Subversion Repositories slepc-dev

/*

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain

   This file is part of SLEPc.

   SLEPc is free software: you can redistribute it and/or modify it under  the

   terms of version 3 of the GNU Lesser General Public License as published by

   the Free Software Foundation.

   SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY

   WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS

   FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for

   more details.

   You  should have received a copy of the GNU Lesser General  Public  License

   along with SLEPc. If not, see <http://www.gnu.org/licenses/>.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*/

static char help[] = "Singular value decomposition of the Lauchli matrix.\n"

  "The command line options are:\n"

  "  -n <n>, where <n> = matrix dimension.\n"

  "  -mu <mu>, where <mu> = subdiagonal value.\n\n";

#include <slepcsvd.h>

#undef __FUNCT__

#define __FUNCT__ "main"

int main( int argc, char **argv )

{

  Mat            A;               /* operator matrix */

  Vec            u,v;             /* left and right singular vectors */

  SVD            svd;             /* singular value problem solver context */

  const SVDType  type;

  PetscReal      error, tol, sigma, mu=PETSC_SQRT_MACHINE_EPSILON;

  PetscErrorCode ierr;

  PetscInt       n=100, i, j, Istart, Iend, nsv, maxit, its, nconv;

  SlepcInitialize(&argc,&argv,(char*)0,help);

  ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscOptionsGetReal(PETSC_NULL,"-mu",&mu,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nLauchli singular value decomposition, (%d x %d) mu=%g\n\n",n+1,n,mu);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

                          Build the Lauchli matrix

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);

  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n);CHKERRQ(ierr);

  ierr = MatSetFromOptions(A);CHKERRQ(ierr);

  ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);

  for (i=Istart;i<Iend;i++) {

    if (i == 0) {

      for (j=0;j<n;j++) {

        ierr = MatSetValue(A,0,j,1.0,INSERT_VALUES);CHKERRQ(ierr);

      }

    } else {

      ierr = MatSetValue(A,i,i-1,mu,INSERT_VALUES);CHKERRQ(ierr);

    }

  }

  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = MatGetVecs(A,&v,&u);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

          Create the singular value solver and set various options

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*

     Create singular value solver context

  */

  ierr = SVDCreate(PETSC_COMM_WORLD,&svd);CHKERRQ(ierr);

  /*

     Set operator

  */

  ierr = SVDSetOperator(svd,A);CHKERRQ(ierr);

  /*

     Use thick-restart Lanczos as default solver

  */

  ierr = SVDSetType(svd,SVDTRLANCZOS);CHKERRQ(ierr);

  /*

     Set solver parameters at runtime

  */

  ierr = SVDSetFromOptions(svd);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

                      Solve the singular value system

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = SVDSolve(svd);CHKERRQ(ierr);

  ierr = SVDGetIterationNumber(svd, &its);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);CHKERRQ(ierr);

  /*

     Optional: Get some information from the solver and display it

  */

  ierr = SVDGetType(svd,&type);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr);

  ierr = SVDGetDimensions(svd,&nsv,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %d\n",nsv);CHKERRQ(ierr);

  ierr = SVDGetTolerances(svd,&tol,&maxit);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

                    Display solution and clean up

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*

     Get number of converged singular triplets

  */

  ierr = SVDGetConverged(svd,&nconv);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %d\n\n",nconv);CHKERRQ(ierr);

  if (nconv>0) {

    /*

       Display singular values and relative errors

    */

    ierr = PetscPrintf(PETSC_COMM_WORLD,

         "          sigma           residual norm\n"

         "  --------------------- ------------------\n" );CHKERRQ(ierr);

    for( i=0; i<nconv; i++ ) {

      /*

         Get converged singular triplets: i-th singular value is stored in sigma

      */

      ierr = SVDGetSingularTriplet(svd,i,&sigma,u,v);CHKERRQ(ierr);

      /*

         Compute the error associated to each singular triplet

      */

      ierr = SVDComputeRelativeError(svd,i,&error);CHKERRQ(ierr);

      ierr = PetscPrintf(PETSC_COMM_WORLD,"       % 6f      ",sigma); CHKERRQ(ierr);

      ierr = PetscPrintf(PETSC_COMM_WORLD," % 12g\n",error);CHKERRQ(ierr);

    }

    ierr = PetscPrintf(PETSC_COMM_WORLD,"\n" );CHKERRQ(ierr);

  }

  /*

     Free work space

  */

  ierr = SVDDestroy(svd);CHKERRQ(ierr);

  ierr = MatDestroy(A);CHKERRQ(ierr);

  ierr = VecDestroy(u);CHKERRQ(ierr);

  ierr = VecDestroy(v);CHKERRQ(ierr);

  ierr = SlepcFinalize();CHKERRQ(ierr);

  return 0;

}