Date: 2026-05-01T10:02:30+00:00

Actual source code: test10.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[] = "Computes the smallest nonzero eigenvalue of the Laplacian of a graph.\n\n"
     12:   "This example illustrates EPSSetDeflationSpace(). The example graph corresponds to a "
     13:   "2-D regular mesh. The command line options are:\n"
     14:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     15:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     17: #include <slepceps.h>

     19: int main (int argc,char **argv)
     20: {
     21:   EPS            eps;             /* eigenproblem solver context */
     22:   Mat            A;               /* operator matrix */
     23:   Vec            x;
     24:   PetscInt       N,n=10,m,i,j,II,Istart,Iend,nev;
     25:   PetscScalar    w;
     26:   PetscBool      flag;

     28:   PetscFunctionBeginUser;
     29:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     31:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     32:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     33:   if (!flag) m=n;
     34:   N = n*m;
     35:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nFiedler vector of a 2-D regular mesh, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

     37:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     38:      Compute the operator matrix that defines the eigensystem, Ax=kx
     39:      In this example, A = L(G), where L is the Laplacian of graph G, i.e.
     40:      Lii = degree of node i, Lij = -1 if edge (i,j) exists in G
     41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     47:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     48:   for (II=Istart;II<Iend;II++) {
     49:     i = II/n; j = II-i*n;
     50:     w = 0.0;
     51:     if (i>0) { PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES)); w=w+1.0; }
     52:     if (i<m-1) { PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES)); w=w+1.0; }
     53:     if (j>0) { PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES)); w=w+1.0; }
     54:     if (j<n-1) { PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES)); w=w+1.0; }
     55:     PetscCall(MatSetValue(A,II,II,w,INSERT_VALUES));
     56:   }

     58:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     59:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

     61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     62:                 Create the eigensolver and set various options
     63:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     65:   /*
     66:      Create eigensolver context
     67:   */
     68:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

     70:   /*
     71:      Set operators. In this case, it is a standard eigenvalue problem
     72:   */
     73:   PetscCall(EPSSetOperators(eps,A,NULL));
     74:   PetscCall(EPSSetProblemType(eps,EPS_HEP));

     76:   /*
     77:      Select portion of spectrum
     78:   */
     79:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL));

     81:   /*
     82:      Set solver parameters at runtime
     83:   */
     84:   PetscCall(EPSSetFromOptions(eps));

     86:   /*
     87:      Attach deflation space: in this case, the matrix has a constant
     88:      nullspace, [1 1 ... 1]^T is the eigenvector of the zero eigenvalue
     89:   */
     90:   PetscCall(MatCreateVecs(A,&x,NULL));
     91:   PetscCall(VecSet(x,1.0));
     92:   PetscCall(EPSSetDeflationSpace(eps,1,&x));
     93:   PetscCall(VecDestroy(&x));

     95:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     96:                       Solve the eigensystem
     97:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     99:   PetscCall(EPSSolve(eps));
    100:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    101:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104:                     Display solution and clean up
    105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    107:   PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    108:   PetscCall(EPSDestroy(&eps));
    109:   PetscCall(MatDestroy(&A));
    110:   PetscCall(SlepcFinalize());
    111:   return 0;
    112: }

    114: /*TEST

    116:    testset:
    117:       args: -eps_nev 4 -m 11 -eps_max_it 500
    118:       output_file: output/test10_1.out
    119:       test:
    120:          suffix: 1
    121:          args: -eps_type {{krylovschur arnoldi gd jd rqcg}}
    122:       test:
    123:          suffix: 1_lobpcg
    124:          args: -eps_type lobpcg -eps_lobpcg_blocksize 6
    125:       test:
    126:          suffix: 1_lanczos
    127:          args: -eps_type lanczos -eps_lanczos_reorthog local
    128:          requires: !single
    129:       test:
    130:          suffix: 1_gd2
    131:          args: -eps_type gd -eps_gd_double_expansion

    133: TEST*/