Date: 2022-10-01T06:40:05+00:00

Actual source code: ex11.c
slepc-3.18.0 2022-10-01
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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:   EPSType        type;
     25:   PetscInt       N,n=10,m,i,j,II,Istart,Iend,nev;
     26:   PetscScalar    w;
     27:   PetscBool      flag,terse;

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

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

     49:   MatGetOwnershipRange(A,&Istart,&Iend);
     50:   for (II=Istart;II<Iend;II++) {
     51:     i = II/n; j = II-i*n;
     52:     w = 0.0;
     53:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); w=w+1.0; }
     54:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); w=w+1.0; }
     55:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); w=w+1.0; }
     56:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); w=w+1.0; }
     57:     MatSetValue(A,II,II,w,INSERT_VALUES);
     58:   }

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

     63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     64:                 Create the eigensolver and set various options
     65:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

     97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     98:                       Solve the eigensystem
     99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    101:   EPSSolve(eps);

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

    111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    112:                     Display solution and clean up
    113:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    115:   /* show detailed info unless -terse option is given by user */
    116:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    117:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    118:   else {
    119:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    120:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
    121:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    122:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    123:   }
    124:   EPSDestroy(&eps);
    125:   MatDestroy(&A);
    126:   SlepcFinalize();
    127:   return 0;
    128: }

    130: /*TEST

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

    142: TEST*/