Stan Math Library  2.9.0
reverse mode automatic differentiation
poisson_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_POISSON_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_POISSON_CCDF_LOG_HPP
3 
13 #include <boost/math/special_functions/fpclassify.hpp>
14 #include <boost/random/poisson_distribution.hpp>
15 #include <boost/random/variate_generator.hpp>
16 #include <cmath>
17 #include <limits>
18 
19 namespace stan {
20 
21  namespace math {
22 
23  template <typename T_n, typename T_rate>
24  typename return_type<T_rate>::type
25  poisson_ccdf_log(const T_n& n, const T_rate& lambda) {
26  static const char* function("stan::math::poisson_ccdf_log");
28  T_partials_return;
29 
34 
35  // Ensure non-zero argument slengths
36  if (!(stan::length(n) && stan::length(lambda)))
37  return 0.0;
38 
39  T_partials_return P(0.0);
40 
41  // Validate arguments
42  check_not_nan(function, "Rate parameter", lambda);
43  check_nonnegative(function, "Rate parameter", lambda);
44  check_consistent_sizes(function,
45  "Random variable", n,
46  "Rate parameter", lambda);
47 
48  // Wrap arguments into vector views
49  VectorView<const T_n> n_vec(n);
50  VectorView<const T_rate> lambda_vec(lambda);
51  size_t size = max_size(n, lambda);
52 
53  // Compute vectorized cdf_log and gradient
55  using stan::math::gamma_q;
56  using boost::math::tgamma;
57  using std::exp;
58  using std::pow;
59  using std::log;
60  using std::exp;
61 
62  OperandsAndPartials<T_rate> operands_and_partials(lambda);
63 
64  // Explicit return for extreme values
65  // The gradients are technically ill-defined, but treated as neg infinity
66  for (size_t i = 0; i < stan::length(n); i++) {
67  if (value_of(n_vec[i]) < 0)
68  return operands_and_partials.to_var(0.0, lambda);
69  }
70 
71  for (size_t i = 0; i < size; i++) {
72  // Explicit results for extreme values
73  // The gradients are technically ill-defined, but treated as zero
74  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
75  return operands_and_partials.to_var(stan::math::negative_infinity(),
76  lambda);
77 
78  const T_partials_return n_dbl = value_of(n_vec[i]);
79  const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
80  const T_partials_return Pi = 1.0 - gamma_q(n_dbl+1, lambda_dbl);
81 
82  P += log(Pi);
83 
85  operands_and_partials.d_x1[i] += exp(-lambda_dbl)
86  * pow(lambda_dbl, n_dbl) / tgamma(n_dbl+1) / Pi;
87  }
88 
89  return operands_and_partials.to_var(P, lambda);
90  }
91  }
92 }
93 #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
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)
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...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:21
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
return_type< T_rate >::type poisson_ccdf_log(const T_n &n, const T_rate &lambda)
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:18
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:15
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
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:15
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132

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