Stan Math Library  2.11.0
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 
18 #include <boost/random/exponential_distribution.hpp>
19 #include <boost/random/variate_generator.hpp>
20 #include <cmath>
21 
22 namespace stan {
23  namespace math {
24 
25  // Pareto(y|y_m, alpha) [y > y_m; y_m > 0; alpha > 0]
26  template <bool propto,
27  typename T_y, typename T_scale, typename T_shape>
28  typename return_type<T_y, T_scale, T_shape>::type
29  pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
30  static const char* function("stan::math::pareto_log");
32  T_partials_return;
33 
38  using std::log;
39 
40  // check if any vectors are zero length
41  if (!(stan::length(y)
42  && stan::length(y_min)
43  && stan::length(alpha)))
44  return 0.0;
45 
46  // set up return value accumulator
47  T_partials_return logp(0.0);
48 
49  // validate args (here done over var, which should be OK)
50  check_not_nan(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  // check if no variables are involved and prop-to
60  return 0.0;
61 
62  VectorView<const T_y> y_vec(y);
63  VectorView<const T_scale> y_min_vec(y_min);
64  VectorView<const T_shape> alpha_vec(alpha);
65  size_t N = max_size(y, y_min, alpha);
66 
67  for (size_t n = 0; n < N; n++) {
68  if (y_vec[n] < y_min_vec[n])
69  return LOG_ZERO;
70  }
71 
72  // set up template expressions wrapping scalars into vector views
74  operands_and_partials(y, y_min, alpha);
75 
77  T_partials_return, T_y> log_y(length(y));
79  for (size_t n = 0; n < length(y); n++)
80  log_y[n] = log(value_of(y_vec[n]));
81  }
82 
84  T_partials_return, T_y> inv_y(length(y));
86  for (size_t n = 0; n < length(y); n++)
87  inv_y[n] = 1 / value_of(y_vec[n]);
88  }
89 
91  T_partials_return, T_scale>
92  log_y_min(length(y_min));
94  for (size_t n = 0; n < length(y_min); n++)
95  log_y_min[n] = log(value_of(y_min_vec[n]));
96  }
97 
99  T_partials_return, T_shape> log_alpha(length(alpha));
101  for (size_t n = 0; n < length(alpha); n++)
102  log_alpha[n] = log(value_of(alpha_vec[n]));
103  }
104 
106 
107  for (size_t n = 0; n < N; n++) {
108  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
109  // log probability
111  logp += log_alpha[n];
113  logp += alpha_dbl * log_y_min[n];
115  logp -= alpha_dbl * log_y[n] + log_y[n];
116 
117  // gradients
119  operands_and_partials.d_x1[n] -= alpha_dbl * inv_y[n] + inv_y[n];
121  operands_and_partials.d_x2[n] += alpha_dbl / value_of(y_min_vec[n]);
123  operands_and_partials.d_x3[n]
124  += 1 / alpha_dbl + log_y_min[n] - log_y[n];
125  }
126  return operands_and_partials.value(logp);
127  }
128 
129  template <typename T_y, typename T_scale, typename T_shape>
130  inline
132  pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
133  return pareto_log<false>(y, y_min, alpha);
134  }
135  }
136 }
137 #endif
VectorView< T_return_type, false, true > d_x2
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
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:29
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
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
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
VectorBuilder allocates type T1 values to be used as intermediate values.
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 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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