/*
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SLEPc - Scalable Library for Eigenvalue Problem Computations
Copyright (c) 2002-2007, Universidad Politecnica de Valencia, Spain
This file is part of SLEPc. See the README file for conditions of use
and additional information.
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*/
static char help[] = "Solves the same eigenproblem as in example ex2, but using a shell matrix. "
"The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"
"The command line options are:\n"
" -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";
#include "slepceps.h"
#include "petscblaslapack.h"
/*
User-defined routines
*/
PetscErrorCode MatLaplacian2D_Mult( Mat A, Vec x, Vec y );
#undef __FUNCT__
#define __FUNCT__ "main"
int main( int argc, char **argv )
{
Mat A; /* operator matrix */
EPS eps; /* eigenproblem solver context */
EPSType type;
PetscReal error, tol, re, im;
PetscScalar kr, ki;
PetscMPIInt size;
PetscErrorCode ierr;
PetscInt N, n=10;
int nev, maxit, i, its, nconv;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(1,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
N = n*n;
ierr = PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%d (%dx%d grid)\n\n",N,n,n);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the operator matrix that defines the eigensystem, Ax=kx
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ierr = MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatShellSetOperation(A,MATOP_MULT,(void(*)())MatLaplacian2D_Mult);CHKERRQ(ierr);
ierr = MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)())MatLaplacian2D_Mult);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the eigensolver and set various options
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/*
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);
/*
Set solver parameters at runtime
*/
ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the eigensystem
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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
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/*
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) {
/*
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;
}
/*
Compute the matrix vector multiplication y<---T*x where T is a nx by nx
tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
DU on the superdiagonal.
*/
static void tv( int nx, PetscScalar *x, PetscScalar *y )
{
PetscScalar dd, dl, du;
int j;
dd = 4.0;
dl = -1.0;
du = -1.0;
y[0] = dd*x[0] + du*x[1];
for( j=1; j<nx-1; j++ )
y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
}
#undef __FUNCT__
#define __FUNCT__ "MatLaplacian2D_Mult"
/*
Matrix-vector product subroutine for the 2D Laplacian.
The matrix used is the 2 dimensional discrete Laplacian on unit square with
zero Dirichlet boundary condition.
Computes y <-- A*x, where A is the block tridiagonal matrix
| T -I |
|-I T -I |
A = | -I T |
| ... -I|
| -I T|
The subroutine TV is called to compute y<--T*x.
*/
PetscErrorCode MatLaplacian2D_Mult( Mat A, Vec x, Vec y )
{
void *ctx;
PetscErrorCode ierr;
int nx, lo, j, one=1;
PetscScalar *px, *py, dmone=-1.0;
PetscFunctionBegin;
ierr = MatShellGetContext( A, &ctx ); CHKERRQ(ierr);
nx = *(int *)ctx;
ierr = VecGetArray( x, &px ); CHKERRQ(ierr);
ierr = VecGetArray( y, &py ); CHKERRQ(ierr);
tv( nx, &px[0], &py[0] );
BLASaxpy_( &nx, &dmone, &px[nx], &one, &py[0], &one );
for( j=2; j<nx; j++ ) {
lo = (j-1)*nx;
tv( nx, &px[lo], &py[lo]);
BLASaxpy_( &nx, &dmone, &px[lo-nx], &one, &py[lo], &one );
BLASaxpy_( &nx, &dmone, &px[lo+nx], &one, &py[lo], &one );
}
lo = (nx-1)*nx;
tv( nx, &px[lo], &py[lo]);
BLASaxpy_( &nx, &dmone, &px[lo-nx], &one, &py[lo], &one );
ierr = VecRestoreArray( x, &px ); CHKERRQ(ierr);
ierr = VecRestoreArray( y, &py ); CHKERRQ(ierr);
PetscFunctionReturn(0);
}