Date: 2021-02-01T14:42:03+00:00

Actual source code: ex3.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

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

     16: #include <slepceps.h>

     18: /*
     19:    User-defined routines
     20: */
     21: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
     22: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);

     24: int main(int argc,char **argv)
     25: {
     26:   Mat            A;               /* operator matrix */
     27:   EPS            eps;             /* eigenproblem solver context */
     28:   EPSType        type;
     29:   PetscMPIInt    size;
     30:   PetscInt       N,n=10,nev;
     31:   PetscBool      terse;

     34:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     35:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     36:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only");

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

     42:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     43:        Create the operator matrix that defines the eigensystem, Ax=kx
     44:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     46:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);
     47:   MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D);
     48:   MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D);
     49:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D);

     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:                 Create the eigensolver and set various options
     53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     55:   /*
     56:      Create eigensolver context
     57:   */
     58:   EPSCreate(PETSC_COMM_WORLD,&eps);

     60:   /*
     61:      Set operators. In this case, it is a standard eigenvalue problem
     62:   */
     63:   EPSSetOperators(eps,A,NULL);
     64:   EPSSetProblemType(eps,EPS_HEP);

     66:   /*
     67:      Set solver parameters at runtime
     68:   */
     69:   EPSSetFromOptions(eps);

     71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     72:                       Solve the eigensystem
     73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     75:   EPSSolve(eps);

     77:   /*
     78:      Optional: Get some information from the solver and display it
     79:   */
     80:   EPSGetType(eps,&type);
     81:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
     82:   EPSGetDimensions(eps,&nev,NULL,NULL);
     83:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

     85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     86:                     Display solution and clean up
     87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     89:   /* show detailed info unless -terse option is given by user */
     90:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
     91:   if (terse) {
     92:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
     93:   } else {
     94:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
     95:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
     96:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
     97:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
     98:   }
     99:   EPSDestroy(&eps);
    100:   MatDestroy(&A);
    101:   SlepcFinalize();
    102:   return ierr;
    103: }

    105: /*
    106:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
    107:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
    108:     DU on the superdiagonal.
    109:  */
    110: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
    111: {
    112:   PetscScalar dd,dl,du;
    113:   int         j;

    115:   dd  = 4.0;
    116:   dl  = -1.0;
    117:   du  = -1.0;

    119:   y[0] =  dd*x[0] + du*x[1];
    120:   for (j=1;j<nx-1;j++)
    121:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
    122:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
    123: }

    125: /*
    126:     Matrix-vector product subroutine for the 2D Laplacian.

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

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

    133:                  | T -I          |
    134:                  |-I  T -I       |
    135:              A = |   -I  T       |
    136:                  |        ...  -I|
    137:                  |           -I T|

    139:     The subroutine TV is called to compute y<--T*x.
    140:  */
    141: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
    142: {
    143:   void              *ctx;
    144:   int               nx,lo,i,j;
    145:   const PetscScalar *px;
    146:   PetscScalar       *py;
    147:   PetscErrorCode    ierr;

    150:   MatShellGetContext(A,&ctx);
    151:   nx = *(int*)ctx;
    152:   VecGetArrayRead(x,&px);
    153:   VecGetArray(y,&py);

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

    158:   for (j=2;j<nx;j++) {
    159:     lo = (j-1)*nx;
    160:     tv(nx,&px[lo],&py[lo]);
    161:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
    162:   }

    164:   lo = (nx-1)*nx;
    165:   tv(nx,&px[lo],&py[lo]);
    166:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

    168:   VecRestoreArrayRead(x,&px);
    169:   VecRestoreArray(y,&py);
    170:   return(0);
    171: }

    173: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
    174: {

    178:   VecSet(diag,4.0);
    179:   return(0);
    180: }

    182: /*TEST

    184:    test:
    185:       suffix: 1
    186:       args: -n 72 -eps_nev 4 -eps_ncv 20 -terse

    188: TEST*/