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pareto_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_LOG_HPP
3
4 #include <boost/random/exponential_distribution.hpp>
5 #include <boost/random/variate_generator.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_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/multiply_log.hpp>
14 #include <stan/math/prim/scal/fun/value_of.hpp>
15 #include <stan/math/prim/scal/meta/include_summand.hpp>
16 #include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
17 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
18 #include <cmath>
19
20 namespace stan {
21 namespace math {
22
23 // Pareto(y|y_m, alpha) [y > y_m; y_m > 0; alpha > 0]
24 template <bool propto,
25 typename T_y, typename T_scale, typename T_shape>
26 typename return_type<T_y, T_scale, T_shape>::type
27 pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
28 static const char* function("stan::math::pareto_log");
29 typedef typename stan::partials_return_type<T_y, T_scale, T_shape>::type
30 T_partials_return;
31
32 using stan::math::value_of;
33 using stan::math::check_positive_finite;
34 using stan::math::check_not_nan;
35 using stan::math::check_consistent_sizes;
36 using std::log;
37
38 // check if any vectors are zero length
39 if (!(stan::length(y)
40 && stan::length(y_min)
41 && stan::length(alpha)))
42 return 0.0;
43
44 // set up return value accumulator
45 T_partials_return logp(0.0);
46
47 // validate args (here done over var, which should be OK)
48 check_not_nan(function, "Random variable", y);
49 check_positive_finite(function, "Scale parameter", y_min);
50 check_positive_finite(function, "Shape parameter", alpha);
51 check_consistent_sizes(function,
52 "Random variable", y,
53 "Scale parameter", y_min,
54 "Shape parameter", alpha);
55
56 // check if no variables are involved and prop-to
57 if (!include_summand<propto, T_y, T_scale, T_shape>::value)
58 return 0.0;
59
60 VectorView<const T_y> y_vec(y);
61 VectorView<const T_scale> y_min_vec(y_min);
62 VectorView<const T_shape> alpha_vec(alpha);
63 size_t N = max_size(y, y_min, alpha);
64
65 for (size_t n = 0; n < N; n++) {
66 if (y_vec[n] < y_min_vec[n])
67 return LOG_ZERO;
68 }
69
70 // set up template expressions wrapping scalars into vector views
71 OperandsAndPartials<T_y, T_scale, T_shape>
72 operands_and_partials(y, y_min, alpha);
73
74 VectorBuilder<include_summand<propto, T_y, T_shape>::value,
75 T_partials_return, T_y> log_y(length(y));
76 if (include_summand<propto, T_y, T_shape>::value) {
77 for (size_t n = 0; n < length(y); n++)
78 log_y[n] = log(value_of(y_vec[n]));
79 }
80
81 VectorBuilder<contains_nonconstant_struct<T_y, T_shape>::value,
82 T_partials_return, T_y> inv_y(length(y));
83 if (contains_nonconstant_struct<T_y, T_shape>::value) {
84 for (size_t n = 0; n < length(y); n++)
85 inv_y[n] = 1 / value_of(y_vec[n]);
86 }
87
88 VectorBuilder<include_summand<propto, T_scale, T_shape>::value,
89 T_partials_return, T_scale>
90 log_y_min(length(y_min));
91 if (include_summand<propto, T_scale, T_shape>::value) {
92 for (size_t n = 0; n < length(y_min); n++)
93 log_y_min[n] = log(value_of(y_min_vec[n]));
94 }
95
96 VectorBuilder<include_summand<propto, T_shape>::value,
97 T_partials_return, T_shape> log_alpha(length(alpha));
98 if (include_summand<propto, T_shape>::value) {
99 for (size_t n = 0; n < length(alpha); n++)
100 log_alpha[n] = log(value_of(alpha_vec[n]));
101 }
102
103 using stan::math::multiply_log;
104
105 for (size_t n = 0; n < N; n++) {
106 const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
107 // log probability
108 if (include_summand<propto, T_shape>::value)
109 logp += log_alpha[n];
110 if (include_summand<propto, T_scale, T_shape>::value)
111 logp += alpha_dbl * log_y_min[n];
112 if (include_summand<propto, T_y, T_shape>::value)
113 logp -= alpha_dbl * log_y[n] + log_y[n];
114
115 // gradients
116 if (!is_constant_struct<T_y>::value)
117 operands_and_partials.d_x1[n] -= alpha_dbl * inv_y[n] + inv_y[n];
118 if (!is_constant_struct<T_scale>::value)
119 operands_and_partials.d_x2[n] += alpha_dbl / value_of(y_min_vec[n]);
120 if (!is_constant_struct<T_shape>::value)
121 operands_and_partials.d_x3[n]
122 += 1 / alpha_dbl + log_y_min[n] - log_y[n];
123 }
124 return operands_and_partials.to_var(logp, y, y_min, alpha);
125 }
126
127 template <typename T_y, typename T_scale, typename T_shape>
128 inline
129 typename return_type<T_y, T_scale, T_shape>::type
130 pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
131 return pareto_log<false>(y, y_min, alpha);
132 }
133 }
134 }
135 #endif
check_not_nan.hpp
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_log
return_type< T_y, T_scale, T_shape >::type pareto_log(const T_y &y, const T_scale &y_min, const T_shape &alpha)
Definition: pareto_log.hpp:27
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::LOG_ZERO
const double LOG_ZERO
Definition: constants.hpp:175
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
include_summand.hpp
multiply_log.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
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
stan::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
stan::math::multiply_log
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: multiply_log.hpp:15
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
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
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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