Automatic Differentiation
 
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double_exponential_cdf.hpp
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1#ifndef STAN_MATH_PRIM_PROB_DOUBLE_EXPONENTIAL_CDF_HPP
2#define STAN_MATH_PRIM_PROB_DOUBLE_EXPONENTIAL_CDF_HPP
3
17#include <cmath>
18
19namespace stan {
20namespace math {
21
36template <typename T_y, typename T_loc, typename T_scale,
38 T_y, T_loc, T_scale>* = nullptr>
40 const T_y& y, const T_loc& mu, const T_scale& sigma) {
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_rep_deriv
44 = std::conditional_t<is_vector<T_y>::value || is_vector<T_loc>::value
46 T_partials_array, T_partials_return>;
47 using std::exp;
48 using T_y_ref = ref_type_if_not_constant_t<T_y>;
49 using T_mu_ref = ref_type_if_not_constant_t<T_loc>;
50 using T_sigma_ref = ref_type_if_not_constant_t<T_scale>;
51 static constexpr const char* function = "double_exponential_cdf";
52 T_y_ref y_ref = y;
53 T_mu_ref mu_ref = mu;
54 T_sigma_ref sigma_ref = sigma;
55
56 T_partials_return cdf(1.0);
57 auto ops_partials = make_partials_propagator(y_ref, mu_ref, sigma_ref);
58
59 decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
60 decltype(auto) mu_val = to_ref(as_value_column_array_or_scalar(mu_ref));
61 decltype(auto) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
62
63 check_not_nan(function, "Random variable", y_val);
64 check_finite(function, "Location parameter", mu_val);
65 check_positive_finite(function, "Scale parameter", sigma_val);
66
67 if (size_zero(y, mu, sigma)) {
68 return 1.0;
69 }
70
71 const auto& inv_sigma = to_ref(inv(sigma_val));
72 const auto& scaled_diff = to_ref_if<!is_constant_all<T_scale>::value>(
73 (y_val - mu_val) * inv_sigma);
74 const auto& exp_scaled_diff = to_ref(exp(scaled_diff));
75
76 T_rep_deriv rep_deriv;
78 using array_bool = Eigen::Array<bool, Eigen::Dynamic, 1>;
79 cdf = forward_as<array_bool>(y_val < mu_val)
80 .select(forward_as<T_partials_array>(exp_scaled_diff * 0.5),
81 1.0 - 0.5 / exp_scaled_diff)
82 .prod();
83 rep_deriv = forward_as<T_rep_deriv>(
84 forward_as<array_bool>(y_val < mu_val)
85 .select((cdf * inv_sigma),
86 forward_as<T_partials_array>(cdf * inv_sigma
87 / (2 * exp_scaled_diff - 1))));
88 } else {
90 cdf = forward_as<bool>(y_val < mu_val)
91 ? forward_as<T_partials_array>(exp_scaled_diff * 0.5).prod()
92 : forward_as<T_partials_array>(1.0 - 0.5 / exp_scaled_diff)
93 .prod();
94 } else {
95 cdf = forward_as<bool>(y_val < mu_val)
96 ? forward_as<T_partials_return>(exp_scaled_diff * 0.5)
97 : forward_as<T_partials_return>(1.0 - 0.5 / exp_scaled_diff);
98 }
99 if (forward_as<bool>(y_val < mu_val)) {
100 rep_deriv = cdf * inv_sigma;
101 } else {
102 rep_deriv = cdf * inv_sigma / (2 * exp_scaled_diff - 1);
103 }
104 }
105
107 partials<0>(ops_partials) = rep_deriv;
108 }
110 partials<1>(ops_partials) = -rep_deriv;
111 }
113 partials<2>(ops_partials) = -rep_deriv * scaled_diff;
114 }
115 return ops_partials.build(cdf);
116}
117
118} // namespace math
119} // namespace stan
120#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.
select_< as_operation_cl_t< T_condition >, as_operation_cl_t< T_then >, as_operation_cl_t< T_else > > select(T_condition &&condition, T_then &&then, T_else &&els)
Selection operation on kernel generator expressions.
Definition select.hpp:148
return_type_t< T_y_cl, T_loc_cl, T_scale_cl > double_exponential_cdf(const T_y_cl &y, const T_loc_cl &mu, const T_scale_cl &sigma)
Returns the double exponential cumulative density function.
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...
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.
fvar< T > inv(const fvar< T > &x)
Definition inv.hpp:12
auto make_partials_propagator(Ops &&... ops)
Construct an partials_propagator.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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...