Actual source code: ex11.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:   EPSType        type;
     25:   PetscInt       N,n=10,m,i,j,II,Istart,Iend,nev;
     26:   PetscScalar    w;
     27:   PetscBool      flag,terse;

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

     32:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     33:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     34:   if (!flag) m=n;
     35:   N = n*m;
     36:   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));

     38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     39:      Compute the operator matrix that defines the eigensystem, Ax=kx
     40:      In this example, A = L(G), where L is the Laplacian of graph G, i.e.
     41:      Lii = degree of node i, Lij = -1 if edge (i,j) exists in G
     42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     48:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     49:   for (II=Istart;II<Iend;II++) {
     50:     i = II/n; j = II-i*n;
     51:     w = 0.0;
     52:     if (i>0) { PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES)); w=w+1.0; }
     53:     if (i<m-1) { PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES)); w=w+1.0; }
     54:     if (j>0) { PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES)); w=w+1.0; }
     55:     if (j<n-1) { PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES)); w=w+1.0; }
     56:     PetscCall(MatSetValue(A,II,II,w,INSERT_VALUES));
     57:   }

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

     62:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     63:                 Create the eigensolver and set various options
     64:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

     96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:                       Solve the eigensystem
     98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    100:   PetscCall(EPSSolve(eps));

    102:   /*
    103:      Optional: Get some information from the solver and display it
    104:   */
    105:   PetscCall(EPSGetType(eps,&type));
    106:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
    107:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    108:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    111:                     Display solution and clean up
    112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    114:   /* show detailed info unless -terse option is given by user */
    115:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    116:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    117:   else {
    118:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    119:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
    120:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    121:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    122:   }
    123:   PetscCall(EPSDestroy(&eps));
    124:   PetscCall(MatDestroy(&A));
    125:   PetscCall(SlepcFinalize());
    126:   return 0;
    127: }

    129: /*TEST

    131:    testset:
    132:       args: -eps_nev 4 -terse
    133:       output_file: output/ex11_1.out
    134:       test:
    135:          suffix: 1
    136:          args: -eps_krylovschur_restart .2
    137:       test:
    138:          suffix: 2
    139:          args: -eps_ncv 20 -eps_target 0 -st_type sinvert -st_ksp_type cg -st_pc_type jacobi

    141: TEST*/