Subversion Repositories slepc-dev

/*

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

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2011, Universitat 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[] = "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);

PetscErrorCode MatLaplacian2D_GetDiagonal(Mat A,Vec diag);

#undef __FUNCT__

#define __FUNCT__ "main"

int main(int argc,char **argv)

{

  Mat            A;               /* operator matrix */

  EPS            eps;             /* eigenproblem solver context */

  const EPSType  type;

  PetscReal      tol=1000*PETSC_MACHINE_EPSILON;

  PetscMPIInt    size;

  PetscInt       N,n=10,nev,maxit;

  PetscErrorCode ierr;

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

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

  if (size != 1) SETERRQ(PETSC_COMM_WORLD,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);

  ierr = MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatLaplacian2D_GetDiagonal);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);

  ierr = EPSSetTolerances(eps,tol,PETSC_DECIDE);CHKERRQ(ierr);

  /*

     Set solver parameters at runtime

  */

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

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

                      Solve the eigensystem

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

  ierr = EPSSolve(eps);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

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

  ierr = EPSPrintSolution(eps,PETSC_NULL);CHKERRQ(ierr);

  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,const 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;

  int               nx,lo,j,one=1;

  const PetscScalar *px;

  PetscScalar       *py,dmone=-1.0;

  PetscErrorCode    ierr;

  PetscFunctionBegin;

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

  nx = *(int*)ctx;

  ierr = VecGetArrayRead(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 = VecRestoreArrayRead(x,&px);CHKERRQ(ierr);

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

  PetscFunctionReturn(0);

}

#undef __FUNCT__

#define __FUNCT__ "MatLaplacian2D_GetDiagonal"

PetscErrorCode MatLaplacian2D_GetDiagonal(Mat A,Vec diag)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  ierr = VecSet(diag,4.0);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}