poisson_cdf_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_POISSON_CDF_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_POISSON_CDF_LOG_HPP
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_less.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_not_nan.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/gamma_q.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <boost/random/poisson_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
#include <limits>
namespace stan {
namespace math {
template <typename T_n, typename T_rate>
typename return_type<T_rate>::type
poisson_cdf_log(const T_n& n, const T_rate& lambda) {
static const char* function("poisson_cdf_log");
typedef typename stan::partials_return_type<T_n, T_rate>::type
T_partials_return;
if (!(stan::length(n) && stan::length(lambda)))
return 0.0;
T_partials_return P(0.0);
check_not_nan(function, "Rate parameter", lambda);
check_nonnegative(function, "Rate parameter", lambda);
check_consistent_sizes(function,
"Random variable", n,
"Rate parameter", lambda);
VectorView<const T_n> n_vec(n);
VectorView<const T_rate> lambda_vec(lambda);
size_t size = max_size(n, lambda);
using std::log;
using std::exp;
OperandsAndPartials<T_rate> operands_and_partials(lambda);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as neg infinity
for (size_t i = 0; i < stan::length(n); i++) {
if (value_of(n_vec[i]) < 0)
return operands_and_partials.value(negative_infinity());
}
for (size_t i = 0; i < size; i++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
continue;
const T_partials_return n_dbl = value_of(n_vec[i]);
const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
const T_partials_return log_Pi = log(gamma_q(n_dbl+1, lambda_dbl));
P += log_Pi;
if (!is_constant_struct<T_rate>::value)
operands_and_partials.d_x1[i] += - exp(n_dbl * log(lambda_dbl)
- lambda_dbl - lgamma(n_dbl+1)
- log_Pi);
}
return operands_and_partials.value(P);
}
}
}
#endif
check_not_nan.hpp
lgamma.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:20
stan
Definition: log_sum_exp.hpp:8
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
stan::math::OperandsAndPartials::value
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
Definition: OperandsAndPartials.hpp:67
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
stan::math::check_nonnegative
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
Definition: check_nonnegative.hpp:61
gamma_q.hpp
stan::return_type::type
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
multiply_log.hpp
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:13
stan::math::poisson_cdf_log
return_type< T_rate >::type poisson_cdf_log(const T_n &n, const T_rate &lambda)
Definition: poisson_cdf_log.hpp:26
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::check_not_nan
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
Definition: check_not_nan.hpp:57
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
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:22
partials_return_type.hpp
OperandsAndPartials.hpp
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
value_of.hpp
stan::VectorView
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
stan::math::check_consistent_sizes
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.
Definition: check_consistent_sizes.hpp:30
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:14
check_consistent_sizes.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130

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