Stan Math Library  2.14.0
reverse mode automatic differentiation
frechet_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_FRECHET_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_FRECHET_LOG_HPP
3 
4 #include <boost/random/weibull_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
23 #include <cmath>
24 
25 namespace stan {
26  namespace math {
27 
28  // Frechet(y|alpha, sigma) [y > 0; alpha > 0; sigma > 0]
29  // FIXME: document
30  template <bool propto,
31  typename T_y, typename T_shape, typename T_scale>
33  frechet_log(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
34  static const char* function("frechet_log");
36  T_partials_return;
37 
38  using std::log;
39 
40  if (!(stan::length(y)
41  && stan::length(alpha)
42  && stan::length(sigma)))
43  return 0.0;
44 
45  T_partials_return logp(0.0);
46  check_positive(function, "Random variable", y);
47  check_positive_finite(function, "Shape parameter", alpha);
48  check_positive_finite(function, "Scale parameter", sigma);
49  check_consistent_sizes(function,
50  "Random variable", y,
51  "Shape parameter", alpha,
52  "Scale parameter", sigma);
53 
55  return 0.0;
56 
57  VectorView<const T_y> y_vec(y);
58  VectorView<const T_shape> alpha_vec(alpha);
59  VectorView<const T_scale> sigma_vec(sigma);
60  size_t N = max_size(y, alpha, sigma);
61 
63  T_partials_return, T_shape> log_alpha(length(alpha));
64  for (size_t i = 0; i < length(alpha); i++)
66  log_alpha[i] = log(value_of(alpha_vec[i]));
67 
69  T_partials_return, T_y> log_y(length(y));
70  for (size_t i = 0; i < length(y); i++)
72  log_y[i] = log(value_of(y_vec[i]));
73 
75  T_partials_return, T_scale> log_sigma(length(sigma));
76  for (size_t i = 0; i < length(sigma); i++)
78  log_sigma[i] = log(value_of(sigma_vec[i]));
79 
81  T_partials_return, T_y> inv_y(length(y));
82  for (size_t i = 0; i < length(y); i++)
84  inv_y[i] = 1.0 / value_of(y_vec[i]);
85 
87  T_partials_return, T_y, T_shape, T_scale>
88  sigma_div_y_pow_alpha(N);
89  for (size_t i = 0; i < N; i++)
91  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
92  sigma_div_y_pow_alpha[i] = pow(inv_y[i] * value_of(sigma_vec[i]),
93  alpha_dbl);
94  }
95 
97  operands_and_partials(y, alpha, sigma);
98  for (size_t n = 0; n < N; n++) {
99  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
101  logp += log_alpha[n];
103  logp -= (alpha_dbl+1.0)*log_y[n];
105  logp += alpha_dbl*log_sigma[n];
107  logp -= sigma_div_y_pow_alpha[n];
108 
110  const T_partials_return inv_y_dbl = value_of(inv_y[n]);
111  operands_and_partials.d_x1[n]
112  += -(alpha_dbl+1.0) * inv_y_dbl
113  + alpha_dbl * sigma_div_y_pow_alpha[n] * inv_y_dbl;
114  }
116  operands_and_partials.d_x2[n]
117  += 1.0/alpha_dbl
118  + (1.0 - sigma_div_y_pow_alpha[n]) * (log_sigma[n] - log_y[n]);
120  operands_and_partials.d_x3[n]
121  += alpha_dbl / value_of(sigma_vec[n])
122  * (1 - sigma_div_y_pow_alpha[n]);
123  }
124  return operands_and_partials.value(logp);
125  }
126 
127  template <typename T_y, typename T_shape, typename T_scale>
128  inline
130  frechet_log(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
131  return frechet_log<false>(y, alpha, sigma);
132  }
133 
134  }
135 }
136 #endif
VectorView< T_return_type, false, true > d_x2
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:14
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
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
return_type< T_y, T_shape, T_scale >::type frechet_log(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Definition: frechet_log.hpp:33
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
VectorBuilder allocates type T1 values to be used as intermediate values.
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:17
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
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.
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
VectorView< T_return_type, false, true > d_x1

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