1 #ifndef STAN_MATH_REV_FUN_LGAMMA_HPP
2 #define STAN_MATH_REV_FUN_LGAMMA_HPP
3 
4 #include <stan/math/rev/meta.hpp>
5 #include <stan/math/rev/core.hpp>
6 #include <stan/math/prim/fun/digamma.hpp>
7 #include <stan/math/prim/fun/lgamma.hpp>
8 
9 namespace stan {
10 namespace math {
11 
12 /**
13  * The log gamma function for variables (C99).
14  *
15  * The derivative is the digamma function,
16  *
17  * \f$\frac{d}{dx} \Gamma(x) = \psi^{(0)}(x)\f$.
18  *
19  * @tparam T Arithmetic or a type inheriting from `EigenBase`.
20  * @param a The variable.
21  * @return Log gamma of the variable.
22  */
23 template <typename T, require_stan_scalar_or_eigen_t<T>* = nullptr>
lgamma(const var_value<T> & a)24 inline auto lgamma(const var_value<T>& a) {
25   return make_callback_var(lgamma(a.val()), [a](auto& vi) mutable {
26     as_array_or_scalar(a.adj())
27         += as_array_or_scalar(vi.adj()) * as_array_or_scalar(digamma(a.val()));
28   });
29 }
30 
31 }  // namespace math
32 }  // namespace stan
33 #endif
34