Stan Math Library  2.20.0
reverse mode automatic differentiation
pareto_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_LPDF_HPP
3 
11 #include <cmath>
12 
13 namespace stan {
14 namespace math {
15 
16 // Pareto(y|y_m, alpha) [y > y_m; y_m > 0; alpha > 0]
17 template <bool propto, typename T_y, typename T_scale, typename T_shape>
19  const T_y& y, const T_scale& y_min, const T_shape& alpha) {
20  static const char* function = "pareto_lpdf";
22  T_partials_return;
23  using std::log;
24  check_not_nan(function, "Random variable", y);
25  check_positive_finite(function, "Scale parameter", y_min);
26  check_positive_finite(function, "Shape parameter", alpha);
27  check_consistent_sizes(function, "Random variable", y, "Scale parameter",
28  y_min, "Shape parameter", alpha);
29  if (size_zero(y, y_min, alpha))
30  return 0;
31 
33  return 0;
34 
35  T_partials_return logp(0);
36 
37  scalar_seq_view<T_y> y_vec(y);
38  scalar_seq_view<T_scale> y_min_vec(y_min);
39  scalar_seq_view<T_shape> alpha_vec(alpha);
40  size_t N = max_size(y, y_min, alpha);
41 
42  for (size_t n = 0; n < N; n++) {
43  if (y_vec[n] < y_min_vec[n])
44  return LOG_ZERO;
45  }
46 
47  operands_and_partials<T_y, T_scale, T_shape> ops_partials(y, y_min, alpha);
48 
50  T_y>
51  log_y(length(y));
53  for (size_t n = 0; n < length(y); n++)
54  log_y[n] = log(value_of(y_vec[n]));
55  }
56 
58  inv_y(length(y));
60  for (size_t n = 0; n < length(y); n++)
61  inv_y[n] = 1 / value_of(y_vec[n]);
62  }
63 
65  T_partials_return, T_scale>
66  log_y_min(length(y_min));
68  for (size_t n = 0; n < length(y_min); n++)
69  log_y_min[n] = log(value_of(y_min_vec[n]));
70  }
71 
73  T_shape>
74  log_alpha(length(alpha));
76  for (size_t n = 0; n < length(alpha); n++)
77  log_alpha[n] = log(value_of(alpha_vec[n]));
78  }
79 
80  for (size_t n = 0; n < N; n++) {
81  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
83  logp += log_alpha[n];
85  logp += alpha_dbl * log_y_min[n];
87  logp -= alpha_dbl * log_y[n] + log_y[n];
88 
90  ops_partials.edge1_.partials_[n] -= alpha_dbl * inv_y[n] + inv_y[n];
92  ops_partials.edge2_.partials_[n] += alpha_dbl / value_of(y_min_vec[n]);
94  ops_partials.edge3_.partials_[n]
95  += 1 / alpha_dbl + log_y_min[n] - log_y[n];
96  }
97  return ops_partials.build(logp);
98 }
99 
100 template <typename T_y, typename T_scale, typename T_shape>
102  const T_y& y, const T_scale& y_min, const T_shape& alpha) {
103  return pareto_lpdf<false>(y, y_min, alpha);
104 }
105 
106 } // namespace math
107 } // namespace stan
108 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
const double LOG_ZERO
Definition: constants.hpp:150
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
return_type< T_y, T_scale, T_shape >::type pareto_lpdf(const T_y &y, const T_scale &y_min, const T_shape &alpha)
Definition: pareto_lpdf.hpp:18
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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