[Trilinos-Users] Smallest Eigenvalues

[Pate Motter]

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 [mailto: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;  
}


_______________________________________________
Trilinos-Users mailing list
Trilinos-Users at software.sandia.gov [mailto:Trilinos-Users at software.sandia.gov]
https://software.sandia.gov/mailman/listinfo/trilinos-users [https://software.sandia.gov/mailman/listinfo/trilinos-users]


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://software.sandia.gov/pipermail/trilinos-users/attachments/20150317/f4a27968/attachment.html>