[petsc-users] Slepc eigen value solver gives strange behavior

[Gong Ding]

Dear Jose,
will you please also take a look at the SVD code for smallest singular value?
It seems work except the time consuming SVDCyclicSetExplicitMatrix routine.
However, I wonder if there exist some more clever method.

  // SVD solver for smallest singular value
  SVD            svd_s;
  EPS            eps_s;
  ST             st_s;
  KSP            ksp_s;
  PC             pc_s;

  PetscErrorCode ierr;

  // Create singular value solver context
  ierr = SVDCreate(PETSC_COMM_WORLD, &svd_s);

  // Set operator
  ierr = SVDSetOperator(svd_s, J);


  // small singular value use eigen value solver on Cyclic Matrix
  ierr = SVDSetWhichSingularTriplets(svd_s, SVD_SMALLEST);
  ierr = SVDSetType(svd_s, SVDCYCLIC);
  ierr = SVDCyclicSetExplicitMatrix(svd_s, PETSC_TRUE); // <-----time consuming
  // shift-and-invert spectral transformation to enhance convergence of 
eigenvalues near zero
  ierr = SVDCyclicGetEPS(svd_s, &eps_s);
  ierr = EPSSetType(eps_s, EPSKRYLOVSCHUR);
  ierr = EPSGetST(eps_s, &st_s);
  ierr = STSetType(st_s, STSINVERT);

  ierr = STGetKSP(st_s, &ksp_s);
  ierr = KSPGetPC(ksp_s, &pc_s);
  // since we have to deal with bad conditioned problem, we choose direct 
solver whenever possible

  // direct solver as preconditioner
  ierr = KSPSetType (ksp_s, (char*) KSPGMRES); assert(!ierr);
  // superlu which use static pivot seems very stable
  ierr = PCSetType  (pc_s, (char*) PCLU); assert(!ierr);
  ierr = PCFactorSetMatSolverPackage (pc_s, "superlu"); assert(!ierr);

  // Set solver parameters at runtime
  ierr = SVDSetFromOptions(svd_s);  assert(!ierr);

  ierr = SVDSetUp(svd_s); assert(!ierr);

  PetscReal sigma_large=1, sigma_small=1;
  PetscInt nconv;
  PetscReal error;

  // find the smallest singular value
  SVDSolve(svd_s);