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exp_mod_normal_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LOG_HPP
#include <boost/random/normal_distribution.hpp>
#include <boost/math/special_functions/fpclassify.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/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <cmath>
namespace stan {
namespace math {
template <bool propto,
typename T_y, typename T_loc, typename T_scale,
typename T_inv_scale>
typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
const T_inv_scale& lambda) {
static const char* function("stan::math::exp_mod_normal_log");
typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
T_inv_scale>::type
T_partials_return;
using stan::is_constant_struct;
using stan::math::check_positive_finite;
using stan::math::check_finite;
using stan::math::check_not_nan;
using stan::math::check_consistent_sizes;
using stan::math::value_of;
using stan::math::include_summand;
using std::log;
// check if any vectors are zero length
if (!(stan::length(y)
&& stan::length(mu)
&& stan::length(sigma)
&& stan::length(lambda)))
return 0.0;
// set up return value accumulator
T_partials_return logp(0.0);
// validate args (here done over var, which should be OK)
check_not_nan(function, "Random variable", y);
check_finite(function, "Location parameter", mu);
check_positive_finite(function, "Inv_scale parameter", lambda);
check_positive_finite(function, "Scale parameter", sigma);
check_consistent_sizes(function,
"Random variable", y,
"Location parameter", mu,
"Scale parameter", sigma,
"Inv_scale paramter", lambda);
// check if no variables are involved and prop-to
if (!include_summand<propto, T_y, T_loc, T_scale, T_inv_scale>::value)
return 0.0;
using boost::math::erfc;
using std::sqrt;
using std::log;
using std::exp;
// set up template expressions wrapping scalars into vector views
OperandsAndPartials<T_y, T_loc, T_scale, T_inv_scale>
operands_and_partials(y, mu, sigma, lambda);
VectorView<const T_y> y_vec(y);
VectorView<const T_loc> mu_vec(mu);
VectorView<const T_scale> sigma_vec(sigma);
VectorView<const T_inv_scale> lambda_vec(lambda);
size_t N = max_size(y, mu, sigma, lambda);
for (size_t n = 0; n < N; n++) {
// pull out values of arguments
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_dbl = value_of(sigma_vec[n]);
const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
const T_partials_return pi_dbl = boost::math::constants::pi<double>();
// log probability
if (include_summand<propto>::value)
logp -= log(2.0);
if (include_summand<propto, T_inv_scale>::value)
logp += log(lambda_dbl);
if (include_summand<propto, T_y, T_loc, T_scale, T_inv_scale>::value)
logp += lambda_dbl
* (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
+ log(erfc((mu_dbl + lambda_dbl * sigma_dbl
* sigma_dbl - y_dbl)
/ (sqrt(2.0) * sigma_dbl)));
// gradients
const T_partials_return deriv_logerfc
= -2.0 / sqrt(pi_dbl)
* exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
/ (std::sqrt(2.0) * sigma_dbl)
* (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
/ (sigma_dbl * std::sqrt(2.0)))
/ erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl
- y_dbl) / (sigma_dbl * std::sqrt(2.0)));
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n]
+= -lambda_dbl
+ deriv_logerfc * -1.0 / (sigma_dbl * std::sqrt(2.0));
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x2[n]
+= lambda_dbl
+ deriv_logerfc / (sigma_dbl * std::sqrt(2.0));
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n]
+= sigma_dbl * lambda_dbl * lambda_dbl
+ deriv_logerfc
* (-mu_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0))
+ lambda_dbl / std::sqrt(2.0)
+ y_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0)));
if (!is_constant_struct<T_inv_scale>::value)
operands_and_partials.d_x4[n]
+= 1 / lambda_dbl + lambda_dbl * sigma_dbl * sigma_dbl
+ mu_dbl - y_dbl + deriv_logerfc * sigma_dbl / std::sqrt(2.0);
}
return operands_and_partials.to_var(logp, y, mu, sigma, lambda);
}
template <typename T_y, typename T_loc, typename T_scale,
typename T_inv_scale>
inline
typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
const T_inv_scale& lambda) {
return exp_mod_normal_log<false>(y, mu, sigma, lambda);
}
}
}
#endif
check_not_nan.hpp
stan::math::sqrt
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:15
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
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::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:36
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
stan::math::exp_mod_normal_log
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_log(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
Definition: exp_mod_normal_log.hpp:25
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::partials_return_type
Definition: partials_return_type.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::d_x4
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
Definition: OperandsAndPartials.hpp:262
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
stan::math::erfc
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
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
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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