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skew_normal_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CCDF_LOG_HPP
3
4 #include <boost/random/variate_generator.hpp>
5 #include <boost/math/distributions.hpp>
6 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
7 #include <stan/math/prim/scal/err/check_finite.hpp>
8 #include <stan/math/prim/scal/err/check_not_nan.hpp>
9 #include <stan/math/prim/scal/err/check_positive.hpp>
10 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
11 #include <stan/math/prim/scal/fun/owens_t.hpp>
12 #include <stan/math/prim/scal/fun/value_of.hpp>
13 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
14 #include <stan/math/prim/scal/meta/include_summand.hpp>
15 #include <stan/math/prim/scal/fun/constants.hpp>
16 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
17 #include <stan/math/prim/scal/meta/VectorView.hpp>
18 #include <cmath>
19
20 namespace stan {
21
22 namespace math {
23
24 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
25 typename return_type<T_y, T_loc, T_scale, T_shape>::type
26 skew_normal_ccdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
27 const T_shape& alpha) {
28 static const char* function("stan::math::skew_normal_ccdf_log");
29 typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
30 T_shape>::type
31 T_partials_return;
32
33 using stan::math::check_positive;
34 using stan::math::check_finite;
35 using stan::math::check_not_nan;
36 using stan::math::check_consistent_sizes;
37 using stan::math::owens_t;
38 using stan::math::value_of;
39
40 T_partials_return ccdf_log(0.0);
41
42 // check if any vectors are zero length
43 if (!(stan::length(y)
44 && stan::length(mu)
45 && stan::length(sigma)
46 && stan::length(alpha)))
47 return ccdf_log;
48
49 check_not_nan(function, "Random variable", y);
50 check_finite(function, "Location parameter", mu);
51 check_not_nan(function, "Scale parameter", sigma);
52 check_positive(function, "Scale parameter", sigma);
53 check_finite(function, "Shape parameter", alpha);
54 check_not_nan(function, "Shape parameter", alpha);
55 check_consistent_sizes(function,
56 "Random variable", y,
57 "Location parameter", mu,
58 "Scale parameter", sigma,
59 "Shape paramter", alpha);
60
61 OperandsAndPartials<T_y, T_loc, T_scale, T_shape>
62 operands_and_partials(y, mu, sigma, alpha);
63
64 using stan::math::SQRT_2;
65 using stan::math::pi;
66 using std::log;
67 using std::exp;
68
69 VectorView<const T_y> y_vec(y);
70 VectorView<const T_loc> mu_vec(mu);
71 VectorView<const T_scale> sigma_vec(sigma);
72 VectorView<const T_shape> alpha_vec(alpha);
73 size_t N = max_size(y, mu, sigma, alpha);
74 const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / stan::math::pi());
75
76 for (size_t n = 0; n < N; n++) {
77 const T_partials_return y_dbl = value_of(y_vec[n]);
78 const T_partials_return mu_dbl = value_of(mu_vec[n]);
79 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
80 const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
81 const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
82 const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
83 const T_partials_return diff_sq = diff * diff;
84 const T_partials_return scaled_diff = diff / SQRT_2;
85 const T_partials_return scaled_diff_sq = diff_sq * 0.5;
86 const T_partials_return ccdf_log_ = 1.0 - 0.5 * erfc(-scaled_diff)
87 + 2 * owens_t(diff, alpha_dbl);
88
89 // ccdf_log
90 ccdf_log += log(ccdf_log_);
91
92 // gradients
93 const T_partials_return deriv_erfc = SQRT_TWO_OVER_PI * 0.5
94 * exp(-scaled_diff_sq) / sigma_dbl;
95 const T_partials_return deriv_owens = erf(alpha_dbl * scaled_diff)
96 * exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI / (-2.0 * pi()) / sigma_dbl;
97 const T_partials_return rep_deriv = (-2.0 * deriv_owens + deriv_erfc)
98 / ccdf_log_;
99
100 if (!is_constant_struct<T_y>::value)
101 operands_and_partials.d_x1[n] -= rep_deriv;
102 if (!is_constant_struct<T_loc>::value)
103 operands_and_partials.d_x2[n] += rep_deriv;
104 if (!is_constant_struct<T_scale>::value)
105 operands_and_partials.d_x3[n] += rep_deriv * diff;
106 if (!is_constant_struct<T_shape>::value)
107 operands_and_partials.d_x4[n] -= -2.0 * exp(-0.5 * diff_sq
108 * (1.0 + alpha_dbl_sq))
109 / ((1 + alpha_dbl_sq) * 2.0 * pi()) / ccdf_log_;
110 }
111
112 return operands_and_partials.to_var(ccdf_log, y, mu, sigma, alpha);
113 }
114 }
115 }
116 #endif
117
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.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::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
VectorView.hpp
stan::math::owens_t
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Definition: owens_t.hpp:14
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::skew_normal_ccdf_log
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_ccdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
Definition: skew_normal_ccdf_log.hpp:26
stan::math::SQRT_2
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:21
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
stan::math::check_positive
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
Definition: check_positive.hpp:68
OperandsAndPartials.hpp
owens_t.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.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: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
is_constant_struct.hpp
stan::math::erfc
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
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

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