static PetscErrorCode PCPreSolve_Eisenstat(PC pc,KSP ksp,Vec b,Vec x)
{
PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;
PetscBool nonzero;
PetscErrorCode ierr;
PetscFunctionBegin;
if (pc->presolvedone < 2) {
if (pc->mat != pc->pmat) SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_SUP,"Cannot have different mat and pmat");
/* swap shell matrix and true matrix */
eis->A = pc->mat;
pc->mat = eis->shell;
}
if (!eis->b[pc->presolvedone-1]) {
ierr = VecDuplicate(b,&eis->b[pc->presolvedone-1]);CHKERRQ(ierr);
ierr = PetscLogObjectParent(pc,eis->b[pc->presolvedone-1]);CHKERRQ(ierr);
}
/* if nonzero initial guess, modify x */
ierr = KSPGetInitialGuessNonzero(ksp,&nonzero);CHKERRQ(ierr);
if (nonzero) {
ierr = VecCopy(x,eis->b[pc->presolvedone-1]);CHKERRQ(ierr);
ierr = MatSOR(eis->A,eis->b[pc->presolvedone-1],eis->omega,SOR_APPLY_UPPER,0.0,1,1,x);CHKERRQ(ierr);
}
/* save true b, other option is to swap pointers */
ierr = VecCopy(b,eis->b[pc->presolvedone-1]);CHKERRQ(ierr);
/* modify b by (L + D/omega)^{-1} */
ierr = MatSOR(eis->A,eis->b[pc->presolvedone-1],eis->omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),0.0,1,1,b);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat C;
Vec u,x,b,e;
PetscInt i,n = 10,midx[3];
PetscErrorCode ierr;
PetscScalar v[3];
PetscReal omega = 1.0,norm;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetReal(NULL,"-omega",&omega,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_SELF,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,n,n,n,n);CHKERRQ(ierr);
ierr = MatSetType(C,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&b);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&u);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&e);CHKERRQ(ierr);
ierr = VecSet(u,1.0);CHKERRQ(ierr);
ierr = VecSet(x,0.0);CHKERRQ(ierr);
v[0] = -1.; v[1] = 2.; v[2] = -1.;
for (i=1; i<n-1; i++) {
midx[0] = i-1; midx[1] = i; midx[2] = i+1;
ierr = MatSetValues(C,1,&i,3,midx,v,INSERT_VALUES);CHKERRQ(ierr);
}
i = 0; midx[0] = 0; midx[1] = 1;
v[0] = 2.0; v[1] = -1.;
ierr = MatSetValues(C,1,&i,2,midx,v,INSERT_VALUES);CHKERRQ(ierr);
i = n-1; midx[0] = n-2; midx[1] = n-1;
v[0] = -1.0; v[1] = 2.;
ierr = MatSetValues(C,1,&i,2,midx,v,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatMult(C,u,b);CHKERRQ(ierr);
for (i=0; i<n; i++) {
ierr = MatSOR(C,b,omega,SOR_FORWARD_SWEEP,0.0,1,1,x);CHKERRQ(ierr);
ierr = VecWAXPY(e,-1.0,x,u);CHKERRQ(ierr);
ierr = VecNorm(e,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"2-norm of error %g\n",(double)norm);CHKERRQ(ierr);
}
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&e);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
static PetscErrorCode PCMult_Eisenstat(Mat mat,Vec b,Vec x)
{
PetscErrorCode ierr;
PC pc;
PC_Eisenstat *eis;
PetscFunctionBegin;
ierr = MatShellGetContext(mat,(void **)&pc);CHKERRQ(ierr);
eis = (PC_Eisenstat*)pc->data;
ierr = MatSOR(eis->A,b,eis->omega,SOR_EISENSTAT,0.0,1,1,x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode PCPostSolve_Eisenstat(PC pc,KSP ksp,Vec b,Vec x)
{
PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;
PetscErrorCode ierr;
PetscFunctionBegin;
/* modify x by (U + D/omega)^{-1} */
ierr = MatSOR(eis->A,x,eis->omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),0.0,1,1,x);CHKERRQ(ierr);
pc->mat = eis->A;
/* get back true b */
ierr = VecCopy(eis->b,b);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
