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pareto_type_2_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_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_greater_or_equal.hpp>
10 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
11 #include <stan/math/prim/scal/err/check_not_nan.hpp>
12 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
13 #include <stan/math/prim/scal/fun/constants.hpp>
14 #include <stan/math/prim/scal/fun/value_of.hpp>
15 #include <stan/math/prim/scal/fun/log1m.hpp>
16 #include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
17 #include <stan/math/prim/scal/meta/VectorView.hpp>
18 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
19 #include <boost/random/variate_generator.hpp>
20 #include <cmath>
21
22 namespace stan {
23 namespace math {
24
25 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
26 typename return_type<T_y, T_loc, T_scale, T_shape>::type
27 pareto_type_2_cdf(const T_y& y, const T_loc& mu,
28 const T_scale& lambda, const T_shape& alpha) {
29 typedef
30 typename stan::partials_return_type<T_y, T_loc, T_scale, T_shape>::type
31 T_partials_return;
32
33 // Check sizes
34 // Size checks
35 if ( !( stan::length(y)
36 && stan::length(mu)
37 && stan::length(lambda)
38 && stan::length(alpha) ) )
39 return 1.0;
40
41 // Check errors
42 static const char* function("stan::math::pareto_type_2_cdf");
43
44 using stan::math::check_greater_or_equal;
45 using stan::math::check_finite;
46 using stan::math::check_positive_finite;
47 using stan::math::check_not_nan;
48 using stan::math::check_greater_or_equal;
49 using stan::math::check_consistent_sizes;
50 using stan::math::check_nonnegative;
51 using stan::math::value_of;
52 using std::log;
53
54 T_partials_return P(1.0);
55
56 check_greater_or_equal(function, "Random variable", y, mu);
57 check_not_nan(function, "Random variable", y);
58 check_nonnegative(function, "Random variable", y);
59 check_positive_finite(function, "Scale parameter", lambda);
60 check_positive_finite(function, "Shape parameter", alpha);
61 check_consistent_sizes(function,
62 "Random variable", y,
63 "Scale parameter", lambda,
64 "Shape parameter", alpha);
65
66 // Wrap arguments in vectors
67 VectorView<const T_y> y_vec(y);
68 VectorView<const T_loc> mu_vec(mu);
69 VectorView<const T_scale> lambda_vec(lambda);
70 VectorView<const T_shape> alpha_vec(alpha);
71 size_t N = max_size(y, mu, lambda, alpha);
72
73 OperandsAndPartials<T_y, T_loc, T_scale, T_shape>
74 operands_and_partials(y, mu, lambda, alpha);
75
76 VectorBuilder<true, T_partials_return,
77 T_y, T_loc, T_scale, T_shape>
78 p1_pow_alpha(N);
79
80 VectorBuilder<contains_nonconstant_struct<T_y, T_loc, T_scale>::value,
81 T_partials_return, T_y, T_loc, T_scale, T_shape>
82 grad_1_2(N);
83
84 VectorBuilder<contains_nonconstant_struct<T_shape, T_y>::value,
85 T_partials_return, T_y, T_loc, T_scale, T_shape>
86 grad_3(N);
87
88 for (size_t i = 0; i < N; i++) {
89 const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
90 const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
91 const T_partials_return temp = 1 + (value_of(y_vec[i])
92 - value_of(mu_vec[i]))
93 / lambda_dbl;
94 p1_pow_alpha[i] = pow(temp, -alpha_dbl);
95
96 if (contains_nonconstant_struct<T_y, T_loc, T_scale>::value)
97 grad_1_2[i] = p1_pow_alpha[i] / temp * alpha_dbl / lambda_dbl;
98
99 if (!is_constant_struct<T_shape>::value)
100 grad_3[i] = log(temp) * p1_pow_alpha[i];
101 }
102
103 // Compute vectorized CDF and its gradients
104
105 for (size_t n = 0; n < N; n++) {
106 // Pull out values
107 const T_partials_return y_dbl = value_of(y_vec[n]);
108 const T_partials_return mu_dbl = value_of(mu_vec[n]);
109 const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
110
111 const T_partials_return Pn = 1.0 - p1_pow_alpha[n];
112
113 // Compute
114 P *= Pn;
115
116 if (!is_constant_struct<T_y>::value)
117 operands_and_partials.d_x1[n] += grad_1_2[n] / Pn;
118 if (!is_constant_struct<T_loc>::value)
119 operands_and_partials.d_x2[n] -= grad_1_2[n] / Pn;
120 if (!is_constant_struct<T_scale>::value)
121 operands_and_partials.d_x3[n] += (mu_dbl - y_dbl)
122 * grad_1_2[n] / lambda_dbl / Pn;
123 if (!is_constant_struct<T_shape>::value)
124 operands_and_partials.d_x4[n] += grad_3[n] / Pn;
125 }
126
127 if (!is_constant_struct<T_y>::value) {
128 for (size_t n = 0; n < stan::length(y); ++n)
129 operands_and_partials.d_x1[n] *= P;
130 }
131 if (!is_constant_struct<T_loc>::value) {
132 for (size_t n = 0; n < stan::length(mu); ++n)
133 operands_and_partials.d_x2[n] *= P;
134 }
135 if (!is_constant_struct<T_scale>::value) {
136 for (size_t n = 0; n < stan::length(lambda); ++n)
137 operands_and_partials.d_x3[n] *= P;
138 }
139 if (!is_constant_struct<T_shape>::value) {
140 for (size_t n = 0; n < stan::length(alpha); ++n)
141 operands_and_partials.d_x4[n] *= P;
142 }
143
144 return operands_and_partials.value(P);
145 }
146 }
147 }
148 #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_greater_or_equal
bool check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Return true if y is greater or equal than low.
Definition: check_greater_or_equal.hpp:84
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::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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
contains_nonconstant_struct.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::pareto_type_2_cdf
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_cdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
Definition: pareto_type_2_cdf.hpp:27
is_constant_struct.hpp
check_nonnegative.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::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:38
VectorView.hpp
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
VectorBuilder.hpp
log1m.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
stan::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
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
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
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::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
check_greater_or_equal.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
stan::math::OperandsAndPartials::d_x4
VectorView< T_return_type, false, true > d_x4
Definition: OperandsAndPartials.hpp:42

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