Stan Math Library  2.20.0
reverse mode automatic differentiation
inv_gamma_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LPDF_HPP
3 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
34 template <bool propto, typename T_y, typename T_shape, typename T_scale>
36  const T_y& y, const T_shape& alpha, const T_scale& beta) {
37  static const char* function = "inv_gamma_lpdf";
39  T_partials_return;
40 
41  check_not_nan(function, "Random variable", y);
42  check_positive_finite(function, "Shape parameter", alpha);
43  check_positive_finite(function, "Scale parameter", beta);
44  check_consistent_sizes(function, "Random variable", y, "Shape parameter",
45  alpha, "Scale parameter", beta);
46  if (size_zero(y, alpha, beta))
47  return 0;
48 
50  return 0;
51 
52  T_partials_return logp(0);
53  scalar_seq_view<T_y> y_vec(y);
54  scalar_seq_view<T_shape> alpha_vec(alpha);
55  scalar_seq_view<T_scale> beta_vec(beta);
56 
57  for (size_t n = 0; n < length(y); n++) {
58  const T_partials_return y_dbl = value_of(y_vec[n]);
59  if (y_dbl <= 0)
60  return LOG_ZERO;
61  }
62 
63  size_t N = max_size(y, alpha, beta);
64  operands_and_partials<T_y, T_shape, T_scale> ops_partials(y, alpha, beta);
65 
66  using std::log;
67 
69  T_y>
70  log_y(length(y));
72  T_y>
73  inv_y(length(y));
74  for (size_t n = 0; n < length(y); n++) {
76  if (value_of(y_vec[n]) > 0)
77  log_y[n] = log(value_of(y_vec[n]));
79  inv_y[n] = 1.0 / value_of(y_vec[n]);
80  }
81 
83  T_shape>
84  lgamma_alpha(length(alpha));
85  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
86  digamma_alpha(length(alpha));
87  for (size_t n = 0; n < length(alpha); n++) {
89  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
91  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
92  }
93 
95  T_partials_return, T_scale>
96  log_beta(length(beta));
98  for (size_t n = 0; n < length(beta); n++)
99  log_beta[n] = log(value_of(beta_vec[n]));
100  }
101 
102  for (size_t n = 0; n < N; n++) {
103  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
104  const T_partials_return beta_dbl = value_of(beta_vec[n]);
105 
107  logp -= lgamma_alpha[n];
109  logp += alpha_dbl * log_beta[n];
111  logp -= (alpha_dbl + 1.0) * log_y[n];
113  logp -= beta_dbl * inv_y[n];
114 
115  if (!is_constant_all<typename is_vector<T_y>::type>::value)
116  ops_partials.edge1_.partials_[n]
117  += -(alpha_dbl + 1) * inv_y[n] + beta_dbl * inv_y[n] * inv_y[n];
118  if (!is_constant_all<typename is_vector<T_shape>::type>::value)
119  ops_partials.edge2_.partials_[n]
120  += -digamma_alpha[n] + log_beta[n] - log_y[n];
121  if (!is_constant_all<typename is_vector<T_scale>::type>::value)
122  ops_partials.edge3_.partials_[n] += alpha_dbl / beta_dbl - inv_y[n];
123  }
124  return ops_partials.build(logp);
125 }
126 
127 template <typename T_y, typename T_shape, typename T_scale>
129  const T_y& y, const T_shape& alpha, const T_scale& beta) {
130  return inv_gamma_lpdf<false>(y, alpha, beta);
131 }
132 
133 } // namespace math
134 } // namespace stan
135 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:21
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
const double LOG_ZERO
Definition: constants.hpp:150
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
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
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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_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_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23
return_type< T_y, T_shape, T_scale >::type inv_gamma_lpdf(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.

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