atan2() [8/11]

var stan::math::atan2 ( double  a, const var &  b  )

inline

Return the principal value of the arc tangent, in radians, of the first scalar divided by the second variable (cmath).

The derivative with respect to the variable is

$\frac{\partial}{\partial y} \arctan \frac{c}{y} = \frac{-c}{c^2 + y^2}$.

$$\mbox{atan2}(x, y) = \begin{cases} \arctan\left(\frac{x}{y}\right) & \mbox{if } -\infty\leq x \leq \infty, -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases}$$

$$\frac{\partial\, \mbox{atan2}(x, y)}{\partial x} = \begin{cases} \frac{y}{x^2+y^2} & \mbox{if } -\infty\leq x\leq \infty, -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases}$$

$$\frac{\partial\, \mbox{atan2}(x, y)}{\partial y} = \begin{cases} -\frac{x}{x^2+y^2} & \mbox{if } -\infty\leq x\leq \infty, -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases}$$

Parameters

a	Numerator scalar.
b	Denominator variable.

Returns

The arc tangent of the fraction, in radians.

Definition at line 93 of file atan2.hpp.