Subversion Repositories slepc-dev

static char help[] = "Computes the smallest nonzero eigenvalue of the Laplacian of a graph.\n\n"

  "This example illustrates EPSAttachDeflationSpace(). The example graph corresponds to a "

  "2-D regular mesh. The command line options are:\n"

  "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"

  "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

#include "slepceps.h"

#undef __FUNCT__

#define __FUNCT__ "main"

int main( int argc, char **argv )

{

  Mat            A;               /* operator matrix */

  Vec            x;

  EPS            eps;             /* eigenproblem solver context */

  EPSType        type;

  PetscReal      error, tol, re, im;

  PetscScalar    kr, ki;

  PetscErrorCode ierr;

  int            nev, maxit, its, nconv;

  PetscInt       N, n=10, m, i, j, II, J, Istart, Iend;

  PetscScalar    v, w;

  PetscTruth     flag;

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

  ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscOptionsGetInt(PETSC_NULL,"-m",&m,&flag);CHKERRQ(ierr);

  if( flag==PETSC_FALSE ) m=n;

  N = n*m;

  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nFiedler vector of a 2-D regular mesh, N=%d (%dx%d grid)\n\n",N,n,m);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     Compute the operator matrix that defines the eigensystem, Ax=kx

     In this example, A = L(G), where L is the Laplacian of graph G, i.e.

     Lii = degree of node i, Lij = -1 if edge (i,j) exists in G

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);

  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);

  ierr = MatSetFromOptions(A);CHKERRQ(ierr);

  ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);

  for( II=Istart; II<Iend; II++ ) {

    v = -1.0; i = II/n; j = II-i*n;

    w = 0.0;

    if(i>0) { J=II-n; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; }

    if(i<m-1) { J=II+n; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; }

    if(j>0) { J=II-1; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; }

    if(j<n-1) { J=II+1; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; }

    MatSetValues(A,1,&II,1,&II,&w,INSERT_VALUES);CHKERRQ(ierr);

  }

  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

                Create the eigensolver and set various options

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*

     Create eigensolver context

  */

  ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);

  /*

     Set operators. In this case, it is a standard eigenvalue problem

  */

  ierr = EPSSetOperators(eps,A,PETSC_NULL);CHKERRQ(ierr);

  ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr);

  /*

     Select portion of spectrum

  */

  ierr = EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);CHKERRQ(ierr);

  /*

     Set solver parameters at runtime

  */

  ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);

  /*

     Attach deflation space: in this case, the matrix has a constant

     nullspace, [1 1 ... 1]^T is the eigenvector of the zero eigenvalue

  */

  ierr = MatGetVecs(A,&x,PETSC_NULL);CHKERRQ(ierr);

  ierr = VecSet(x,1.0);CHKERRQ(ierr);

  ierr = EPSAttachDeflationSpace(eps,1,&x,PETSC_FALSE);CHKERRQ(ierr);

  ierr = VecDestroy(x);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

                      Solve the eigensystem

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = EPSSolve(eps);CHKERRQ(ierr);

  ierr = EPSGetIterationNumber(eps, &its);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);CHKERRQ(ierr);

  /*

     Optional: Get some information from the solver and display it

  */

  ierr = EPSGetType(eps,&type);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr);

  ierr = EPSGetDimensions(eps,&nev,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);CHKERRQ(ierr);

  ierr = EPSGetTolerances(eps,&tol,&maxit);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

                    Display solution and clean up

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*

     Get number of converged approximate eigenpairs

  */

  ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr);

  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv);

         CHKERRQ(ierr);

  if (nconv>0) {

    /*

       Display eigenvalues and relative errors

    */

    ierr = PetscPrintf(PETSC_COMM_WORLD,

         "           k          ||Ax-kx||/||kx||\n"

         "   ----------------- ------------------\n" );CHKERRQ(ierr);

    for( i=0; i<nconv; i++ ) {

      /*

        Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and

        ki (imaginary part)

      */

      ierr = EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

      /*

         Compute the relative error associated to each eigenpair

      */

      ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr);

#ifdef PETSC_USE_COMPLEX

      re = PetscRealPart(kr);

      im = PetscImaginaryPart(kr);

#else

      re = kr;

      im = ki;

#endif 

      if (im!=0.0) {

        ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",re,im,error);CHKERRQ(ierr);

      } else {

        ierr = PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",re,error);CHKERRQ(ierr);

      }

    }

    ierr = PetscPrintf(PETSC_COMM_WORLD,"\n" );CHKERRQ(ierr);

  }

  /*

     Free work space

  */

  ierr = EPSDestroy(eps);CHKERRQ(ierr);

  ierr = MatDestroy(A);CHKERRQ(ierr);

  ierr = SlepcFinalize();CHKERRQ(ierr);

  return 0;

}