Atomic Forward Jacobian Sparsity Patterns

atomic_two_for_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 Forward Jacobian Sparsity Patterns
Syntax

ok = afun.for_sparse_jac(q, r, s, x)

Deprecated 2016-06-27

ok = afun.for_sparse_jac(q, r, s)

Purpose
This function is used by ForSparseJac to compute Jacobian sparsity patterns. For a fixed matrix @(@ R \in \B{R}^{n \times q} @)@, the Jacobian of @(@ f( x + R * u) @)@ with respect to @(@ u \in \B{R}^q @)@ is @[@ S(x) = f^{(1)} (x) * R @]@ Given a sparsity pattern for @(@ R @)@, for_sparse_jac computes a sparsity pattern for @(@ S(x) @)@.

Implementation
If you are using ForSparseJac , ForSparseHes , or RevSparseHes , one of the versions of 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 columns in @(@ R \in \B{R}^{n \times q} @)@ and the Jacobian @(@ S(x) \in \B{R}^{m \times q} @)@.

r
This argument has prototype



     const atomic_sparsity& r

and is a atomic_sparsity pattern for @(@ R \in \B{R}^{n \times q} @)@.

s
This argument has prototype



    atomic_sparsity& s

The input values of its elements are not specified (must not matter). Upon return, s is a atomic_sparsity pattern for @(@ S(x) \in \B{R}^{m \times q} @)@.

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.

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/for_sparse_jac.hpp