Date: 2021-02-01T14:42:13+00:00

Actual source code: ex28.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[] = "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;
     36:   ST             st;

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

     42:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     43:   N = n*n;
     44:   PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem with shell matrices, N=%D (%Dx%D 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:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&K);
     52:   MatShellSetOperation(K,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D);
     53:   MatShellSetOperation(K,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D);
     54:   MatShellSetOperation(K,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D);

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

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

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

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

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

     94:   PEPSolve(pep);

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

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

    108:   /* show detailed info unless -terse option is given by user */
    109:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    110:   if (terse) {
    111:     PEPErrorView(pep,PEP_ERROR_RELATIVE,NULL);
    112:   } else {
    113:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    114:     PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    115:     PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    116:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    117:   }
    118:   PEPDestroy(&pep);
    119:   MatDestroy(&M);
    120:   MatDestroy(&C);
    121:   MatDestroy(&K);
    122:   SlepcFinalize();
    123:   return ierr;
    124: }

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

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

    140:   y[0] =  dd*x[0] + du*x[1];
    141:   for (j=1;j<nx-1;j++)
    142:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
    143:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
    144: }

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

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

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

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

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

    171:   MatShellGetContext(A,&ctx);
    172:   nx = *(int*)ctx;
    173:   VecGetArrayRead(x,&px);
    174:   VecGetArray(y,&py);

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

    179:   for (j=2;j<nx;j++) {
    180:     lo = (j-1)*nx;
    181:     tv(nx,&px[lo],&py[lo]);
    182:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
    183:   }

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

    189:   VecRestoreArrayRead(x,&px);
    190:   VecRestoreArray(y,&py);
    191:   return(0);
    192: }

    194: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
    195: {

    199:   VecSet(diag,4.0);
    200:   return(0);
    201: }

    203: /*
    204:     Matrix-vector product subroutine for the Null matrix.
    205:  */
    206: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y)
    207: {

    211:   VecSet(y,0.0);
    212:   return(0);
    213: }

    215: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag)
    216: {

    220:   VecSet(diag,0.0);
    221:   return(0);
    222: }

    224: /*
    225:     Matrix-vector product subroutine for the Identity matrix.
    226:  */
    227: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y)
    228: {
    229:   PetscErrorCode    ierr;

    232:   VecCopy(x,y);
    233:   return(0);
    234: }

    236: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag)
    237: {

    241:   VecSet(diag,1.0);
    242:   return(0);
    243: }

    245: /*TEST

    247:    test:
    248:       suffix: 1
    249:       args: -pep_type {{toar qarnoldi linear}} -pep_nev 4 -terse
    250:       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/"

    252: TEST*/