gamma_lcdf.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LCDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LCDF_HPP
#include <boost/random/gamma_distribution.hpp>
#include <boost/random/variate_generator.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_greater_or_equal.hpp>
#include <stan/math/prim/scal/err/check_less_or_equal.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/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/gamma_p.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/meta/length.hpp>
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/VectorView.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/return_type.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
#include <cmath>
#include <limits>
namespace stan {
namespace math {
template <typename T_y, typename T_shape, typename T_inv_scale>
typename return_type<T_y, T_shape, T_inv_scale>::type
gamma_lcdf(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
return 0.0;
typedef typename stan::partials_return_type<T_y, T_shape,
T_inv_scale>::type
T_partials_return;
static const char* function("gamma_lcdf");
using boost::math::tools::promote_args;
using std::exp;
T_partials_return P(0.0);
check_positive_finite(function, "Shape parameter", alpha);
check_positive_finite(function, "Scale parameter", beta);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_consistent_sizes(function,
"Random variable", y,
"Shape parameter", alpha,
"Scale Parameter", beta);
VectorView<const T_y> y_vec(y);
VectorView<const T_shape> alpha_vec(alpha);
VectorView<const T_inv_scale> beta_vec(beta);
size_t N = max_size(y, alpha, beta);
OperandsAndPartials<T_y, T_shape, T_inv_scale>
operands_and_partials(y, alpha, beta);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++) {
if (value_of(y_vec[i]) == 0)
return operands_and_partials.value(negative_infinity());
}
using boost::math::tgamma;
using std::exp;
using std::pow;
using std::log;
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape> gamma_vec(stan::length(alpha));
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape>
digamma_vec(stan::length(alpha));
if (!is_constant_struct<T_shape>::value) {
for (size_t i = 0; i < stan::length(alpha); i++) {
const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
gamma_vec[i] = tgamma(alpha_dbl);
digamma_vec[i] = digamma(alpha_dbl);
}
}
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
return operands_and_partials.value(0.0);
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return beta_dbl = value_of(beta_vec[n]);
const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
P += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
* pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x2[n]
-= grad_reg_inc_gamma(alpha_dbl, beta_dbl
* y_dbl, gamma_vec[n],
digamma_vec[n]) / Pn;
if (!is_constant_struct<T_inv_scale>::value)
operands_and_partials.d_x3[n] += y_dbl * exp(-beta_dbl * y_dbl)
* pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
}
return operands_and_partials.value(P);
}
}
}
#endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
check_positive_finite.hpp
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
digamma.hpp
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
return_type.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
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
include_summand.hpp
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::check_positive_finite
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
Definition: check_positive_finite.hpp:26
stan::partials_return_type
Definition: partials_return_type.hpp:16
check_less_or_equal.hpp
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
VectorView.hpp
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:40
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
length.hpp
stan::math::gamma_p
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:14
gamma_p.hpp
grad_reg_inc_gamma.hpp
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
constants.hpp
stan::math::grad_reg_inc_gamma
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6)
Gradient of the regularized incomplete gamma functions igamma(a, z)
Definition: grad_reg_inc_gamma.hpp:40
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
check_greater_or_equal.hpp
value_of.hpp
stan::math::gamma_lcdf
return_type< T_y, T_shape, T_inv_scale >::type gamma_lcdf(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
Definition: gamma_lcdf.hpp:34
stan::math::tgamma
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
Definition: tgamma.hpp:20
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
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
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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