Stan Math Library  2.20.0
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 
12 #include <cmath>
13 #include <limits>
14 
15 namespace stan {
16 namespace math {
17 
18 // Poisson CDF
19 template <typename T_n, typename T_rate>
20 typename return_type<T_rate>::type poisson_cdf(const T_n& n,
21  const T_rate& lambda) {
22  static const char* function = "poisson_cdf";
23  typedef
24  typename stan::partials_return_type<T_n, T_rate>::type T_partials_return;
25 
26  if (size_zero(n, lambda))
27  return 1.0;
28 
29  T_partials_return P(1.0);
30 
31  check_not_nan(function, "Rate parameter", lambda);
32  check_nonnegative(function, "Rate parameter", lambda);
33  check_consistent_sizes(function, "Random variable", n, "Rate parameter",
34  lambda);
35 
36  scalar_seq_view<T_n> n_vec(n);
37  scalar_seq_view<T_rate> lambda_vec(lambda);
38  size_t size = max_size(n, lambda);
39 
40  using std::exp;
41  using std::pow;
42 
43  operands_and_partials<T_rate> ops_partials(lambda);
44 
45  // Explicit return for extreme values
46  // The gradients are technically ill-defined, but treated as zero
47  for (size_t i = 0; i < stan::length(n); i++) {
48  if (value_of(n_vec[i]) < 0)
49  return ops_partials.build(0.0);
50  }
51 
52  for (size_t i = 0; i < size; i++) {
53  // Explicit results for extreme values
54  // The gradients are technically ill-defined, but treated as zero
55  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
56  continue;
57 
58  const T_partials_return n_dbl = value_of(n_vec[i]);
59  const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
60  const T_partials_return Pi = gamma_q(n_dbl + 1, lambda_dbl);
61 
62  P *= Pi;
63 
65  ops_partials.edge1_.partials_[i]
66  -= exp(-lambda_dbl) * pow(lambda_dbl, n_dbl) / tgamma(n_dbl + 1) / Pi;
67  }
68 
70  for (size_t i = 0; i < stan::length(lambda); ++i)
71  ops_partials.edge1_.partials_[i] *= P;
72  }
73  return ops_partials.build(P);
74 }
75 
76 } // namespace math
77 } // namespace stan
78 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
return_type< T_rate >::type poisson_cdf(const T_n &n, const T_rate &lambda)
Definition: poisson_cdf.hpp:20
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
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
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:16
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
Definition: tgamma.hpp:21
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:13
internal::ops_partials_edge< double, Op1 > edge1_

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