Automatic Differentiation
 
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gumbel_cdf.hpp
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1#ifndef STAN_MATH_PRIM_PROB_GUMBEL_CDF_HPP
2#define STAN_MATH_PRIM_PROB_GUMBEL_CDF_HPP
3
16#include <cmath>
17
18namespace stan {
19namespace math {
20
36template <typename T_y, typename T_loc, typename T_scale,
38 T_y, T_loc, T_scale>* = nullptr>
39return_type_t<T_y, T_loc, T_scale> gumbel_cdf(const T_y& y, const T_loc& mu,
40 const T_scale& beta) {
41 using T_partials_return = partials_return_t<T_y, T_loc, T_scale>;
42 using T_partials_array = Eigen::Array<T_partials_return, Eigen::Dynamic, 1>;
43 using T_y_ref = ref_type_if_not_constant_t<T_y>;
44 using T_mu_ref = ref_type_if_not_constant_t<T_loc>;
45 using T_beta_ref = ref_type_if_not_constant_t<T_scale>;
46 static constexpr const char* function = "gumbel_cdf";
47 check_consistent_sizes(function, "Random variable", y, "Location parameter",
48 mu, "Scale parameter", beta);
49 T_y_ref y_ref = y;
50 T_mu_ref mu_ref = mu;
51 T_beta_ref beta_ref = beta;
52
53 decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
54 decltype(auto) mu_val = to_ref(as_value_column_array_or_scalar(mu_ref));
55 decltype(auto) beta_val = to_ref(as_value_column_array_or_scalar(beta_ref));
56
57 check_not_nan(function, "Random variable", y_val);
58 check_finite(function, "Location parameter", mu_val);
59 check_positive(function, "Scale parameter", beta_val);
60
61 if (size_zero(y, mu, beta)) {
62 return 1.0;
63 }
64
65 auto ops_partials = make_partials_propagator(y_ref, mu_ref, beta_ref);
66
67 const auto& scaled_diff
68 = to_ref_if<!is_constant_all<T_y, T_loc, T_scale>::value>((y_val - mu_val)
69 / beta_val);
70 const auto& exp_m_scaled_diff
71 = to_ref_if<!is_constant_all<T_y, T_loc, T_scale>::value>(
72 exp(-scaled_diff));
73 const auto& cdf_n = to_ref_if<!is_constant_all<T_y, T_loc, T_scale>::value>(
74 exp(-exp_m_scaled_diff));
75
76 T_partials_return cdf(1.0);
79 cdf = forward_as<T_partials_array>(cdf_n).prod();
80 } else {
81 cdf = forward_as<T_partials_return>(cdf_n);
82 }
83
85 const auto& rep_deriv_tmp = exp(-scaled_diff - exp_m_scaled_diff);
86 const auto& rep_deriv
87 = to_ref_if<!is_constant_all<T_loc>::value
90 >= 2>(cdf * rep_deriv_tmp / (beta_val * cdf_n));
92 partials<0>(ops_partials) = rep_deriv;
93 }
95 partials<1>(ops_partials) = -rep_deriv;
96 }
98 partials<2>(ops_partials) = -rep_deriv * scaled_diff;
99 }
100 }
101 return ops_partials.build(cdf);
102}
103
104} // namespace math
105} // namespace stan
106#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_loc_cl, T_scale_cl > gumbel_cdf(const T_y_cl &y, const T_loc_cl &mu, const T_scale_cl &beta)
Returns the gumbel 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.
bool size_zero(const T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition size_zero.hpp:19
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_finite(const char *function, const char *name, const T_y &y)
Return true if all values in y are finite.
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition beta.hpp:51
auto make_partials_propagator(Ops &&... ops)
Construct an partials_propagator.
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 ...
If the input type T is either an eigen matrix with 1 column or 1 row at compile time or a standard ve...
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...