Stan Math Library  2.10.0
reverse mode automatic differentiation
pareto_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_LOG_HPP
3 
15 #include <boost/random/exponential_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 #include <limits>
19 
20 namespace stan {
21  namespace math {
22 
23  template <typename T_y, typename T_scale, typename T_shape>
24  typename return_type<T_y, T_scale, T_shape>::type
25  pareto_cdf_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
27  T_partials_return;
28 
29  // Size checks
30  if ( !( stan::length(y) && stan::length(y_min) && stan::length(alpha) ) )
31  return 0.0;
32 
33  // Check errors
34  static const char* function("stan::math::pareto_cdf_log");
35 
42  using std::log;
43  using std::exp;
44 
45  T_partials_return P(0.0);
46 
47  check_not_nan(function, "Random variable", y);
48  check_nonnegative(function, "Random variable", y);
49  check_positive_finite(function, "Scale parameter", y_min);
50  check_positive_finite(function, "Shape parameter", alpha);
51  check_consistent_sizes(function,
52  "Random variable", y,
53  "Scale parameter", y_min,
54  "Shape parameter", alpha);
55 
56  // Wrap arguments in vectors
57  VectorView<const T_y> y_vec(y);
58  VectorView<const T_scale> y_min_vec(y_min);
59  VectorView<const T_shape> alpha_vec(alpha);
60  size_t N = max_size(y, y_min, alpha);
61 
63  operands_and_partials(y, y_min, alpha);
64 
65  // Explicit return for extreme values
66  // The gradients are technically ill-defined, but treated as zero
67 
68  for (size_t i = 0; i < stan::length(y); i++) {
69  if (value_of(y_vec[i]) < value_of(y_min_vec[i]))
70  return operands_and_partials.value(stan::math::negative_infinity());
71  }
72 
73  // Compute vectorized cdf_log and its gradients
74 
75  for (size_t n = 0; n < N; n++) {
76  // Explicit results for extreme values
77  // The gradients are technically ill-defined, but treated as zero
78  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
79  return operands_and_partials.value(0.0);
80  }
81 
82  // Pull out values
83  const T_partials_return log_dbl = log(value_of(y_min_vec[n])
84  / value_of(y_vec[n]));
85  const T_partials_return y_min_inv_dbl = 1.0 / value_of(y_min_vec[n]);
86  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
87 
88  // Compute
89  const T_partials_return Pn = 1.0 - exp(alpha_dbl * log_dbl);
90 
91  P += log(Pn);
92 
94  operands_and_partials.d_x1[n]
95  += alpha_dbl * y_min_inv_dbl * exp((alpha_dbl + 1) * log_dbl) / Pn;
97  operands_and_partials.d_x2[n]
98  -= alpha_dbl * y_min_inv_dbl * exp(alpha_dbl * log_dbl) / Pn;
100  operands_and_partials.d_x3[n]
101  -= exp(alpha_dbl * log_dbl) * log_dbl / Pn;
102  }
103 
104  return operands_and_partials.value(P);
105  }
106  }
107 }
108 #endif
VectorView< T_return_type, false, true > d_x2
bool check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Return true if y is greater or equal than low.
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
return_type< T_y, T_scale, T_shape >::type pareto_cdf_log(const T_y &y, const T_scale &y_min, const T_shape &alpha)
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132

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