template<typename Base >

template<typename VectorBase >

VectorBase CppAD::ADFun< Base >::Forward	(	size_t	q,
		size_t	r,
		const VectorBase &	xq
	)

forward mode user API, one order multiple directions.

One order, multiple directions, forward mode Taylor coefficieints.

Template Parameters

Base	The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD<Base>.
VectorBase	is a Simple Vector class with eleements of type Base.

Parameters

q	is the order for this forward mode computation, q > 0. There must be at least q Taylor coefficients per variable before this call. After this call there will be q+1 Taylor coefficients per variable.
r	is the number of directions for this calculation. If q != 1, r must be the same as in the previous call to Forward where q was equal to one.
xq	contains Taylor coefficients for the independent variables. The size of xq must either be r*n, For j = 0 , ... , n-1, ell = 0, ... , r-1, xq[ ( r*j + ell ] is the q-th order coefficient for the j-th independent variable and the ell-th direction.

Returns

contains Taylor coefficients for the dependent variables. The size of the return value y is r*m. For i = 0, ... , m-1, ell = 0, ... , r-1, y[ r*i + ell ] is the q-th order coefficient for the i-th dependent variable and the ell-th direction.

taylor_

The Taylor coefficients up to order q-1 are inputs and the coefficents of order q are outputs. Let N = num_var_tape_, and C = cap_order_taylor_. Note that for i = 1 , ..., N-1, taylor_[ (C-1)*r*i + i + 0 ] is the zero order cofficent, for the i-th varaible, and all directions. For i = 1 , ..., N-1, k = 1 , ..., q, ell = 0 , ..., r-1, taylor_[ (C-1)*r*i + i + (k-1)*r + ell + 1 ] is the k-th order cofficent, for the i-th varaible, and ell-th direction. (The first independent variable has index one on the tape and there is no variable with index zero.)

Definition at line 324 of file forward.hpp.

Referenced by CppAD::BenderQuad(), CppAD::ipopt::solve_callback< Dvector, ADvector, FG_eval >::cache_new_x(), CppAD::ipopt::solve_callback< Dvector, ADvector, FG_eval >::eval_jac_g(), CppAD::FunCheck(), and CppAD::JacobianFor().