atomic_four_define¶

Defining Atomic Functions: Fourth Generation¶

Syntax¶

Define Class¶

class atomic_user : public CppAD::atomic_four< Base > {
      …
};

Constructor¶

atomic_user afun ( ctor_arg_list )

Call¶

afun ( ax , ay )

afun ( call_id , ax , ay )

Callbacks¶

ok = afun . for_type ( call_id ,
      type_x , type_y
)
ok = afun . forward ( call_id ,
      select_y , order_low , order_up , taylor_x , taylor_y
)
ok = afun . reverse ( call_id ,
      select_x , order_up , taylor_x , taylor_y , partial_x , partial_y
)
ok = afun . jac_sparsity ( call_id ,
      dependency , ident_zero_x , select_x select_y , pattern_out
)
ok = afun . hes_sparsity ( call_id ,
      ident_zero_x , select_x , select_y , pattern_out
)
ok = afun . rev_depend ( call_id ,
      ident_zero_x , depend_x , depend_y
)

Purpose¶

Speed¶

In some cases, it is possible to compute derivatives of a function

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

more efficiently than by coding it using AD < Base > Atomic operations and letting CppAD do the rest. The class atomic_four < Base > is used to create a new atomic operation corresponding to a function \(g(x)\) where the user specifies how to compute the derivatives and sparsity patterns for \(g(x)\).

Reduce Memory¶

If the function \(g(x)\) is used many times during the recording of an ADFun object, an atomic version of \(g(x)\) removes the need for repeated copies of the corresponding AD < Base > operations and variables in the recording.

Virtual Functions¶

The callback functions are implemented by defining the virtual functions in the atomic_user class. These functions compute derivatives, sparsity patterns, and dependency relations. Each virtual function has a default implementation that returns ok == false . The for_type and forward function (for the case order_up == 0 ) are used by an atomic function Call . Hence, they are required for one to use an atomic function. Other functions and orders are only required if they are used for your calculations. For example, forward for the case order_up == 2 can just return ok == false unless you require forward mode calculation of second derivatives.

Contents¶

Name	Title
atomic_four_ctor	Atomic Function Constructor
atomic_four_call	Calling an Atomic Function
atomic_four_for_type	Atomic Function Forward Type Calculation
atomic_four_forward	Atomic Function Forward Mode
atomic_four_reverse	Atomic Function Reverse Mode
atomic_four_jac_sparsity	Atomic Function Jacobian Sparsity Patterns
atomic_four_hes_sparsity	Atomic Function Hessian Sparsity Patterns
atomic_four_rev_depend	Atomic Function Reverse Dependency