Stan Math Library  2.9.0
reverse mode automatic differentiation
pareto_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_LOG_HPP
3 
4 #include <boost/random/exponential_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 namespace stan {
21  namespace math {
22 
23  // Pareto(y|y_m, alpha) [y > y_m; y_m > 0; alpha > 0]
24  template <bool propto,
25  typename T_y, typename T_scale, typename T_shape>
26  typename return_type<T_y, T_scale, T_shape>::type
27  pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
28  static const char* function("stan::math::pareto_log");
30  T_partials_return;
31 
36  using std::log;
37 
38  // check if any vectors are zero length
39  if (!(stan::length(y)
40  && stan::length(y_min)
41  && stan::length(alpha)))
42  return 0.0;
43 
44  // set up return value accumulator
45  T_partials_return logp(0.0);
46 
47  // validate args (here done over var, which should be OK)
48  check_not_nan(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  // check if no variables are involved and prop-to
58  return 0.0;
59 
60  VectorView<const T_y> y_vec(y);
61  VectorView<const T_scale> y_min_vec(y_min);
62  VectorView<const T_shape> alpha_vec(alpha);
63  size_t N = max_size(y, y_min, alpha);
64 
65  for (size_t n = 0; n < N; n++) {
66  if (y_vec[n] < y_min_vec[n])
67  return LOG_ZERO;
68  }
69 
70  // set up template expressions wrapping scalars into vector views
72  operands_and_partials(y, y_min, alpha);
73 
75  T_partials_return, T_y> log_y(length(y));
77  for (size_t n = 0; n < length(y); n++)
78  log_y[n] = log(value_of(y_vec[n]));
79  }
80 
82  T_partials_return, T_y> inv_y(length(y));
84  for (size_t n = 0; n < length(y); n++)
85  inv_y[n] = 1 / value_of(y_vec[n]);
86  }
87 
89  T_partials_return, T_scale>
90  log_y_min(length(y_min));
92  for (size_t n = 0; n < length(y_min); n++)
93  log_y_min[n] = log(value_of(y_min_vec[n]));
94  }
95 
97  T_partials_return, T_shape> log_alpha(length(alpha));
99  for (size_t n = 0; n < length(alpha); n++)
100  log_alpha[n] = log(value_of(alpha_vec[n]));
101  }
102 
104 
105  for (size_t n = 0; n < N; n++) {
106  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
107  // log probability
109  logp += log_alpha[n];
111  logp += alpha_dbl * log_y_min[n];
113  logp -= alpha_dbl * log_y[n] + log_y[n];
114 
115  // gradients
117  operands_and_partials.d_x1[n] -= alpha_dbl * inv_y[n] + inv_y[n];
119  operands_and_partials.d_x2[n] += alpha_dbl / value_of(y_min_vec[n]);
121  operands_and_partials.d_x3[n]
122  += 1 / alpha_dbl + log_y_min[n] - log_y[n];
123  }
124  return operands_and_partials.to_var(logp, y, y_min, alpha);
125  }
126 
127  template <typename T_y, typename T_scale, typename T_shape>
128  inline
130  pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
131  return pareto_log<false>(y, y_min, alpha);
132  }
133  }
134 }
135 #endif
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
return_type< T_y, T_scale, T_shape >::type pareto_log(const T_y &y, const T_scale &y_min, const T_shape &alpha)
Definition: pareto_log.hpp:27
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)
const double LOG_ZERO
Definition: constants.hpp:175
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
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...
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
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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
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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