| Stan Math Library 2.6.3 probability, sampling & optimization

- Main Page
- Namespaces
- Classes
- Files

- File List
- File Members

All Classes Namespaces Files Functions Variables Typedefs Enumerator Friends Macros
exp_mod_normal_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_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 <typename T_y, typename T_loc, typename T_scale,
22 typename T_inv_scale>
23 typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
24 exp_mod_normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
25 const T_inv_scale& lambda) {
26 static const char* function("stan::math::exp_mod_normal_cdf");
27 typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
28 T_inv_scale>::type
29 T_partials_return;
30
31 using stan::math::check_positive_finite;
32 using stan::math::check_finite;
33 using stan::math::check_not_nan;
34 using stan::math::check_consistent_sizes;
35 using stan::math::value_of;
36
37 T_partials_return cdf(1.0);
38 // check if any vectors are zero length
39 if (!(stan::length(y)
40 && stan::length(mu)
41 && stan::length(sigma)
42 && stan::length(lambda)))
43 return cdf;
44
45 check_not_nan(function, "Random variable", y);
46 check_finite(function, "Location parameter", mu);
47 check_not_nan(function, "Scale parameter", sigma);
48 check_positive_finite(function, "Scale parameter", sigma);
49 check_positive_finite(function, "Inv_scale parameter", lambda);
50 check_not_nan(function, "Inv_scale parameter", lambda);
51 check_consistent_sizes(function,
52 "Random variable", y,
53 "Location parameter", mu,
54 "Scale parameter", sigma,
55 "Inv_scale paramter", lambda);
56
57 OperandsAndPartials<T_y, T_loc, T_scale, T_inv_scale>
58 operands_and_partials(y, mu, sigma, lambda);
59
60 using stan::math::SQRT_2;
61 using std::exp;
62
63 VectorView<const T_y> y_vec(y);
64 VectorView<const T_loc> mu_vec(mu);
65 VectorView<const T_scale> sigma_vec(sigma);
66 VectorView<const T_inv_scale> lambda_vec(lambda);
67 size_t N = max_size(y, mu, sigma, lambda);
68 const double sqrt_pi = std::sqrt(stan::math::pi());
69 for (size_t n = 0; n < N; n++) {
70 if (boost::math::isinf(y_vec[n])) {
71 if (y_vec[n] < 0.0)
72 return operands_and_partials.to_var(0.0, y, mu, sigma, lambda);
73 }
74
75 const T_partials_return y_dbl = value_of(y_vec[n]);
76 const T_partials_return mu_dbl = value_of(mu_vec[n]);
77 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
78 const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
79 const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
80 const T_partials_return v = lambda_dbl * sigma_dbl;
81 const T_partials_return v_sq = v * v;
82 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (SQRT_2
83 * sigma_dbl);
84 const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
85 const T_partials_return erf_calc = 0.5 * (1 + erf(-v / SQRT_2
86 + scaled_diff));
87 const T_partials_return deriv_1 = lambda_dbl * exp(0.5 * v_sq - u)
88 * erf_calc;
89 const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
90 * exp(0.5 * v_sq - (scaled_diff - (v / SQRT_2))
91 * (scaled_diff - (v / SQRT_2)) - u) / sigma_dbl;
92 const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
93 * exp(-scaled_diff_sq) / sigma_dbl;
94
95 const T_partials_return cdf_ = 0.5 * (1 + erf(u / (v * SQRT_2)))
96 - exp(-u + v_sq * 0.5) * (erf_calc);
97
98 cdf *= cdf_;
99
100 if (!is_constant_struct<T_y>::value)
101 operands_and_partials.d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
102 / cdf_;
103 if (!is_constant_struct<T_loc>::value)
104 operands_and_partials.d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
105 / cdf_;
106 if (!is_constant_struct<T_scale>::value)
107 operands_and_partials.d_x3[n] += (-deriv_1 * v - deriv_3
108 * scaled_diff * SQRT_2 - deriv_2
109 * sigma_dbl * SQRT_2
110 * (-SQRT_2 * 0.5
111 * (-lambda_dbl + scaled_diff
112 * SQRT_2 / sigma_dbl) - SQRT_2
113 * lambda_dbl)) / cdf_;
114 if (!is_constant_struct<T_inv_scale>::value)
115 operands_and_partials.d_x4[n] += exp(0.5 * v_sq - u)
116 * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
117 * exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
118 - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc) / cdf_;
119 }
120
121 if (!is_constant_struct<T_y>::value) {
122 for (size_t n = 0; n < stan::length(y); ++n)
123 operands_and_partials.d_x1[n] *= cdf;
124 }
125 if (!is_constant_struct<T_loc>::value) {
126 for (size_t n = 0; n < stan::length(mu); ++n)
127 operands_and_partials.d_x2[n] *= cdf;
128 }
129 if (!is_constant_struct<T_scale>::value) {
130 for (size_t n = 0; n < stan::length(sigma); ++n)
131 operands_and_partials.d_x3[n] *= cdf;
132 }
133 if (!is_constant_struct<T_inv_scale>::value) {
134 for (size_t n = 0; n < stan::length(lambda); ++n)
135 operands_and_partials.d_x4[n] *= cdf;
136 }
137
138 return operands_and_partials.to_var(cdf, y, mu, sigma, lambda);
139 }
140 }
141 }
142 #endif
143
144
145
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::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::exp_mod_normal_cdf
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
Definition: exp_mod_normal_cdf.hpp:24
stan::math::erf
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
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
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::SQRT_2
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:21
boost::math::isinf
bool isinf(const stan::math::var &v)
Checks if the given number is infinite.
Definition: boost_isinf.hpp:22
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::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
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 Home Page ] © 2011–2015, Stan Development Team.