Date: 2015-09-03T15:05:04+00:00

Actual source code: test8.c
slepc-3.6.1 2015-09-03
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, 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:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
     44:   PetscMPIInt    size;
     45:   PetscInt       N,n=10,nev;

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

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

     56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     57:      Compute the operator matrix that defines the eigensystem, Ax=kx
     58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     67:                 Create the eigensolver and set various options
     68:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

     82:   /*
     83:      Set solver parameters at runtime
     84:   */
     85:   EPSSetFromOptions(eps);

     87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88:                       Solve the eigensystem
     89:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     91:   EPSSolve(eps);

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

    101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    102:                     Display solution and clean up
    103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    105:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    106:   EPSDestroy(&eps);
    107:   MatDestroy(&A);
    108:   SlepcFinalize();
    109:   return 0;
    110: }

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

    122:   dd  = 4.0;
    123:   dl  = -1.0;
    124:   du  = -1.0;

    126:   y[0] =  dd*x[0] + du*x[1];
    127:   for (j=1;j<nx-1;j++)
    128:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
    129:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
    130: }

    134: /*
    135:     Matrix-vector product subroutine for the 2D Laplacian.

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

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

    142:                  | T -I          |
    143:                  |-I  T -I       |
    144:              A = |   -I  T       |
    145:                  |        ...  -I|
    146:                  |           -I T|

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

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

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

    167:   for (j=2;j<nx;j++) {
    168:     lo = (j-1)*nx;
    169:     tv(nx,&px[lo],&py[lo]);
    170:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
    171:   }

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

    177:   VecRestoreArrayRead(x,&px);
    178:   VecRestoreArray(y,&py);
    179:   return(0);
    180: }

    184: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
    185: {

    189:   VecSet(diag,4.0);
    190:   return(0);
    191: }