Stan Math Library  2.20.0
reverse mode automatic differentiation
pareto_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_HPP
3 
11 #include <cmath>
12 #include <limits>
13 
14 namespace stan {
15 namespace math {
16 
17 template <typename T_y, typename T_scale, typename T_shape>
19  const T_y& y, const T_scale& y_min, const T_shape& alpha) {
21  T_partials_return;
22 
23  if (size_zero(y, y_min, alpha))
24  return 1.0;
25 
26  static const char* function = "pareto_cdf";
27 
28  using std::exp;
29  using std::log;
30 
31  T_partials_return P(1.0);
32 
33  check_not_nan(function, "Random variable", y);
34  check_nonnegative(function, "Random variable", y);
35  check_positive_finite(function, "Scale parameter", y_min);
36  check_positive_finite(function, "Shape parameter", alpha);
37  check_consistent_sizes(function, "Random variable", y, "Scale parameter",
38  y_min, "Shape parameter", alpha);
39 
40  scalar_seq_view<T_y> y_vec(y);
41  scalar_seq_view<T_scale> y_min_vec(y_min);
42  scalar_seq_view<T_shape> alpha_vec(alpha);
43  size_t N = max_size(y, y_min, alpha);
44 
45  operands_and_partials<T_y, T_scale, T_shape> ops_partials(y, y_min, alpha);
46 
47  // Explicit return for extreme values
48  // The gradients are technically ill-defined, but treated as zero
49  for (size_t i = 0; i < stan::length(y); i++) {
50  if (value_of(y_vec[i]) < value_of(y_min_vec[i]))
51  return ops_partials.build(0.0);
52  }
53 
54  for (size_t n = 0; n < N; n++) {
55  // Explicit results for extreme values
56  // The gradients are technically ill-defined, but treated as zero
57  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
58  continue;
59  }
60 
61  const T_partials_return log_dbl
62  = log(value_of(y_min_vec[n]) / value_of(y_vec[n]));
63  const T_partials_return y_min_inv_dbl = 1.0 / value_of(y_min_vec[n]);
64  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
65 
66  const T_partials_return Pn = 1.0 - exp(alpha_dbl * log_dbl);
67 
68  P *= Pn;
69 
71  ops_partials.edge1_.partials_[n]
72  += alpha_dbl * y_min_inv_dbl * exp((alpha_dbl + 1) * log_dbl) / Pn;
74  ops_partials.edge2_.partials_[n]
75  += -alpha_dbl * y_min_inv_dbl * exp(alpha_dbl * log_dbl) / Pn;
77  ops_partials.edge3_.partials_[n]
78  += -exp(alpha_dbl * log_dbl) * log_dbl / Pn;
79  }
80 
82  for (size_t n = 0; n < stan::length(y); ++n)
83  ops_partials.edge1_.partials_[n] *= P;
84  }
86  for (size_t n = 0; n < stan::length(y_min); ++n)
87  ops_partials.edge2_.partials_[n] *= P;
88  }
90  for (size_t n = 0; n < stan::length(alpha); ++n)
91  ops_partials.edge3_.partials_[n] *= P;
92  }
93  return ops_partials.build(P);
94 }
95 
96 } // namespace math
97 } // namespace stan
98 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
return_type< T_y, T_scale, T_shape >::type pareto_cdf(const T_y &y, const T_scale &y_min, const T_shape &alpha)
Definition: pareto_cdf.hpp:18
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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