Stan Math Library  2.8.0
reverse mode automatic differentiation
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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 
4 #include <boost/random/exponential_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
15 #include <cmath>
16 #include <limits>
17 
18 
19 namespace stan {
20  namespace math {
21 
22  template <typename T_y, typename T_scale, typename T_shape>
23  typename return_type<T_y, T_scale, T_shape>::type
24  pareto_cdf(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
26  T_partials_return;
27 
28  // Check sizes
29  // Size checks
30  if ( !( stan::length(y) && stan::length(y_min) && stan::length(alpha) ) )
31  return 1.0;
32 
33  // Check errors
34  static const char* function("stan::math::pareto_cdf");
35 
42  using std::log;
43  using std::exp;
44 
45  T_partials_return P(1.0);
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.to_var(0.0, y, y_min, alpha);
71  }
72 
73  // Compute vectorized CDF 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  continue;
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 *= Pn;
92 
94  operands_and_partials.d_x1[n]
95  += alpha_dbl * y_min_inv_dbl * exp((alpha_dbl + 1) * log_dbl)
96  / Pn;
98  operands_and_partials.d_x2[n]
99  += - alpha_dbl * y_min_inv_dbl * exp(alpha_dbl * log_dbl) / Pn;
101  operands_and_partials.d_x3[n]
102  += - exp(alpha_dbl * log_dbl) * log_dbl / Pn;
103  }
104 
106  for (size_t n = 0; n < stan::length(y); ++n)
107  operands_and_partials.d_x1[n] *= P;
108  }
110  for (size_t n = 0; n < stan::length(y_min); ++n)
111  operands_and_partials.d_x2[n] *= P;
112  }
114  for (size_t n = 0; n < stan::length(alpha); ++n)
115  operands_and_partials.d_x3[n] *= P;
116  }
117 
118  return operands_and_partials.to_var(P, y, y_min, alpha);
119  }
120  }
121 }
122 #endif
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
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:24
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_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 metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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.

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