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exp_mod_normal_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LOG_HPP
3
4 #include <boost/random/normal_distribution.hpp>
5 #include <boost/math/special_functions/fpclassify.hpp>
6 #include <boost/random/variate_generator.hpp>
7 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
8 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
9 #include <stan/math/prim/scal/err/check_finite.hpp>
10 #include <stan/math/prim/scal/err/check_not_nan.hpp>
11 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
12 #include <stan/math/prim/scal/fun/constants.hpp>
13 #include <stan/math/prim/scal/meta/include_summand.hpp>
14 #include <stan/math/prim/scal/fun/value_of.hpp>
15 #include <cmath>
16
17 namespace stan {
18
19 namespace math {
20
21 template <bool propto,
22 typename T_y, typename T_loc, typename T_scale,
23 typename T_inv_scale>
24 typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
25 exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
26 const T_inv_scale& lambda) {
27 static const char* function("stan::math::exp_mod_normal_log");
28 typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
29 T_inv_scale>::type
30 T_partials_return;
31
32 using stan::is_constant_struct;
33 using stan::math::check_positive_finite;
34 using stan::math::check_finite;
35 using stan::math::check_not_nan;
36 using stan::math::check_consistent_sizes;
37 using stan::math::value_of;
38 using stan::math::include_summand;
39 using std::log;
40
41 // check if any vectors are zero length
42 if (!(stan::length(y)
43 && stan::length(mu)
44 && stan::length(sigma)
45 && stan::length(lambda)))
46 return 0.0;
47
48 // set up return value accumulator
49 T_partials_return logp(0.0);
50
51 // validate args (here done over var, which should be OK)
52 check_not_nan(function, "Random variable", y);
53 check_finite(function, "Location parameter", mu);
54 check_positive_finite(function, "Inv_scale parameter", lambda);
55 check_positive_finite(function, "Scale parameter", sigma);
56 check_consistent_sizes(function,
57 "Random variable", y,
58 "Location parameter", mu,
59 "Scale parameter", sigma,
60 "Inv_scale paramter", lambda);
61
62 // check if no variables are involved and prop-to
63 if (!include_summand<propto, T_y, T_loc, T_scale, T_inv_scale>::value)
64 return 0.0;
65
66 using boost::math::erfc;
67 using std::sqrt;
68 using std::log;
69 using std::exp;
70
71 // set up template expressions wrapping scalars into vector views
72 OperandsAndPartials<T_y, T_loc, T_scale, T_inv_scale>
73 operands_and_partials(y, mu, sigma, lambda);
74
75 VectorView<const T_y> y_vec(y);
76 VectorView<const T_loc> mu_vec(mu);
77 VectorView<const T_scale> sigma_vec(sigma);
78 VectorView<const T_inv_scale> lambda_vec(lambda);
79 size_t N = max_size(y, mu, sigma, lambda);
80
81 for (size_t n = 0; n < N; n++) {
82 // pull out values of arguments
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]);
87
88 const T_partials_return pi_dbl = boost::math::constants::pi<double>();
89
90 // log probability
91 if (include_summand<propto>::value)
92 logp -= log(2.0);
93 if (include_summand<propto, T_inv_scale>::value)
94 logp += log(lambda_dbl);
95 if (include_summand<propto, T_y, T_loc, T_scale, T_inv_scale>::value)
96 logp += lambda_dbl
97 * (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
98 + log(erfc((mu_dbl + lambda_dbl * sigma_dbl
99 * sigma_dbl - y_dbl)
100 / (sqrt(2.0) * sigma_dbl)));
101
102 // gradients
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)
106 / (std::sqrt(2.0) * sigma_dbl)
107 * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
108 / (sigma_dbl * std::sqrt(2.0)))
109 / erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl
110 - y_dbl) / (sigma_dbl * std::sqrt(2.0)));
111
112 if (!is_constant_struct<T_y>::value)
113 operands_and_partials.d_x1[n]
114 += -lambda_dbl
115 + deriv_logerfc * -1.0 / (sigma_dbl * std::sqrt(2.0));
116 if (!is_constant_struct<T_loc>::value)
117 operands_and_partials.d_x2[n]
118 += lambda_dbl
119 + deriv_logerfc / (sigma_dbl * std::sqrt(2.0));
120 if (!is_constant_struct<T_scale>::value)
121 operands_and_partials.d_x3[n]
122 += sigma_dbl * lambda_dbl * lambda_dbl
123 + deriv_logerfc
124 * (-mu_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0))
125 + lambda_dbl / std::sqrt(2.0)
126 + y_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0)));
127 if (!is_constant_struct<T_inv_scale>::value)
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);
131 }
132 return operands_and_partials.to_var(logp, y, mu, sigma, lambda);
133 }
134
135 template <typename T_y, typename T_loc, typename T_scale,
136 typename T_inv_scale>
137 inline
138 typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
139 exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
140 const T_inv_scale& lambda) {
141 return exp_mod_normal_log<false>(y, mu, sigma, lambda);
142 }
143 }
144 }
145 #endif
146
147
148
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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