Stan Math Library  2.11.0
reverse mode automatic differentiation
gamma_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LOG_HPP
3 
21 #include <boost/random/gamma_distribution.hpp>
22 #include <boost/random/variate_generator.hpp>
23 #include <cmath>
24 
25 namespace stan {
26 
27  namespace math {
28 
51  template <bool propto,
52  typename T_y, typename T_shape, typename T_inv_scale>
53  typename return_type<T_y, T_shape, T_inv_scale>::type
54  gamma_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
55  static const char* function("stan::math::gamma_log");
56  typedef typename stan::partials_return_type<T_y, T_shape,
57  T_inv_scale>::type
58  T_partials_return;
59 
66 
67  // check if any vectors are zero length
68  if (!(stan::length(y)
69  && stan::length(alpha)
70  && stan::length(beta)))
71  return 0.0;
72 
73  // set up return value accumulator
74  T_partials_return logp(0.0);
75 
76  // validate args (here done over var, which should be OK)
77  check_not_nan(function, "Random variable", y);
78  check_positive_finite(function, "Shape parameter", alpha);
79  check_positive_finite(function, "Inverse scale parameter", beta);
80  check_consistent_sizes(function,
81  "Random variable", y,
82  "Shape parameter", alpha,
83  "Inverse scale parameter", beta);
84 
85  // check if no variables are involved and prop-to
87  return 0.0;
88 
89  // set up template expressions wrapping scalars into vector views
90  VectorView<const T_y> y_vec(y);
91  VectorView<const T_shape> alpha_vec(alpha);
92  VectorView<const T_inv_scale> beta_vec(beta);
93 
94  for (size_t n = 0; n < length(y); n++) {
95  const T_partials_return y_dbl = value_of(y_vec[n]);
96  if (y_dbl < 0)
97  return LOG_ZERO;
98  }
99 
100  size_t N = max_size(y, alpha, beta);
102  operands_and_partials(y, alpha, beta);
103 
104  using boost::math::lgamma;
106  using boost::math::digamma;
107  using std::log;
108 
110  T_partials_return, T_y> log_y(length(y));
112  for (size_t n = 0; n < length(y); n++) {
113  if (value_of(y_vec[n]) > 0)
114  log_y[n] = log(value_of(y_vec[n]));
115  }
116  }
117 
119  T_partials_return, T_shape> lgamma_alpha(length(alpha));
121  T_partials_return, T_shape> digamma_alpha(length(alpha));
122  for (size_t n = 0; n < length(alpha); n++) {
124  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
126  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
127  }
128 
130  T_partials_return, T_inv_scale> log_beta(length(beta));
132  for (size_t n = 0; n < length(beta); n++)
133  log_beta[n] = log(value_of(beta_vec[n]));
134  }
135 
136  for (size_t n = 0; n < N; n++) {
137  // pull out values of arguments
138  const T_partials_return y_dbl = value_of(y_vec[n]);
139  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
140  const T_partials_return beta_dbl = value_of(beta_vec[n]);
141 
143  logp -= lgamma_alpha[n];
145  logp += alpha_dbl * log_beta[n];
147  logp += (alpha_dbl-1.0) * log_y[n];
149  logp -= beta_dbl * y_dbl;
150 
151  // gradients
153  operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl - beta_dbl;
155  operands_and_partials.d_x2[n] += -digamma_alpha[n] + log_beta[n]
156  + log_y[n];
158  operands_and_partials.d_x3[n] += alpha_dbl / beta_dbl - y_dbl;
159  }
160  return operands_and_partials.value(logp);
161  }
162 
163  template <typename T_y, typename T_shape, typename T_inv_scale>
164  inline
166  gamma_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
167  return gamma_log<false>(y, alpha, beta);
168  }
169  }
170 }
171 
172 #endif
VectorView< T_return_type, false, true > d_x2
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
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: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
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
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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.
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
return_type< T_y, T_shape, T_inv_scale >::type gamma_log(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_log.hpp:54
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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