Atomic Reverse Jacobian Sparsity Patterns

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atomic_two_rev_sparse_jac

$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$ This is cppad-20221105 documentation. Here is a link to its current documentation . Atomic Reverse Jacobian Sparsity Patterns
Syntax

ok = afun.rev_sparse_jac(q, rt, st, x)

Deprecated 2016-06-27

ok = afun.rev_sparse_jac(q, rt, st)

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

For a fixed matrix

$R \in \B{R}^{q \times m}$ , the Jacobian of

$R * f( x )$ with respect to

$x \in \B{R}^n$ is

$S(x) = R * f^{(1)} (x)$ Given a sparsity pattern for

$R$ , rev_sparse_jac computes a sparsity pattern for

$S(x)$ .

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

q
The argument q has prototype



    size_t q

It specifies the number of rows in

$R \in \B{R}^{q \times m}$ and the Jacobian

$S(x) \in \B{R}^{q \times n}$ .

rt
This argument has prototype



     const atomic_sparsity& rt

and is a atomic_sparsity pattern for

$R^\R{T} \in \B{R}^{m \times q}$ .

st
This argument has prototype



    atomic_sparsity& st

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

$S(x)^\R{T} \in \B{R}^{n \times q}$ .

x
The argument has prototype



    const CppAD::vector<Base>& x

and size is equal to the n . This is the 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.

ok
The return value ok has prototype



    bool ok

If it is true, the corresponding evaluation succeeded, otherwise it failed.

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