Atomic Forward Hessian Sparsity Patterns

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atomic_two_for_sparse_hes

$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$ This is cppad-20221105 documentation. Here is a link to its current documentation . Atomic Forward Hessian Sparsity Patterns
Syntax
ok = afun.for_sparse_hes(vx, r, s, h, x)

Deprecated 2016-06-27
ok = afun.for_sparse_hes(vx, r, s, h)

Purpose
This function is used by ForSparseHes to compute Hessian sparsity patterns. If you are using ForSparseHes , one of the versions of this virtual function must be defined by the atomic_user class.

Given a sparsity pattern for a diagonal matrix

$R \in \B{R}^{n \times n}$ , and a row vector

$S \in \B{R}^{1 \times m}$ , this routine computes the sparsity pattern for

$H(x) = R^\R{T} \cdot (S \cdot f)^{(2)}( x ) \cdot R$

Implementation
If you are using and ForSparseHes , this virtual function must be defined by the atomic_user class.

vx
The argument vx has prototype



     const CppAD:vector<bool>& vx

vx.size() == n , and for

$j = 0 , \ldots , n-1$ , vx[j] is true if and only if ax[j] is a variable or dynamic parameter in the corresponding call to



    afun(ax, ay)

r
This argument has prototype



     const CppAD:vector<bool>& r

and is a atomic_sparsity pattern for the diagonal of

$R \in \B{R}^{n \times n}$ .

s
The argument s has prototype



     const CppAD:vector<bool>& s

and its size is m . It is a sparsity pattern for

$S \in \B{R}^{1 \times m}$ .

h
This argument has prototype



     atomic_sparsity& h

The input value of its elements are not specified (must not matter). Upon return, h is a atomic_sparsity pattern for

$H(x) \in \B{R}^{n \times n}$ which is defined above.

x
The argument has prototype



    const CppAD::vector<Base>& x

and size is equal to the n . This is the Value value corresponding to the parameters in the vector ax (when the atomic function was called). To be specific, if



    if( Parameter(ax[i]) == true )

        x[i] = Value( ax[i] );

    else

        x[i] = CppAD::numeric_limits<Base>::quiet_NaN();

The version of this function with out the x argument is deprecated; i.e., you should include the argument even if you do not use it.

Input File: include/cppad/core/atomic/two/for_sparse_hes.hpp