Stan Math Library  2.9.0
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 
30  namespace math {
31 
48  template <bool propto,
49  typename T_y, typename T_shape, typename T_scale>
50  typename return_type<T_y, T_shape, T_scale>::type
51  inv_gamma_log(const T_y& y, const T_shape& alpha, const T_scale& beta) {
52  static const char* function("stan::math::inv_gamma_log");
54  T_partials_return;
55 
59  using boost::math::tools::promote_args;
62 
63  // check if any vectors are zero length
64  if (!(stan::length(y)
65  && stan::length(alpha)
66  && stan::length(beta)))
67  return 0.0;
68 
69  // set up return value accumulator
70  T_partials_return logp(0.0);
71 
72  check_not_nan(function, "Random variable", y);
73  check_positive_finite(function, "Shape parameter", alpha);
74  check_positive_finite(function, "Scale parameter", beta);
75  check_consistent_sizes(function,
76  "Random variable", y,
77  "Shape parameter", alpha,
78  "Scale parameter", beta);
79 
80  // check if no variables are involved and prop-to
82  return 0.0;
83 
84  // set up template expressions wrapping scalars into vector views
85  VectorView<const T_y> y_vec(y);
86  VectorView<const T_shape> alpha_vec(alpha);
87  VectorView<const T_scale> beta_vec(beta);
88 
89  for (size_t n = 0; n < length(y); n++) {
90  const T_partials_return y_dbl = value_of(y_vec[n]);
91  if (y_dbl <= 0)
92  return LOG_ZERO;
93  }
94 
95  size_t N = max_size(y, alpha, beta);
97  operands_and_partials(y, alpha, beta);
98 
99  using stan::math::lgamma;
100  using stan::math::digamma;
101  using std::log;
102 
104  T_partials_return, T_y> log_y(length(y));
106  T_partials_return, T_y> inv_y(length(y));
107  for (size_t n = 0; n < length(y); n++) {
109  if (value_of(y_vec[n]) > 0)
110  log_y[n] = log(value_of(y_vec[n]));
112  inv_y[n] = 1.0 / value_of(y_vec[n]);
113  }
114 
116  T_partials_return, T_shape> lgamma_alpha(length(alpha));
118  T_partials_return, T_shape> digamma_alpha(length(alpha));
119  for (size_t n = 0; n < length(alpha); n++) {
121  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
123  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
124  }
125 
127  T_partials_return, T_scale> log_beta(length(beta));
129  for (size_t n = 0; n < length(beta); n++)
130  log_beta[n] = log(value_of(beta_vec[n]));
131  }
132 
133  for (size_t n = 0; n < N; n++) {
134  // pull out values of arguments
135  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
136  const T_partials_return beta_dbl = value_of(beta_vec[n]);
137 
139  logp -= lgamma_alpha[n];
141  logp += alpha_dbl * log_beta[n];
143  logp -= (alpha_dbl+1.0) * log_y[n];
145  logp -= beta_dbl * inv_y[n];
146 
147  // gradients
148  if (!is_constant<typename is_vector<T_y>::type>::value)
149  operands_and_partials.d_x1[n]
150  += -(alpha_dbl+1) * inv_y[n] + beta_dbl * inv_y[n] * inv_y[n];
151  if (!is_constant<typename is_vector<T_shape>::type>::value)
152  operands_and_partials.d_x2[n]
153  += -digamma_alpha[n] + log_beta[n] - log_y[n];
154  if (!is_constant<typename is_vector<T_scale>::type>::value)
155  operands_and_partials.d_x3[n] += alpha_dbl / beta_dbl - inv_y[n];
156  }
157  return operands_and_partials.to_var(logp, y, alpha, beta);
158  }
159 
160  template <typename T_y, typename T_shape, typename T_scale>
161  inline
163  inv_gamma_log(const T_y& y, const T_shape& alpha, const T_scale& beta) {
164  return inv_gamma_log<false>(y, alpha, beta);
165  }
166  }
167 }
168 
169 #endif
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:15
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)
const double LOG_ZERO
Definition: constants.hpp:175
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...
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...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
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
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.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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