Automatic Differentiation
 
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exponential_cdf.hpp
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1#ifndef STAN_MATH_PRIM_PROB_EXPONENTIAL_CDF_HPP
2#define STAN_MATH_PRIM_PROB_EXPONENTIAL_CDF_HPP
3
15#include <cmath>
16
17namespace stan {
18namespace math {
19
32template <typename T_y, typename T_inv_scale,
34 T_y, T_inv_scale>* = nullptr>
36 const T_inv_scale& beta) {
37 using T_partials_return = partials_return_t<T_y, T_inv_scale>;
38 using T_partials_array = Eigen::Array<T_partials_return, Eigen::Dynamic, 1>;
39 using T_y_ref = ref_type_if_not_constant_t<T_y>;
41 static constexpr const char* function = "exponential_cdf";
42 T_y_ref y_ref = y;
43 T_beta_ref beta_ref = beta;
44
45 decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
46 decltype(auto) beta_val = to_ref(as_value_column_array_or_scalar(beta_ref));
47
48 check_nonnegative(function, "Random variable", y_val);
49 check_positive_finite(function, "Inverse scale parameter", beta_val);
50
51 if (size_zero(y, beta)) {
52 return 1.0;
53 }
54
55 auto ops_partials = make_partials_propagator(y_ref, beta_ref);
56
57 constexpr bool any_derivatives = !is_constant_all<T_y, T_inv_scale>::value;
58 const auto& exp_val = to_ref_if<any_derivatives>(exp(-beta_val * y_val));
59 const auto& one_m_exp = to_ref_if<any_derivatives>(1 - exp_val);
60
61 T_partials_return cdf(1.0);
63 cdf = forward_as<T_partials_array>(one_m_exp).prod();
64 } else {
65 cdf = forward_as<T_partials_return>(one_m_exp);
66 }
67
68 if (any_derivatives) {
69 const auto& rep_deriv = to_ref_if<(
71 exp_val / one_m_exp * cdf);
73 partials<0>(ops_partials) = beta_val * rep_deriv;
74 }
76 partials<1>(ops_partials) = y_val * rep_deriv;
77 }
78 }
79 return ops_partials.build(cdf);
80}
81
82} // namespace math
83} // namespace stan
84#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_inv_scale_cl > exponential_cdf(const T_y_cl &y, const T_inv_scale_cl &beta)
Calculates the exponential cumulative distribution function for the given y and beta.
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
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...
ref_type_t< T && > to_ref(T &&a)
This evaluates expensive Eigen expressions.
Definition to_ref.hpp:17
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.
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...