1 #ifndef STAN_MATH_PRIM_FUN_LOG_INV_LOGIT_HPP
2 #define STAN_MATH_PRIM_FUN_LOG_INV_LOGIT_HPP
3 
4 #include <stan/math/prim/meta.hpp>
5 #include <stan/math/prim/fun/exp.hpp>
6 #include <stan/math/prim/fun/log1p.hpp>
7 #include <stan/math/prim/functor/apply_scalar_unary.hpp>
8 #include <cmath>
9 
10 namespace stan {
11 namespace math {
12 
13 /**
14  * Returns the natural logarithm of the inverse logit of the
15  * specified argument.
16  *
17    \f[
18    \mbox{log\_inv\_logit}(x) =
19    \begin{cases}
20      \ln\left(\frac{1}{1+\exp(-x)}\right)& \mbox{if } -\infty\leq x \leq \infty
21  \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \f]
22 
23    \f[
24    \frac{\partial\, \mbox{log\_inv\_logit}(x)}{\partial x} =
25    \begin{cases}
26      \frac{1}{1+\exp(x)} & \mbox{if } -\infty\leq x\leq \infty \\[6pt]
27      \textrm{NaN} & \mbox{if } x = \textrm{NaN}
28    \end{cases}
29    \f]
30  *
31  * @param u argument
32  * @return log of the inverse logit of argument
33  */
log_inv_logit(double u)34 inline double log_inv_logit(double u) {
35   using std::exp;
36   if (u < 0.0) {
37     return u - log1p(exp(u));  // prevent underflow
38   }
39   return -log1p(exp(-u));
40 }
41 
42 /**
43  * Returns the natural logarithm of the inverse logit of the
44  * specified argument.
45  *
46  * @param u argument
47  * @return log of the inverse logit of argument
48  */
log_inv_logit(int u)49 inline double log_inv_logit(int u) {
50   return log_inv_logit(static_cast<double>(u));
51 }
52 
53 /**
54  * Structure to wrap log_inv_logit() so it can be vectorized.
55  */
56 struct log_inv_logit_fun {
57   /**
58    * Return the natural logarithm of the inverse logit
59    * of the specified argument.
60    *
61    * @tparam T argument scalar type
62    * @param x argument
63    * @return natural log of inverse logit of argument
64    */
65   template <typename T>
funstan::math::log_inv_logit_fun66   static inline T fun(const T& x) {
67     return log_inv_logit(x);
68   }
69 };
70 
71 /**
72  * Return the elementwise application of
73  * <code>log_inv_logit()</code> to specified argument container.
74  * The return type promotes the underlying scalar argument type to
75  * double if it is an integer, and otherwise is the argument type.
76  *
77  * @tparam T type of container
78  * @param x container
79  * @return elementwise log_inv_logit of members of container
80  */
81 template <typename T,
82           require_not_nonscalar_prim_or_rev_kernel_expression_t<T>* = nullptr>
log_inv_logit(const T & x)83 inline auto log_inv_logit(const T& x) {
84   return apply_scalar_unary<log_inv_logit_fun, T>::apply(x);
85 }
86 
87 }  // namespace math
88 }  // namespace stan
89 
90 #endif
91