Date: 2026-05-01T10:02:39+00:00

Actual source code: ex13.c

      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[] = "Generalized Symmetric eigenproblem.\n\n"
     12:   "The problem is Ax = lambda Bx, with:\n"
     13:   "   A = Laplacian operator in 2-D\n"
     14:   "   B = diagonal matrix with all values equal to 4 except nulldim zeros\n\n"
     15:   "The command line options are:\n"
     16:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     17:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n"
     18:   "  -nulldim <k>, where <k> = dimension of the nullspace of B.\n\n";

     20: #include <slepceps.h>

     22: int main(int argc,char **argv)
     23: {
     24:   Mat            A,B;         /* matrices */
     25:   EPS            eps;         /* eigenproblem solver context */
     26:   EPSType        type;
     27:   PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,nulldim=0;
     28:   PetscBool      flag,terse;

     30:   PetscFunctionBeginUser;
     31:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     33:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     34:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     35:   if (!flag) m=n;
     36:   N = n*m;
     37:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-nulldim",&nulldim,NULL));
     38:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid), null(B)=%" PetscInt_FMT "\n\n",N,n,m,nulldim));

     40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     41:      Compute the matrices that define the eigensystem, Ax=kBx
     42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     44:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     45:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     46:   PetscCall(MatSetFromOptions(A));

     48:   PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
     49:   PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N));
     50:   PetscCall(MatSetFromOptions(B));

     52:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     53:   for (II=Istart;II<Iend;II++) {
     54:     i = II/n; j = II-i*n;
     55:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
     56:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
     57:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
     58:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
     59:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
     60:     if (II>=nulldim) PetscCall(MatSetValue(B,II,II,4.0,INSERT_VALUES));
     61:   }

     63:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     64:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
     65:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
     66:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));

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

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

     77:   /*
     78:      Set operators. In this case, it is a generalized eigenvalue problem
     79:   */
     80:   PetscCall(EPSSetOperators(eps,A,B));
     81:   PetscCall(EPSSetProblemType(eps,EPS_GHEP));

     83:   /*
     84:      Set solver parameters at runtime
     85:   */
     86:   PetscCall(EPSSetFromOptions(eps));

     88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     89:                       Solve the eigensystem
     90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     92:   PetscCall(EPSSolve(eps));

     94:   /*
     95:      Optional: Get some information from the solver and display it
     96:   */
     97:   PetscCall(EPSGetType(eps,&type));
     98:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
     99:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    100:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    103:                     Display solution and clean up
    104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    106:   /* show detailed info unless -terse option is given by user */
    107:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    108:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    109:   else {
    110:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    111:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
    112:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    113:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    114:   }
    115:   PetscCall(EPSDestroy(&eps));
    116:   PetscCall(MatDestroy(&A));
    117:   PetscCall(MatDestroy(&B));
    118:   PetscCall(SlepcFinalize());
    119:   return 0;
    120: }

    122: /*TEST

    124:    test:
    125:       suffix: 1
    126:       args: -eps_nev 4 -eps_ncv 22 -eps_tol 1e-5 -st_type sinvert -terse
    127:       filter: grep -v Solution

    129:    test:
    130:       suffix: 2
    131:       args: -n 110 -nulldim 6 -eps_nev 4 -eps_ncv 18 -eps_tol 1e-5 -eps_purify 1 -st_type sinvert -st_matstructure {{different subset}} -terse
    132:       requires: !single

    134:    test:
    135:       suffix: 3
    136:       args: -eps_nev 3 -eps_tol 1e-5 -mat_type sbaij -st_type sinvert -terse

    138:    test:
    139:       suffix: 4
    140:       args: -eps_nev 4 -eps_tol 1e-4 -eps_smallest_real -eps_type {{gd lobpcg rqcg}} -terse
    141:       output_file: output/ex13_1.out
    142:       filter: grep -v Solution

    144:    test:
    145:       suffix: 5_primme
    146:       args: -n 10 -m 12 -eps_nev 4 -eps_target 0.9 -eps_max_it 15000 -eps_type primme -st_pc_type jacobi -terse
    147:       requires: primme defined(SLEPC_HAVE_PRIMME3) !single

    149:    test:
    150:       suffix: 6
    151:       nsize: 2
    152:       args: -eps_type ciss -rg_type ellipse -rg_ellipse_center 1.4 -rg_ellipse_radius 0.1 -eps_ciss_partitions 2 -terse
    153:       requires: !single

    155: TEST*/