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[] = "Estimates the 2-norm condition number of a matrix A, that is, the ratio of the largest to the smallest singular values of A. "

  "The matrix is a Grcar matrix.\n\n"

  "The command line options are:\n"

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

#include "slepcsvd.h"

/*

   This example computes the singular values of an nxn Grcar matrix,

   which is a nonsymmetric Toeplitz matrix:

              |  1  1  1  1               |

              | -1  1  1  1  1            |

              |    -1  1  1  1  1         |

              |       .  .  .  .  .       |

          A = |          .  .  .  .  .    |

              |            -1  1  1  1  1 |

              |               -1  1  1  1 |

              |                  -1  1  1 |

              |                     -1  1 |

 */

#undef __FUNCT__

#define __FUNCT__ "main"

int main( int argc, char **argv )

{

  PetscErrorCode ierr;

  Mat            A;               /* Grcar matrix */

  SVD            svd;             /* singular value solver context */

  PetscInt       N=30, Istart, Iend, i, col[5], nconv1, nconv2;

  PetscScalar    value[] = { -1, 1, 1, 1, 1 };

  PetscReal      sigma_1, sigma_n;

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

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

  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%d\n\n",N);CHKERRQ(ierr);

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

        Generate the matrix

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

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

  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);

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

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

  for( i=Istart; i<Iend; i++ ) {

    col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;

    if (i==0) {

      ierr = MatSetValues(A,1,&i,4,col+1,value+1,INSERT_VALUES);CHKERRQ(ierr);

    }

    else {

      ierr = MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);CHKERRQ(ierr);

    }

  }

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

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

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

             Create the singular value solver and set the solution method

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

  /*

     Create singular value context

  */

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

  /*

     Set operator

  */

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

  /*

     Set solver parameters at runtime

  */

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

  ierr = SVDSetDimensions(svd,1,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);

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

                      Solve the eigensystem

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

  /*

     First request an eigenvalue from one end of the spectrum

  */

  ierr = SVDSetWhichSingularTriplets(svd,SVD_LARGEST);CHKERRQ(ierr);

  ierr = SVDSolve(svd);CHKERRQ(ierr);

  /*

     Get number of converged singular values

  */

  ierr = SVDGetConverged(svd,&nconv1);CHKERRQ(ierr);

  /*

     Get converged singular values: largest singular value is stored in sigma_1.

     In this example, we are not interested in the singular vectors

  */

  if (nconv1 > 0) {

    ierr = SVDGetSingularTriplet(svd,0,&sigma_1,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

  } else {

    ierr = PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");CHKERRQ(ierr);

  }

  /*

     Request an eigenvalue from the other end of the spectrum

  */

  ierr = SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);CHKERRQ(ierr);

  ierr = SVDSolve(svd);CHKERRQ(ierr);

  /*

     Get number of converged eigenpairs

  */

  ierr = SVDGetConverged(svd,&nconv2);CHKERRQ(ierr);

  /*

     Get converged singular values: smallest singular value is stored in sigma_n.

     As before, we are not interested in the singular vectors

  */

  if (nconv2 > 0) {

    ierr = SVDGetSingularTriplet(svd,0,&sigma_n,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

  } else {

    ierr = PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");CHKERRQ(ierr);

  }

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

                    Display solution and clean up

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

  if (nconv1 > 0 && nconv2 > 0) {

    ierr = PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%6f, sigma_n=%6f\n",sigma_1,sigma_n);CHKERRQ(ierr);

    ierr = PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%6f\n\n",sigma_1/sigma_n);CHKERRQ(ierr);

  }  

  /*

     Free work space

  */

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

  ierr = MatDestroy(A);CHKERRQ(ierr);

  ierr = SlepcFinalize();CHKERRQ(ierr);

  return 0;

}