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.