#include "petscts.h" PetscErrorCode TSSetCostHessianProducts(TS ts,PetscInt numcost,Vec *lambda2,Vec *mu2,Vec dir)Logically Collective on TS
|ts||- the TS context obtained from TSCreate()|
|numcost||- number of cost functions|
|lambda2||- Hessian-vector product with respect to the initial condition variables, the dimension and parallel layout of these vectors is the same as the ODE solution vector|
|mu2||- Hessian-vector product with respect to the parameters, the number of entries in these vectors is the same as the number of parameters|
|dir||- the direction vector that are multiplied with the Hessian of the cost functions|
Notes: Hessian of the cost function is completely different from Hessian of the ODE/DAE system
For second-order adjoint, one needs to call this function and then TSAdjointSetForward() before TSSolve().
After TSAdjointSolve() is called, the lamba2 and the mu2 will contain the computed second-order adjoint sensitivities, and can be used to produce Hessian-vector product (not the full Hessian matrix). Users must provide a direction vector; it is usually generated by an optimization solver.
Passing NULL for lambda2 disables the second-order calculation.