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@(@\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 Function Hessian Sparsity Patterns

Syntax

Preferred
ok = afun.hes_sparsity( call_id,
    ident_zero_x, select_x, select_y, pattern_out
)

Deprecated 2022-05-16
ok = afun.hes_sparsity( call_id,
    select_x, select_y, pattern_out
)

Prototype 

template <class Base>
bool atomic_four<Base>::hes_sparsity(
    size_t                                  call_id      ,
    const vector<bool>&                     ident_zero_x ,
    const vector<bool>&                     select_x     ,
    const vector<bool>&                     select_y     ,
    sparse_rc< vector<size_t> >&            pattern_out  )

Implementation
This function must be defined if afun is used to define an ADFun object f , and Hessian sparsity patterns are computed for f .

Base
See Base .

vector
is the CppAD_vector template class.

call_id
See call_id .

ident_zero_x
This can sometimes be used to create more efficient sparsity patterns. If you do not see a way to do this, you can just ignore it. This argument has size equal to the number of arguments to this atomic function; i.e. the size of ax . If ident_zero_x[j] is true, the argument ax[j] is a constant parameter that is identically zero. An identically zero value times any other value can be treated as being identically zero.

select_x
This argument has size equal to the number of arguments to this atomic function; i.e. the size of ax . It specifies which domain components are included in the calculation of pattern_out . If select_x[j] is false, then there will be no indices k such that either of the following hold:
    pattern_out.row()[k] == j
    pattern_out.col()[k] == j
 .

select_y
This argument has size equal to the number of results to this atomic function; i.e. the size of ay . It specifies which range component functions @(@ g_i (x) @)@ are included in of pattern_out .

pattern_out
This input value of pattern_out does not matter. Upon return it is the union, with respect to i such that select_y[i] is true, of the sparsity pattern for Hessian of @(@ g_i (x) @)@. To be specific, there are non-negative indices r , c , and k such that
    pattern_out.row()[k] == r
    pattern_out.col()[k] == c
 if and only if there exists an index i such that, select_y[i] is true, select_x[r] is true, select_x[c] is true, and @[@ \partial_{x(r)} \partial_{x(c)} g_i(x) @]@ is possibly non-zero. Note that the sparsity pattern should be symmetric.

ok
If this calculation succeeded, ok is true. Otherwise it is false.

Example
The following is an example hes_sparsity definition taken from atomic_four_norm_sq.cpp : 
        // Use deprecated version of this callback to test that is still works
        // (missing the ident_zero_x argument).
        bool hes_sparsity(
            size_t                                     call_id     ,
            // const CppAD::vector<bool>&              ident_zero_x,
            const CppAD::vector<bool>&                 select_x    ,
            const CppAD::vector<bool>&                 select_y    ,
            CppAD::sparse_rc< CppAD::vector<size_t> >& pattern_out ) override
        {   size_t n = select_x.size();
# ifndef NDEBUG
            size_t m = select_y.size();
            assert( call_id == 0 );
            assert( m == 1 );
# endif
            // nnz
            size_t nnz = 0;
            if( select_y[0] )
            {   for(size_t j = 0; j < n; ++j)
                {   if( select_x[j] )
                        ++nnz;
                }
            }
            // pattern_out
            pattern_out.resize(n, n, nnz);
            size_t k = 0;
            if( select_y[0] )
            {   for(size_t j = 0; j < n; ++j)
                {   if( select_x[j] )
                        pattern_out.set(k++, j, j);
                }
            }
            return true;
        }
Input File: include/cppad/core/atomic/four/hes_sparsity.hpp