1 #ifndef STAN_MATH_PRIM_FUN_MULTIPLY_LOG_HPP
2 #define STAN_MATH_PRIM_FUN_MULTIPLY_LOG_HPP
3
4 #include <stan/math/prim/meta.hpp>
5 #include <stan/math/prim/fun/log.hpp>
6 #include <stan/math/prim/functor/apply_scalar_binary.hpp>
7 #include <cmath>
8
9 namespace stan {
10 namespace math {
11
12 /**
13 * Calculate the value of the first argument
14 * times log of the second argument while behaving
15 * properly with 0 inputs.
16 *
17 * \f$ a * \log b \f$.
18 *
19 \f[
20 \mbox{multiply\_log}(x, y) =
21 \begin{cases}
22 0 & \mbox{if } x=y=0\\
23 x\ln y & \mbox{if } x, y\neq 0 \\[6pt]
24 \end{cases}
25 \f]
26
27 \f[
28 \frac{\partial\, \mbox{multiply\_log}(x, y)}{\partial x} =
29 \begin{cases}
30 \ln y \\[6pt]
31 \end{cases}
32 \f]
33
34 \f[
35 \frac{\partial\, \mbox{multiply\_log}(x, y)}{\partial y} =
36 \begin{cases}
37 \frac{x}{y} \\[6pt]
38 \end{cases}
39 \f]
40 *
41 * @tparam T_a type of the first variable
42 * @tparam T_b type of the second variable
43 * @param a the first variable
44 * @param b the second variable
45 * @return a * log(b)
46 */
47 template <typename T_a, typename T_b,
48 require_all_arithmetic_t<T_a, T_b>* = nullptr>
multiply_log(const T_a a,const T_b b)49 inline return_type_t<T_a, T_b> multiply_log(const T_a a, const T_b b) {
50 using std::log;
51 if (b == 0.0 && a == 0.0) {
52 return 0.0;
53 }
54
55 return a * log(b);
56 }
57
58 /**
59 * Enables the vectorised application of the multiply_log
60 * function, when the first and/or second arguments are containers.
61 *
62 * @tparam T1 type of first input
63 * @tparam T2 type of second input
64 * @param a First input
65 * @param b Second input
66 * @return multiply_log function applied to the two inputs.
67 */
68 template <typename T1, typename T2, require_any_container_t<T1, T2>* = nullptr,
69 require_all_not_var_matrix_t<T1, T2>* = nullptr>
multiply_log(const T1 & a,const T2 & b)70 inline auto multiply_log(const T1& a, const T2& b) {
71 return apply_scalar_binary(
72 a, b, [&](const auto& c, const auto& d) { return multiply_log(c, d); });
73 }
74
75 } // namespace math
76 } // namespace stan
77
78 #endif
79