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pareto_type_2_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LOG_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/VectorView.hpp>
16 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
17 #include <stan/math/prim/scal/meta/include_summand.hpp>
18 #include <cmath>
19
20
21 namespace stan {
22 namespace math {
23
24 // pareto_type_2(y|lambda, alpha) [y >= 0; lambda > 0; alpha > 0]
25 template <bool propto,
26 typename T_y, typename T_loc, typename T_scale, typename T_shape>
27 typename return_type<T_y, T_loc, T_scale, T_shape>::type
28 pareto_type_2_log(const T_y& y, const T_loc& mu, const T_scale& lambda,
29 const T_shape& alpha) {
30 static const char* function("stan::math::pareto_type_2_log");
31 typedef
32 typename stan::partials_return_type<T_y, T_loc, T_scale, T_shape>::type
33 T_partials_return;
34
35 using std::log;
36 using stan::math::value_of;
37 using stan::math::check_finite;
38 using stan::math::check_greater_or_equal;
39 using stan::math::check_positive_finite;
40 using stan::math::check_nonnegative;
41 using stan::math::check_not_nan;
42 using stan::math::check_consistent_sizes;
43 using std::log;
44
45 // check if any vectors are zero length
46 if (!(stan::length(y)
47 && stan::length(mu)
48 && stan::length(lambda)
49 && stan::length(alpha)))
50 return 0.0;
51
52 // set up return value accumulator
53 T_partials_return logp(0.0);
54
55 // validate args (here done over var, which should be OK)
56 check_greater_or_equal(function, "Random variable", y, mu);
57 check_not_nan(function, "Random variable", y);
58 check_positive_finite(function, "Scale parameter", lambda);
59 check_positive_finite(function, "Shape parameter", alpha);
60 check_consistent_sizes(function,
61 "Random variable", y,
62 "Scale parameter", lambda,
63 "Shape parameter", alpha);
64
65
66 // check if no variables are involved and prop-to
67 if (!include_summand<propto, T_y, T_loc, T_scale, T_shape>::value)
68 return 0.0;
69
70 VectorView<const T_y> y_vec(y);
71 VectorView<const T_loc> mu_vec(mu);
72 VectorView<const T_scale> lambda_vec(lambda);
73 VectorView<const T_shape> alpha_vec(alpha);
74 size_t N = max_size(y, mu, lambda, alpha);
75
76 // set up template expressions wrapping scalars into vector views
77 OperandsAndPartials<T_y, T_loc, T_scale, T_shape>
78 operands_and_partials(y, mu, lambda, alpha);
79
80 VectorBuilder<include_summand<propto, T_y, T_loc, T_scale, T_shape>
81 ::value,
82 T_partials_return, T_y, T_loc, T_scale>
83 log1p_scaled_diff(N);
84 if (include_summand<propto, T_y, T_loc, T_scale, T_shape>::value) {
85 for (size_t n = 0; n < N; n++)
86 log1p_scaled_diff[n] = log1p((value_of(y_vec[n])
87 - value_of(mu_vec[n]))
88 / value_of(lambda_vec[n]));
89 }
90
91 VectorBuilder<include_summand<propto, T_scale>::value,
92 T_partials_return, T_scale> log_lambda(length(lambda));
93 if (include_summand<propto, T_scale>::value) {
94 for (size_t n = 0; n < length(lambda); n++)
95 log_lambda[n] = log(value_of(lambda_vec[n]));
96 }
97
98 VectorBuilder<include_summand<propto, T_shape>::value,
99 T_partials_return, T_shape> log_alpha(length(alpha));
100 if (include_summand<propto, T_shape>::value) {
101 for (size_t n = 0; n < length(alpha); n++)
102 log_alpha[n] = log(value_of(alpha_vec[n]));
103 }
104
105 VectorBuilder<!is_constant_struct<T_shape>::value,
106 T_partials_return, T_shape> inv_alpha(length(alpha));
107 if (!is_constant_struct<T_shape>::value) {
108 for (size_t n = 0; n < length(alpha); n++)
109 inv_alpha[n] = 1 / value_of(alpha_vec[n]);
110 }
111
112 for (size_t n = 0; n < N; n++) {
113 const T_partials_return y_dbl = value_of(y_vec[n]);
114 const T_partials_return mu_dbl = value_of(mu_vec[n]);
115 const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
116 const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
117 const T_partials_return sum_dbl = lambda_dbl + y_dbl - mu_dbl;
118 const T_partials_return inv_sum = 1.0 / sum_dbl;
119 const T_partials_return alpha_div_sum = alpha_dbl / sum_dbl;
120 const T_partials_return deriv_1_2 = inv_sum + alpha_div_sum;
121
122 // // log probability
123 if (include_summand<propto, T_shape>::value)
124 logp += log_alpha[n];
125 if (include_summand<propto, T_scale>::value)
126 logp -= log_lambda[n];
127 if (include_summand<propto, T_y, T_scale, T_shape>::value)
128 logp -= (alpha_dbl + 1.0) * log1p_scaled_diff[n];
129
130 // gradients
131 if (!is_constant_struct<T_y>::value)
132 operands_and_partials.d_x1[n] -= deriv_1_2;
133 if (!is_constant_struct<T_loc>::value)
134 operands_and_partials.d_x2[n] += deriv_1_2;
135 if (!is_constant_struct<T_scale>::value)
136 operands_and_partials.d_x3[n] -= alpha_div_sum * (mu_dbl - y_dbl)
137 / lambda_dbl + inv_sum;
138 if (!is_constant_struct<T_shape>::value)
139 operands_and_partials.d_x4[n] += inv_alpha[n] - log1p_scaled_diff[n];
140 }
141 return operands_and_partials.to_var(logp, y, mu, lambda, alpha);
142 }
143
144 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
145 inline
146 typename return_type<T_y, T_loc, T_scale, T_shape>::type
147 pareto_type_2_log(const T_y& y, const T_loc& mu,
148 const T_scale& lambda, const T_shape& alpha) {
149 return pareto_type_2_log<false>(y, mu, lambda, alpha);
150 }
151 }
152 }
153 #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
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
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:36
stan::return_type::type
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
VectorView.hpp
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
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::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::log1p
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:16
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
stan::math::pareto_type_2_log
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_log(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
Definition: pareto_type_2_log.hpp:28

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