Automatic Differentiation
 
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pareto_type_2_lccdf.hpp
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1#ifndef STAN_MATH_PRIM_PROB_PARETO_TYPE_2_LCCDF_HPP
2#define STAN_MATH_PRIM_PROB_PARETO_TYPE_2_LCCDF_HPP
3
16#include <cmath>
17
18namespace stan {
19namespace math {
20
21template <typename T_y, typename T_loc, typename T_scale, typename T_shape,
23 T_y, T_loc, T_scale, T_shape>* = nullptr>
25 const T_y& y, const T_loc& mu, const T_scale& lambda,
26 const T_shape& alpha) {
28 using T_y_ref = ref_type_if_not_constant_t<T_y>;
29 using T_mu_ref = ref_type_if_not_constant_t<T_loc>;
30 using T_lambda_ref = ref_type_if_not_constant_t<T_scale>;
31 using T_alpha_ref = ref_type_if_not_constant_t<T_shape>;
32 static constexpr const char* function = "pareto_type_2_lccdf";
33 check_consistent_sizes(function, "Random variable", y, "Location parameter",
34 mu, "Scale parameter", lambda, "Shape parameter",
35 alpha);
36
37 if (size_zero(y, mu, lambda, alpha)) {
38 return 0;
39 }
40
41 T_y_ref y_ref = y;
42 T_mu_ref mu_ref = mu;
43 T_lambda_ref lambda_ref = lambda;
44 T_alpha_ref alpha_ref = alpha;
45
46 decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
47 decltype(auto) mu_val = to_ref(as_value_column_array_or_scalar(mu_ref));
48 decltype(auto) lambda_val
50 decltype(auto) alpha_val = to_ref(as_value_column_array_or_scalar(alpha_ref));
51
52 check_nonnegative(function, "Random variable", y_val);
53 check_positive_finite(function, "Scale parameter", lambda_val);
54 check_positive_finite(function, "Shape parameter", alpha_val);
55 check_greater_or_equal(function, "Random variable", y_val, mu_val);
56
57 auto ops_partials
58 = make_partials_propagator(y_ref, mu_ref, lambda_ref, alpha_ref);
59
60 const auto& log_temp = to_ref_if<!is_constant_all<T_shape>::value>(
61 log1p((y_val - mu_val) / lambda_val));
62 T_partials_return P = -sum(alpha_val * log_temp);
63
65 auto rep_deriv = to_ref_if<(!is_constant_all<T_y>::value
68 >= 2>(alpha_val / (y_val - mu_val + lambda_val));
70 partials<0>(ops_partials) = -rep_deriv;
71 }
73 edge<2>(ops_partials).partials_
74 = rep_deriv * (y_val - mu_val) / lambda_val;
75 }
77 partials<1>(ops_partials) = std::move(rep_deriv);
78 }
79 }
80 size_t N = max_size(y, mu, lambda, alpha);
83 using Log_temp_scalar = partials_return_t<T_y, T_loc, T_scale>;
84 using Log_temp_array = Eigen::Array<Log_temp_scalar, Eigen::Dynamic, 1>;
87 partials<3>(ops_partials) = -forward_as<Log_temp_array>(log_temp);
88 } else {
89 partials<3>(ops_partials) = Log_temp_array::Constant(
90 N, 1, -forward_as<Log_temp_scalar>(log_temp));
91 }
92 } else {
93 forward_as<internal::broadcast_array<T_partials_return>>(
94 partials<3>(ops_partials))
95 = -log_temp * N / max_size(y, mu, lambda);
96 }
97 }
98
99 return ops_partials.build(P);
100}
101
102} // namespace math
103} // namespace stan
104#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_shape_cl > pareto_type_2_lccdf(const T_y_cl &y, const T_loc_cl &mu, const T_scale_cl &lambda, const T_shape_cl &alpha)
Returns the pareto type 2 log complementaty cumulative density function.
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
void check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low, Idxs... idxs)
Throw an exception if y is not greater or equal than low.
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
fvar< T > log1p(const fvar< T > &x)
Definition log1p.hpp:12
auto sum(const std::vector< T > &m)
Return the sum of the entries of the specified standard vector.
Definition sum.hpp:23
int64_t max_size(const T1 &x1, const Ts &... xs)
Calculate the size of the largest input.
Definition max_size.hpp:20
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.
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...