Automatic Differentiation
 
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pareto_cdf.hpp
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1#ifndef STAN_MATH_OPENCL_PRIM_PARETO_CDF_HPP
2#define STAN_MATH_OPENCL_PRIM_PARETO_CDF_HPP
3#ifdef STAN_OPENCL
4
12
13namespace stan {
14namespace math {
15
28template <
29 typename T_y_cl, typename T_scale_cl, typename T_shape_cl,
31 T_shape_cl>* = nullptr,
32 require_any_not_stan_scalar_t<T_y_cl, T_scale_cl, T_shape_cl>* = nullptr>
34 const T_y_cl& y, const T_scale_cl& y_min, const T_shape_cl& alpha) {
35 static constexpr const char* function = "pareto_cdf(OpenCL)";
37 using std::isfinite;
38 using std::isnan;
39
40 check_consistent_sizes(function, "Random variable", y, "Location parameter",
41 y_min, "Scale parameter", alpha);
42 const size_t N = max_size(y, y_min, alpha);
43 if (N == 0) {
44 return 1.0;
45 }
46
47 const auto& y_col = as_column_vector_or_scalar(y);
48 const auto& y_min_col = as_column_vector_or_scalar(y_min);
49 const auto& alpha_col = as_column_vector_or_scalar(alpha);
50
51 const auto& y_val = value_of(y_col);
52 const auto& y_min_val = value_of(y_min_col);
53 const auto& alpha_val = value_of(alpha_col);
54
55 auto check_y_nonnegative
56 = check_cl(function, "Random variable", y_val, "nonnegative");
57 auto y_not_nonnegative_expr = 0 <= y_val;
58 auto check_y_min_positive_finite
59 = check_cl(function, "Scale parameter", y_min_val, "positive finite");
60 auto y_min_positive_finite_expr = 0 < y_min_val && isfinite(y_min_val);
61 auto check_alpha_positive_finite
62 = check_cl(function, "Shape parameter", alpha_val, "positive finite");
63 auto alpha_positive_finite_expr = 0 < alpha_val && isfinite(alpha_val);
64
65 auto any_y_lower_than_y_min = colwise_max(cast<char>(y_val < y_min_val));
66 auto cond = y_val == INFTY;
67 auto log_dbl = log(elt_divide(y_min_val, y_val));
68 auto y_min_inv = elt_divide(1.0, y_min_val);
69 auto cdf_n = 1.0 - exp(elt_multiply(alpha_val, log_dbl));
70 auto cdf_expr = colwise_prod(select(cond, 1.0, cdf_n));
71 auto y_y_min_deriv = elt_multiply(alpha_val, y_min_inv);
72 auto y_min_alpha_deriv
73 = elt_divide(exp(elt_multiply(alpha_val, log_dbl)), cdf_n);
74
75 auto y_deriv = elt_divide(
76 elt_multiply(y_y_min_deriv, exp(elt_multiply(alpha_val + 1.0, log_dbl))),
77 cdf_n);
78 auto y_min_deriv = elt_multiply(-y_y_min_deriv, y_min_alpha_deriv);
79 auto alpha_deriv = elt_multiply(y_min_alpha_deriv, -log_dbl);
80
81 matrix_cl<double> cdf_cl;
82 matrix_cl<char> any_y_lower_than_y_min_cl;
83 matrix_cl<double> y_min_deriv_cl;
84 matrix_cl<double> y_deriv_cl;
85 matrix_cl<double> alpha_deriv_cl;
86
87 results(check_y_nonnegative, check_y_min_positive_finite,
88 check_alpha_positive_finite, any_y_lower_than_y_min_cl, cdf_cl,
89 y_deriv_cl, y_min_deriv_cl, alpha_deriv_cl)
90 = expressions(y_not_nonnegative_expr, y_min_positive_finite_expr,
91 alpha_positive_finite_expr, any_y_lower_than_y_min,
92 cdf_expr, calc_if<!is_constant<T_y_cl>::value>(y_deriv),
95
96 if (from_matrix_cl(any_y_lower_than_y_min_cl).maxCoeff()) {
97 return 0;
98 }
99
100 T_partials_return cdf = from_matrix_cl(cdf_cl).prod();
101
102 auto ops_partials = make_partials_propagator(y_col, y_min_col, alpha_col);
104 results(y_min_deriv_cl, y_deriv_cl, alpha_deriv_cl) = expressions(
105 calc_if<!is_constant<T_scale_cl>::value>(y_min_deriv_cl * cdf),
106 calc_if<!is_constant<T_y_cl>::value>(y_deriv_cl * cdf),
107 calc_if<!is_constant<T_shape_cl>::value>(alpha_deriv_cl * cdf));
108
110 partials<0>(ops_partials) = std::move(y_deriv_cl);
111 }
113 partials<1>(ops_partials) = std::move(y_min_deriv_cl);
114 }
116 partials<2>(ops_partials) = std::move(alpha_deriv_cl);
117 }
118 }
119 return ops_partials.build(cdf);
120}
121
122} // namespace math
123} // namespace stan
124#endif
125#endif
Represents an arithmetic matrix on the OpenCL device.
Definition matrix_cl.hpp:47
elt_multiply_< as_operation_cl_t< T_a >, as_operation_cl_t< T_b > > elt_multiply(T_a &&a, T_b &&b)
isfinite_< as_operation_cl_t< T > > isfinite(T &&a)
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
auto check_cl(const char *function, const char *var_name, T &&y, const char *must_be)
Constructs a check on opencl matrix or expression.
Definition check_cl.hpp:219
results_cl< T_results... > results(T_results &&... results)
Deduces types for constructing results_cl object.
auto as_column_vector_or_scalar(T &&a)
as_column_vector_or_scalar of a kernel generator expression.
auto colwise_prod(T &&a)
Column wise product - reduction of a kernel generator expression.
elt_divide_< as_operation_cl_t< T_a >, as_operation_cl_t< T_b > > elt_divide(T_a &&a, T_b &&b)
auto colwise_max(T &&a)
Column wise max - reduction of a kernel generator expression.
calc_if_< true, as_operation_cl_t< T > > calc_if(T &&a)
Definition calc_if.hpp:121
expressions_cl< T_expressions... > expressions(T_expressions &&... expressions)
Deduces types for constructing expressions_cl object.
return_type_t< T_y_cl, T_scale_cl, T_shape_cl > pareto_cdf(const T_y_cl &y, const T_scale_cl &y_min, const T_shape_cl &alpha)
Returns the Pareto cumulative density function.
auto from_matrix_cl(const T &src)
Copies the source matrix that is stored on the OpenCL device to the destination Eigen matrix.
Definition copy.hpp:61
require_all_t< is_prim_or_rev_kernel_expression< std::decay_t< Types > >... > require_all_prim_or_rev_kernel_expression_t
Require type satisfies is_prim_or_rev_kernel_expression.
typename return_type< Ts... >::type return_type_t
Convenience type for the return type of the specified template parameters.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition value_of.hpp:18
fvar< T > log(const fvar< T > &x)
Definition log.hpp:15
void check_consistent_sizes(const char *)
Trivial no input case, this function is a no-op.
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.
static constexpr double INFTY
Positive infinity.
Definition constants.hpp:46
fvar< T > exp(const fvar< T > &x)
Definition exp.hpp:13
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 ...
bool isnan(const stan::math::var &a)
Checks if the given number is NaN.
Definition std_isnan.hpp:18
Metaprogramming struct to detect whether a given type is constant in the mathematical sense (not the ...
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...