I'm afraid I don't know
>> whether Trilinos even has a function to invert a sparse matrix, but if
>> you were only interested in solving linear systems, it certainly has
>> functions for that.
>>
>> Best wishes,
>> Alicia Klinvex
>>
>>
>>
>> ----- Original Message -----
>> From: "Antonella Longo" <longo at pi.ingv.it>
>> To: trilinos-users at software.sandia.gov
>> Cc: "Deepak Garg" <deepak.garg at pi.ingv.it>
>> Sent: Wednesday, September 10, 2014 9:10:46 AM
>> Subject: [Trilinos-Users] problems with transpose,	inverse and products
>> with Epetra_CRSMatrix
>>
>> We are making computations with Epetra_CRSMatrices,
>> but we could not find any mathematical functions for
>> these matrices.
>> In particular we need to compute the transpose and
>> the inverse of an Epetra_CRSMatrix, to calculate
>> the product of two Epetra_CRSMatrices, and the
>> product of an Epetra_CRSMatrix with an Epetra_Vector.
>> Does there exist any standard functions for these operations?
>> We checked the functions of the above mentioned classes but we found
>> nothing. 
>>
>> Thanks for your kind attention.
>>
>> Antonella Longo and Deepak Garg
>>
>>
>>
>> -----------------------------------------------
>> Antonella Longo
>> Istituto Nazionale di Geofisica e Vulcanologia
>> Sezione di Pisa
>> Via Uguccione della Faggiola, 32
>> Pisa, Italy
>> Tel. office: 050 8311939
>> Cell.: 339 7532089
>>
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>
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