Date: 2017-05-17T08:27:06+00:00

Actual source code: ex28.c
slepc-3.7.4 2017-05-17
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, 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[] = "A quadratic eigenproblem defined using shell matrices.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = number of grid subdivisions in x and y dimensions.\n\n";

     26: #include <slepcpep.h>

     28: /*
     29:    User-defined routines
     30: */
     31: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
     32: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);
     33: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y);
     34: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag);
     35: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y);
     36: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag);

     40: int main(int argc,char **argv)
     41: {
     42:   Mat            M,C,K,A[3];      /* problem matrices */
     43:   PEP            pep;             /* polynomial eigenproblem solver context */
     44:   PEPType        type;
     45:   PetscInt       N,n=10,nev;
     46:   PetscMPIInt    size;
     47:   PetscBool      terse;
     49:   ST             st;

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

     55:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     56:   N = n*n;
     57:   PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem with shell matrices, N=%D (%Dx%D grid)\n\n",N,n,n);

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     63:   /* K is the 2-D Laplacian */
     64:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&K);
     65:   MatSetFromOptions(K);
     66:   MatShellSetOperation(K,MATOP_MULT,(void(*)())MatMult_Laplacian2D);
     67:   MatShellSetOperation(K,MATOP_MULT_TRANSPOSE,(void(*)())MatMult_Laplacian2D);
     68:   MatShellSetOperation(K,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Laplacian2D);

     70:   /* C is the zero matrix */
     71:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&C);
     72:   MatSetFromOptions(C);
     73:   MatShellSetOperation(C,MATOP_MULT,(void(*)())MatMult_Zero);
     74:   MatShellSetOperation(C,MATOP_MULT_TRANSPOSE,(void(*)())MatMult_Zero);
     75:   MatShellSetOperation(C,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Zero);

     77:   /* M is the identity matrix */
     78:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&M);
     79:   MatSetFromOptions(M);
     80:   MatShellSetOperation(M,MATOP_MULT,(void(*)())MatMult_Identity);
     81:   MatShellSetOperation(M,MATOP_MULT_TRANSPOSE,(void(*)())MatMult_Identity);
     82:   MatShellSetOperation(M,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Identity);

     84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     85:                 Create the eigensolver and set various options
     86:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     88:   /*
     89:      Create eigensolver context
     90:   */
     91:   PEPCreate(PETSC_COMM_WORLD,&pep);

     93:   /*
     94:      Set matrices and problem type
     95:   */
     96:   A[0] = K; A[1] = C; A[2] = M;
     97:   PEPSetOperators(pep,3,A);
     98:   PEPGetST(pep,&st);
     99:   STSetMatMode(st,ST_MATMODE_SHELL);

    101:   /*
    102:      Set solver parameters at runtime
    103:   */
    104:   PEPSetFromOptions(pep);

    106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    107:                       Solve the eigensystem
    108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    110:   PEPSolve(pep);

    112:   /*
    113:      Optional: Get some information from the solver and display it
    114:   */
    115:   PEPGetType(pep,&type);
    116:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    117:   PEPGetDimensions(pep,&nev,NULL,NULL);
    118:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    121:                     Display solution and clean up
    122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    124:   /* show detailed info unless -terse option is given by user */
    125:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    126:   if (terse) {
    127:     PEPErrorView(pep,PEP_ERROR_RELATIVE,NULL);
    128:   } else {
    129:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    130:     PEPReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    131:     PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    132:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    133:   }
    134:   PEPDestroy(&pep);
    135:   MatDestroy(&M);
    136:   MatDestroy(&C);
    137:   MatDestroy(&K);
    138:   SlepcFinalize();
    139:   return ierr;
    140: }

    142: /*
    143:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
    144:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
    145:     DU on the superdiagonal.
    146:  */
    147: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
    148: {
    149:   PetscScalar dd,dl,du;
    150:   int         j;

    152:   dd  = 4.0;
    153:   dl  = -1.0;
    154:   du  = -1.0;

    156:   y[0] =  dd*x[0] + du*x[1];
    157:   for (j=1;j<nx-1;j++)
    158:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
    159:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
    160: }

    164: /*
    165:     Matrix-vector product subroutine for the 2D Laplacian.

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

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

    172:                  | T -I          |
    173:                  |-I  T -I       |
    174:              A = |   -I  T       |
    175:                  |        ...  -I|
    176:                  |           -I T|

    178:     The subroutine TV is called to compute y<--T*x.
    179:  */
    180: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
    181: {
    182:   void              *ctx;
    183:   int               nx,lo,i,j;
    184:   const PetscScalar *px;
    185:   PetscScalar       *py;
    186:   PetscErrorCode    ierr;

    189:   MatShellGetContext(A,&ctx);
    190:   nx = *(int*)ctx;
    191:   VecGetArrayRead(x,&px);
    192:   VecGetArray(y,&py);

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

    197:   for (j=2;j<nx;j++) {
    198:     lo = (j-1)*nx;
    199:     tv(nx,&px[lo],&py[lo]);
    200:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
    201:   }

    203:   lo = (nx-1)*nx;
    204:   tv(nx,&px[lo],&py[lo]);
    205:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

    207:   VecRestoreArrayRead(x,&px);
    208:   VecRestoreArray(y,&py);
    209:   return(0);
    210: }

    214: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
    215: {

    219:   VecSet(diag,4.0);
    220:   return(0);
    221: }

    225: /*
    226:     Matrix-vector product subroutine for the Null matrix.
    227:  */
    228: PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y)
    229: {

    233:   VecSet(y,0.0);
    234:   return(0);
    235: }

    239: PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag)
    240: {

    244:   VecSet(diag,0.0);
    245:   return(0);
    246: }

    250: /*
    251:     Matrix-vector product subroutine for the Identity matrix.
    252:  */
    253: PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y)
    254: {
    255:   PetscErrorCode    ierr;

    258:   VecCopy(x,y);
    259:   return(0);
    260: }

    264: PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag)
    265: {

    269:   VecSet(diag,1.0);
    270:   return(0);
    271: }