Date: 2023-11-27T17:19:07+00:00

Actual source code: ex28.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[] = "A quadratic eigenproblem defined using shell matrices.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions in x and y dimensions.\n\n";

     15: #include <slepcpep.h>

     17: /*
     18:    User-defined routines
     19: */
     20: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
     21: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);
     22: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y);
     23: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag);
     24: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y);
     25: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag);

     27: int main(int argc,char **argv)
     28: {
     29:   Mat            M,C,K,A[3];      /* problem matrices */
     30:   PEP            pep;             /* polynomial eigenproblem solver context */
     31:   PEPType        type;
     32:   PetscInt       N,n=10,nev;
     33:   PetscMPIInt    size;
     34:   PetscBool      terse;
     35:   ST             st;

     37:   PetscFunctionBeginUser;
     38:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
     39:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
     40:   PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only");

     42:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     43:   N = n*n;
     44:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem with shell matrices, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,n));

     46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     47:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     48:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     50:   /* K is the 2-D Laplacian */
     51:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&K));
     52:   PetscCall(MatShellSetOperation(K,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D));
     53:   PetscCall(MatShellSetOperation(K,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D));
     54:   PetscCall(MatShellSetOperation(K,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D));

     56:   /* C is the zero matrix */
     57:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&C));
     58:   PetscCall(MatShellSetOperation(C,MATOP_MULT,(void(*)(void))MatMult_Zero));
     59:   PetscCall(MatShellSetOperation(C,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Zero));
     60:   PetscCall(MatShellSetOperation(C,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Zero));

     62:   /* M is the identity matrix */
     63:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&M));
     64:   PetscCall(MatShellSetOperation(M,MATOP_MULT,(void(*)(void))MatMult_Identity));
     65:   PetscCall(MatShellSetOperation(M,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Identity));
     66:   PetscCall(MatShellSetOperation(M,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Identity));

     68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     69:                 Create the eigensolver and set various options
     70:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     72:   /*
     73:      Create eigensolver context
     74:   */
     75:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));

     77:   /*
     78:      Set matrices and problem type
     79:   */
     80:   A[0] = K; A[1] = C; A[2] = M;
     81:   PetscCall(PEPSetOperators(pep,3,A));
     82:   PetscCall(PEPGetST(pep,&st));
     83:   PetscCall(STSetMatMode(st,ST_MATMODE_SHELL));

     85:   /*
     86:      Set solver parameters at runtime
     87:   */
     88:   PetscCall(PEPSetFromOptions(pep));

     90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     91:                       Solve the eigensystem
     92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     94:   PetscCall(PEPSolve(pep));

     96:   /*
     97:      Optional: Get some information from the solver and display it
     98:   */
     99:   PetscCall(PEPGetType(pep,&type));
    100:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
    101:   PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL));
    102:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:                     Display solution and clean up
    106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    108:   /* show detailed info unless -terse option is given by user */
    109:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    110:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,NULL));
    111:   else {
    112:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    113:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    114:     PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    115:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    116:   }
    117:   PetscCall(PEPDestroy(&pep));
    118:   PetscCall(MatDestroy(&M));
    119:   PetscCall(MatDestroy(&C));
    120:   PetscCall(MatDestroy(&K));
    121:   PetscCall(SlepcFinalize());
    122:   return 0;
    123: }

    125: /*
    126:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
    127:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
    128:     DU on the superdiagonal.
    129:  */
    130: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
    131: {
    132:   PetscScalar dd,dl,du;
    133:   int         j;

    135:   dd  = 4.0;
    136:   dl  = -1.0;
    137:   du  = -1.0;

    139:   y[0] =  dd*x[0] + du*x[1];
    140:   for (j=1;j<nx-1;j++)
    141:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
    142:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
    143: }

    145: /*
    146:     Matrix-vector product subroutine for the 2D Laplacian.

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

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

    153:                  | T -I          |
    154:                  |-I  T -I       |
    155:              A = |   -I  T       |
    156:                  |        ...  -I|
    157:                  |           -I T|

    159:     The subroutine TV is called to compute y<--T*x.
    160:  */
    161: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
    162: {
    163:   void              *ctx;
    164:   int               nx,lo,i,j;
    165:   const PetscScalar *px;
    166:   PetscScalar       *py;

    168:   PetscFunctionBeginUser;
    169:   PetscCall(MatShellGetContext(A,&ctx));
    170:   nx = *(int*)ctx;
    171:   PetscCall(VecGetArrayRead(x,&px));
    172:   PetscCall(VecGetArray(y,&py));

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

    177:   for (j=2;j<nx;j++) {
    178:     lo = (j-1)*nx;
    179:     tv(nx,&px[lo],&py[lo]);
    180:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
    181:   }

    183:   lo = (nx-1)*nx;
    184:   tv(nx,&px[lo],&py[lo]);
    185:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

    187:   PetscCall(VecRestoreArrayRead(x,&px));
    188:   PetscCall(VecRestoreArray(y,&py));
    189:   PetscFunctionReturn(PETSC_SUCCESS);
    190: }

    192: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
    193: {
    194:   PetscFunctionBeginUser;
    195:   PetscCall(VecSet(diag,4.0));
    196:   PetscFunctionReturn(PETSC_SUCCESS);
    197: }

    199: /*
    200:     Matrix-vector product subroutine for the Null matrix.
    201:  */
    202: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y)
    203: {
    204:   PetscFunctionBeginUser;
    205:   PetscCall(VecSet(y,0.0));
    206:   PetscFunctionReturn(PETSC_SUCCESS);
    207: }

    209: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag)
    210: {
    211:   PetscFunctionBeginUser;
    212:   PetscCall(VecSet(diag,0.0));
    213:   PetscFunctionReturn(PETSC_SUCCESS);
    214: }

    216: /*
    217:     Matrix-vector product subroutine for the Identity matrix.
    218:  */
    219: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y)
    220: {
    221:   PetscFunctionBeginUser;
    222:   PetscCall(VecCopy(x,y));
    223:   PetscFunctionReturn(PETSC_SUCCESS);
    224: }

    226: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag)
    227: {
    228:   PetscFunctionBeginUser;
    229:   PetscCall(VecSet(diag,1.0));
    230:   PetscFunctionReturn(PETSC_SUCCESS);
    231: }

    233: /*TEST

    235:    test:
    236:       suffix: 1
    237:       args: -pep_type {{toar qarnoldi linear}} -pep_nev 4 -terse
    238:       filter: grep -v Solution | sed -e "s/2.7996[1-8]i/2.79964i/g" | sed -e "s/2.7570[5-9]i/2.75708i/g" | sed -e "s/0.00000-2.79964i, 0.00000+2.79964i/0.00000+2.79964i, 0.00000-2.79964i/" | sed -e "s/0.00000-2.75708i, 0.00000+2.75708i/0.00000+2.75708i, 0.00000-2.75708i/"

    240: TEST*/