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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 
4 #include <boost/random/gamma_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 
23 namespace stan {
24 
25  namespace math {
26 
49  template <bool propto,
50  typename T_y, typename T_shape, typename T_inv_scale>
51  typename return_type<T_y, T_shape, T_inv_scale>::type
52  gamma_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
53  static const char* function("stan::math::gamma_log");
54  typedef typename stan::partials_return_type<T_y, T_shape,
55  T_inv_scale>::type
56  T_partials_return;
57 
64 
65  // check if any vectors are zero length
66  if (!(stan::length(y)
67  && stan::length(alpha)
68  && stan::length(beta)))
69  return 0.0;
70 
71  // set up return value accumulator
72  T_partials_return logp(0.0);
73 
74  // validate args (here done over var, which should be OK)
75  check_not_nan(function, "Random variable", y);
76  check_positive_finite(function, "Shape parameter", alpha);
77  check_positive_finite(function, "Inverse scale parameter", beta);
78  check_consistent_sizes(function,
79  "Random variable", y,
80  "Shape parameter", alpha,
81  "Inverse scale parameter", beta);
82 
83  // check if no variables are involved and prop-to
85  return 0.0;
86 
87  // set up template expressions wrapping scalars into vector views
88  VectorView<const T_y> y_vec(y);
89  VectorView<const T_shape> alpha_vec(alpha);
90  VectorView<const T_inv_scale> beta_vec(beta);
91 
92  for (size_t n = 0; n < length(y); n++) {
93  const T_partials_return y_dbl = value_of(y_vec[n]);
94  if (y_dbl < 0)
95  return LOG_ZERO;
96  }
97 
98  size_t N = max_size(y, alpha, beta);
100  operands_and_partials(y, alpha, beta);
101 
102  using boost::math::lgamma;
104  using boost::math::digamma;
105  using std::log;
106 
108  T_partials_return, T_y> log_y(length(y));
110  for (size_t n = 0; n < length(y); n++) {
111  if (value_of(y_vec[n]) > 0)
112  log_y[n] = log(value_of(y_vec[n]));
113  }
114  }
115 
117  T_partials_return, T_shape> lgamma_alpha(length(alpha));
119  T_partials_return, T_shape> digamma_alpha(length(alpha));
120  for (size_t n = 0; n < length(alpha); n++) {
122  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
124  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
125  }
126 
128  T_partials_return, T_inv_scale> log_beta(length(beta));
130  for (size_t n = 0; n < length(beta); n++)
131  log_beta[n] = log(value_of(beta_vec[n]));
132  }
133 
134  for (size_t n = 0; n < N; n++) {
135  // pull out values of arguments
136  const T_partials_return y_dbl = value_of(y_vec[n]);
137  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
138  const T_partials_return beta_dbl = value_of(beta_vec[n]);
139 
141  logp -= lgamma_alpha[n];
143  logp += alpha_dbl * log_beta[n];
145  logp += (alpha_dbl-1.0) * log_y[n];
147  logp -= beta_dbl * y_dbl;
148 
149  // gradients
151  operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl - beta_dbl;
153  operands_and_partials.d_x2[n] += -digamma_alpha[n] + log_beta[n]
154  + log_y[n];
156  operands_and_partials.d_x3[n] += alpha_dbl / beta_dbl - y_dbl;
157  }
158  return operands_and_partials.to_var(logp, y, alpha, beta);
159  }
160 
161  template <typename T_y, typename T_shape, typename T_inv_scale>
162  inline
164  gamma_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
165  return gamma_log<false>(y, alpha, beta);
166  }
167  }
168 }
169 
170 #endif
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
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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:52
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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