Atomic Function Jacobian Sparsity Patterns

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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 Jacobian Sparsity Patterns
Syntax

ok = afun.jac_sparsity(

    parameter_x, type_x, dependency, select_x, select_y, pattern_out

)

Prototype


template <class Base>
bool atomic_three<Base>::jac_sparsity(
    const vector<Base>&                     parameter_x  ,
    const vector<ad_type_enum>&             type_x       ,
    bool                                    dependency   ,
    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 Jacobian sparsity patterns are computed for f . (Computing Hessian sparsity patterns and optimizing requires Jacobian sparsity patterns.)

Base
See Base .

parameter_x
See parameter_x .

type_x
See type_x .

dependency
If dependency is true, then pattern_out is a dependency pattern for this atomic function. Otherwise it is a sparsity pattern for the derivative of the atomic function.

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



    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 components are included in the calculation of pattern_out . If select_y[i] is false, then there will be no indices k such that



    pattern_out.row()[k] == i

.

pattern_out
This input value of pattern_out does not matter. Upon return it is a dependency or sparsity pattern for the Jacobian of

$g(x)$ , the function corresponding to afun ; dependency above. To be specific, there are non-negative indices i , j , k such that



    pattern_out.row()[k] == i

    pattern_out.col()[k] == j

if and only if select_x[j] is true, select_y[j] is true, and

$g_i(x)$ depends on the value of

$x_j$ (and the partial of

$g_i(x)$ with respect to

$x_j$ is possibly non-zero).

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

Examples
The file atomic_three_jac_sparsity.cpp contains an example and test that uses this routine.

Input File: include/cppad/core/atomic/three/jac_sparsity.hpp