Date: 2013-09-02T10:05:36+00:00

Actual source code: ex3.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Solves the same eigenproblem as in example ex2, but using a shell matrix. "
     23:   "The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"
     24:   "The command line options are:\n"
     25:   "  -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";

     27: #include <slepceps.h>
     28: #include <petscblaslapack.h>

     30: /*
     31:    User-defined routines
     32: */
     33: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
     34: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);

     38: int main(int argc,char **argv)
     39: {
     40:   Mat            A;               /* operator matrix */
     41:   EPS            eps;             /* eigenproblem solver context */
     42:   EPSType        type;
     43:   PetscMPIInt    size;
     44:   PetscInt       N,n=10,nev;

     47:   SlepcInitialize(&argc,&argv,(char*)0,help);
     48:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     49:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only");

     51:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     52:   N = n*n;
     53:   PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%D (%Dx%D grid)\n\n",N,n,n);

     55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     56:      Compute the operator matrix that defines the eigensystem, Ax=kx
     57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     59:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);
     60:   MatSetFromOptions(A);
     61:   MatShellSetOperation(A,MATOP_MULT,(void(*)())MatMult_Laplacian2D);
     62:   MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)())MatMult_Laplacian2D);
     63:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Laplacian2D);

     65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     66:                 Create the eigensolver and set various options
     67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     69:   /*
     70:      Create eigensolver context
     71:   */
     72:   EPSCreate(PETSC_COMM_WORLD,&eps);

     74:   /*
     75:      Set operators. In this case, it is a standard eigenvalue problem
     76:   */
     77:   EPSSetOperators(eps,A,NULL);
     78:   EPSSetProblemType(eps,EPS_HEP);

     80:   /*
     81:      Set solver parameters at runtime
     82:   */
     83:   EPSSetFromOptions(eps);

     85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     86:                       Solve the eigensystem
     87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     89:   EPSSolve(eps);

     91:   /*
     92:      Optional: Get some information from the solver and display it
     93:   */
     94:   EPSGetType(eps,&type);
     95:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
     96:   EPSGetDimensions(eps,&nev,NULL,NULL);
     97:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

     99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    100:                     Display solution and clean up
    101:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    103:   EPSPrintSolution(eps,NULL);
    104:   EPSDestroy(&eps);
    105:   MatDestroy(&A);
    106:   SlepcFinalize();
    107:   return 0;
    108: }

    110: /*
    111:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
    112:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
    113:     DU on the superdiagonal.
    114:  */
    115: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
    116: {
    117:   PetscScalar dd,dl,du;
    118:   int         j;

    120:   dd  = 4.0;
    121:   dl  = -1.0;
    122:   du  = -1.0;

    124:   y[0] =  dd*x[0] + du*x[1];
    125:   for (j=1;j<nx-1;j++)
    126:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
    127:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
    128: }

    132: /*
    133:     Matrix-vector product subroutine for the 2D Laplacian.

    135:     The matrix used is the 2 dimensional discrete Laplacian on unit square with
    136:     zero Dirichlet boundary condition.

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

    140:                  | T -I          |
    141:                  |-I  T -I       |
    142:              A = |   -I  T       |
    143:                  |        ...  -I|
    144:                  |           -I T|

    146:     The subroutine TV is called to compute y<--T*x.
    147:  */
    148: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
    149: {
    150:   void              *ctx;
    151:   int               nx,lo,i,j;
    152:   const PetscScalar *px;
    153:   PetscScalar       *py;
    154:   PetscErrorCode    ierr;

    157:   MatShellGetContext(A,&ctx);
    158:   nx = *(int*)ctx;
    159:   VecGetArrayRead(x,&px);
    160:   VecGetArray(y,&py);

    162:   tv(nx,&px[0],&py[0]);
    163:   for (i=0;i<nx;i++) py[i] -= px[nx+i];

    165:   for (j=2;j<nx;j++) {
    166:     lo = (j-1)*nx;
    167:     tv(nx,&px[lo],&py[lo]);
    168:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
    169:   }

    171:   lo = (nx-1)*nx;
    172:   tv(nx,&px[lo],&py[lo]);
    173:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

    175:   VecRestoreArrayRead(x,&px);
    176:   VecRestoreArray(y,&py);
    177:   return(0);
    178: }

    182: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
    183: {

    187:   VecSet(diag,4.0);
    188:   return(0);
    189: }