template<typename Base >

template<typename VectorBase >

VectorBase CppAD::ADFun< Base >::Reverse	(	size_t	q,
		const VectorBase &	w
	)

reverse mode sweep

Use reverse mode to compute derivative of forward mode Taylor coefficients.

The function $X : {\bf R} \times {\bf R}^{n \times q} \rightarrow {\bf R}$ is defined by

$X(t , u) = \sum_{k=0}^{q-1} u^{(k)} t^k$

The function $Y : {\bf R} \times {\bf R}^{n \times q} \rightarrow {\bf R}$ is defined by

$Y(t , u) = F[ X(t, u) ]$

The function $W : {\bf R}^{n \times q} \rightarrow {\bf R}$ is defined by

$W(u) = \sum_{k=0}^{q-1} ( w^{(k)} )^{\rm T} \frac{1}{k !} \frac{ \partial^k } { t^k } Y(0, u)$

Template Parameters

Base	base type for the operator; i.e., this operation sequence was recorded using AD< Base > and computations by this routine are done using type Base.
VectorBase	is a Simple Vector class with elements of type Base.

Parameters

q is the number of the number of Taylor coefficients that are being differentiated (per variable).

w

is the weighting for each of the Taylor coefficients corresponding to dependent variables. If the argument w has size m * q , for $k = 0 , \ldots , q-1$ and $i = 0, \ldots , m-1$ ,

$w_i^{(k)} = w [ i * q + k ]$

If the argument w has size m , for $k = 0 , \ldots , q-1$ and $i = 0, \ldots , m-1$ ,

$w_i^{(k)} = \left\{ \begin{array}{ll} w [ i ] & {\rm if} \; k = q-1 \\ 0 & {\rm otherwise} \end{array} \right.$

Returns: Is a vector such that for $j = 0 , \ldots , n-1$ and $k = 0 , \ldots , q-1$
$dw[ j * q + k ] = W^{(1)} ( x )_{j,k}$
where the matrix is the value for that corresponding to the forward mode Taylor coefficients for the independent variables as specified by previous calls to Forward.

Definition at line 91 of file reverse.hpp.

Referenced by CppAD::BenderQuad(), CppAD::ipopt::solve_callback< Dvector, ADvector, FG_eval >::eval_grad_f(), CppAD::ipopt::solve_callback< Dvector, ADvector, FG_eval >::eval_jac_g(), and CppAD::JacobianRev().