1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LOG_HPP
4 #include <boost/random/normal_distribution.hpp>
5 #include <boost/math/special_functions/fpclassify.hpp>
6 #include <boost/random/variate_generator.hpp>
21 template <
bool propto,
22 typename T_y,
typename T_loc,
typename T_scale,
24 typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
26 const T_inv_scale& lambda) {
27 static const char*
function(
"stan::math::exp_mod_normal_log");
49 T_partials_return logp(0.0);
58 "Location parameter", mu,
59 "Scale parameter", sigma,
60 "Inv_scale paramter", lambda);
73 operands_and_partials(y, mu, sigma, lambda);
79 size_t N =
max_size(y, mu, sigma, lambda);
81 for (
size_t n = 0; n < N; n++) {
83 const T_partials_return y_dbl =
value_of(y_vec[n]);
84 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
85 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
86 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
88 const T_partials_return pi_dbl = boost::math::constants::pi<double>();
94 logp +=
log(lambda_dbl);
97 * (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
98 +
log(
erfc((mu_dbl + lambda_dbl * sigma_dbl
100 / (
sqrt(2.0) * sigma_dbl)));
103 const T_partials_return deriv_logerfc
104 = -2.0 /
sqrt(pi_dbl)
105 *
exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
107 * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
109 /
erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl
110 - y_dbl) / (sigma_dbl *
std::sqrt(2.0)));
113 operands_and_partials.
d_x1[n]
115 + deriv_logerfc * -1.0 / (sigma_dbl *
std::sqrt(2.0));
117 operands_and_partials.
d_x2[n]
119 + deriv_logerfc / (sigma_dbl *
std::sqrt(2.0));
121 operands_and_partials.
d_x3[n]
122 += sigma_dbl * lambda_dbl * lambda_dbl
124 * (-mu_dbl / (sigma_dbl * sigma_dbl *
std::sqrt(2.0))
126 + y_dbl / (sigma_dbl * sigma_dbl *
std::sqrt(2.0)));
128 operands_and_partials.
d_x4[n]
129 += 1 / lambda_dbl + lambda_dbl * sigma_dbl * sigma_dbl
130 + mu_dbl - y_dbl + deriv_logerfc * sigma_dbl /
std::sqrt(2.0);
132 return operands_and_partials.
to_var(logp, y, mu, sigma, lambda);
135 template <
typename T_y,
typename T_loc,
typename T_scale,
136 typename T_inv_scale>
140 const T_inv_scale& lambda) {
141 return exp_mod_normal_log<false>(y, mu, sigma, lambda);
fvar< T > sqrt(const fvar< T > &x)
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > log(const fvar< T > &x)
size_t length(const std::vector< T > &x)
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)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
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)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > erfc(const fvar< T > &x)
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.