static char help[] = "Solves a problem associated to the Brusselator wave model in chemical reactions, illustrating the use of shell matrices.\n\n"
"The command line options are:\n\n"
" -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
" -L <L>, where <L> = bifurcation parameter.\n"
" -alpha <alpha>, -beta <beta>, -delta1 <delta1>, -delta2 <delta2>,\n"
" where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";
#include "slepceps.h"
/*
This example computes the eigenvalues with largest real part of the
following matrix
A = [ tau1*T+(beta-1)*I alpha^2*I
-beta*I tau2*T-alpha^2*I ],
where
T = tridiag{1,-2,1}
h = 1/(n+1)
tau1 = delta1/(h*L)^2
tau2 = delta2/(h*L)^2
*/
/*
Matrix operations
*/
extern int MatBrussel_Mult(Mat,Vec,Vec);
extern int MatBrussel_Shift(PetscScalar*,Mat);
extern int MatBrussel_GetDiagonal(Mat,Vec);
typedef struct {
Mat T;
Vec x1, x2, y1, y2;
PetscScalar alpha, beta, tau1, tau2, sigma;
} CTX_BRUSSEL;
#undef __FUNCT__
#define __FUNCT__ "main"
int main( int argc, char **argv )
{
Mat A; /* eigenvalue problem matrix */
EPS eps; /* eigenproblem solver context */
EPSType type;
PetscReal error, tol, re, im;
PetscScalar delta1, delta2, L, h, kr, ki, value[3];
int N=30, n, nev, ierr, maxit, i, its, nconv,
col[3], Istart, Iend, FirstBlock=0, LastBlock=0;
CTX_BRUSSEL *ctx;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&N,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%d\n\n",N);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Generate the matrix
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create shell matrix context and set default parameters
*/
ierr = PetscNew(CTX_BRUSSEL,&ctx);CHKERRQ(ierr);
ctx->alpha = 2.0;
ctx->beta = 5.45;
delta1 = 0.008;
delta2 = 0.004;
L = 0.51302;
/*
Look the command line for user-provided parameters
*/
ierr = PetscOptionsGetScalar(PETSC_NULL,"-L",&L,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(PETSC_NULL,"-alpha",&ctx->alpha,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(PETSC_NULL,"-beta",&ctx->beta,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(PETSC_NULL,"-delta1",&delta1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(PETSC_NULL,"-delta2",&delta2,PETSC_NULL);CHKERRQ(ierr);
/*
Create matrix T
*/
ierr = MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&ctx->T);CHKERRQ(ierr);
ierr = MatSetFromOptions(ctx->T);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(ctx->T,&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(ctx->T,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
if (LastBlock) {
i=N-1; col[0]=N-2; col[1]=N-1;
ierr = MatSetValues(ctx->T,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(ctx->T,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatGetLocalSize(ctx->T,&n,PETSC_NULL);CHKERRQ(ierr);
/*
Fill the remaining information in the shell matrix context
and create auxiliary vectors
*/
h = 1.0 / (double)(N+1);
ctx->tau1 = delta1 / ((h*L)*(h*L));
ctx->tau2 = delta2 / ((h*L)*(h*L));
ctx->sigma = 0.0;
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n,PETSC_DECIDE,PETSC_NULL,&ctx->x1);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n,PETSC_DECIDE,PETSC_NULL,&ctx->x2);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n,PETSC_DECIDE,PETSC_NULL,&ctx->y1);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,n,PETSC_DECIDE,PETSC_NULL,&ctx->y2);CHKERRQ(ierr);
/*
Create the shell matrix
*/
ierr = MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);CHKERRQ(ierr);
ierr = MatShellSetOperation(A,MATOP_MULT,(void(*)())MatBrussel_Mult);CHKERRQ(ierr);
ierr = MatShellSetOperation(A,MATOP_SHIFT,(void(*)())MatBrussel_Shift);CHKERRQ(ierr);
ierr = MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatBrussel_GetDiagonal);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);
/*
Force to use ARPACK if it is installed and ask for the rightmost eigenvalues
*/
#if defined(SLEPC_HAVE_ARPACK)
ierr = EPSSetType(eps,EPSARPACK);CHKERRQ(ierr);
#else
ierr = EPSSetType(eps, EPSLAPACK);CHKERRQ(ierr);
#endif
ierr = EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);CHKERRQ(ierr);
/*
Set other solver options 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);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 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);
#if defined(PETSC_USE_COMPLEX)
re = PetscRealPart(kr);
im = PetscImaginaryPart(kr);
#else
re = kr;
im = ki;
#endif
if( im != 0.0 ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," % 6f %+6f i",re,im);CHKERRQ(ierr);
} else {
ierr = PetscPrintf(PETSC_COMM_WORLD," % 6f ",re); CHKERRQ(ierr);
}
ierr = PetscPrintf(PETSC_COMM_WORLD," % 12f\n",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(ctx->T);CHKERRQ(ierr);
ierr = VecDestroy(ctx->x1);CHKERRQ(ierr);
ierr = VecDestroy(ctx->x2);CHKERRQ(ierr);
ierr = VecDestroy(ctx->y1);CHKERRQ(ierr);
ierr = VecDestroy(ctx->y2);CHKERRQ(ierr);
ierr = PetscFree(ctx);CHKERRQ(ierr);
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}
#undef __FUNC__
#define __FUNC__ "MatBrussel_Mult"
int MatBrussel_Mult(Mat A,Vec x,Vec y)
{
int n, ierr;
PetscScalar alpha, *px, *py;
MPI_Comm comm;
CTX_BRUSSEL *ctx;
ierr = MatShellGetContext(A,(void**)&ctx);CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
ierr = MatGetLocalSize(ctx->T,&n,PETSC_NULL);CHKERRQ(ierr);
ierr = VecGetArray(x,&px);CHKERRQ(ierr);
ierr = VecGetArray(y,&py);CHKERRQ(ierr);
ierr = VecPlaceArray(ctx->x1,px);CHKERRQ(ierr);
ierr = VecPlaceArray(ctx->x2,px+n);CHKERRQ(ierr);
ierr = VecPlaceArray(ctx->y1,py);CHKERRQ(ierr);
ierr = VecPlaceArray(ctx->y2,py+n);CHKERRQ(ierr);
ierr = MatMult(ctx->T,ctx->x1,ctx->y1);CHKERRQ(ierr);
ierr = VecScale(&ctx->tau1,ctx->y1);CHKERRQ(ierr);
alpha = ctx->beta - 1.0 - ctx->sigma;
ierr = VecAXPY(&alpha,ctx->x1,ctx->y1);CHKERRQ(ierr);
alpha = ctx->alpha * ctx->alpha;
ierr = VecAXPY(&alpha,ctx->x2,ctx->y1);CHKERRQ(ierr);
ierr = MatMult(ctx->T,ctx->x2,ctx->y2);CHKERRQ(ierr);
ierr = VecScale(&ctx->tau2,ctx->y2);CHKERRQ(ierr);
alpha = -ctx->beta;
ierr = VecAXPY(&alpha,ctx->x1,ctx->y2);CHKERRQ(ierr);
alpha = -ctx->alpha * ctx->alpha - ctx->sigma;
ierr = VecAXPY(&alpha,ctx->x2,ctx->y2);CHKERRQ(ierr);
ierr = VecRestoreArray(x,&px);CHKERRQ(ierr);
ierr = VecRestoreArray(y,&py);CHKERRQ(ierr);
return 0;
}
#undef __FUNCT__
#define __FUNCT__ "MatBrussel_Shift"
int MatBrussel_Shift( PetscScalar* a, Mat Y )
{
CTX_BRUSSEL *ctx;
int ierr;
ierr = MatShellGetContext( Y, (void**)&ctx ); CHKERRQ(ierr);
ctx->sigma += *a;
PetscFunctionReturn(0);
}
#undef __FUNC__
#define __FUNC__ "MatBrussel_GetDiagonal"
int MatBrussel_GetDiagonal(Mat A,Vec diag)
{
Vec d1, d2;
int n, ierr;
PetscScalar alpha, *pd;
MPI_Comm comm;
CTX_BRUSSEL *ctx;
ierr = MatShellGetContext(A,(void**)&ctx);CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
ierr = MatGetLocalSize(ctx->T,&n,PETSC_NULL);CHKERRQ(ierr);
ierr = VecGetArray(diag,&pd);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(comm,n,PETSC_DECIDE,pd,&d1);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(comm,n,PETSC_DECIDE,pd+n,&d2);CHKERRQ(ierr);
alpha = -2.0*ctx->tau1 + ctx->beta - 1.0 - ctx->sigma;
ierr = VecSet(&alpha,d1);CHKERRQ(ierr);
alpha = -2.0*ctx->tau2 - ctx->alpha*ctx->alpha - ctx->sigma;
ierr = VecSet(&alpha,d2);CHKERRQ(ierr);
ierr = VecDestroy(d1);CHKERRQ(ierr);
ierr = VecDestroy(d2);CHKERRQ(ierr);
ierr = VecRestoreArray(diag,&pd);CHKERRQ(ierr);
return 0;
}