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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 
27  namespace math {
28 
29  // Frechet(y|alpha, sigma) [y > 0; alpha > 0; sigma > 0]
30  // FIXME: document
31  template <bool propto,
32  typename T_y, typename T_shape, typename T_scale>
33  typename return_type<T_y, T_shape, T_scale>::type
34  frechet_log(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
35  static const char* function("stan::math::frechet_log");
37  T_partials_return;
38 
45  using std::log;
46 
47  // check if any vectors are zero length
48  if (!(stan::length(y)
49  && stan::length(alpha)
50  && stan::length(sigma)))
51  return 0.0;
52 
53  // set up return value accumulator
54  T_partials_return logp(0.0);
55  check_positive(function, "Random variable", y);
56  check_positive_finite(function, "Shape parameter", alpha);
57  check_positive_finite(function, "Scale parameter", sigma);
58  check_consistent_sizes(function,
59  "Random variable", y,
60  "Shape parameter", alpha,
61  "Scale parameter", sigma);
62 
63  // check if no variables are involved and prop-to
65  return 0.0;
66 
67  VectorView<const T_y> y_vec(y);
68  VectorView<const T_shape> alpha_vec(alpha);
69  VectorView<const T_scale> sigma_vec(sigma);
70  size_t N = max_size(y, alpha, sigma);
71 
73  T_partials_return, T_shape> log_alpha(length(alpha));
74  for (size_t i = 0; i < length(alpha); i++)
76  log_alpha[i] = log(value_of(alpha_vec[i]));
77 
79  T_partials_return, T_y> log_y(length(y));
80  for (size_t i = 0; i < length(y); i++)
82  log_y[i] = log(value_of(y_vec[i]));
83 
85  T_partials_return, T_scale> log_sigma(length(sigma));
86  for (size_t i = 0; i < length(sigma); i++)
88  log_sigma[i] = log(value_of(sigma_vec[i]));
89 
91  T_partials_return, T_y> inv_y(length(y));
92  for (size_t i = 0; i < length(y); i++)
94  inv_y[i] = 1.0 / value_of(y_vec[i]);
95 
97  T_partials_return, T_y, T_shape, T_scale>
98  sigma_div_y_pow_alpha(N);
99  for (size_t i = 0; i < N; i++)
101  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
102  sigma_div_y_pow_alpha[i] = pow(inv_y[i] * value_of(sigma_vec[i]),
103  alpha_dbl);
104  }
105 
107  operands_and_partials(y, alpha, sigma);
108  for (size_t n = 0; n < N; n++) {
109  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
111  logp += log_alpha[n];
113  logp -= (alpha_dbl+1.0)*log_y[n];
115  logp += alpha_dbl*log_sigma[n];
117  logp -= sigma_div_y_pow_alpha[n];
118 
120  const T_partials_return inv_y_dbl = value_of(inv_y[n]);
121  operands_and_partials.d_x1[n]
122  += -(alpha_dbl+1.0) * inv_y_dbl
123  + alpha_dbl * sigma_div_y_pow_alpha[n] * inv_y_dbl;
124  }
126  operands_and_partials.d_x2[n]
127  += 1.0/alpha_dbl
128  + (1.0 - sigma_div_y_pow_alpha[n]) * (log_sigma[n] - log_y[n]);
130  operands_and_partials.d_x3[n]
131  += alpha_dbl / value_of(sigma_vec[n])
132  * (1 - sigma_div_y_pow_alpha[n]);
133  }
134  return operands_and_partials.to_var(logp, y, alpha, sigma);
135  }
136 
137  template <typename T_y, typename T_shape, typename T_scale>
138  inline
140  frechet_log(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
141  return frechet_log<false>(y, alpha, sigma);
142  }
143  }
144 }
145 #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
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)
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...
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:34
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...
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
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
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
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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