Stan Math Library  2.12.0
reverse mode automatic differentiation
inv_gamma_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LOG_HPP
3 
4 #include <boost/random/gamma_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
26 #include <cmath>
27 
28 namespace stan {
29  namespace math {
30 
47  template <bool propto,
48  typename T_y, typename T_shape, typename T_scale>
49  typename return_type<T_y, T_shape, T_scale>::type
50  inv_gamma_log(const T_y& y, const T_shape& alpha, const T_scale& beta) {
51  static const char* function("inv_gamma_log");
53  T_partials_return;
54 
56  using boost::math::tools::promote_args;
57 
58  if (!(stan::length(y)
59  && stan::length(alpha)
60  && stan::length(beta)))
61  return 0.0;
62 
63  T_partials_return logp(0.0);
64 
65  check_not_nan(function, "Random variable", y);
66  check_positive_finite(function, "Shape parameter", alpha);
67  check_positive_finite(function, "Scale parameter", beta);
68  check_consistent_sizes(function,
69  "Random variable", y,
70  "Shape parameter", alpha,
71  "Scale parameter", beta);
72 
74  return 0.0;
75 
76  VectorView<const T_y> y_vec(y);
77  VectorView<const T_shape> alpha_vec(alpha);
78  VectorView<const T_scale> beta_vec(beta);
79 
80  for (size_t n = 0; n < length(y); n++) {
81  const T_partials_return y_dbl = value_of(y_vec[n]);
82  if (y_dbl <= 0)
83  return LOG_ZERO;
84  }
85 
86  size_t N = max_size(y, alpha, beta);
88  operands_and_partials(y, alpha, beta);
89 
90  using std::log;
91 
93  T_partials_return, T_y> log_y(length(y));
95  T_partials_return, T_y> inv_y(length(y));
96  for (size_t n = 0; n < length(y); n++) {
98  if (value_of(y_vec[n]) > 0)
99  log_y[n] = log(value_of(y_vec[n]));
101  inv_y[n] = 1.0 / value_of(y_vec[n]);
102  }
103 
105  T_partials_return, T_shape> lgamma_alpha(length(alpha));
107  T_partials_return, T_shape> digamma_alpha(length(alpha));
108  for (size_t n = 0; n < length(alpha); n++) {
110  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
112  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
113  }
114 
116  T_partials_return, T_scale> log_beta(length(beta));
118  for (size_t n = 0; n < length(beta); n++)
119  log_beta[n] = log(value_of(beta_vec[n]));
120  }
121 
122  for (size_t n = 0; n < N; n++) {
123  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
124  const T_partials_return beta_dbl = value_of(beta_vec[n]);
125 
127  logp -= lgamma_alpha[n];
129  logp += alpha_dbl * log_beta[n];
131  logp -= (alpha_dbl+1.0) * log_y[n];
133  logp -= beta_dbl * inv_y[n];
134 
135  if (!is_constant<typename is_vector<T_y>::type>::value)
136  operands_and_partials.d_x1[n]
137  += -(alpha_dbl+1) * inv_y[n] + beta_dbl * inv_y[n] * inv_y[n];
138  if (!is_constant<typename is_vector<T_shape>::type>::value)
139  operands_and_partials.d_x2[n]
140  += -digamma_alpha[n] + log_beta[n] - log_y[n];
141  if (!is_constant<typename is_vector<T_scale>::type>::value)
142  operands_and_partials.d_x3[n] += alpha_dbl / beta_dbl - inv_y[n];
143  }
144  return operands_and_partials.value(logp);
145  }
146 
147  template <typename T_y, typename T_shape, typename T_scale>
148  inline
150  inv_gamma_log(const T_y& y, const T_shape& alpha, const T_scale& beta) {
151  return inv_gamma_log<false>(y, alpha, beta);
152  }
153 
154  }
155 }
156 #endif
VectorView< T_return_type, false, true > d_x2
Metaprogramming struct to detect whether a given type is constant in the mathematical sense (not the ...
Definition: is_constant.hpp:22
return_type< T_y, T_shape, T_scale >::type inv_gamma_log(const T_y &y, const T_shape &alpha, const T_scale &beta)
The log of an inverse gamma density for y with the specified shape and scale parameters.
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:14
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: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
const double LOG_ZERO
Definition: constants.hpp:172
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
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
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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