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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
ok = afun.hes_sparsity(
    parameter_x, type_x, select_x, select_y, pattern_out
)

Prototype 

template <class Base>
bool atomic_three<Base>::hes_sparsity(
    const vector<Base>&                     parameter_x  ,
    const vector<ad_type_enum>&             type_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 .

parameter_x
See parameter_x .

type_x
See type_x .

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 i , r , c , and k such that
    pattern_out.row()[k] == r
    pattern_out.col()[k] == c
 if and only if 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.

Examples
The file atomic_three_hes_sparsity.cpp contains an example and test that uses this routine.
Input File: include/cppad/core/atomic/three/hes_sparsity.hpp