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exp_mod_normal_cdf.hpp
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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 <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/fun/is_inf.hpp>
13 #include <stan/math/prim/scal/meta/include_summand.hpp>
14 #include <stan/math/prim/scal/fun/value_of.hpp>
15 #include <boost/random/normal_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18
19 namespace stan {
20 namespace math {
21
22 template <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_cdf(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_cdf");
28 typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
29 T_inv_scale>::type
30 T_partials_return;
31
32 T_partials_return cdf(1.0);
33 if (!(stan::length(y)
34 && stan::length(mu)
35 && stan::length(sigma)
36 && stan::length(lambda)))
37 return cdf;
38
39 check_not_nan(function, "Random variable", y);
40 check_finite(function, "Location parameter", mu);
41 check_not_nan(function, "Scale parameter", sigma);
42 check_positive_finite(function, "Scale parameter", sigma);
43 check_positive_finite(function, "Inv_scale parameter", lambda);
44 check_not_nan(function, "Inv_scale parameter", lambda);
45 check_consistent_sizes(function,
46 "Random variable", y,
47 "Location parameter", mu,
48 "Scale parameter", sigma,
49 "Inv_scale paramter", lambda);
50
51 OperandsAndPartials<T_y, T_loc, T_scale, T_inv_scale>
52 operands_and_partials(y, mu, sigma, lambda);
53
54 using std::exp;
55
56 VectorView<const T_y> y_vec(y);
57 VectorView<const T_loc> mu_vec(mu);
58 VectorView<const T_scale> sigma_vec(sigma);
59 VectorView<const T_inv_scale> lambda_vec(lambda);
60 size_t N = max_size(y, mu, sigma, lambda);
61 const double sqrt_pi = std::sqrt(pi());
62 for (size_t n = 0; n < N; n++) {
63 if (is_inf(y_vec[n])) {
64 if (y_vec[n] < 0.0)
65 return operands_and_partials.value(0.0);
66 }
67
68 const T_partials_return y_dbl = value_of(y_vec[n]);
69 const T_partials_return mu_dbl = value_of(mu_vec[n]);
70 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
71 const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
72 const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
73 const T_partials_return v = lambda_dbl * sigma_dbl;
74 const T_partials_return v_sq = v * v;
75 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (SQRT_2
76 * sigma_dbl);
77 const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
78 const T_partials_return erf_calc = 0.5 * (1 + erf(-v / SQRT_2
79 + scaled_diff));
80 const T_partials_return deriv_1 = lambda_dbl * exp(0.5 * v_sq - u)
81 * erf_calc;
82 const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
83 * exp(0.5 * v_sq - (scaled_diff - (v / SQRT_2))
84 * (scaled_diff - (v / SQRT_2)) - u) / sigma_dbl;
85 const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
86 * exp(-scaled_diff_sq) / sigma_dbl;
87
88 const T_partials_return cdf_ = 0.5 * (1 + erf(u / (v * SQRT_2)))
89 - exp(-u + v_sq * 0.5) * (erf_calc);
90
91 cdf *= cdf_;
92
93 if (!is_constant_struct<T_y>::value)
94 operands_and_partials.d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
95 / cdf_;
96 if (!is_constant_struct<T_loc>::value)
97 operands_and_partials.d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
98 / cdf_;
99 if (!is_constant_struct<T_scale>::value)
100 operands_and_partials.d_x3[n] += (-deriv_1 * v - deriv_3
101 * scaled_diff * SQRT_2 - deriv_2
102 * sigma_dbl * SQRT_2
103 * (-SQRT_2 * 0.5
104 * (-lambda_dbl + scaled_diff
105 * SQRT_2 / sigma_dbl) - SQRT_2
106 * lambda_dbl)) / cdf_;
107 if (!is_constant_struct<T_inv_scale>::value)
108 operands_and_partials.d_x4[n] += exp(0.5 * v_sq - u)
109 * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
110 * exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
111 - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc) / cdf_;
112 }
113
114 if (!is_constant_struct<T_y>::value) {
115 for (size_t n = 0; n < stan::length(y); ++n)
116 operands_and_partials.d_x1[n] *= cdf;
117 }
118 if (!is_constant_struct<T_loc>::value) {
119 for (size_t n = 0; n < stan::length(mu); ++n)
120 operands_and_partials.d_x2[n] *= cdf;
121 }
122 if (!is_constant_struct<T_scale>::value) {
123 for (size_t n = 0; n < stan::length(sigma); ++n)
124 operands_and_partials.d_x3[n] *= cdf;
125 }
126 if (!is_constant_struct<T_inv_scale>::value) {
127 for (size_t n = 0; n < stan::length(lambda); ++n)
128 operands_and_partials.d_x4[n] *= cdf;
129 }
130 return operands_and_partials.value(cdf);
131 }
132
133 }
134 }
135 #endif
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::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_inf.hpp
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:25
stan::math::erf
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
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::SQRT_2
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:20
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
stan::math::is_inf
int is_inf(const fvar< T > &x)
Returns 1 if the input's value is infinite and 0 otherwise.
Definition: is_inf.hpp:21
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::pi
double pi()
Return the value of pi.
Definition: constants.hpp:85
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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