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 = ts->ptime;
PetscErrorCode ierr;
PetscReal h = ts->time_step;
Mat J,Jp;
PetscFunctionBegin;
rk->status = TS_STEP_INCOMPLETE;
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]);CHKERRQ(ierr);
for (j=i+1; j<s; j++) {
ierr = VecAXPY(VecSensiTemp[nadj],-h*A[j*s+i],VecDeltaLam[nadj*s+j]);CHKERRQ(ierr);
}
}
/* 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);
if (ts->vec_costintegral) {
ierr = TSAdjointComputeDRDYFunction(ts,rk->stage_time,Y[i],ts->vecs_drdy);CHKERRQ(ierr);
}
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(J,VecSensiTemp[nadj],VecDeltaLam[nadj*s+i]);CHKERRQ(ierr);
if (ts->vec_costintegral) {
ierr = VecAXPY(VecDeltaLam[nadj*s+i],-h*b[i],ts->vecs_drdy[nadj]);CHKERRQ(ierr);
}
}
/* Stage values of mu */
if(ts->vecs_sensip) {
ierr = TSAdjointComputeRHSJacobian(ts,rk->stage_time,Y[i],ts->Jacp);CHKERRQ(ierr);
if (ts->vec_costintegral) {
ierr = TSAdjointComputeDRDPFunction(ts,rk->stage_time,Y[i],ts->vecs_drdp);CHKERRQ(ierr);
}
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(ts->Jacp,VecSensiTemp[nadj],VecDeltaMu[nadj*s+i]);CHKERRQ(ierr);
if (ts->vec_costintegral) {
ierr = VecAXPY(VecDeltaMu[nadj*s+i],-h*b[i],ts->vecs_drdp[nadj]);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);
}
}
rk->status = TS_STEP_COMPLETE;
PetscFunctionReturn(0);
}
static PetscErrorCode TSAdjointStep_Theta(TS ts)
{
TS_Theta *th = (TS_Theta*)ts->data;
Vec *VecsDeltaLam = th->VecsDeltaLam,*VecsDeltaMu = th->VecsDeltaMu,*VecsSensiTemp = th->VecsSensiTemp;
PetscInt nadj;
PetscErrorCode ierr;
Mat J,Jp;
KSP ksp;
PetscReal shift;
PetscFunctionBegin;
th->status = TS_STEP_INCOMPLETE;
ierr = SNESGetKSP(ts->snes,&ksp);CHKERRQ(ierr);
ierr = TSGetIJacobian(ts,&J,&Jp,NULL,NULL);CHKERRQ(ierr);
/* If endpoint=1, th->ptime and th->X0 will be used; if endpoint=0, th->stage_time and th->X will be used. */
th->stage_time = ts->ptime + (th->endpoint ? ts->time_step : (1.-th->Theta)*ts->time_step); /* time_step is negative*/
th->ptime = ts->ptime + ts->time_step;
/* Build RHS */
if (ts->vec_costintegral) { /* Cost function has an integral term */
if (th->endpoint) {
ierr = TSAdjointComputeDRDYFunction(ts,ts->ptime,ts->vec_sol,ts->vecs_drdy);CHKERRQ(ierr);
}else {
ierr = TSAdjointComputeDRDYFunction(ts,th->stage_time,th->X,ts->vecs_drdy);CHKERRQ(ierr);
}
}
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]);CHKERRQ(ierr);
ierr = VecScale(VecsSensiTemp[nadj],-1./(th->Theta*ts->time_step));CHKERRQ(ierr);
if (ts->vec_costintegral) {
ierr = VecAXPY(VecsSensiTemp[nadj],1.,ts->vecs_drdy[nadj]);CHKERRQ(ierr);
}
}
/* Build LHS */
shift = -1./(th->Theta*ts->time_step);
if (th->endpoint) {
ierr = TSComputeIJacobian(ts,ts->ptime,ts->vec_sol,th->Xdot,shift,J,Jp,PETSC_FALSE);CHKERRQ(ierr);
}else {
ierr = TSComputeIJacobian(ts,th->stage_time,th->X,th->Xdot,shift,J,Jp,PETSC_FALSE);CHKERRQ(ierr);
}
ierr = KSPSetOperators(ksp,J,Jp);CHKERRQ(ierr);
/* Solve LHS X = RHS */
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = KSPSolveTranspose(ksp,VecsSensiTemp[nadj],VecsDeltaLam[nadj]);CHKERRQ(ierr);
}
/* Update sensitivities, and evaluate integrals if there is any */
if(th->endpoint) { /* two-stage case */
if (th->Theta!=1.) {
shift = -1./((th->Theta-1.)*ts->time_step);
ierr = TSComputeIJacobian(ts,th->ptime,th->X0,th->Xdot,shift,J,Jp,PETSC_FALSE);CHKERRQ(ierr);
if (ts->vec_costintegral) {
ierr = TSAdjointComputeDRDYFunction(ts,th->ptime,th->X0,ts->vecs_drdy);CHKERRQ(ierr);
}
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(J,VecsDeltaLam[nadj],ts->vecs_sensi[nadj]);CHKERRQ(ierr);
if (ts->vec_costintegral) {
ierr = VecAXPY(ts->vecs_sensi[nadj],-1.,ts->vecs_drdy[nadj]);CHKERRQ(ierr);
}
ierr = VecScale(ts->vecs_sensi[nadj],1./shift);CHKERRQ(ierr);
}
}else { /* backward Euler */
shift = 0.0;
ierr = TSComputeIJacobian(ts,ts->ptime,ts->vec_sol,th->Xdot,shift,J,Jp,PETSC_FALSE);CHKERRQ(ierr); /* get -f_y */
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(J,VecsDeltaLam[nadj],VecsSensiTemp[nadj]);CHKERRQ(ierr);
ierr = VecAXPY(ts->vecs_sensi[nadj],ts->time_step,VecsSensiTemp[nadj]);CHKERRQ(ierr);
if (ts->vec_costintegral) {
ierr = VecAXPY(ts->vecs_sensi[nadj],-ts->time_step,ts->vecs_drdy[nadj]);CHKERRQ(ierr);
}
}
}
if (ts->vecs_sensip) { /* sensitivities wrt parameters */
ierr = TSAdjointComputeRHSJacobian(ts,ts->ptime,ts->vec_sol,ts->Jacp);CHKERRQ(ierr);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);CHKERRQ(ierr);
ierr = VecAXPY(ts->vecs_sensip[nadj],-ts->time_step*th->Theta,VecsDeltaMu[nadj]);CHKERRQ(ierr);
}
if (th->Theta!=1.) {
ierr = TSAdjointComputeRHSJacobian(ts,th->ptime,th->X0,ts->Jacp);CHKERRQ(ierr);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);CHKERRQ(ierr);
ierr = VecAXPY(ts->vecs_sensip[nadj],-ts->time_step*(1.-th->Theta),VecsDeltaMu[nadj]);CHKERRQ(ierr);
}
}
if (ts->vec_costintegral) {
ierr = TSAdjointComputeDRDPFunction(ts,ts->ptime,ts->vec_sol,ts->vecs_drdp);CHKERRQ(ierr);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = VecAXPY(ts->vecs_sensip[nadj],-ts->time_step*th->Theta,ts->vecs_drdp[nadj]);CHKERRQ(ierr);
}
if (th->Theta!=1.) {
ierr = TSAdjointComputeDRDPFunction(ts,th->ptime,th->X0,ts->vecs_drdp);CHKERRQ(ierr);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = VecAXPY(ts->vecs_sensip[nadj],-ts->time_step*(1.-th->Theta),ts->vecs_drdp[nadj]);CHKERRQ(ierr);
}
}
}
}
}else { /* one-stage case */
shift = 0.0;
ierr = TSComputeIJacobian(ts,th->stage_time,th->X,th->Xdot,shift,J,Jp,PETSC_FALSE);CHKERRQ(ierr); /* get -f_y */
if (ts->vec_costintegral) {
ierr = TSAdjointComputeDRDYFunction(ts,th->stage_time,th->X,ts->vecs_drdy);CHKERRQ(ierr);
}
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(J,VecsDeltaLam[nadj],VecsSensiTemp[nadj]);CHKERRQ(ierr);
ierr = VecAXPY(ts->vecs_sensi[nadj],ts->time_step,VecsSensiTemp[nadj]);CHKERRQ(ierr);
if (ts->vec_costintegral) {
ierr = VecAXPY(ts->vecs_sensi[nadj],-ts->time_step,ts->vecs_drdy[nadj]);CHKERRQ(ierr);
}
}
if (ts->vecs_sensip) {
ierr = TSAdjointComputeRHSJacobian(ts,th->stage_time,th->X,ts->Jacp);CHKERRQ(ierr);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);CHKERRQ(ierr);
ierr = VecAXPY(ts->vecs_sensip[nadj],-ts->time_step,VecsDeltaMu[nadj]);CHKERRQ(ierr);
}
if (ts->vec_costintegral) {
ierr = TSAdjointComputeDRDPFunction(ts,th->stage_time,th->X,ts->vecs_drdp);CHKERRQ(ierr);
for (nadj=0; nadj<ts->numcost; nadj++) {
ierr = VecAXPY(ts->vecs_sensip[nadj],-ts->time_step,ts->vecs_drdp[nadj]);CHKERRQ(ierr);
}
}
}
}
th->status = TS_STEP_COMPLETE;
PetscFunctionReturn(0);
}