CppAD: A C++ Algorithmic Differentiation Package  20171217
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Macros
template<typename Base >
template<typename VectorBase , typename SizeVector >
void CppAD::ADFun< Base >::subgraph_reverse ( size_t  q,
size_t  ell,
SizeVector &  col,
VectorBase &  dw 

Use reverse mode to compute derivative of Taylor coefficients on a subgraph.

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

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

qis the number of Taylor coefficient we are differentiating.
ellis the component of the range that is selected for differentiation.
colis the set of indices j = col[c] where the return value is defined. If an index j is not in col, then either its derivative is zero, or it is not in select_domain.
dwIs a vector $ dw $ such that for j = col[c], $ k = 0 , \ldots , q-1 $

\[ dw[ j * q + k ] = W^{(1)} ( x )_{j,k} \]

where the matrix $ x $ is the value for $ u $ that corresponding to the forward mode Taylor coefficients for the independent variables as specified by previous calls to Forward.
The element process_range[ell] is set to true by this operation.
some of the elements of this vector are set to have value ell (so it can not longer be used to determine the subgraph corresponding to the ell-th dependent variable).

Definition at line 259 of file subgraph_reverse.hpp.