chi_square_lpdf.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LPDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LPDF_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_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/VectorBuilder.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <boost/random/chi_squared_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
namespace stan {
namespace math {
template <bool propto,
typename T_y, typename T_dof>
typename return_type<T_y, T_dof>::type
chi_square_lpdf(const T_y& y, const T_dof& nu) {
static const char* function("chi_square_lpdf");
typedef typename stan::partials_return_type<T_y, T_dof>::type
T_partials_return;
if (!(stan::length(y)
&& stan::length(nu)))
return 0.0;
T_partials_return logp(0.0);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_positive_finite(function, "Degrees of freedom parameter", nu);
check_consistent_sizes(function,
"Random variable", y,
"Degrees of freedom parameter", nu);
VectorView<const T_y> y_vec(y);
VectorView<const T_dof> nu_vec(nu);
size_t N = max_size(y, nu);
for (size_t n = 0; n < length(y); n++)
if (value_of(y_vec[n]) < 0)
return LOG_ZERO;
if (!include_summand<propto, T_y, T_dof>::value)
return 0.0;
using boost::math::digamma;
using boost::math::lgamma;
using std::log;
VectorBuilder<include_summand<propto, T_y, T_dof>::value,
T_partials_return, T_y> log_y(length(y));
for (size_t i = 0; i < length(y); i++)
if (include_summand<propto, T_y, T_dof>::value)
log_y[i] = log(value_of(y_vec[i]));
VectorBuilder<include_summand<propto, T_y>::value,
T_partials_return, T_y> inv_y(length(y));
for (size_t i = 0; i < length(y); i++)
if (include_summand<propto, T_y>::value)
inv_y[i] = 1.0 / value_of(y_vec[i]);
VectorBuilder<include_summand<propto, T_dof>::value,
T_partials_return, T_dof> lgamma_half_nu(length(nu));
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof>
digamma_half_nu_over_two(length(nu));
for (size_t i = 0; i < length(nu); i++) {
T_partials_return half_nu = 0.5 * value_of(nu_vec[i]);
if (include_summand<propto, T_dof>::value)
lgamma_half_nu[i] = lgamma(half_nu);
if (!is_constant_struct<T_dof>::value)
digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
}
OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return half_y = 0.5 * y_dbl;
const T_partials_return nu_dbl = value_of(nu_vec[n]);
const T_partials_return half_nu = 0.5 * nu_dbl;
if (include_summand<propto, T_dof>::value)
logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
if (include_summand<propto, T_y, T_dof>::value)
logp += (half_nu-1.0) * log_y[n];
if (include_summand<propto, T_y>::value)
logp -= half_y;
if (!is_constant_struct<T_y>::value) {
operands_and_partials.d_x1[n] += (half_nu-1.0)*inv_y[n] - 0.5;
}
if (!is_constant_struct<T_dof>::value) {
operands_and_partials.d_x2[n] += NEG_LOG_TWO_OVER_TWO
- digamma_half_nu_over_two[n] + log_y[n]*0.5;
}
}
return operands_and_partials.value(logp);
}
template <typename T_y, typename T_dof>
inline
typename return_type<T_y, T_dof>::type
chi_square_lpdf(const T_y& y, const T_dof& nu) {
return chi_square_lpdf<false>(y, nu);
}
}
}
#endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
stan::math::chi_square_lpdf
return_type< T_y, T_dof >::type chi_square_lpdf(const T_y &y, const T_dof &nu)
The log of a chi-squared density for y with the specified degrees of freedom parameter.
Definition: chi_square_lpdf.hpp:48
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
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
stan::math::LOG_ZERO
const double LOG_ZERO
Definition: constants.hpp:172
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:35
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::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
VectorBuilder.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
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::NEG_LOG_TWO_OVER_TWO
const double NEG_LOG_TWO_OVER_TWO
Definition: constants.hpp:188
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_consistent_sizes.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
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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