/*
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SLEPc - Scalable Library for Eigenvalue Problem Computations
Copyright (c) 2002-2011, Universitat 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/>.
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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);
PetscErrorCode MatLaplacian2D_GetDiagonal(Mat A,Vec diag);
#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc,char **argv)
{
Mat A; /* operator matrix */
EPS eps; /* eigenproblem solver context */
const EPSType type;
PetscReal tol=1000*PETSC_MACHINE_EPSILON;
PetscMPIInt size;
PetscInt N,n=10,nev,maxit;
PetscErrorCode ierr;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,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);
ierr = MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatLaplacian2D_GetDiagonal);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);
ierr = EPSSetTolerances(eps,tol,PETSC_DECIDE);CHKERRQ(ierr);
/*
Set solver parameters at runtime
*/
ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the eigensystem
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ierr = EPSSolve(eps);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
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ierr = EPSPrintSolution(eps,PETSC_NULL);CHKERRQ(ierr);
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,const 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;
int nx,lo,j,one=1;
const PetscScalar *px;
PetscScalar *py,dmone=-1.0;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = MatShellGetContext(A,&ctx);CHKERRQ(ierr);
nx = *(int*)ctx;
ierr = VecGetArrayRead(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 = VecRestoreArrayRead(x,&px);CHKERRQ(ierr);
ierr = VecRestoreArray(y,&py);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "MatLaplacian2D_GetDiagonal"
PetscErrorCode MatLaplacian2D_GetDiagonal(Mat A,Vec diag)
{
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = VecSet(diag,4.0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}