[Trilinos-Users] Smallest Eigenvalues

[Alicia Klinvex]

If your matrix has the potential to be indefinite, here are some additional
options (although BKS will certainly work too):

1.  Use TraceMin-Davidson, and ask it to compute the harmonic Ritz values.
This is brand new, so if you try this and see any wonky behavior, let me
know.
2.  Use spectrum folding.  This method has the potential to be very slow
(since you are in essence squaring the condition number of your matrix),
but it will allow you to use any eigensolver you wish.  Example:
http://trilinos.org/docs/dev/packages/anasazi/doc/html/LOBPCGCustomStatusTest_8cpp-example.html

If you decide to stick with BKS and have trouble getting your driver to
work, let us know :-)

- Alicia

On Tue, Mar 17, 2015 at 6:51 PM, Pate Motter <pate.motter at colorado.edu>
wrote:

> Hi Alicia,
>
> Thank you for the information. This is not guaranteed to be an SPD matrix
> so the first option is probably the best. I remember seeing an example
> going through that process, but could not get it to work either. I will
> retry that though as it could have been an error elsewhere.
>
> -Pate
>
> On 3/17/2015 4:47:03 PM, Alicia Klinvex <aklinvex at purdue.edu> wrote:
> Hello Pate,
>
> If you want to find the smallest eigenvalues, I'd recommend one of the
> following options:
> 1.  Using BKS in shift-and-invert mode.  There are several examples
> demonstrating how to do this on the Anasazi page.  If you want to go this
> route, you will have to create a linear solver (either direct or iterative)
> and pass it to the BKS solver manager.
> 2.  Pick a different eigensolver.  Is your matrix symmetric positive
> definite?  If so, you can use LOBPCG, RTR, or TraceMin-Davidson.  If your
> matrix is not SPD, your choices are more limited, and we can discuss your
> options further.
>
> Let me know which route you want to go, and I'll try to help you with it
> :-)
>
> Best wishes,
> Alicia
>
> On Tue, Mar 17, 2015 at 6:16 PM, Pate Motter <pate.motter at colorado.edu>
> wrote:
>
>> Hi,
>>
>> I am having difficulties converging when finding the smallest magnitude
>> eigenvalues in a sparse, square, real matrix. I am trying to use a
>> combination of Tpetra and Anasazi to accomplish this based on a few of the
>> examples I was able to find online. It currently works for finding largest
>> magnitude.
>>
>> Thanks,
>> Pate Motter
>>
>> RCP<MV> calcEigenValues(const RCP<MAT> &A, std::string eigenType) {
>>   //  Get norm
>>   ST mat_norm = A->getFrobeniusNorm();
>>
>>   // Eigensolver parameters
>>   int nev = 1;
>>   int blockSize = 1;
>>   int numBlocks = 10*nev / blockSize;
>>   ST tol = 1e-6;
>>
>>   //  Create parameters to pass to the solver
>>   Teuchos::ParameterList MyPL;
>>   MyPL.set("Block Size", blockSize );
>>   MyPL.set("Convergence Tolerance", tol);
>>   MyPL.set("Num Blocks", numBlocks);
>>
>>   //  Default to largest magnitude
>>   if (eigenType.compare("SM") == 0) {
>>     MyPL.set("Which", "SM");
>>   } else if (eigenType.compare("SR") == 0) {
>>     MyPL.set("Which", "SR");
>>   } else if (eigenType.compare("LR") == 0) {
>>     MyPL.set("Which", "LR");
>>   } else {
>>     MyPL.set("Which", "LM");
>>   }
>>
>>   //  Create multivector for a initial vector to start the solver
>>   RCP<MV> ivec = rcp (new MV(A->getRowMap(), blockSize));
>>   MVT::MvRandom(*ivec);
>>
>>   //  Create eigenproblem
>>   RCP<Anasazi::BasicEigenproblem<ST, MV, OP> > MyProblem =
>>     Teuchos::rcp(new Anasazi::BasicEigenproblem<ST, MV, OP>(A, ivec));
>>
>>   MyProblem->setHermitian(false);
>>   MyProblem->setNEV(nev);
>>   MyProblem->setProblem();
>>
>>   Anasazi::BlockKrylovSchurSolMgr<ST, MV, OP> MySolverMgr(MyProblem,
>> MyPL);
>>
>>   //  Solve the problem
>>   Anasazi::ReturnType returnCode = MySolverMgr.solve();
>>   if (returnCode != Anasazi::Converged) {
>>     *fos << "unconverged" << ", ";
>>   }
>>
>>   //  Get the results
>>   Anasazi::Eigensolution<ST, MV> sol = MyProblem->getSolution();
>>   std::vector<Anasazi::Value<ST> > evals = sol.Evals;
>>   RCP<MV> evecs = sol.Evecs;
>>   int numev = sol.numVecs;
>>
>>   //  Compute residual
>>   if (numev > 0) {
>>     Teuchos::SerialDenseMatrix<int, ST> T(numev,numev);
>>     for (int i = 0; i < numev; i++) {
>>       T(i,i) = evals[i].realpart;
>>     }
>>     std::vector<ST> normR(sol.numVecs);
>>     MV Kvec(A->getRowMap(), MVT::GetNumberVecs(*evecs));
>>     OPT::Apply(*A, *evecs, Kvec);
>>     MVT::MvTimesMatAddMv(-1.0, *evecs, T, 1.0, Kvec);
>>     MVT::MvNorm(Kvec, normR);
>>     for (int i=0; i<numev; i++) {
>>       *fos << evals[i].realpart << ", " << normR[i]/mat_norm << ", ";
>>     }
>>   }
>> return evecs;
>> }
>>
>>
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>
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