Defining Atomic Functions: Second Generation

@(@\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 . 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

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

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