Date: 2022-11-02T11:46:56+00:00

Actual source code: test10.c
slepc-3.18.1 2022-11-02
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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[] = "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;

     29:   SlepcInitialize(&argc,&argv,(char*)0,help);

     31:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     32:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     33:   if (!flag) m=n;
     34:   N = n*m;
     35:   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:   MatCreate(PETSC_COMM_WORLD,&A);
     44:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     45:   MatSetFromOptions(A);
     46:   MatSetUp(A);

     48:   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) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); w=w+1.0; }
     53:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); w=w+1.0; }
     54:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); w=w+1.0; }
     55:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); w=w+1.0; }
     56:     MatSetValue(A,II,II,w,INSERT_VALUES);
     57:   }

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

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

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

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

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

     82:   /*
     83:      Set solver parameters at runtime
     84:   */
     85:   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:   MatCreateVecs(A,&x,NULL);
     92:   VecSet(x,1.0);
     93:   EPSSetDeflationSpace(eps,1,&x);
     94:   VecDestroy(&x);

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

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

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:                     Display solution and clean up
    106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    108:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    109:   EPSDestroy(&eps);
    110:   MatDestroy(&A);
    111:   SlepcFinalize();
    112:   return 0;
    113: }

    115: /*TEST

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

    134: TEST*/