log_inv_logit_diff() [1/10]

template<typename T >

fvar< T > stan::math::log_inv_logit_diff ( const fvar< T > &  x, const fvar< T > &  y  )

inline

Returns fvar with the natural logarithm of the difference of the inverse logits of the specified arguments and its gradients.

$$\mathrm{log\_inv\_logit\_diff}(x,y) = \ln\left(\frac{1}{1+\exp(-x)}-\frac{1}{1+\exp(-y)}\right)$$

$$\frac{\partial }{\partial x} = -\frac{e^x}{e^y-e^x}-\frac{e^x}{e^x+1}$$

$$\frac{\partial }{\partial x} = -\frac{e^y}{e^x-e^y}-\frac{e^y}{e^y+1}$$

Template Parameters

T	inner type of the fvar

Parameters

x	Argument.
y	Argument.

Returns

Fvar with result of log difference of inverse logits of arguments and gradients.

Definition at line 38 of file log_inv_logit_diff.hpp.