\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

atan2

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AD Two Argument Inverse Tangent Function

Syntax

theta = atan2 ( y , x )

Purpose

Determines an angle \(\theta \in [ - \pi , + \pi ]\) such that

\begin{eqnarray} \sin ( \theta ) & = & y / \sqrt{ x^2 + y^2 } \\ \cos ( \theta ) & = & x / \sqrt{ x^2 + y^2 } \end{eqnarray}

y

The argument y has one of the following prototypes

      const AD < Base > & y

      const VecAD < Base >:: reference & y

x

The argument x has one of the following prototypes

      const AD < Base > & x

      const VecAD < Base >:: reference & x

theta

The result theta has prototype

AD < Base > theta

Operation Sequence

The AD of Base operation sequence used to calculate theta is Independent of x and y .

Example

The file atan2.cpp contains an example and test of this function.