\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

atomic_two

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Defining Atomic Functions: Second Generation

Deprecated 2019-01-01

Using the atomic_base class has been deprecated. Use atomic_three instead.

Syntax

atomic_user afun ( ctor_arg_list )

afun ( ax , ay )

ok = afun . forward ( p , q , vx , vy , tx , ty )

ok = afun . reverse ( q , tx , ty , px , py )

ok = afun . for_sparse_jac ( q , r , s , x )

ok = afun . rev_sparse_jac ( q , r , s , x )

ok = afun . for_sparse_hes ( vx , r , s , h , x )

ok = afun . rev_sparse_hes ( vx , s , t , q , r , u , v , x )

atomic_base < Base >:: clear ()

See Also

checkpoint

Purpose

Speed

In some cases, the user knows how to compute derivatives of a function

\[y = f(x) \; {\rm where} \; f : \B{R}^n \rightarrow \B{R}^m\]

more efficiently than by coding it using AD < Base > atomic_base operations and letting CppAD do the rest. In this case atomic_base < Base > can use the user code for \(f(x)\), and its derivatives, as AD < Base > atomic operations.

Reduce Memory

If the function \(f(x)\) is used often, using an atomic version of \(f(x)\) remove the need for repeated copies of the corresponding AD < Base > operations.

Virtual Functions

User defined derivatives are implemented by defining the following virtual functions in the atomic_base class: forward , reverse , for_sparse_jac , rev_sparse_jac , and rev_sparse_hes . These virtual functions have a default implementation that returns ok == false . The forward function, for the case q == 0 , must be implemented. Otherwise, only those functions required by the your calculations need to be implemented. For example, forward for the case q == 2 can just return ok == false unless you require forward mode calculation of second derivatives.

Examples

See atomic_two_example .

Contents

Name	Title
atomic_two_ctor	Atomic Function Constructor
atomic_two_option	Set Atomic Function Options
atomic_two_afun	Using AD Version of Atomic Function
atomic_two_forward	Atomic Forward Mode
atomic_two_reverse	Atomic Reverse Mode
atomic_two_for_sparse_jac	Atomic Forward Jacobian Sparsity Patterns
atomic_two_rev_sparse_jac	Atomic Reverse Jacobian Sparsity Patterns
atomic_two_for_sparse_hes	Atomic Forward Hessian Sparsity Patterns
atomic_two_rev_sparse_hes	Atomic Reverse Hessian Sparsity Patterns
atomic_two_clear	Free Static Variables