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/*

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

      SLEPc - Scalable Library for Eigenvalue Problem Computations

      Copyright (c) 2002-2007, Universidad Politecnica de Valencia, Spain

      This file is part of SLEPc. See the README file for conditions of use

      and additional information.

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

*/

static char help[] = "Solves the same eigenproblem as in example ex2, but using a shell matrix. "

  "The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"

  "The command line options are:\n"

  "  -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";

#include "slepceps.h"

#include "petscblaslapack.h"

/*

   User-defined routines

*/

PetscErrorCode MatLaplacian2D_Mult( Mat A, Vec x, Vec y );

#undef __FUNCT__

#define __FUNCT__ "main"

int main( int argc, char **argv )

{

  Mat            A;               /* operator matrix */

  EPS            eps;             /* eigenproblem solver context */

  const EPSType  type;

  PetscReal      error, tol, re, im;

  PetscScalar    kr, ki;

  PetscMPIInt    size;

  PetscErrorCode ierr;

  PetscInt       N, n=10, nev, maxit, i, its, nconv;

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

  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);

  if (size != 1) SETERRQ(1,"This is a uniprocessor example only!");

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

  N = n*n;

  ierr = PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%d (%dx%d grid)\n\n",N,n,n);CHKERRQ(ierr);

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

     Compute the operator matrix that defines the eigensystem, Ax=kx

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

  ierr = MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);CHKERRQ(ierr);

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

  ierr = MatShellSetOperation(A,MATOP_MULT,(void(*)())MatLaplacian2D_Mult);CHKERRQ(ierr);

  ierr = MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)())MatLaplacian2D_Mult);CHKERRQ(ierr);

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

                Create the eigensolver and set various options

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

  /*

     Create eigensolver context

  */

  ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);

  /*

     Set operators. In this case, it is a standard eigenvalue problem

  */

  ierr = EPSSetOperators(eps,A,PETSC_NULL);CHKERRQ(ierr);

  ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr);

  /*

     Set solver parameters at runtime

  */

  ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);

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

                      Solve the eigensystem

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

  ierr = EPSSolve(eps);CHKERRQ(ierr);

  ierr = EPSGetIterationNumber(eps, &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 = EPSGetType(eps,&type);CHKERRQ(ierr);

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

  ierr = EPSGetDimensions(eps,&nev,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);CHKERRQ(ierr);

  ierr = EPSGetTolerances(eps,&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 approximate eigenpairs

  */

  ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %d\n\n",nconv);

         CHKERRQ(ierr);

  if (nconv>0) {

    /*

       Display eigenvalues and relative errors

    */

    ierr = PetscPrintf(PETSC_COMM_WORLD,

         "           k          ||Ax-kx||/||kx||\n"

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

    for( i=0; i<nconv; i++ ) {

      /*

        Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and

        ki (imaginary part)

      */

      ierr = EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

      /*

         Compute the relative error associated to each eigenpair

      */

      ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr);

#ifdef PETSC_USE_COMPLEX

      re = PetscRealPart(kr);

      im = PetscImaginaryPart(kr);

#else

      re = kr;

      im = ki;

#endif 

      if (im!=0.0) {

        ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",re,im,error);CHKERRQ(ierr);

      } else {

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

      }

    }

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

  }

  /*

     Free work space

  */

  ierr = EPSDestroy(eps);CHKERRQ(ierr);

  ierr = MatDestroy(A);CHKERRQ(ierr);

  ierr = SlepcFinalize();CHKERRQ(ierr);

  return 0;

}

/*

    Compute the matrix vector multiplication y<---T*x where T is a nx by nx

    tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and

    DU on the superdiagonal.

 */  

static void tv( int nx, PetscScalar *x, PetscScalar *y )

{

  PetscScalar dd, dl, du;

  int         j;

  dd  = 4.0;

  dl  = -1.0;

  du  = -1.0;

  y[0] =  dd*x[0] + du*x[1];

  for( j=1; j<nx-1; j++ )

    y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];

  y[nx-1] = dl*x[nx-2] + dd*x[nx-1];

}

#undef __FUNCT__

#define __FUNCT__ "MatLaplacian2D_Mult"

/*

    Matrix-vector product subroutine for the 2D Laplacian.

    The matrix used is the 2 dimensional discrete Laplacian on unit square with

    zero Dirichlet boundary condition.

    Computes y <-- A*x, where A is the block tridiagonal matrix

                 | T -I          |

                 |-I  T -I       |

             A = |   -I  T       |

                 |        ...  -I|

                 |           -I T|

    The subroutine TV is called to compute y<--T*x.

 */

PetscErrorCode MatLaplacian2D_Mult( Mat A, Vec x, Vec y )

{

  void           *ctx;

  PetscErrorCode ierr;

  int            nx, lo, j, one=1;

  PetscScalar    *px, *py, dmone=-1.0;

  PetscFunctionBegin;

  ierr = MatShellGetContext( A, &ctx ); CHKERRQ(ierr);

  nx = *(int *)ctx;

  ierr = VecGetArray( x, &px ); CHKERRQ(ierr);

  ierr = VecGetArray( y, &py ); CHKERRQ(ierr);

  tv( nx, &px[0], &py[0] );

  BLASaxpy_( &nx, &dmone, &px[nx], &one, &py[0], &one );

  for( j=2; j<nx; j++ ) {

    lo = (j-1)*nx;

    tv( nx, &px[lo], &py[lo]);

    BLASaxpy_( &nx, &dmone, &px[lo-nx], &one, &py[lo], &one );

    BLASaxpy_( &nx, &dmone, &px[lo+nx], &one, &py[lo], &one );

  }

  lo = (nx-1)*nx;

  tv( nx, &px[lo], &py[lo]);

  BLASaxpy_( &nx, &dmone, &px[lo-nx], &one, &py[lo], &one );

  ierr = VecRestoreArray( x, &px ); CHKERRQ(ierr);

  ierr = VecRestoreArray( y, &py ); CHKERRQ(ierr);

  PetscFunctionReturn(0);

}