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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 <boost/random/variate_generator.hpp>
5 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
6 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
7 #include <stan/math/prim/scal/err/check_finite.hpp>
8 #include <stan/math/prim/scal/err/check_greater_or_equal.hpp>
9 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
10 #include <stan/math/prim/scal/err/check_not_nan.hpp>
11 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
12 #include <stan/math/prim/scal/fun/constants.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <stan/math/prim/scal/fun/log1m.hpp>
15 #include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
16 #include <stan/math/prim/scal/meta/VectorView.hpp>
17 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
18 #include <cmath>
19
20 namespace stan {
21 namespace math {
22
23 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
24 typename return_type<T_y, T_loc, T_scale, T_shape>::type
25 pareto_type_2_cdf(const T_y& y, const T_loc& mu,
26 const T_scale& lambda, const T_shape& alpha) {
27 typedef
28 typename stan::partials_return_type<T_y, T_loc, T_scale, T_shape>::type
29 T_partials_return;
30
31 // Check sizes
32 // Size checks
33 if ( !( stan::length(y)
34 && stan::length(mu)
35 && stan::length(lambda)
36 && stan::length(alpha) ) )
37 return 1.0;
38
39 // Check errors
40 static const char* function("stan::math::pareto_type_2_cdf");
41
42 using stan::math::check_greater_or_equal;
43 using stan::math::check_finite;
44 using stan::math::check_positive_finite;
45 using stan::math::check_not_nan;
46 using stan::math::check_greater_or_equal;
47 using stan::math::check_consistent_sizes;
48 using stan::math::check_nonnegative;
49 using stan::math::value_of;
50 using std::log;
51
52 T_partials_return P(1.0);
53
54 check_greater_or_equal(function, "Random variable", y, mu);
55 check_not_nan(function, "Random variable", y);
56 check_nonnegative(function, "Random variable", y);
57 check_positive_finite(function, "Scale parameter", lambda);
58 check_positive_finite(function, "Shape parameter", alpha);
59 check_consistent_sizes(function,
60 "Random variable", y,
61 "Scale parameter", lambda,
62 "Shape parameter", alpha);
63
64 // Wrap arguments in vectors
65 VectorView<const T_y> y_vec(y);
66 VectorView<const T_loc> mu_vec(mu);
67 VectorView<const T_scale> lambda_vec(lambda);
68 VectorView<const T_shape> alpha_vec(alpha);
69 size_t N = max_size(y, mu, lambda, alpha);
70
71 OperandsAndPartials<T_y, T_loc, T_scale, T_shape>
72 operands_and_partials(y, mu, lambda, alpha);
73
74 VectorBuilder<true, T_partials_return,
75 T_y, T_loc, T_scale, T_shape>
76 p1_pow_alpha(N);
77
78 VectorBuilder<contains_nonconstant_struct<T_y, T_loc, T_scale>::value,
79 T_partials_return, T_y, T_loc, T_scale, T_shape>
80 grad_1_2(N);
81
82 VectorBuilder<contains_nonconstant_struct<T_shape, T_y>::value,
83 T_partials_return, T_y, T_loc, T_scale, T_shape>
84 grad_3(N);
85
86 for (size_t i = 0; i < N; i++) {
87 const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
88 const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
89 const T_partials_return temp = 1 + (value_of(y_vec[i])
90 - value_of(mu_vec[i]))
91 / lambda_dbl;
92 p1_pow_alpha[i] = pow(temp, -alpha_dbl);
93
94 if (contains_nonconstant_struct<T_y, T_loc, T_scale>::value)
95 grad_1_2[i] = p1_pow_alpha[i] / temp * alpha_dbl / lambda_dbl;
96
97 if (!is_constant_struct<T_shape>::value)
98 grad_3[i] = log(temp) * p1_pow_alpha[i];
99 }
100
101 // Compute vectorized CDF and its gradients
102
103 for (size_t n = 0; n < N; n++) {
104 // Pull out values
105 const T_partials_return y_dbl = value_of(y_vec[n]);
106 const T_partials_return mu_dbl = value_of(mu_vec[n]);
107 const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
108
109 const T_partials_return Pn = 1.0 - p1_pow_alpha[n];
110
111 // Compute
112 P *= Pn;
113
114 if (!is_constant_struct<T_y>::value)
115 operands_and_partials.d_x1[n] += grad_1_2[n] / Pn;
116 if (!is_constant_struct<T_loc>::value)
117 operands_and_partials.d_x2[n] -= grad_1_2[n] / Pn;
118 if (!is_constant_struct<T_scale>::value)
119 operands_and_partials.d_x3[n] += (mu_dbl - y_dbl)
120 * grad_1_2[n] / lambda_dbl / Pn;
121 if (!is_constant_struct<T_shape>::value)
122 operands_and_partials.d_x4[n] += grad_3[n] / Pn;
123 }
124
125 if (!is_constant_struct<T_y>::value) {
126 for (size_t n = 0; n < stan::length(y); ++n)
127 operands_and_partials.d_x1[n] *= P;
128 }
129 if (!is_constant_struct<T_loc>::value) {
130 for (size_t n = 0; n < stan::length(mu); ++n)
131 operands_and_partials.d_x2[n] *= P;
132 }
133 if (!is_constant_struct<T_scale>::value) {
134 for (size_t n = 0; n < stan::length(lambda); ++n)
135 operands_and_partials.d_x3[n] *= P;
136 }
137 if (!is_constant_struct<T_shape>::value) {
138 for (size_t n = 0; n < stan::length(alpha); ++n)
139 operands_and_partials.d_x4[n] *= P;
140 }
141
142 return operands_and_partials.to_var(P, y, mu, lambda, alpha);
143 }
144 }
145 }
146 #endif
check_not_nan.hpp
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::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
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:25
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::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
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:16
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
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
log1m.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
Definition: VectorBuilder.hpp:61
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
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 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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