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cauchy_cdf_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_LOG_HPP
#include <boost/random/cauchy_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_finite.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/square.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/log1p.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <cmath>
namespace stan {
namespace math {
template <typename T_y, typename T_loc, typename T_scale>
typename return_type<T_y, T_loc, T_scale>::type
cauchy_cdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
T_partials_return;
// Size checks
if ( !( stan::length(y) && stan::length(mu)
&& stan::length(sigma) ) )
return 0.0;
static const char* function("stan::math::cauchy_cdf");
using stan::math::check_positive_finite;
using stan::math::check_finite;
using stan::math::check_not_nan;
using stan::math::check_consistent_sizes;
using boost::math::tools::promote_args;
using stan::math::value_of;
T_partials_return cdf_log(0.0);
check_not_nan(function, "Random variable", y);
check_finite(function, "Location parameter", mu);
check_positive_finite(function, "Scale parameter", sigma);
check_consistent_sizes(function,
"Random variable", y,
"Location parameter", mu,
"Scale Parameter", sigma);
// Wrap arguments in vectors
VectorView<const T_y> y_vec(y);
VectorView<const T_loc> mu_vec(mu);
VectorView<const T_scale> sigma_vec(sigma);
size_t N = max_size(y, mu, sigma);
OperandsAndPartials<T_y, T_loc, T_scale>
operands_and_partials(y, mu, sigma);
// Compute CDFLog and its gradients
using std::atan;
using stan::math::pi;
using std::log;
// Compute vectorized CDF and gradient
for (size_t n = 0; n < N; n++) {
// Pull out values
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return mu_dbl = value_of(mu_vec[n]);
const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
// Compute
const T_partials_return Pn = atan(z) / pi() + 0.5;
cdf_log += log(Pn);
const T_partials_return rep_deriv
= 1.0 / (pi() * Pn * (z * z * sigma_dbl + sigma_dbl));
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += rep_deriv;
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x2[n] -= rep_deriv;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] -= rep_deriv * z;
}
return operands_and_partials.to_var(cdf_log, y, mu, sigma);
}
}
}
#endif
check_not_nan.hpp
stan::math::cauchy_cdf_log
return_type< T_y, T_loc, T_scale >::type cauchy_cdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
Definition: cauchy_cdf_log.hpp:24
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
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::atan
fvar< T > atan(const fvar< T > &x)
Definition: atan.hpp:12
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
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::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
stan::math::check_finite
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
Definition: check_finite.hpp:62
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
check_finite.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
log1p.hpp
stan::math::pi
double pi()
Return the value of pi.
Definition: constants.hpp:86
value_of.hpp
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_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

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