Stan Math Library  2.20.0
reverse mode automatic differentiation
gamma_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LPDF_HPP
3 
14 #include <cmath>
15 
16 namespace stan {
17 namespace math {
18 
41 template <bool propto, typename T_y, typename T_shape, typename T_inv_scale>
43  const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
44  static const char* function = "gamma_lpdf";
46  T_partials_return;
47 
48  if (size_zero(y, alpha, beta))
49  return 0.0;
50 
51  T_partials_return logp(0.0);
52 
53  check_not_nan(function, "Random variable", y);
54  check_positive_finite(function, "Shape parameter", alpha);
55  check_positive_finite(function, "Inverse scale parameter", beta);
56  check_consistent_sizes(function, "Random variable", y, "Shape parameter",
57  alpha, "Inverse scale parameter", beta);
58 
60  return 0.0;
61 
62  scalar_seq_view<T_y> y_vec(y);
63  scalar_seq_view<T_shape> alpha_vec(alpha);
64  scalar_seq_view<T_inv_scale> beta_vec(beta);
65 
66  for (size_t n = 0; n < length(y); n++) {
67  const T_partials_return y_dbl = value_of(y_vec[n]);
68  if (y_dbl < 0)
69  return LOG_ZERO;
70  }
71 
72  size_t N = max_size(y, alpha, beta);
73  operands_and_partials<T_y, T_shape, T_inv_scale> ops_partials(y, alpha, beta);
74 
75  using std::log;
76 
78  T_y>
79  log_y(length(y));
81  for (size_t n = 0; n < length(y); n++) {
82  if (value_of(y_vec[n]) > 0)
83  log_y[n] = log(value_of(y_vec[n]));
84  }
85  }
86 
88  T_shape>
89  lgamma_alpha(length(alpha));
90  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
91  digamma_alpha(length(alpha));
92  for (size_t n = 0; n < length(alpha); n++) {
94  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
96  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
97  }
98 
100  T_partials_return, T_inv_scale>
101  log_beta(length(beta));
103  for (size_t n = 0; n < length(beta); n++)
104  log_beta[n] = log(value_of(beta_vec[n]));
105  }
106 
107  for (size_t n = 0; n < N; n++) {
108  const T_partials_return y_dbl = value_of(y_vec[n]);
109  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
110  const T_partials_return beta_dbl = value_of(beta_vec[n]);
111 
113  logp -= lgamma_alpha[n];
115  logp += alpha_dbl * log_beta[n];
117  logp += (alpha_dbl - 1.0) * log_y[n];
119  logp -= beta_dbl * y_dbl;
120 
122  ops_partials.edge1_.partials_[n] += (alpha_dbl - 1) / y_dbl - beta_dbl;
124  ops_partials.edge2_.partials_[n]
125  += -digamma_alpha[n] + log_beta[n] + log_y[n];
127  ops_partials.edge3_.partials_[n] += alpha_dbl / beta_dbl - y_dbl;
128  }
129  return ops_partials.build(logp);
130 }
131 
132 template <typename T_y, typename T_shape, typename T_inv_scale>
134  const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
135  return gamma_lpdf<false>(y, alpha, beta);
136 }
137 
138 } // namespace math
139 } // namespace stan
140 #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.
return_type< T_y, T_shape, T_inv_scale >::type gamma_lpdf(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
The log of a gamma density for y with the specified shape and inverse scale parameters.
Definition: gamma_lpdf.hpp:42
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

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