Stan Math Library  2.20.0
reverse mode automatic differentiation
frechet_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_FRECHET_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_FRECHET_LPDF_HPP
3 
5 #include <boost/random/weibull_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 
19 namespace stan {
20 namespace math {
21 
22 // Frechet(y|alpha, sigma) [y > 0; alpha > 0; sigma > 0]
23 // FIXME: document
24 template <bool propto, typename T_y, typename T_shape, typename T_scale>
26  const T_y& y, const T_shape& alpha, const T_scale& sigma) {
27  static const char* function = "frechet_lpdf";
29  T_partials_return;
30  using std::log;
31  check_positive(function, "Random variable", y);
32  check_positive_finite(function, "Shape parameter", alpha);
33  check_positive_finite(function, "Scale parameter", sigma);
34  check_consistent_sizes(function, "Random variable", y, "Shape parameter",
35  alpha, "Scale parameter", sigma);
36 
37  if (size_zero(y, alpha, sigma))
38  return 0;
40  return 0;
41 
42  T_partials_return logp(0);
43 
44  scalar_seq_view<T_y> y_vec(y);
45  scalar_seq_view<T_shape> alpha_vec(alpha);
46  scalar_seq_view<T_scale> sigma_vec(sigma);
47  size_t N = max_size(y, alpha, sigma);
48 
50  T_shape>
51  log_alpha(length(alpha));
52  for (size_t i = 0; i < length(alpha); i++)
54  log_alpha[i] = log(value_of(alpha_vec[i]));
55 
57  T_y>
58  log_y(length(y));
59  for (size_t i = 0; i < length(y); i++)
61  log_y[i] = log(value_of(y_vec[i]));
62 
64  T_partials_return, T_scale>
65  log_sigma(length(sigma));
66  for (size_t i = 0; i < length(sigma); i++)
68  log_sigma[i] = log(value_of(sigma_vec[i]));
69 
71  T_partials_return, T_y>
72  inv_y(length(y));
73  for (size_t i = 0; i < length(y); i++)
75  inv_y[i] = 1.0 / value_of(y_vec[i]);
76 
78  T_partials_return, T_y, T_shape, T_scale>
79  sigma_div_y_pow_alpha(N);
80  for (size_t i = 0; i < N; i++)
82  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
83  sigma_div_y_pow_alpha[i]
84  = pow(inv_y[i] * value_of(sigma_vec[i]), alpha_dbl);
85  }
86 
87  operands_and_partials<T_y, T_shape, T_scale> ops_partials(y, alpha, sigma);
88  for (size_t n = 0; n < N; n++) {
89  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
91  logp += log_alpha[n];
93  logp -= (alpha_dbl + 1.0) * log_y[n];
95  logp += alpha_dbl * log_sigma[n];
97  logp -= sigma_div_y_pow_alpha[n];
98 
100  const T_partials_return inv_y_dbl = value_of(inv_y[n]);
101  ops_partials.edge1_.partials_[n]
102  += -(alpha_dbl + 1.0) * inv_y_dbl
103  + alpha_dbl * sigma_div_y_pow_alpha[n] * inv_y_dbl;
104  }
106  ops_partials.edge2_.partials_[n]
107  += 1.0 / alpha_dbl
108  + (1.0 - sigma_div_y_pow_alpha[n]) * (log_sigma[n] - log_y[n]);
110  ops_partials.edge3_.partials_[n] += alpha_dbl / value_of(sigma_vec[n])
111  * (1 - sigma_div_y_pow_alpha[n]);
112  }
113  return ops_partials.build(logp);
114 }
115 
116 template <typename T_y, typename T_shape, typename T_scale>
118  const T_y& y, const T_shape& alpha, const T_scale& sigma) {
119  return frechet_lpdf<false>(y, alpha, sigma);
120 }
121 
122 } // namespace math
123 } // namespace stan
124 #endif
return_type< T_y, T_shape, T_scale >::type frechet_lpdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
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
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
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_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:16
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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