Date: 2013-09-02T10:05:27+00:00

Actual source code: test10.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Computes the smallest nonzero eigenvalue of the Laplacian of a graph.\n\n"
     23:   "This example illustrates EPSSetDeflationSpace(). The example graph corresponds to a "
     24:   "2-D regular mesh. The command line options are:\n"
     25:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     26:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     28: #include <slepceps.h>

     32: int main (int argc,char **argv)
     33: {
     34:   EPS            eps;             /* eigenproblem solver context */
     35:   Mat            A;               /* operator matrix */
     36:   Vec            x;
     37:   EPSType        type;
     38:   PetscInt       N,n=10,m,i,j,II,Istart,Iend,nev;
     39:   PetscScalar    w;
     40:   PetscBool      flag;

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

     45:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     46:   PetscOptionsGetInt(NULL,"-m",&m,&flag);
     47:   if (!flag) m=n;
     48:   N = n*m;
     49:   PetscPrintf(PETSC_COMM_WORLD,"\nFiedler vector of a 2-D regular mesh, N=%D (%Dx%D grid)\n\n",N,n,m);

     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:      Compute the operator matrix that defines the eigensystem, Ax=kx
     53:      In this example, A = L(G), where L is the Laplacian of graph G, i.e.
     54:      Lii = degree of node i, Lij = -1 if edge (i,j) exists in G
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     57:   MatCreate(PETSC_COMM_WORLD,&A);
     58:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     59:   MatSetFromOptions(A);
     60:   MatSetUp(A);

     62:   MatGetOwnershipRange(A,&Istart,&Iend);
     63:   for (II=Istart;II<Iend;II++) {
     64:     i = II/n; j = II-i*n;
     65:     w = 0.0;
     66:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); w=w+1.0; }
     67:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); w=w+1.0; }
     68:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); w=w+1.0; }
     69:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); w=w+1.0; }
     70:     MatSetValue(A,II,II,w,INSERT_VALUES);
     71:   }

     73:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     74:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     76:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     77:                 Create the eigensolver and set various options
     78:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     80:   /*
     81:      Create eigensolver context
     82:   */
     83:   EPSCreate(PETSC_COMM_WORLD,&eps);

     85:   /*
     86:      Set operators. In this case, it is a standard eigenvalue problem
     87:   */
     88:   EPSSetOperators(eps,A,NULL);
     89:   EPSSetProblemType(eps,EPS_HEP);

     91:   /*
     92:      Select portion of spectrum
     93:   */
     94:   EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);

     96:   /*
     97:      Set solver parameters at runtime
     98:   */
     99:   EPSSetFromOptions(eps);

    101:   /*
    102:      Attach deflation space: in this case, the matrix has a constant
    103:      nullspace, [1 1 ... 1]^T is the eigenvector of the zero eigenvalue
    104:   */
    105:   MatGetVecs(A,&x,NULL);
    106:   VecSet(x,1.0);
    107:   EPSSetDeflationSpace(eps,1,&x);
    108:   VecDestroy(&x);

    110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    111:                       Solve the eigensystem
    112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    114:   EPSSolve(eps);

    116:   /*
    117:      Optional: Get some information from the solver and display it
    118:   */
    119:   EPSGetType(eps,&type);
    120:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    121:   EPSGetDimensions(eps,&nev,NULL,NULL);
    122:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:                     Display solution and clean up
    126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    128:   EPSPrintSolution(eps,NULL);
    129:   EPSDestroy(&eps);
    130:   MatDestroy(&A);
    131:   SlepcFinalize();
    132:   return 0;
    133: }