Date: 2022-03-31T15:29:12+00:00

Actual source code: test8.c
slepc-3.17.0 2022-03-31
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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>
     17: #include <petscblaslapack.h>

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

     25: int main(int argc,char **argv)
     26: {
     27:   Mat            A;               /* operator matrix */
     28:   EPS            eps;             /* eigenproblem solver context */
     29:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
     30:   PetscMPIInt    size;
     31:   PetscInt       N,n=10,nev;

     33:   SlepcInitialize(&argc,&argv,(char*)0,help);
     34:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     37:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     38:   N = n*n;
     39:   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);

     41:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     42:      Compute the operator matrix that defines the eigensystem, Ax=kx
     43:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     51:                 Create the eigensolver and set various options
     52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     54:   /*
     55:      Create eigensolver context
     56:   */
     57:   EPSCreate(PETSC_COMM_WORLD,&eps);

     59:   /*
     60:      Set operators. In this case, it is a standard eigenvalue problem
     61:   */
     62:   EPSSetOperators(eps,A,NULL);
     63:   EPSSetProblemType(eps,EPS_HEP);
     64:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);

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

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

     75:   EPSSolve(eps);
     76:   EPSGetDimensions(eps,&nev,NULL,NULL);
     77:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

     79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     80:                     Display solution and clean up
     81:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     83:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
     84:   EPSDestroy(&eps);
     85:   MatDestroy(&A);
     86:   SlepcFinalize();
     87:   return 0;
     88: }

     90: /*
     91:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
     92:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
     93:     DU on the superdiagonal.
     94:  */
     95: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
     96: {
     97:   PetscScalar dd,dl,du;
     98:   int         j;

    100:   dd  = 4.0;
    101:   dl  = -1.0;
    102:   du  = -1.0;

    104:   y[0] =  dd*x[0] + du*x[1];
    105:   for (j=1;j<nx-1;j++)
    106:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
    107:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
    108: }

    110: /*
    111:     Matrix-vector product subroutine for the 2D Laplacian.

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

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

    118:                  | T -I          |
    119:                  |-I  T -I       |
    120:              A = |   -I  T       |
    121:                  |        ...  -I|
    122:                  |           -I T|

    124:     The subroutine TV is called to compute y<--T*x.
    125:  */
    126: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
    127: {
    128:   void              *ctx;
    129:   int               nx,lo,i,j;
    130:   const PetscScalar *px;
    131:   PetscScalar       *py;

    134:   MatShellGetContext(A,&ctx);
    135:   nx = *(int*)ctx;
    136:   VecGetArrayRead(x,&px);
    137:   VecGetArray(y,&py);

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

    142:   for (j=2;j<nx;j++) {
    143:     lo = (j-1)*nx;
    144:     tv(nx,&px[lo],&py[lo]);
    145:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
    146:   }

    148:   lo = (nx-1)*nx;
    149:   tv(nx,&px[lo],&py[lo]);
    150:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

    152:   VecRestoreArrayRead(x,&px);
    153:   VecRestoreArray(y,&py);
    154:   PetscFunctionReturn(0);
    155: }

    157: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
    158: {
    160:   VecSet(diag,4.0);
    161:   PetscFunctionReturn(0);
    162: }

    164: /*TEST

    166:    testset:
    167:       args: -n 20 -eps_nev 4 -eps_ncv 11 -eps_max_it 40000
    168:       requires: !single
    169:       output_file: output/test8_1.out
    170:       test:
    171:          suffix: 1
    172:          args: -eps_type {{power subspace arnoldi}}
    173:       test:
    174:          suffix: 1_lanczos
    175:          args: -eps_type lanczos -eps_lanczos_reorthog local
    176:       test:
    177:          suffix: 1_lapack
    178:          args: -eps_type lapack
    179:          timeoutfactor: 2
    180:       test:
    181:          suffix: 1_elemental
    182:          args: -eps_type elemental
    183:          requires: elemental
    184:       test:
    185:          suffix: 1_krylovschur_vecs
    186:          args: -bv_type vecs -bv_orthog_refine always -eps_ncv 10
    187:       test:
    188:          suffix: 1_jd
    189:          args: -eps_type jd -eps_jd_blocksize 3
    190:       test:
    191:          suffix: 1_gd
    192:          args: -eps_type gd -eps_gd_blocksize 3 -eps_tol 1e-8
    193:       test:
    194:          suffix: 1_gd2
    195:          args: -eps_type gd -eps_gd_double_expansion
    196:       test:
    197:          suffix: 1_primme
    198:          args: -eps_type primme -eps_conv_abs
    199:          requires: primme

    201:    testset:
    202:       args: -eps_nev 4 -eps_smallest_real -eps_max_it 600
    203:       output_file: output/test8_2.out
    204:       test:
    205:          suffix: 2
    206:          args: -eps_type {{rqcg lobpcg}}
    207:       test:
    208:          suffix: 2_lanczos
    209:          args: -eps_type lanczos -eps_lanczos_reorthog local
    210:       test:
    211:          suffix: 2_arpack
    212:          args: -eps_type arpack -eps_ncv 6
    213:          requires: arpack !single
    214:       test:
    215:          suffix: 2_primme
    216:          args: -eps_type primme -eps_conv_abs -eps_primme_method lobpcg_orthobasisw -eps_ncv 24
    217:          requires: primme

    219:    testset:
    220:       args: -eps_nev 12 -eps_mpd 9 -eps_smallest_real -eps_max_it 1000
    221:       output_file: output/test8_3.out
    222:       test:
    223:          suffix: 3_rqcg
    224:          args: -eps_type rqcg
    225:       test:
    226:          suffix: 3_lanczos
    227:          args: -eps_type lanczos -eps_lanczos_reorthog local
    228:       test:
    229:          suffix: 3_lobpcg
    230:          args: -eps_type lobpcg -eps_lobpcg_blocksize 3 -eps_lobpcg_locking 0 -st_ksp_type preonly -st_pc_type jacobi
    231:          requires: !__float128
    232:       test:
    233:          suffix: 3_lobpcg_quad
    234:          args: -eps_type lobpcg -eps_lobpcg_blocksize 3 -eps_lobpcg_locking 0 -st_ksp_type preonly -st_pc_type jacobi -eps_tol 1e-25
    235:          requires: __float128
    236: TEST*/