Automatic Differentiation
 
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exp_mod_normal_cdf.hpp
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1#ifndef STAN_MATH_PRIM_PROB_EXP_MOD_NORMAL_CDF_HPP
2#define STAN_MATH_PRIM_PROB_EXP_MOD_NORMAL_CDF_HPP
3
21#include <cmath>
22
23namespace stan {
24namespace math {
25
26template <typename T_y, typename T_loc, typename T_scale, typename T_inv_scale,
28 T_y, T_loc, T_scale, T_inv_scale>* = nullptr>
30 const T_y& y, const T_loc& mu, const T_scale& sigma,
31 const T_inv_scale& lambda) {
33 using T_partials_array = Eigen::Array<T_partials_return, Eigen::Dynamic, 1>;
34 using T_y_ref = ref_type_if_not_constant_t<T_y>;
35 using T_mu_ref = ref_type_if_not_constant_t<T_loc>;
36 using T_sigma_ref = ref_type_if_not_constant_t<T_scale>;
37 using T_lambda_ref = ref_type_if_not_constant_t<T_inv_scale>;
38 static constexpr const char* function = "exp_mod_normal_cdf";
39 check_consistent_sizes(function, "Random variable", y, "Location parameter",
40 mu, "Scale parameter", sigma, "Inv_scale paramter",
41 lambda);
42 T_y_ref y_ref = y;
43 T_mu_ref mu_ref = mu;
44 T_sigma_ref sigma_ref = sigma;
45 T_lambda_ref lambda_ref = lambda;
46
47 decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
48 decltype(auto) mu_val = to_ref(as_value_column_array_or_scalar(mu_ref));
49 decltype(auto) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
50 decltype(auto) lambda_val
52
53 check_not_nan(function, "Random variable", y_val);
54 check_finite(function, "Location parameter", mu_val);
55 check_positive_finite(function, "Scale parameter", sigma_val);
56 check_positive_finite(function, "Inv_scale parameter", lambda_val);
57
58 if (size_zero(y, mu, sigma, lambda)) {
59 return 1.0;
60 }
61
62 auto ops_partials
63 = make_partials_propagator(y_ref, mu_ref, sigma_ref, lambda_ref);
64
65 using T_y_val_scalar = scalar_type_t<decltype(y_val)>;
67 if ((forward_as<Eigen::Array<T_y_val_scalar, Eigen::Dynamic, 1>>(y_val)
69 .any()) {
70 return ops_partials.build(0.0);
71 }
72 } else {
73 if (forward_as<T_y_val_scalar>(y_val) == NEGATIVE_INFTY) {
74 return ops_partials.build(0.0);
75 }
76 }
77
78 const auto& inv_sigma
79 = to_ref_if<!is_constant_all<T_y, T_loc, T_scale>::value>(inv(sigma_val));
80 const auto& diff = to_ref(y_val - mu_val);
81 const auto& v = to_ref(lambda_val * sigma_val);
82 const auto& scaled_diff = to_ref(diff * INV_SQRT_TWO * inv_sigma);
83 const auto& scaled_diff_diff
84 = to_ref_if<!is_constant_all<T_y, T_loc, T_scale, T_inv_scale>::value>(
85 scaled_diff - v * INV_SQRT_TWO);
86 const auto& erf_calc = to_ref(0.5 * (1 + erf(scaled_diff_diff)));
87
88 const auto& exp_term
89 = to_ref_if<!is_constant_all<T_y, T_loc, T_scale, T_inv_scale>::value>(
90 exp(0.5 * square(v) - lambda_val * diff));
91 const auto& cdf_n
92 = to_ref(0.5 + 0.5 * erf(scaled_diff) - exp_term * erf_calc);
93
94 T_partials_return cdf(1.0);
95 if (is_vector<decltype(cdf_n)>::value) {
96 cdf = forward_as<T_partials_array>(cdf_n).prod();
97 } else {
98 cdf = forward_as<T_partials_return>(cdf_n);
99 }
100
102 const auto& exp_term_2
105 exp(-square(scaled_diff_diff)));
107 constexpr bool need_deriv_refs = !is_constant_all<T_y, T_loc>::value
109 const auto& deriv_1
110 = to_ref_if<need_deriv_refs>(lambda_val * exp_term * erf_calc);
111 const auto& deriv_2 = to_ref_if<need_deriv_refs>(
112 INV_SQRT_TWO_PI * exp_term * exp_term_2 * inv_sigma);
113 const auto& sq_scaled_diff = square(scaled_diff);
114 const auto& exp_m_sq_scaled_diff = exp(-sq_scaled_diff);
115 const auto& deriv_3 = to_ref_if<need_deriv_refs>(
116 INV_SQRT_TWO_PI * exp_m_sq_scaled_diff * inv_sigma);
118 const auto& deriv = to_ref_if<(!is_constant_all<T_loc>::value
120 cdf * (deriv_1 - deriv_2 + deriv_3) / cdf_n);
122 partials<0>(ops_partials) = deriv;
123 }
125 partials<1>(ops_partials) = -deriv;
126 }
127 }
129 edge<2>(ops_partials).partials_
130 = -cdf
131 * ((deriv_1 - deriv_2) * v
132 + (deriv_3 - deriv_2) * scaled_diff * SQRT_TWO)
133 / cdf_n;
134 }
135 }
137 edge<3>(ops_partials).partials_
138 = cdf * exp_term
139 * (INV_SQRT_TWO_PI * sigma_val * exp_term_2
140 - (v * sigma_val - diff) * erf_calc)
141 / cdf_n;
142 }
143 }
144 return ops_partials.build(cdf);
145}
146
147} // namespace math
148} // namespace stan
149#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, T_inv_scale_cl > exp_mod_normal_cdf(const T_y_cl &y, const T_loc_cl &mu, const T_scale_cl &sigma, const T_inv_scale_cl &lambda)
Returns the double exponential cumulative density function.
T_actual && forward_as(T_actual &&a)
Assume which type we get.
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
T to_ref_if(T &&a)
No-op that should be optimized away.
Definition to_ref.hpp:29
fvar< T > erf(const fvar< T > &x)
Definition erf.hpp:15
static constexpr double INV_SQRT_TWO
The value of 1 over the square root of 2, .
static constexpr double INV_SQRT_TWO_PI
The value of 1 over the square root of , .
static constexpr double NEGATIVE_INFTY
Negative infinity.
Definition constants.hpp:51
static constexpr double SQRT_TWO
The value of the square root of 2, .
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.
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 > 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 scalar_type< T >::type scalar_type_t
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...