1 #ifndef STAN_MATH_OPENCL_PRIM_CAUCHY_LCCDF_HPP
2 #define STAN_MATH_OPENCL_PRIM_CAUCHY_LCCDF_HPP
3 #ifdef STAN_OPENCL
4
5 #include <stan/math/prim/meta.hpp>
6 #include <stan/math/prim/err.hpp>
7 #include <stan/math/prim/fun/constants.hpp>
8 #include <stan/math/prim/fun/elt_divide.hpp>
9 #include <stan/math/prim/fun/elt_multiply.hpp>
10 #include <stan/math/opencl/kernel_generator.hpp>
11 #include <stan/math/prim/functor/operands_and_partials.hpp>
12
13 namespace stan {
14 namespace math {
15
16 /** \ingroup opencl
17 * Returns the cauchy log complementary cumulative distribution function
18 * for the given location, and scale. If given containers of matching sizes
19 * returns the log sum of probabilities.
20 *
21 * @tparam T_y_cl type of scalar outcome
22 * @tparam T_loc_cl type of location
23 * @tparam T_scale_cl type of scale
24 * @param y (Sequence of) scalar(s).
25 * @param mu (Sequence of) location(s).
26 * @param sigma (Sequence of) scale(s).
27 * @return The log of the product of densities.
28 */
29 template <
30 typename T_y_cl, typename T_loc_cl, typename T_scale_cl,
31 require_all_prim_or_rev_kernel_expression_t<T_y_cl, T_loc_cl,
32 T_scale_cl>* = nullptr,
33 require_any_not_stan_scalar_t<T_y_cl, T_loc_cl, T_scale_cl>* = nullptr>
cauchy_lccdf(const T_y_cl & y,const T_loc_cl & mu,const T_scale_cl & sigma)34 return_type_t<T_y_cl, T_loc_cl, T_scale_cl> cauchy_lccdf(
35 const T_y_cl& y, const T_loc_cl& mu, const T_scale_cl& sigma) {
36 static const char* function = "cauchy_lccdf(OpenCL)";
37 using T_partials_return = partials_return_t<T_y_cl, T_loc_cl, T_scale_cl>;
38 using std::isfinite;
39 using std::isnan;
40
41 check_consistent_sizes(function, "Random variable", y, "Location parameter",
42 mu, "Scale parameter", sigma);
43 const size_t N = max_size(y, mu, sigma);
44 if (N == 0) {
45 return 0.0;
46 }
47
48 const auto& y_col = as_column_vector_or_scalar(y);
49 const auto& mu_col = as_column_vector_or_scalar(mu);
50 const auto& sigma_col = as_column_vector_or_scalar(sigma);
51
52 const auto& y_val = value_of(y_col);
53 const auto& mu_val = value_of(mu_col);
54 const auto& sigma_val = value_of(sigma_col);
55
56 auto check_y_not_nan
57 = check_cl(function, "Random variable", y_val, "not NaN");
58 auto y_not_nan_expr = !isnan(y_val);
59 auto check_mu_finite
60 = check_cl(function, "Location parameter", mu_val, "finite");
61 auto mu_finite_expr = isfinite(mu_val);
62 auto check_sigma_positive_finite
63 = check_cl(function, "Scale parameter", sigma_val, "positive finite");
64 auto sigma_positive_finite_expr = 0 < sigma_val && isfinite(sigma_val);
65
66 auto sigma_inv = elt_divide(1.0, sigma_val);
67 auto z = elt_multiply(y_val - mu_val, sigma_inv);
68 auto Pn = 0.5 - elt_divide(atan(z), pi());
69 auto ccdf_log_expr = colwise_sum(log(Pn));
70 auto rep_deriv = elt_divide(
71 1.0,
72 elt_multiply(Pn * pi(), elt_multiply(square(z), sigma_val) + sigma_val));
73 auto sigma_deriv = elt_multiply(rep_deriv, z);
74
75 matrix_cl<double> ccdf_log_cl;
76 matrix_cl<double> y_deriv_cl;
77 matrix_cl<double> mu_deriv_cl;
78 matrix_cl<double> sigma_deriv_cl;
79
80 results(check_y_not_nan, check_mu_finite, check_sigma_positive_finite,
81 ccdf_log_cl, y_deriv_cl, mu_deriv_cl, sigma_deriv_cl)
82 = expressions(y_not_nan_expr, mu_finite_expr, sigma_positive_finite_expr,
83 ccdf_log_expr,
84 calc_if<!is_constant<T_y_cl>::value>(-rep_deriv),
85 calc_if<!is_constant<T_loc_cl>::value>(rep_deriv),
86 calc_if<!is_constant<T_scale_cl>::value>(sigma_deriv));
87
88 T_partials_return ccdf_log = sum(from_matrix_cl(ccdf_log_cl));
89
90 operands_and_partials<decltype(y_col), decltype(mu_col), decltype(sigma_col)>
91 ops_partials(y_col, mu_col, sigma_col);
92
93 if (!is_constant<T_y_cl>::value) {
94 ops_partials.edge1_.partials_ = std::move(y_deriv_cl);
95 }
96 if (!is_constant<T_loc_cl>::value) {
97 ops_partials.edge2_.partials_ = std::move(mu_deriv_cl);
98 }
99 if (!is_constant<T_scale_cl>::value) {
100 ops_partials.edge3_.partials_ = std::move(sigma_deriv_cl);
101 }
102 return ops_partials.build(ccdf_log);
103 }
104
105 } // namespace math
106 } // namespace stan
107 #endif
108 #endif
109