The AD Power Function

@(@\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 . The AD Power Function
Syntax
z = pow(x, y)

See Also
pow_int

Purpose
Determines the value of the power function which is defined by @[@ {\rm pow} (x, y) = x^y @]@

If y is a Variable
If y is a variable, the pow function may use logarithms and exponentiation to compute derivatives. This will not work if x is less than or equal zero.

If y is a Parameter
If y is a parameter, a different method is used to compute the derivatives; see pow_forward . In the special case where x is zero, zero is returned as the derivative. This is correct when y minus the order of the derivative is greater than zero. If y minus the order of the derivative is zero, then y is an integer. If y minus the order of the derivative is less than zero, the actual derivative is infinite.

If y is an Integer
If the value of y is an integer, the pow_int function can be used to compute this value using only multiplication (and division if y is negative). This will work even if x is less than or equal zero.

x
The argument x has one of the following prototypes



    const Base&                    x

    const AD<Base>&                x

    const VecAD<Base>::reference&  x

y
The argument y has one of the following prototypes



    const Base&                    y

    const AD<Base>&                y

    const VecAD<Base>::reference&  y

z
If both x and y are Base objects, the result z is also a Base object. Otherwise, it has prototype



    AD<Base> z

Operation Sequence
This is an AD of Base atomic operation and hence is part of the current AD of Base operation sequence .

Example
The files pow.cpp and pow_nan.cpp are examples tests of this function.

Input File: include/cppad/core/pow.hpp