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double_exponential_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_DOUBLE_EXPONENTIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_DOUBLE_EXPONENTIAL_CDF_HPP
3
4 #include <boost/random/uniform_01.hpp>
5 #include <boost/random/variate_generator.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/value_of.hpp>
12 #include <stan/math/prim/scal/fun/log1m.hpp>
13 #include <stan/math/prim/scal/fun/constants.hpp>
14 #include <stan/math/prim/scal/meta/include_summand.hpp>
15 #include <stan/math/prim/scal/fun/sign.hpp>
16 #include <cmath>
17
18 namespace stan {
19
20 namespace math {
21
36 template <typename T_y, typename T_loc, typename T_scale>
37 typename return_type<T_y, T_loc, T_scale>::type
38 double_exponential_cdf(const T_y& y,
39 const T_loc& mu, const T_scale& sigma) {
40 static const char* function("stan::math::double_exponential_cdf");
41 typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
42 T_partials_return;
43
44 // Size checks
45 if ( !( stan::length(y) && stan::length(mu)
46 && stan::length(sigma) ) )
47 return 1.0;
48
49 using stan::math::value_of;
50 using stan::math::check_finite;
51 using stan::math::check_positive_finite;
52 using stan::math::check_not_nan;
53 using boost::math::tools::promote_args;
54 using std::exp;
55
56 T_partials_return cdf(1.0);
57
58 check_not_nan(function, "Random variable", y);
59 check_finite(function, "Location parameter", mu);
60 check_positive_finite(function, "Scale parameter", sigma);
61
62 OperandsAndPartials<T_y, T_loc, T_scale>
63 operands_and_partials(y, mu, sigma);
64
65 VectorView<const T_y> y_vec(y);
66 VectorView<const T_loc> mu_vec(mu);
67 VectorView<const T_scale> sigma_vec(sigma);
68 size_t N = max_size(y, mu, sigma);
69
70 // cdf
71 for (size_t n = 0; n < N; n++) {
72 const T_partials_return y_dbl = value_of(y_vec[n]);
73 const T_partials_return mu_dbl = value_of(mu_vec[n]);
74 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
75 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (sigma_dbl);
76 const T_partials_return exp_scaled_diff = exp(scaled_diff);
77
78 if (y_dbl < mu_dbl)
79 cdf *= exp_scaled_diff * 0.5;
80 else
81 cdf *= 1.0 - 0.5 / exp_scaled_diff;
82 }
83
84 // gradients
85 for (size_t n = 0; n < N; n++) {
86 const T_partials_return y_dbl = value_of(y_vec[n]);
87 const T_partials_return mu_dbl = value_of(mu_vec[n]);
88 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
89 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / sigma_dbl;
90 const T_partials_return exp_scaled_diff = exp(scaled_diff);
91 const T_partials_return inv_sigma = 1.0 / sigma_dbl;
92
93 if (y_dbl < mu_dbl) {
94 if (!is_constant_struct<T_y>::value)
95 operands_and_partials.d_x1[n] += inv_sigma * cdf;
96 if (!is_constant_struct<T_loc>::value)
97 operands_and_partials.d_x2[n] -= inv_sigma * cdf;
98 if (!is_constant_struct<T_scale>::value)
99 operands_and_partials.d_x3[n] -= scaled_diff * inv_sigma * cdf;
100 } else {
101 const T_partials_return rep_deriv = cdf * inv_sigma
102 / (2.0 * exp_scaled_diff - 1.0);
103 if (!is_constant_struct<T_y>::value)
104 operands_and_partials.d_x1[n] += rep_deriv;
105 if (!is_constant_struct<T_loc>::value)
106 operands_and_partials.d_x2[n] -= rep_deriv;
107 if (!is_constant_struct<T_scale>::value)
108 operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff;
109 }
110 }
111 return operands_and_partials.to_var(cdf, y, mu, sigma);
112 }
113 }
114 }
115 #endif
check_not_nan.hpp
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::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::double_exponential_cdf
return_type< T_y, T_loc, T_scale >::type double_exponential_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Calculates the double exponential cumulative density function.
Definition: double_exponential_cdf.hpp:38
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
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
log1m.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
sign.hpp
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
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
stan::partials_return_type::type
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
Definition: partials_return_type.hpp:26
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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