All Classes Namespaces Files Functions Variables Typedefs Enumerator Friends Macros Groups
scaled_inv_chi_square_ccdf_log.hpp
Go to the documentation of this file.
#ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CCDF_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CCDF_LOG_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/value_of.hpp>
#include <stan/math/prim/scal/fun/gamma_q.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/square.hpp>
#include <stan/math/prim/scal/meta/VectorView.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/length.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
#include <boost/random/chi_squared_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <limits>
#include <cmath>
namespace stan {
namespace math {
template <typename T_y, typename T_dof, typename T_scale>
typename return_type<T_y, T_dof, T_scale>::type
scaled_inv_chi_square_ccdf_log(const T_y& y, const T_dof& nu,
const T_scale& s) {
typedef typename stan::partials_return_type<T_y, T_dof, T_scale>::type
T_partials_return;
// Size checks
if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
return 0.0;
static const char* function("stan::math::scaled_inv_chi_square_ccdf_log");
using stan::math::check_positive_finite;
using stan::math::check_not_nan;
using stan::math::check_consistent_sizes;
using stan::math::check_nonnegative;
using stan::math::value_of;
using std::exp;
T_partials_return P(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_positive_finite(function, "Scale parameter", s);
check_consistent_sizes(function,
"Random variable", y,
"Degrees of freedom parameter", nu,
"Scale parameter", s);
// Wrap arguments in vectors
VectorView<const T_y> y_vec(y);
VectorView<const T_dof> nu_vec(nu);
VectorView<const T_scale> s_vec(s);
size_t N = max_size(y, nu, s);
OperandsAndPartials<T_y, T_dof, T_scale>
operands_and_partials(y, nu, s);
// 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.to_var(0.0, y, nu, s);
}
// Compute cdf_log and its gradients
using stan::math::gamma_q;
using stan::math::digamma;
using boost::math::tgamma;
using std::exp;
using std::pow;
using std::log;
// Cache a few expensive function calls if nu is a parameter
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof> gamma_vec(stan::length(nu));
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof> digamma_vec(stan::length(nu));
if (!is_constant_struct<T_dof>::value) {
for (size_t i = 0; i < stan::length(nu); i++) {
const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
gamma_vec[i] = tgamma(half_nu_dbl);
digamma_vec[i] = digamma(half_nu_dbl);
}
}
// Compute vectorized cdf_log and gradient
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.to_var(stan::math::negative_infinity(),
y, nu, s);
}
// Pull out values
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return y_inv_dbl = 1.0 / y_dbl;
const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
const T_partials_return s_dbl = value_of(s_vec[n]);
const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
* y_inv_dbl;
const T_partials_return half_nu_s2_overx_dbl
= 2.0 * half_nu_dbl * half_s2_overx_dbl;
// Compute
const T_partials_return Pn = 1.0 - gamma_q(half_nu_dbl,
half_nu_s2_overx_dbl);
const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
* pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
P += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] -= half_nu_s2_overx_dbl * y_inv_dbl
* gamma_p_deriv / Pn;
if (!is_constant_struct<T_dof>::value)
operands_and_partials.d_x2[n]
-= (0.5 * stan::math::grad_reg_inc_gamma(half_nu_dbl,
half_nu_s2_overx_dbl,
gamma_vec[n],
digamma_vec[n])
- half_s2_overx_dbl * gamma_p_deriv)
/ Pn;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] += 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
* gamma_p_deriv / Pn;
}
return operands_and_partials.to_var(P, y, nu, s);
}
}
}
#endif
check_not_nan.hpp
lgamma.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
check_positive_finite.hpp
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:15
square.hpp
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
stan::math::grad_reg_inc_gamma
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
Definition: grad_reg_inc_gamma.hpp:15
gamma_q.hpp
VectorView.hpp
stan::math::scaled_inv_chi_square_ccdf_log
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_ccdf_log(const T_y &y, const T_dof &nu, const T_scale &s)
Definition: scaled_inv_chi_square_ccdf_log.hpp:31
include_summand.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::d_x3
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
Definition: OperandsAndPartials.hpp:259
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
length.hpp
grad_reg_inc_gamma.hpp
stan::VectorBuilder
Definition: VectorBuilder.hpp:61
constants.hpp
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::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
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
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::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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