petsc-3.14.6 2021-03-30

TSSetRHSHessianProduct

Sets the function that computes the vector-Hessian-vector product. The Hessian is the second-order derivative of G (RHSFunction) w.r.t. the state variable.

Synopsis

#include "petscts.h"  
PetscErrorCode TSSetRHSHessianProduct(TS ts,Vec *rhshp1,PetscErrorCode (*rhshessianproductfunc1)(TS,PetscReal,Vec,Vec*,Vec,Vec*,void*),
                                          Vec *rhshp2,PetscErrorCode (*rhshessianproductfunc2)(TS,PetscReal,Vec,Vec*,Vec,Vec*,void*),
                                          Vec *rhshp3,PetscErrorCode (*rhshessianproductfunc3)(TS,PetscReal,Vec,Vec*,Vec,Vec*,void*),
                                          Vec *rhshp4,PetscErrorCode (*rhshessianproductfunc4)(TS,PetscReal,Vec,Vec*,Vec,Vec*,void*),
                                    void *ctx)

Logically Collective on TS

Input Parameters

	ts	- TS context obtained from TSCreate()
	rhshp1	- an array of vectors storing the result of vector-Hessian-vector product for G_UU
	hessianproductfunc1	- vector-Hessian-vector product function for G_UU
	rhshp2	- an array of vectors storing the result of vector-Hessian-vector product for G_UP
	hessianproductfunc2	- vector-Hessian-vector product function for G_UP
	rhshp3	- an array of vectors storing the result of vector-Hessian-vector product for G_PU
	hessianproductfunc3	- vector-Hessian-vector product function for G_PU
	rhshp4	- an array of vectors storing the result of vector-Hessian-vector product for G_PP
	hessianproductfunc4	- vector-Hessian-vector product function for G_PP

Calling sequence of ihessianproductfunc

rhshessianproductfunc (TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx);

	t	- current timestep
	U	- input vector (current ODE solution)
	Vl	- an array of input vectors to be left-multiplied with the Hessian
	Vr	- input vector to be right-multiplied with the Hessian
	VHV	- an array of output vectors for vector-Hessian-vector product
	ctx	- [optional] user-defined function context

Notes

The first Hessian function and the working array are required. As an example to implement the callback functions, the second callback function calculates the vector-Hessian-vector product $ Vl_n^T*G_UP*Vr where the vector Vl_n (n-th element in the array Vl) and Vr are of size N and M respectively, and the Hessian G_UP is of size N x N x M. Each entry of G_UP corresponds to the derivative $ G_UP[i][j][k] = \frac{\partial^2 G[i]}{\partial U[j] \partial P[k]}. The result of the vector-Hessian-vector product for Vl_n needs to be stored in vector VHV_n with j-th entry being $ VHV_n[j] = \sum_i \sum_k {Vl_n[i] * G_UP[i][j][k] * Vr[k]} If the cost function is a scalar, there will be only one vector in Vl and VHV.

Level

intermediate

Location

src/ts/interface/sensitivity/tssen.c

Examples

src/ts/tutorials/ex20opt_p.c.html
src/ts/tutorials/ex20opt_ic.c.html

Index of all Sensitivity routines
Table of Contents for all manual pages
Index of all manual pages