Stan Math Library  2.15.0
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 
22 #include <boost/random/gamma_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 
26 namespace stan {
27  namespace math {
28 
51  template <bool propto,
52  typename T_y, typename T_shape, typename T_inv_scale>
54  gamma_lpdf(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
55  static const char* function("gamma_lpdf");
56  typedef typename stan::partials_return_type<T_y, T_shape,
57  T_inv_scale>::type
58  T_partials_return;
59 
61 
62  if (!(stan::length(y)
63  && stan::length(alpha)
64  && stan::length(beta)))
65  return 0.0;
66 
67  T_partials_return logp(0.0);
68 
69  check_not_nan(function, "Random variable", y);
70  check_positive_finite(function, "Shape parameter", alpha);
71  check_positive_finite(function, "Inverse scale parameter", beta);
72  check_consistent_sizes(function,
73  "Random variable", y,
74  "Shape parameter", alpha,
75  "Inverse scale parameter", beta);
76 
78  return 0.0;
79 
81  scalar_seq_view<const T_shape> alpha_vec(alpha);
83 
84  for (size_t n = 0; n < length(y); n++) {
85  const T_partials_return y_dbl = value_of(y_vec[n]);
86  if (y_dbl < 0)
87  return LOG_ZERO;
88  }
89 
90  size_t N = max_size(y, alpha, beta);
92  operands_and_partials(y, alpha, beta);
93 
94  using boost::math::lgamma;
96  using std::log;
97 
99  T_partials_return, T_y> log_y(length(y));
101  for (size_t n = 0; n < length(y); n++) {
102  if (value_of(y_vec[n]) > 0)
103  log_y[n] = log(value_of(y_vec[n]));
104  }
105  }
106 
108  T_partials_return, T_shape> lgamma_alpha(length(alpha));
110  T_partials_return, T_shape> digamma_alpha(length(alpha));
111  for (size_t n = 0; n < length(alpha); n++) {
113  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
115  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
116  }
117 
119  T_partials_return, T_inv_scale> log_beta(length(beta));
121  for (size_t n = 0; n < length(beta); n++)
122  log_beta[n] = log(value_of(beta_vec[n]));
123  }
124 
125  for (size_t n = 0; n < N; n++) {
126  const T_partials_return y_dbl = value_of(y_vec[n]);
127  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
128  const T_partials_return beta_dbl = value_of(beta_vec[n]);
129 
131  logp -= lgamma_alpha[n];
133  logp += alpha_dbl * log_beta[n];
135  logp += (alpha_dbl-1.0) * log_y[n];
137  logp -= beta_dbl * y_dbl;
138 
140  operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl - beta_dbl;
142  operands_and_partials.d_x2[n] += -digamma_alpha[n] + log_beta[n]
143  + log_y[n];
145  operands_and_partials.d_x3[n] += alpha_dbl / beta_dbl - y_dbl;
146  }
147  return operands_and_partials.value(logp);
148  }
149 
150  template <typename T_y, typename T_shape, typename T_inv_scale>
151  inline
153  gamma_lpdf(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
154  return gamma_lpdf<false>(y, alpha, beta);
155  }
156 
157  }
158 }
159 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:20
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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
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:54
VectorBuilder allocates type T1 values to be used as intermediate values.
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.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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