Subversion Repositories slepc-dev

/*

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain

   This file is part of SLEPc.

   SLEPc is free software: you can redistribute it and/or modify it under  the

   terms of version 3 of the GNU Lesser General Public License as published by

   the Free Software Foundation.

   SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY

   WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS

   FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for

   more details.

   You  should have received a copy of the GNU Lesser General  Public  License

   along with SLEPc. If not, see <http://www.gnu.org/licenses/>.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*/

static char help[] = "Generalized Symmetric eigenproblem.\n\n"

  "The problem is Ax = lambda Bx, with:\n"

  "   A = Laplacian operator in 2-D\n"

  "   B = diagonal matrix with all values equal to 4 except nulldim zeros\n\n"

  "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"

  "  -nulldim <k>, where <k> = dimension of the nullspace of B.\n\n";

#include <slepceps.h>

#undef __FUNCT__

#define __FUNCT__ "main"

int main( int argc, char **argv )

{

  Mat            A, B;            /* matrices */

  EPS            eps;             /* eigenproblem solver context */

  ST             st;              /* spectral transformation context */

  const EPSType  type;

  PetscReal      error, tol, re, im;

  PetscScalar    kr, ki;

  PetscErrorCode ierr;

  PetscInt       N, n=10, m, Istart, Iend, II, nev, maxit, i, j, its, nconv, nulldim=0;

  PetscBool      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) m=n;

  N = n*m;

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

  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%d (%dx%d grid), null(B)=%d\n\n",N,n,m,nulldim);CHKERRQ(ierr);

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

     Compute the matrices that define the eigensystem, Ax=kBx

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

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

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

  ierr = MatSetFromOptions(B);CHKERRQ(ierr);

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

  for( II=Istart; II<Iend; II++ ) {

    i = II/n; j = II-i*n;  

    if(i>0) { ierr = MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }

    if(i<m-1) { ierr = MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }

    if(j>0) { ierr = MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }

    if(j<n-1) { ierr = MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }

    ierr = MatSetValue(A,II,II,4.0,INSERT_VALUES);CHKERRQ(ierr);

    if (II>=nulldim) { ierr = MatSetValue(B,II,II,4.0,INSERT_VALUES);CHKERRQ(ierr); }

  }

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

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

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

  ierr = MatAssemblyEnd(B,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 generalized eigenvalue problem

  */

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

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

  /*

     Use shift-and-invert to avoid solving linear systems with a singular B

     in case nulldim>0

  */

  ierr = EPSGetST(eps,&st);CHKERRQ(ierr);

  ierr = EPSSetTarget(eps,0.0);CHKERRQ(ierr);

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

  ierr = STSetType(st,STSINVERT);CHKERRQ(ierr);

  /*

     Set solver parameters at runtime

  */

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

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

                      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,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-kBx||/||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 = MatDestroy(&B);CHKERRQ(ierr);

  ierr = SlepcFinalize();CHKERRQ(ierr);

  return 0;

}