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Up-> CppAD AD ADValued atomic atomic_base

AD-> ad_ctor ad_assign Convert ADValued BoolValued VecAD base_require

ADValued-> Arithmetic unary_standard_math binary_math CondExp Discrete numeric_limits atomic

atomic-> checkpoint atomic_base

atomic_base-> atomic_ctor atomic_option atomic_afun atomic_forward atomic_reverse atomic_for_sparse_jac atomic_rev_sparse_jac atomic_for_sparse_hes atomic_rev_sparse_hes atomic_base_clear atomic_get_started.cpp atomic_norm_sq.cpp atomic_reciprocal.cpp atomic_set_sparsity.cpp atomic_tangent.cpp atomic_eigen_mat_mul.cpp atomic_eigen_mat_inv.cpp atomic_eigen_cholesky.cpp atomic_mat_mul.cpp

Headings-> Syntax Purpose Virtual Functions Contents Examples ---..Getting Started ---..Scalar Function ---..Vector Range ---..Hessian Sparsity Patterns General Case

@(@\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}} }@)@User Defined Atomic AD Functions
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)
ok = afun.rev_sparse_jac(q, r, s)
ok = afun.for_sparse_hes(vx, r, s, h)
ok = afun.rev_sparse_hes(vx, s, t, q, r, u, v)
atomic_base<Base>::clear()

Purpose
In some cases, the user knows how to compute derivatives of a function @[@ y = f(x) \; {\rm where} \; f : B^n \rightarrow B^m @]@ more efficiently than by coding it using AD<Base> atomic 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.

Virtual Functions
User defined derivatives are implemented by defining the following virtual functions in the base_atomic 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.

Contents

atomic_ctor	Atomic Function Constructor
atomic_option	Set Atomic Function Options
atomic_afun	Using AD Version of Atomic Function
atomic_forward	Atomic Forward Mode
atomic_reverse	Atomic Reverse Mode
atomic_for_sparse_jac	Atomic Forward Jacobian Sparsity Patterns
atomic_rev_sparse_jac	Atomic Reverse Jacobian Sparsity Patterns
atomic_for_sparse_hes	Atomic Forward Hessian Sparsity Patterns
atomic_rev_sparse_hes	Atomic Reverse Hessian Sparsity Patterns
atomic_base_clear	Free Static Variables
atomic_get_started.cpp	Getting Started with Atomic Operations: Example and Test
atomic_norm_sq.cpp	Atomic Euclidean Norm Squared: Example and Test
atomic_reciprocal.cpp	Reciprocal as an Atomic Operation: Example and Test
atomic_set_sparsity.cpp	Atomic Sparsity with Set Patterns: Example and Test
atomic_tangent.cpp	Tan and Tanh as User Atomic Operations: Example and Test
atomic_eigen_mat_mul.cpp	Atomic Eigen Matrix Multiply: Example and Test
atomic_eigen_mat_inv.cpp	Atomic Eigen Matrix Inverse: Example and Test
atomic_eigen_cholesky.cpp	Atomic Eigen Cholesky Factorization: Example and Test
atomic_mat_mul.cpp	User Atomic Matrix Multiply: Example and Test

Examples

Getting Started
The file atomic_get_started.cpp contains an example and test that shows the minimal amount of information required to create a user defined atomic operation.

Scalar Function
The file atomic_reciprocal.cpp contains an example and test where the user provides the code for computing derivatives. This example is simple because the domain and range are scalars.

Vector Range
The file atomic_tangent.cpp contains another example where the user provides the code for computing derivatives. This example is more complex because the range has two components.

Hessian Sparsity Patterns
The file atomic_rev_sparse_hes.cpp contains an minimal example where the user provides the code for computing Hessian sparsity patterns.

General Case
The file atomic_mat_mul.cpp contains a more general example where the user provides the code for computing derivatives. This example is more complex because both the domain and range dimensions are arbitrary.

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Input File: omh/atomic_base.omh