Stan Math Library  2.11.0
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 
15 #include <boost/random/exponential_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 #include <limits>
19 
20 
21 namespace stan {
22  namespace math {
23 
24  template <typename T_y, typename T_scale, typename T_shape>
25  typename return_type<T_y, T_scale, T_shape>::type
26  pareto_cdf(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
28  T_partials_return;
29 
30  // Check sizes
31  // Size checks
32  if ( !( stan::length(y) && stan::length(y_min) && stan::length(alpha) ) )
33  return 1.0;
34 
35  // Check errors
36  static const char* function("stan::math::pareto_cdf");
37 
44  using std::log;
45  using std::exp;
46 
47  T_partials_return P(1.0);
48 
49  check_not_nan(function, "Random variable", y);
50  check_nonnegative(function, "Random variable", y);
51  check_positive_finite(function, "Scale parameter", y_min);
52  check_positive_finite(function, "Shape parameter", alpha);
53  check_consistent_sizes(function,
54  "Random variable", y,
55  "Scale parameter", y_min,
56  "Shape parameter", alpha);
57 
58  // Wrap arguments in vectors
59  VectorView<const T_y> y_vec(y);
60  VectorView<const T_scale> y_min_vec(y_min);
61  VectorView<const T_shape> alpha_vec(alpha);
62  size_t N = max_size(y, y_min, alpha);
63 
65  operands_and_partials(y, y_min, alpha);
66 
67  // Explicit return for extreme values
68  // The gradients are technically ill-defined, but treated as zero
69 
70  for (size_t i = 0; i < stan::length(y); i++) {
71  if (value_of(y_vec[i]) < value_of(y_min_vec[i]))
72  return operands_and_partials.value(0.0);
73  }
74 
75  // Compute vectorized CDF and its gradients
76 
77  for (size_t n = 0; n < N; n++) {
78  // Explicit results for extreme values
79  // The gradients are technically ill-defined, but treated as zero
80  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
81  continue;
82  }
83 
84  // Pull out values
85  const T_partials_return log_dbl = log(value_of(y_min_vec[n])
86  / value_of(y_vec[n]));
87  const T_partials_return y_min_inv_dbl = 1.0 / value_of(y_min_vec[n]);
88  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
89 
90  // Compute
91  const T_partials_return Pn = 1.0 - exp(alpha_dbl * log_dbl);
92 
93  P *= Pn;
94 
96  operands_and_partials.d_x1[n]
97  += alpha_dbl * y_min_inv_dbl * exp((alpha_dbl + 1) * log_dbl)
98  / Pn;
100  operands_and_partials.d_x2[n]
101  += - alpha_dbl * y_min_inv_dbl * exp(alpha_dbl * log_dbl) / Pn;
103  operands_and_partials.d_x3[n]
104  += - exp(alpha_dbl * log_dbl) * log_dbl / Pn;
105  }
106 
108  for (size_t n = 0; n < stan::length(y); ++n)
109  operands_and_partials.d_x1[n] *= P;
110  }
112  for (size_t n = 0; n < stan::length(y_min); ++n)
113  operands_and_partials.d_x2[n] *= P;
114  }
116  for (size_t n = 0; n < stan::length(alpha); ++n)
117  operands_and_partials.d_x3[n] *= P;
118  }
119 
120  return operands_and_partials.value(P);
121  }
122  }
123 }
124 #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
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:26
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.
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

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