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Up-> cppad_swig library a_fun a_fun_reverse

cppad_swig-> testing swig_xam.i library whats_new_2018

library-> module a_double vector a_fun sparse error xam.m4

a_fun-> independent abort_recording a_fun_ctor a_fun_jacobian a_fun_hessian a_fun_forward a_fun_reverse a_fun_optimize a_fun_property

a_fun_reverse-> a_fun_reverse_xam.cpp a_fun_reverse_xam.m a_fun_reverse_xam.pm a_fun_reverse_xam.py

Headings-> Syntax af Notation ---..f(x) ---..X(t), S ---..Y(t), T ---..G(T) q yq xq Example

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@ Reverse Mode AD
Syntax
xq = af.reverse(q, yq)

af
This object has prototype
     a_fun af
Note that it is effectively const, but some details that are not visible to the user may change, so it is not declared const.

Notation

f(x)
We use the notation @(@ f: \B{R}^n \rightarrow \B{R}^m @)@ for the function corresponding to af . Note that n is the size of ax and m is the size of ay in to the constructor for af .

X(t), S
This is the same function as X(t) in the previous call to af.forward . We use @(@ S \in \B{R}^{n \times q} @)@ to denote the Taylor coefficients of @(@ X(t) @)@.

Y(t), T
This is the same function as Y(t) in the previous call to af.forward . We use @(@ T \in \B{R}^{m \times q} @)@ to denote the Taylor coefficients of @(@ Y(t) @)@. We also use the notation @(@ T(S) @)@ to express the fact that the Taylor coefficients for @(@ Y(t) @)@ are a function of the Taylor coefficients of @(@ X(t) @)@.

G(T)
We use the notation @(@ G : \B{R}^{m \times p} \rightarrow \B{R} @)@ for a function that the calling routine chooses.

q
This argument has prototype
     int q
Its value is the number of the Taylor coefficient (for each variable) that we are computing the derivative with respect to. It must be greater than zero, and less than or equal p + 1 , the number of Taylor coefficient stored in af . (The number of Taylor coefficients is equal to p+1 where p is the order for the previous forward call using af .)

yq
This argument has prototype
     const vec_double& yq
and its size must be m*q . For 0 <= i < m and 0 <= k < q , yq[ i * q + k ] is the partial derivative of @(@ G(T) @)@ with respect to the k-th order Taylor coefficient for the i-th component function; i.e., the partial derivative of @(@ G(T) @)@ w.r.t. @(@ Y_i^{(k)} (t) / k ! @)@.

xq
The result has prototype
     vec_double xq
and its size is n*q . For 0 <= j < n and 0 <= k < q , yq[ j * q + k ] is the partial derivative of @(@ G(T(S)) @)@ with respect to the k-th order Taylor coefficient for the j-th component function; i.e., the partial derivative of @(@ G(T(S)) @)@ w.r.t. @(@ S_j^{(k)} (t) / k ! @)@.

Example
C++ , Octave , Perl , Python .

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Input File: lib/a_fun.cpp