CppAD: A C++ Algorithmic Differentiation Package
20171217
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Multiple direction Taylor coefficient for op = AtanOp.
The C++ source code corresponding to this operation is
z = atan(x)
The auxillary result is
y = 1 + x * x
The value of y, and its derivatives, are computed along with the value and derivatives of z.
Base | base type for the operator; i.e., this operation was recorded using AD< Base > and computations by this routine are done using type Base. |
q | order of the Taylor coefficients that we are computing. |
r | number of directions for Taylor coefficients that we are computing. |
i_z | variable index corresponding to the last (primary) result for this operation; i.e. the row index in taylor corresponding to z. The auxillary result is called y has index i_z - 1. |
i_x | variable index corresponding to the argument for this operator; i.e. the row index in taylor corresponding to x. |
cap_order | maximum number of orders that will fit in the taylor array. |
tpv = (cap_order-1) * r + 1
which is the number of Taylor coefficients per variabletaylor | Input: taylor [ i_x * tpv + 0 ] is the zero order Taylor coefficient for all directions and taylor [ i_x * tpv + (k-1)*r + ell + 1 for k = 1 , ... , q, ell = 0 , ..., r-1, is the k-th order Taylor coefficient corresponding to x and the ell-th direction. Input: taylor [ i_z * tpv + 0 ] , is the zero order Taylor coefficient for all directions and taylor [ i_z * tpv + (k-1)*r + ell + 1 ] , for k = 1 , ... , q-1, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to z and the ell-th direction. Input: taylor [ (i_z-1) * tpv + 0 ] , is the zero order Taylor coefficient for all directions and taylor [ (i_z-1) * tpv + (k-1)*r + ell + 1 ] , for k = 1 , ... , q-1, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to the auxillary result y and the ell-th direction. Output: taylor [ i_z * tpv + (q-1)*r + ell + 1] , ell = 0, ..., r-1, is the q-th order Taylor coefficient corresponding to z and the ell-th direction. |
Definition at line 96 of file atan_op.hpp.
Referenced by forward2sweep().