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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 $R \in B^{n \times n}$, and a row vector $S \in B^{1 \times m}$, 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 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 $R \in B^{n \times n}$.

s
The argument s has prototype       const CppAD:vector<bool>& s  and its size is m . It is a sparsity pattern for $S \in B^{1 \times m}$.

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 $H(x) \in B^{n \times n}$ 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.

Examples
The file atomic_for_sparse_hes.cpp contains an example and test that uses this routine. It returns true if the test passes and false if it fails.