static PetscErrorCode TSAdjointStep_RK(TS ts)
{
TS_RK *rk = (TS_RK*)ts->data;
RKTableau tab = rk->tableau;
const PetscInt s = tab->s;
const PetscReal *A = tab->A,*b = tab->b,*c = tab->c;
PetscScalar *w = rk->work;
Vec *Y = rk->Y,*VecDeltaLam = rk->VecDeltaLam,*VecDeltaMu = rk->VecDeltaMu,*VecSensiTemp = rk->VecSensiTemp;
PetscInt i,j,nadj;
PetscReal t;
PetscErrorCode ierr;
PetscReal h = ts->time_step;
Mat J,Jp;
PetscFunctionBegin;
t = ts->ptime;
rk->status = TS_STEP_INCOMPLETE;
h = ts->time_step;
ierr = TSPreStep(ts);CHKERRQ(ierr);
for (i=s-1; i>=0; i--) {
rk->stage_time = t + h*(1.0-c[i]);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = VecCopy(ts->vecs_sensi[nadj],VecSensiTemp[nadj]);CHKERRQ(ierr);
ierr = VecScale(VecSensiTemp[nadj],-h*b[i]);
for (j=i+1; j<s; j++) {
ierr = VecAXPY(VecSensiTemp[nadj],-h*A[j*s+i],VecDeltaLam[nadj*s+j]);
}
}
/* Stage values of lambda */
ierr = TSGetRHSJacobian(ts,&J,&Jp,NULL,NULL);CHKERRQ(ierr);
ierr = TSComputeRHSJacobian(ts,rk->stage_time,Y[i],J,Jp);CHKERRQ(ierr);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(J,VecSensiTemp[nadj],VecDeltaLam[nadj*s+i]);CHKERRQ(ierr);
}
/* Stage values of mu */
if(ts->vecs_sensip) {
ierr = TSAdjointComputeRHSJacobian(ts,rk->stage_time,Y[i],ts->Jacp);CHKERRQ(ierr);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(ts->Jacp,VecSensiTemp[nadj],VecDeltaMu[nadj*s+i]);CHKERRQ(ierr);
}
}
}
for (j=0; j<s; j++) w[j] = 1.0;
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecDeltaLam[nadj*s]);CHKERRQ(ierr);
if(ts->vecs_sensip) {
ierr = VecMAXPY(ts->vecs_sensip[nadj],s,w,&VecDeltaMu[nadj*s]);CHKERRQ(ierr);
}
}
ts->ptime += ts->time_step;
ts->steps++;
rk->status = TS_STEP_COMPLETE;
PetscFunctionReturn(0);
}
PetscErrorCode RHSFunctionHeat(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx)
{
PetscErrorCode ierr;
Mat A;
PetscFunctionBeginUser;
ierr = TSGetRHSJacobian(ts,&A,NULL,NULL,&ctx);CHKERRQ(ierr);
ierr = RHSMatrixHeat(ts,t,globalin,A,NULL,ctx);CHKERRQ(ierr);
/* ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
ierr = MatMult(A,globalin,globalout);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
