@(@\newcommand{\W}[1]{ \; #1 \; }
\newcommand{\R}[1]{ {\rm #1} }
\newcommand{\B}[1]{ {\bf #1} }
\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }
\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }
\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }
\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@This is cppad-20221105 documentation. Here is a link to its
current documentation
.
Computing a Jacobian With Constants that Change
Purpose
In this example we use two levels of taping so that a derivative
can have constant parameters that can be changed. To be specific,
we consider the function @(@
f : \B{R}^2 \rightarrow \B{R}^2
@)@
@[@
f(x) = p \left( \begin{array}{c}
\sin( x_0 ) \\
\sin( x_1 )
\end{array} \right)
@]@
were @(@
p \in \B{R}
@)@ is a parameter.
The Jacobian of this function is
@[@
g(x,p) = p \left( \begin{array}{cc}
\cos( x_0 ) & 0 \\
0 & \cos( x_1 )
\end{array} \right)
@]@
In this example we use two levels of AD to avoid computing
the partial of @(@
f(x)
@)@ with respect to @(@
p
@)@,
but still allow for the evaluation of @(@
g(x, p)
@)@
at different values of @(@
p
@)@.
Input File: example/general/change_param.cpp
