1 #ifndef STAN_MATH_PRIM_FUN_PHI_HPP
2 #define STAN_MATH_PRIM_FUN_PHI_HPP
3 
4 #include <stan/math/prim/meta.hpp>
5 #include <stan/math/prim/err.hpp>
6 #include <stan/math/prim/fun/constants.hpp>
7 #include <stan/math/prim/fun/erf.hpp>
8 #include <stan/math/prim/fun/erfc.hpp>
9 #include <stan/math/prim/fun/Phi.hpp>
10 #include <stan/math/prim/functor/apply_scalar_unary.hpp>
11 
12 namespace stan {
13 namespace math {
14 
15 /**
16  * The unit normal cumulative distribution function.
17  *
18  * The return value for a specified input is the probability that
19  * a random unit normal variate is less than or equal to the
20  * specified value, defined by
21  *
22  * \f$\Phi(x) = \int_{-\infty}^x \mbox{\sf Norm}(x|0, 1) \ dx\f$
23  *
24  * This function can be used to implement the inverse link function
25  * for probit regression.
26  *
27  * Phi will underflow to 0 below -37.5 and overflow to 1 above 8
28  *
29  * @param x Argument.
30  * @return Probability random sample is less than or equal to argument.
31  */
Phi(double x)32 inline double Phi(double x) {
33   check_not_nan("Phi", "x", x);
34   if (x < -37.5) {
35     return 0;
36   } else if (x < -5.0) {
37     return 0.5 * erfc(-INV_SQRT_TWO * x);
38   } else if (x > 8.25) {
39     return 1;
40   } else {
41     return 0.5 * (1.0 + erf(INV_SQRT_TWO * x));
42   }
43 }
44 
45 /**
46  * Structure to wrap Phi() so it can be vectorized.
47  *
48  * @tparam T type of argument
49  * @param x argument
50  * @return Unit normal CDF of x.
51  */
52 struct Phi_fun {
53   template <typename T>
funstan::math::Phi_fun54   static inline T fun(const T& x) {
55     return Phi(x);
56   }
57 };
58 
59 /**
60  * Vectorized version of Phi().
61  *
62  * @tparam T type of container
63  * @param x container
64  * @return Unit normal CDF of each value in x.
65  */
66 template <
67     typename T,
68     require_all_not_nonscalar_prim_or_rev_kernel_expression_t<T>* = nullptr,
69     require_not_var_matrix_t<T>* = nullptr>
Phi(const T & x)70 inline auto Phi(const T& x) {
71   return apply_scalar_unary<Phi_fun, T>::apply(x);
72 }
73 
74 }  // namespace math
75 }  // namespace stan
76 
77 #endif
78