| Stan Math Library 2.6.3 probability, sampling & optimization

- Main Page
- Namespaces
- Classes
- Files

- File List
- File Members

All Classes Namespaces Files Functions Variables Typedefs Enumerator Friends Macros
poisson_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_POISSON_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_POISSON_CDF_HPP
3
4 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
5 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
6 #include <stan/math/prim/scal/err/check_less.hpp>
7 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
8 #include <stan/math/prim/scal/err/check_not_nan.hpp>
9 #include <stan/math/prim/scal/fun/constants.hpp>
10 #include <stan/math/prim/scal/fun/multiply_log.hpp>
11 #include <stan/math/prim/scal/fun/gamma_q.hpp>
12 #include <stan/math/prim/scal/fun/value_of.hpp>
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 // 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("stan::math::poisson_cdf");
28 typedef typename stan::partials_return_type<T_n, T_rate>::type
29 T_partials_return;
30
31 using stan::math::check_not_nan;
32 using stan::math::check_nonnegative;
33 using stan::math::value_of;
34 using stan::math::check_consistent_sizes;
35
36 // Ensure non-zero argument slengths
37 if (!(stan::length(n) && stan::length(lambda)))
38 return 1.0;
39
40 T_partials_return P(1.0);
41
42 // Validate arguments
43 check_not_nan(function, "Rate parameter", lambda);
44 check_nonnegative(function, "Rate parameter", lambda);
45 check_consistent_sizes(function,
46 "Random variable", n,
47 "Rate parameter", lambda);
48
49 // Wrap arguments into vector views
50 VectorView<const T_n> n_vec(n);
51 VectorView<const T_rate> lambda_vec(lambda);
52 size_t size = max_size(n, lambda);
53
54 // Compute vectorized CDF and gradient
55 using stan::math::value_of;
56 using stan::math::gamma_q;
57 using boost::math::tgamma;
58 using std::exp;
59 using std::pow;
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 zero
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 continue;
76
77 const T_partials_return n_dbl = value_of(n_vec[i]);
78 const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
79 const T_partials_return Pi = gamma_q(n_dbl+1, lambda_dbl);
80
81 P *= Pi;
82
83 if (!is_constant_struct<T_rate>::value)
84 operands_and_partials.d_x1[i] -= exp(-lambda_dbl)
85 * pow(lambda_dbl, n_dbl) / tgamma(n_dbl+1) / Pi;
86 }
87
88 if (!is_constant_struct<T_rate>::value) {
89 for (size_t i = 0; i < stan::length(lambda); ++i)
90 operands_and_partials.d_x1[i] *= P;
91 }
92
93 return operands_and_partials.to_var(P, lambda);
94 }
95 }
96 }
97 #endif
check_not_nan.hpp
stan::math::check_not_nan
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
Definition: check_not_nan.hpp:63
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::OperandsAndPartials::to_var
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)
Definition: OperandsAndPartials.hpp:322
gamma_q.hpp
multiply_log.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
check_nonnegative.hpp
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:16
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
stan::math::poisson_cdf
return_type< T_rate >::type poisson_cdf(const T_n &n, const T_rate &lambda)
Definition: poisson_cdf.hpp:26
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
stan::math::max
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:21
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Definition: size.hpp:11
stan::math::check_consistent_sizes
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.
Definition: check_consistent_sizes.hpp:31
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
value_of.hpp
stan::math::tgamma
fvar< T > tgamma(const fvar< T > &x)
Definition: tgamma.hpp:15
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
stan::partials_return_type::type
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
Definition: partials_return_type.hpp:26
check_less.hpp
stan::math::gamma_q
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:15
check_consistent_sizes.hpp

[ Stan Home Page ] © 2011–2015, Stan Development Team.