static char help[] = "Simple example that solves an eigensystem with the "
"EPS object. The standard symmetric eigenvalue problem to be solved "
"corresponds to the Laplacian operator in 1 dimension.\n\n"
"The command line options are:\n\n"
" -n <n>, where <n> = number of grid subdivisions = matrix dimension.\n\n";
#include "slepceps.h"
#undef __FUNCT__
#define __FUNCT__ "main"
int main( int argc, char **argv )
{
Vec *x; /* basis vectors */
Mat A; /* operator matrix */
EPS eps; /* eigenproblem solver context */
EPSType type;
PetscReal *error, tol;
PetscScalar *kr, *ki;
int n=30, nev, ierr, maxit, i, its, nconv,
col[3], Istart, Iend, FirstBlock=0, LastBlock=0;
PetscScalar value[3];
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\n1-D Laplacian Eigenproblem, n=%d\n\n",n);
CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the operator matrix that defines the eigensystem, Ax=kx
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,&A);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
if (Istart==0) FirstBlock=PETSC_TRUE;
if (Iend==n) LastBlock=PETSC_TRUE;
value[0]=-1.0; value[1]=2.0; value[2]=-1.0;
for( i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++ ) {
col[0]=i-1; col[1]=i; col[2]=i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
if (LastBlock) {
i=n-1; col[0]=n-2; col[1]=n-1;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
if (FirstBlock) {
i=0; col[0]=0; col[1]=1; value[0]=2.0; value[1]=-1.0;
ierr = MatSetValues(A,1,&i,2,col,value,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);
/*
Set solver parameters at runtime
*/
ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the eigensystem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = EPSSolve(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 eigenpairs: %d\n\n",nconv);
CHKERRQ(ierr);
if (nconv>0) {
/*
Get converged eigenpairs: i-th eigenvalue is stored in kr[i] (real part) and
ki[i] (imaginary part), and the corresponding eigenvector is stored in x
*/
ierr = EPSGetSolution(eps,&kr,&ki,&x);CHKERRQ(ierr);
/*
Compute the relative error associated to each eigenpair
*/
ierr = PetscMalloc(nconv*sizeof(PetscReal),&error);CHKERRQ(ierr);
ierr = EPSComputeError(eps,error);CHKERRQ(ierr);
/*
Display eigenvalues and relative errors
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,
" k ||Ax-kx||/|k|\n"
" ----------------- -----------------\n" );CHKERRQ(ierr);
for( i=0; i<nconv; i++ ) {
if (ki[i]!=0.0) {
ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12f\n",kr[i],ki[i],error[i]);
CHKERRQ(ierr); }
else {
ierr = PetscPrintf(PETSC_COMM_WORLD," %12f %12f\n",kr[i],error[i]);
CHKERRQ(ierr); }
}
ierr = PetscPrintf(PETSC_COMM_WORLD,"\n" );CHKERRQ(ierr);
ierr = PetscFree(error);CHKERRQ(ierr);
}
/*
Free work space
*/
ierr = EPSDestroy(eps);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}