logit()

double stan::math::opencl_kernels::logit

(

double

x

)

Return the log odds applied to the kernel generator expression.

The logit function is defined as for $x \in [0, 1]$ by returning the log odds of $x$ treated as a probability,

$\mbox{logit}(x) = \log \left( \frac{x}{1 - x} \right)$.

The inverse to this function is inv_logit.

$$\mbox{logit}(x) = \begin{cases} \textrm{NaN}& \mbox{if } x < 0 \textrm{ or } x > 1\\ \ln\frac{x}{1-x} & \mbox{if } 0\leq x \leq 1 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases}$$

$$\frac{\partial\, \mbox{logit}(x)}{\partial x} = \begin{cases} \textrm{NaN}& \mbox{if } x < 0 \textrm{ or } x > 1\\ \frac{1}{x-x^2}& \mbox{if } 0\leq x\leq 1 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases}$$

Parameters

x

argument

Returns

log odds of argument

Definition at line 52 of file logit.hpp.