Date: 2023-11-27T17:18:39+00:00

Actual source code: ex3.c
slepc-3.20.1 2023-11-27
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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;

     33:   PetscFunctionBeginUser;
     34:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
     35:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
     36:   PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only");

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

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

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

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

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

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

     75:   PetscCall(EPSSolve(eps));

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

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

     89:   /* show detailed info unless -terse option is given by user */
     90:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
     91:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
     92:   else {
     93:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
     94:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
     95:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
     96:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
     97:   }
     98:   PetscCall(EPSDestroy(&eps));
     99:   PetscCall(MatDestroy(&A));
    100:   PetscCall(SlepcFinalize());
    101:   return 0;
    102: }

    104: /*
    105:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
    106:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
    107:     DU on the superdiagonal.
    108:  */
    109: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
    110: {
    111:   PetscScalar dd,dl,du;
    112:   int         j;

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

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

    124: /*
    125:     Matrix-vector product subroutine for the 2D Laplacian.

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

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

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

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

    147:   PetscFunctionBeginUser;
    148:   PetscCall(MatShellGetContext(A,&ctx));
    149:   nx = *(int*)ctx;
    150:   PetscCall(VecGetArrayRead(x,&px));
    151:   PetscCall(VecGetArray(y,&py));

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

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

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

    166:   PetscCall(VecRestoreArrayRead(x,&px));
    167:   PetscCall(VecRestoreArray(y,&py));
    168:   PetscFunctionReturn(PETSC_SUCCESS);
    169: }

    171: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
    172: {
    173:   PetscFunctionBeginUser;
    174:   PetscCall(VecSet(diag,4.0));
    175:   PetscFunctionReturn(PETSC_SUCCESS);
    176: }

    178: /*TEST

    180:    test:
    181:       suffix: 1
    182:       args: -n 72 -eps_nev 4 -eps_ncv 20 -terse
    183:       requires: !single

    185: TEST*/