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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 <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/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 <boost/random/uniform_01.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19
20 namespace stan {
21
22 namespace math {
23
38 template <typename T_y, typename T_loc, typename T_scale>
39 typename return_type<T_y, T_loc, T_scale>::type
40 double_exponential_cdf(const T_y& y,
41 const T_loc& mu, const T_scale& sigma) {
42 static const char* function("stan::math::double_exponential_cdf");
43 typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
44 T_partials_return;
45
46 // Size checks
47 if ( !( stan::length(y) && stan::length(mu)
48 && stan::length(sigma) ) )
49 return 1.0;
50
51 using stan::math::value_of;
52 using stan::math::check_finite;
53 using stan::math::check_positive_finite;
54 using stan::math::check_not_nan;
55 using boost::math::tools::promote_args;
56 using std::exp;
57
58 T_partials_return cdf(1.0);
59
60 check_not_nan(function, "Random variable", y);
61 check_finite(function, "Location parameter", mu);
62 check_positive_finite(function, "Scale parameter", sigma);
63
64 OperandsAndPartials<T_y, T_loc, T_scale>
65 operands_and_partials(y, mu, sigma);
66
67 VectorView<const T_y> y_vec(y);
68 VectorView<const T_loc> mu_vec(mu);
69 VectorView<const T_scale> sigma_vec(sigma);
70 size_t N = max_size(y, mu, sigma);
71
72 // cdf
73 for (size_t n = 0; n < N; n++) {
74 const T_partials_return y_dbl = value_of(y_vec[n]);
75 const T_partials_return mu_dbl = value_of(mu_vec[n]);
76 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
77 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (sigma_dbl);
78 const T_partials_return exp_scaled_diff = exp(scaled_diff);
79
80 if (y_dbl < mu_dbl)
81 cdf *= exp_scaled_diff * 0.5;
82 else
83 cdf *= 1.0 - 0.5 / exp_scaled_diff;
84 }
85
86 // gradients
87 for (size_t n = 0; n < N; n++) {
88 const T_partials_return y_dbl = value_of(y_vec[n]);
89 const T_partials_return mu_dbl = value_of(mu_vec[n]);
90 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
91 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / sigma_dbl;
92 const T_partials_return exp_scaled_diff = exp(scaled_diff);
93 const T_partials_return inv_sigma = 1.0 / sigma_dbl;
94
95 if (y_dbl < mu_dbl) {
96 if (!is_constant_struct<T_y>::value)
97 operands_and_partials.d_x1[n] += inv_sigma * cdf;
98 if (!is_constant_struct<T_loc>::value)
99 operands_and_partials.d_x2[n] -= inv_sigma * cdf;
100 if (!is_constant_struct<T_scale>::value)
101 operands_and_partials.d_x3[n] -= scaled_diff * inv_sigma * cdf;
102 } else {
103 const T_partials_return rep_deriv = cdf * inv_sigma
104 / (2.0 * exp_scaled_diff - 1.0);
105 if (!is_constant_struct<T_y>::value)
106 operands_and_partials.d_x1[n] += rep_deriv;
107 if (!is_constant_struct<T_loc>::value)
108 operands_and_partials.d_x2[n] -= rep_deriv;
109 if (!is_constant_struct<T_scale>::value)
110 operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff;
111 }
112 }
113 return operands_and_partials.value(cdf);
114 }
115 }
116 }
117 #endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:40
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
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::OperandsAndPartials::value
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
Definition: OperandsAndPartials.hpp:68
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
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::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:40
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:38
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:41
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
log1m.hpp
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:62
constants.hpp
sign.hpp
check_finite.hpp
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
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
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:39

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