Stan Math Library  2.12.0
reverse mode automatic differentiation
poisson_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_POISSON_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_POISSON_CDF_HPP
3 
15 #include <boost/random/poisson_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 #include <limits>
19 
20 namespace stan {
21  namespace math {
22 
23  // Poisson CDF
24  template <typename T_n, typename T_rate>
25  typename return_type<T_rate>::type
26  poisson_cdf(const T_n& n, const T_rate& lambda) {
27  static const char* function("poisson_cdf");
29  T_partials_return;
30 
31  if (!(stan::length(n) && stan::length(lambda)))
32  return 1.0;
33 
34  T_partials_return P(1.0);
35 
36  check_not_nan(function, "Rate parameter", lambda);
37  check_nonnegative(function, "Rate parameter", lambda);
38  check_consistent_sizes(function,
39  "Random variable", n,
40  "Rate parameter", lambda);
41 
42  VectorView<const T_n> n_vec(n);
43  VectorView<const T_rate> lambda_vec(lambda);
44  size_t size = max_size(n, lambda);
45 
46  using boost::math::tgamma;
47  using std::exp;
48  using std::pow;
49  using std::exp;
50 
51  OperandsAndPartials<T_rate> operands_and_partials(lambda);
52 
53  // Explicit return for extreme values
54  // The gradients are technically ill-defined, but treated as zero
55  for (size_t i = 0; i < stan::length(n); i++) {
56  if (value_of(n_vec[i]) < 0)
57  return operands_and_partials.value(0.0);
58  }
59 
60  for (size_t i = 0; i < size; i++) {
61  // Explicit results for extreme values
62  // The gradients are technically ill-defined, but treated as zero
63  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
64  continue;
65 
66  const T_partials_return n_dbl = value_of(n_vec[i]);
67  const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
68  const T_partials_return Pi = gamma_q(n_dbl+1, lambda_dbl);
69 
70  P *= Pi;
71 
73  operands_and_partials.d_x1[i] -= exp(-lambda_dbl)
74  * pow(lambda_dbl, n_dbl) / tgamma(n_dbl+1) / Pi;
75  }
76 
78  for (size_t i = 0; i < stan::length(lambda); ++i)
79  operands_and_partials.d_x1[i] *= P;
80  }
81  return operands_and_partials.value(P);
82  }
83 
84  }
85 }
86 #endif
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
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
This class builds partial derivatives with respect to a set of operands.
return_type< T_rate >::type poisson_cdf(const T_n &n, const T_rate &lambda)
Definition: poisson_cdf.hpp:26
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:22
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.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
fvar< T > tgamma(const fvar< T > &x)
Definition: tgamma.hpp:14
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
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
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:14
VectorView< T_return_type, false, true > d_x1

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