1 #ifndef STAN_MATH_PRIM_FUN_INV_CLOGLOG_HPP
2 #define STAN_MATH_PRIM_FUN_INV_CLOGLOG_HPP
3
4 #include <stan/math/prim/meta.hpp>
5 #include <stan/math/prim/fun/exp.hpp>
6 #include <stan/math/prim/functor/apply_scalar_unary.hpp>
7 #include <stan/math/prim/functor/apply_vector_unary.hpp>
8 #include <cmath>
9
10 namespace stan {
11 namespace math {
12
13 /**
14 * The inverse complementary log-log function.
15 *
16 * The function is defined by
17 *
18 * <code>inv_cloglog(x) = 1 - exp(-exp(x))</code>.
19 *
20 * This function can be used to implement the inverse link
21 * function for complementary-log-log regression.
22 *
23 *
24 \f[
25 \mbox{inv\_cloglog}(y) =
26 \begin{cases}
27 \mbox{cloglog}^{-1}(y) & \mbox{if } -\infty\leq y \leq \infty \\[6pt]
28 \textrm{NaN} & \mbox{if } y = \textrm{NaN}
29 \end{cases}
30 \f]
31 \f[
32 \frac{\partial\, \mbox{inv\_cloglog}(y)}{\partial y} =
33 \begin{cases}
34 \frac{\partial\, \mbox{cloglog}^{-1}(y)}{\partial y} & \mbox{if }
35 -\infty\leq y\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } y = \textrm{NaN}
36 \end{cases}
37 \f]
38 \f[
39 \mbox{cloglog}^{-1}(y) = 1 - \exp \left( - \exp(y) \right)
40 \f]
41 \f[
42 \frac{\partial \, \mbox{cloglog}^{-1}(y)}{\partial y} = \exp(y-\exp(y))
43 \f]
44 *
45 * @param x Argument.
46 * @return Inverse complementary log-log of the argument.
47 */
inv_cloglog(double x)48 inline double inv_cloglog(double x) {
49 using std::exp;
50 return 1 - exp(-exp(x));
51 }
52
53 /**
54 * Structure to wrap inv_cloglog() so that it can be vectorized.
55 *
56 * @tparam T type of variable
57 * @param x variable
58 * @return 1 - exp(-exp(x)).
59 */
60 struct inv_cloglog_fun {
61 template <typename T>
funstan::math::inv_cloglog_fun62 static inline T fun(const T& x) {
63 return inv_cloglog(x);
64 }
65 };
66
67 /**
68 * Vectorized version of inv_cloglog().
69 *
70 * @tparam Container type of container
71 * @param x container
72 * @return 1 - exp(-exp()) applied to each value in x.
73 */
74 template <typename Container,
75 require_not_container_st<std::is_arithmetic, Container>* = nullptr,
76 require_not_var_matrix_t<Container>* = nullptr,
77 require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
78 Container>* = nullptr>
inv_cloglog(const Container & x)79 inline auto inv_cloglog(const Container& x) {
80 return apply_scalar_unary<inv_cloglog_fun, Container>::apply(x);
81 }
82
83 /**
84 * Version of inv_cloglog() that accepts std::vectors, Eigen Matrix/Array
85 * objects or expressions, and containers of these.
86 *
87 * @tparam Container Type of x
88 * @param x Container
89 * @return 1 - exp(-exp()) applied to each value in x.
90 */
91 template <typename Container,
92 require_container_st<std::is_arithmetic, Container>* = nullptr>
inv_cloglog(const Container & x)93 inline auto inv_cloglog(const Container& x) {
94 return apply_vector_unary<Container>::apply(
95 x, [](const auto& v) { return 1 - (-v.array().exp()).exp(); });
96 }
97
98 } // namespace math
99 } // namespace stan
100
101 #endif
102