Automatic Differentiation
 
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rayleigh_cdf.hpp
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1#ifndef STAN_MATH_PRIM_PROB_RAYLEIGH_CDF_HPP
2#define STAN_MATH_PRIM_PROB_RAYLEIGH_CDF_HPP
3
17#include <cmath>
18
19namespace stan {
20namespace math {
21
22template <typename T_y, typename T_scale,
24 T_y, T_scale>* = nullptr>
25return_type_t<T_y, T_scale> rayleigh_cdf(const T_y& y, const T_scale& sigma) {
26 using T_partials_return = partials_return_t<T_y, T_scale>;
27 using T_y_ref = ref_type_if_not_constant_t<T_y>;
28 using T_sigma_ref = ref_type_if_not_constant_t<T_scale>;
29 static constexpr const char* function = "rayleigh_cdf";
30 check_consistent_sizes(function, "Random variable", y, "Scale parameter",
31 sigma);
32
33 T_y_ref y_ref = y;
34 T_sigma_ref sigma_ref = sigma;
35
36 decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
37 decltype(auto) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
38
39 check_nonnegative(function, "Random variable", y_val);
40 check_positive(function, "Scale parameter", sigma_val);
41
42 if (size_zero(y, sigma)) {
43 return 1.0;
44 }
45
46 auto ops_partials = make_partials_propagator(y_ref, sigma_ref);
47
48 const auto& inv_sigma
49 = to_ref_if<!is_constant_all<T_scale>::value>(inv(sigma_val));
50 const auto& inv_sigma_square
51 = to_ref_if<!is_constant_all<T_y, T_scale>::value>(square(inv_sigma));
52 const auto& exp_val = to_ref_if<!is_constant_all<T_y, T_scale>::value>(
53 exp(-0.5 * square(y_val) * inv_sigma_square));
54
55 T_partials_return cdf = prod(1 - exp_val);
56
58 const auto& common_deriv = to_ref_if<(!is_constant_all<T_y>::value
60 y_val * inv_sigma_square * exp_val / (1.0 - exp_val) * cdf);
62 partials<0>(ops_partials) = common_deriv;
63 }
65 partials<1>(ops_partials) = -y_val * inv_sigma * common_deriv;
66 }
67 }
68
69 return ops_partials.build(cdf);
70}
71
72} // namespace math
73} // namespace stan
74#endif
require_all_not_t< is_nonscalar_prim_or_rev_kernel_expression< std::decay_t< Types > >... > require_all_not_nonscalar_prim_or_rev_kernel_expression_t
Require none of the types satisfy is_nonscalar_prim_or_rev_kernel_expression.
return_type_t< T_y_cl, T_scale_cl > rayleigh_cdf(const T_y_cl &y, const T_scale_cl &sigma)
Returns the Rayleigh cumulative distribution function for the given location, and scale.
typename return_type< Ts... >::type return_type_t
Convenience type for the return type of the specified template parameters.
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
bool size_zero(const T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition size_zero.hpp:19
value_type_t< T > prod(const T &m)
Calculates product of given kernel generator expression elements.
Definition prod.hpp:21
T to_ref_if(T &&a)
No-op that should be optimized away.
Definition to_ref.hpp:29
auto as_value_column_array_or_scalar(T &&a)
Extract the value from an object and for eigen vectors and std::vectors convert to an eigen column ar...
void check_consistent_sizes(const char *)
Trivial no input case, this function is a no-op.
ref_type_t< T && > to_ref(T &&a)
This evaluates expensive Eigen expressions.
Definition to_ref.hpp:17
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
fvar< T > inv(const fvar< T > &x)
Definition inv.hpp:12
auto make_partials_propagator(Ops &&... ops)
Construct an partials_propagator.
fvar< T > square(const fvar< T > &x)
Definition square.hpp:12
fvar< T > exp(const fvar< T > &x)
Definition exp.hpp:13
typename ref_type_if<!is_constant< T >::value, T >::type ref_type_if_not_constant_t
Definition ref_type.hpp:62
typename partials_return_type< Args... >::type partials_return_t
The lgamma implementation in stan-math is based on either the reentrant safe lgamma_r implementation ...
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...