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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 <stan/math/prim/scal/meta/is_constant_struct.hpp>
5 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
6 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
7 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
8 #include <stan/math/prim/scal/err/check_finite.hpp>
9 #include <stan/math/prim/scal/err/check_not_nan.hpp>
10 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
11 #include <stan/math/prim/scal/fun/constants.hpp>
12 #include <stan/math/prim/scal/meta/include_summand.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <boost/random/normal_distribution.hpp>
15 #include <boost/random/variate_generator.hpp>
16 #include <cmath>
17
18 namespace stan {
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("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 std::log;
34
35 if (!(stan::length(y)
36 && stan::length(mu)
37 && stan::length(sigma)
38 && stan::length(lambda)))
39 return 0.0;
40
41 T_partials_return logp(0.0);
42
43 check_not_nan(function, "Random variable", y);
44 check_finite(function, "Location parameter", mu);
45 check_positive_finite(function, "Inv_scale parameter", lambda);
46 check_positive_finite(function, "Scale parameter", sigma);
47 check_consistent_sizes(function,
48 "Random variable", y,
49 "Location parameter", mu,
50 "Scale parameter", sigma,
51 "Inv_scale paramter", lambda);
52
53 if (!include_summand<propto, T_y, T_loc, T_scale, T_inv_scale>::value)
54 return 0.0;
55
56 using boost::math::erfc;
57 using std::sqrt;
58 using std::log;
59 using std::exp;
60
61 OperandsAndPartials<T_y, T_loc, T_scale, T_inv_scale>
62 operands_and_partials(y, mu, sigma, lambda);
63
64 VectorView<const T_y> y_vec(y);
65 VectorView<const T_loc> mu_vec(mu);
66 VectorView<const T_scale> sigma_vec(sigma);
67 VectorView<const T_inv_scale> lambda_vec(lambda);
68 size_t N = max_size(y, mu, sigma, lambda);
69
70 for (size_t n = 0; n < N; n++) {
71 const T_partials_return y_dbl = value_of(y_vec[n]);
72 const T_partials_return mu_dbl = value_of(mu_vec[n]);
73 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
74 const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
75
76 const T_partials_return pi_dbl = boost::math::constants::pi<double>();
77
78 if (include_summand<propto>::value)
79 logp -= log(2.0);
80 if (include_summand<propto, T_inv_scale>::value)
81 logp += log(lambda_dbl);
82 if (include_summand<propto, T_y, T_loc, T_scale, T_inv_scale>::value)
83 logp += lambda_dbl
84 * (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
85 + log(erfc((mu_dbl + lambda_dbl * sigma_dbl
86 * sigma_dbl - y_dbl)
87 / (sqrt(2.0) * sigma_dbl)));
88
89 const T_partials_return deriv_logerfc
90 = -2.0 / sqrt(pi_dbl)
91 * exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
92 / (std::sqrt(2.0) * sigma_dbl)
93 * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
94 / (sigma_dbl * std::sqrt(2.0)))
95 / erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl
96 - y_dbl) / (sigma_dbl * std::sqrt(2.0)));
97
98 if (!is_constant_struct<T_y>::value)
99 operands_and_partials.d_x1[n]
100 += -lambda_dbl
101 + deriv_logerfc * -1.0 / (sigma_dbl * std::sqrt(2.0));
102 if (!is_constant_struct<T_loc>::value)
103 operands_and_partials.d_x2[n]
104 += lambda_dbl
105 + deriv_logerfc / (sigma_dbl * std::sqrt(2.0));
106 if (!is_constant_struct<T_scale>::value)
107 operands_and_partials.d_x3[n]
108 += sigma_dbl * lambda_dbl * lambda_dbl
109 + deriv_logerfc
110 * (-mu_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0))
111 + lambda_dbl / std::sqrt(2.0)
112 + y_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0)));
113 if (!is_constant_struct<T_inv_scale>::value)
114 operands_and_partials.d_x4[n]
115 += 1 / lambda_dbl + lambda_dbl * sigma_dbl * sigma_dbl
116 + mu_dbl - y_dbl + deriv_logerfc * sigma_dbl / std::sqrt(2.0);
117 }
118 return operands_and_partials.value(logp);
119 }
120
121 template <typename T_y, typename T_loc, typename T_scale,
122 typename T_inv_scale>
123 inline
124 typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
125 exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
126 const T_inv_scale& lambda) {
127 return exp_mod_normal_log<false>(y, mu, sigma, lambda);
128 }
129
130 }
131 }
132 #endif
133
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
stan::math::sqrt
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
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:60
check_positive_finite.hpp
stan
Definition: log_sum_exp.hpp:8
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:14
stan::math::OperandsAndPartials::value
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
Definition: OperandsAndPartials.hpp:67
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:35
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::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:13
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
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:40
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
partials_return_type.hpp
OperandsAndPartials.hpp
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:60
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::erfc
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
value_of.hpp
stan::VectorView
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
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::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
stan::math::OperandsAndPartials::d_x4
VectorView< T_return_type, false, true > d_x4
Definition: OperandsAndPartials.hpp:41

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