Stan Math Library  2.8.0
reverse mode automatic differentiation
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poisson_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_POISSON_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_POISSON_LOG_HPP
3 
15 #include <boost/math/special_functions/fpclassify.hpp>
16 #include <boost/random/poisson_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <limits>
19 
20 namespace stan {
21 
22  namespace math {
23 
24  // Poisson(n|lambda) [lambda > 0; n >= 0]
25  template <bool propto, typename T_n, typename T_rate>
26  typename return_type<T_rate>::type
27  poisson_log(const T_n& n, const T_rate& lambda) {
29  T_partials_return;
30 
31  static const char* function("stan::math::poisson_log");
32 
33  using boost::math::lgamma;
39 
40  // check if any vectors are zero length
41  if (!(stan::length(n)
42  && stan::length(lambda)))
43  return 0.0;
44 
45  // set up return value accumulator
46  T_partials_return logp(0.0);
47 
48  // validate args
49  check_nonnegative(function, "Random variable", n);
50  check_not_nan(function, "Rate parameter", lambda);
51  check_nonnegative(function, "Rate parameter", lambda);
52  check_consistent_sizes(function,
53  "Random variable", n,
54  "Rate parameter", lambda);
55 
56  // check if no variables are involved and prop-to
58  return 0.0;
59 
60  // set up expression templates wrapping scalars/vecs into vector views
61  VectorView<const T_n> n_vec(n);
62  VectorView<const T_rate> lambda_vec(lambda);
63  size_t size = max_size(n, lambda);
64 
65  for (size_t i = 0; i < size; i++)
66  if (boost::math::isinf(lambda_vec[i]))
67  return LOG_ZERO;
68  for (size_t i = 0; i < size; i++)
69  if (lambda_vec[i] == 0 && n_vec[i] != 0)
70  return LOG_ZERO;
71 
72  // return accumulator with gradients
73  OperandsAndPartials<T_rate> operands_and_partials(lambda);
74 
76  for (size_t i = 0; i < size; i++) {
77  if (!(lambda_vec[i] == 0 && n_vec[i] == 0)) {
79  logp -= lgamma(n_vec[i] + 1.0);
81  logp += multiply_log(n_vec[i], value_of(lambda_vec[i]))
82  - value_of(lambda_vec[i]);
83  }
84 
85  // gradients
87  operands_and_partials.d_x1[i]
88  += n_vec[i] / value_of(lambda_vec[i]) - 1.0;
89  }
90 
91 
92  return operands_and_partials.to_var(logp, lambda);
93  }
94 
95  template <typename T_n,
96  typename T_rate>
97  inline
99  poisson_log(const T_n& n, const T_rate& lambda) {
100  return poisson_log<false>(n, lambda);
101  }
102  }
103 }
104 #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
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...
bool isinf(const stan::math::var &v)
Checks if the given number is infinite.
Definition: boost_isinf.hpp:22
A variable implementation that stores operands and derivatives with respect to the variable...
return_type< T_rate >::type poisson_log(const T_n &n, const T_rate &lambda)
Definition: poisson_log.hpp:27
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)
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
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 metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type

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