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frechet_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_FRECHET_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_FRECHET_LOG_HPP
3
4 #include <boost/random/weibull_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_nonnegative.hpp>
9 #include <stan/math/prim/scal/err/check_not_nan.hpp>
10 #include <stan/math/prim/scal/err/check_positive.hpp>
11 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
12 #include <stan/math/prim/scal/fun/log1m.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/length.hpp>
16 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
17 #include <stan/math/prim/scal/meta/VectorView.hpp>
18 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
19 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
20 #include <stan/math/prim/scal/meta/return_type.hpp>
21 #include <stan/math/prim/scal/fun/constants.hpp>
22 #include <stan/math/prim/scal/meta/include_summand.hpp>
23 #include <cmath>
24
25 namespace stan {
26 namespace math {
27
28 // Frechet(y|alpha, sigma) [y > 0; alpha > 0; sigma > 0]
29 // FIXME: document
30 template <bool propto,
31 typename T_y, typename T_shape, typename T_scale>
32 typename return_type<T_y, T_shape, T_scale>::type
33 frechet_log(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
34 static const char* function("frechet_log");
35 typedef typename stan::partials_return_type<T_y, T_shape, T_scale>::type
36 T_partials_return;
37
38 using std::log;
39
40 if (!(stan::length(y)
41 && stan::length(alpha)
42 && stan::length(sigma)))
43 return 0.0;
44
45 T_partials_return logp(0.0);
46 check_positive(function, "Random variable", y);
47 check_positive_finite(function, "Shape parameter", alpha);
48 check_positive_finite(function, "Scale parameter", sigma);
49 check_consistent_sizes(function,
50 "Random variable", y,
51 "Shape parameter", alpha,
52 "Scale parameter", sigma);
53
54 if (!include_summand<propto, T_y, T_shape, T_scale>::value)
55 return 0.0;
56
57 VectorView<const T_y> y_vec(y);
58 VectorView<const T_shape> alpha_vec(alpha);
59 VectorView<const T_scale> sigma_vec(sigma);
60 size_t N = max_size(y, alpha, sigma);
61
62 VectorBuilder<include_summand<propto, T_shape>::value,
63 T_partials_return, T_shape> log_alpha(length(alpha));
64 for (size_t i = 0; i < length(alpha); i++)
65 if (include_summand<propto, T_shape>::value)
66 log_alpha[i] = log(value_of(alpha_vec[i]));
67
68 VectorBuilder<include_summand<propto, T_y, T_shape>::value,
69 T_partials_return, T_y> log_y(length(y));
70 for (size_t i = 0; i < length(y); i++)
71 if (include_summand<propto, T_y, T_shape>::value)
72 log_y[i] = log(value_of(y_vec[i]));
73
74 VectorBuilder<include_summand<propto, T_shape, T_scale>::value,
75 T_partials_return, T_scale> log_sigma(length(sigma));
76 for (size_t i = 0; i < length(sigma); i++)
77 if (include_summand<propto, T_shape, T_scale>::value)
78 log_sigma[i] = log(value_of(sigma_vec[i]));
79
80 VectorBuilder<include_summand<propto, T_y, T_shape, T_scale>::value,
81 T_partials_return, T_y> inv_y(length(y));
82 for (size_t i = 0; i < length(y); i++)
83 if (include_summand<propto, T_y, T_shape, T_scale>::value)
84 inv_y[i] = 1.0 / value_of(y_vec[i]);
85
86 VectorBuilder<include_summand<propto, T_y, T_shape, T_scale>::value,
87 T_partials_return, T_y, T_shape, T_scale>
88 sigma_div_y_pow_alpha(N);
89 for (size_t i = 0; i < N; i++)
90 if (include_summand<propto, T_y, T_shape, T_scale>::value) {
91 const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
92 sigma_div_y_pow_alpha[i] = pow(inv_y[i] * value_of(sigma_vec[i]),
93 alpha_dbl);
94 }
95
96 OperandsAndPartials<T_y, T_shape, T_scale>
97 operands_and_partials(y, alpha, sigma);
98 for (size_t n = 0; n < N; n++) {
99 const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
100 if (include_summand<propto, T_shape>::value)
101 logp += log_alpha[n];
102 if (include_summand<propto, T_y, T_shape>::value)
103 logp -= (alpha_dbl+1.0)*log_y[n];
104 if (include_summand<propto, T_shape, T_scale>::value)
105 logp += alpha_dbl*log_sigma[n];
106 if (include_summand<propto, T_y, T_shape, T_scale>::value)
107 logp -= sigma_div_y_pow_alpha[n];
108
109 if (!is_constant_struct<T_y>::value) {
110 const T_partials_return inv_y_dbl = value_of(inv_y[n]);
111 operands_and_partials.d_x1[n]
112 += -(alpha_dbl+1.0) * inv_y_dbl
113 + alpha_dbl * sigma_div_y_pow_alpha[n] * inv_y_dbl;
114 }
115 if (!is_constant_struct<T_shape>::value)
116 operands_and_partials.d_x2[n]
117 += 1.0/alpha_dbl
118 + (1.0 - sigma_div_y_pow_alpha[n]) * (log_sigma[n] - log_y[n]);
119 if (!is_constant_struct<T_scale>::value)
120 operands_and_partials.d_x3[n]
121 += alpha_dbl / value_of(sigma_vec[n])
122 * (1 - sigma_div_y_pow_alpha[n]);
123 }
124 return operands_and_partials.value(logp);
125 }
126
127 template <typename T_y, typename T_shape, typename T_scale>
128 inline
129 typename return_type<T_y, T_shape, T_scale>::type
130 frechet_log(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
131 return frechet_log<false>(y, alpha, sigma);
132 }
133
134 }
135 }
136 #endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
check_positive_finite.hpp
check_positive.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:14
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_constant_struct.hpp
return_type.hpp
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:35
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
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::frechet_log
return_type< T_y, T_shape, T_scale >::type frechet_log(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Definition: frechet_log.hpp:33
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
VectorView.hpp
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:40
stan::math::check_positive
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
Definition: check_positive.hpp:66
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
length.hpp
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
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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:38

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