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cauchy_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LOG_HPP
3
4 #include <boost/random/cauchy_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_finite.hpp>
9 #include <stan/math/prim/scal/err/check_not_nan.hpp>
10 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
11 #include <stan/math/prim/scal/fun/constants.hpp>
12 #include <stan/math/prim/scal/fun/square.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <stan/math/prim/scal/fun/log1p.hpp>
15 #include <stan/math/prim/scal/meta/include_summand.hpp>
16 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
17 #include <cmath>
18
19 namespace stan {
20
21 namespace math {
22
40 template <bool propto,
41 typename T_y, typename T_loc, typename T_scale>
42 typename return_type<T_y, T_loc, T_scale>::type
43 cauchy_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
44 static const char* function("stan::math::cauchy_log");
45 typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
46 T_partials_return;
47
48 using stan::is_constant_struct;
49 using stan::math::check_positive_finite;
50 using stan::math::check_finite;
51 using stan::math::check_not_nan;
52 using stan::math::check_consistent_sizes;
53 using stan::math::value_of;
54
55 // check if any vectors are zero length
56 if (!(stan::length(y)
57 && stan::length(mu)
58 && stan::length(sigma)))
59 return 0.0;
60
61 // set up return value accumulator
62 T_partials_return logp(0.0);
63
64 // validate args (here done over var, which should be OK)
65 check_not_nan(function, "Random variable", y);
66 check_finite(function, "Location parameter", mu);
67 check_positive_finite(function, "Scale parameter", sigma);
68 check_consistent_sizes(function,
69 "Random variable", y,
70 "Location parameter", mu,
71 "Scale parameter", sigma);
72
73 // check if no variables are involved and prop-to
74 if (!include_summand<propto, T_y, T_loc, T_scale>::value)
75 return 0.0;
76
77 using stan::math::log1p;
78 using stan::math::square;
79 using std::log;
80
81 // set up template expressions wrapping scalars into vector views
82 VectorView<const T_y> y_vec(y);
83 VectorView<const T_loc> mu_vec(mu);
84 VectorView<const T_scale> sigma_vec(sigma);
85 size_t N = max_size(y, mu, sigma);
86
87 VectorBuilder<true, T_partials_return, T_scale> inv_sigma(length(sigma));
88 VectorBuilder<true, T_partials_return,
89 T_scale> sigma_squared(length(sigma));
90 VectorBuilder<include_summand<propto, T_scale>::value,
91 T_partials_return, T_scale> log_sigma(length(sigma));
92 for (size_t i = 0; i < length(sigma); i++) {
93 const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
94 inv_sigma[i] = 1.0 / sigma_dbl;
95 sigma_squared[i] = sigma_dbl * sigma_dbl;
96 if (include_summand<propto, T_scale>::value) {
97 log_sigma[i] = log(sigma_dbl);
98 }
99 }
100
101 OperandsAndPartials<T_y, T_loc, T_scale>
102 operands_and_partials(y, mu, sigma);
103
104 for (size_t n = 0; n < N; n++) {
105 // pull out values of arguments
106 const T_partials_return y_dbl = value_of(y_vec[n]);
107 const T_partials_return mu_dbl = value_of(mu_vec[n]);
108
109 // reusable subexpression values
110 const T_partials_return y_minus_mu
111 = y_dbl - mu_dbl;
112 const T_partials_return y_minus_mu_squared
113 = y_minus_mu * y_minus_mu;
114 const T_partials_return y_minus_mu_over_sigma
115 = y_minus_mu * inv_sigma[n];
116 const T_partials_return y_minus_mu_over_sigma_squared
117 = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
118
119 // log probability
120 if (include_summand<propto>::value)
121 logp += NEG_LOG_PI;
122 if (include_summand<propto, T_scale>::value)
123 logp -= log_sigma[n];
124 if (include_summand<propto, T_y, T_loc, T_scale>::value)
125 logp -= log1p(y_minus_mu_over_sigma_squared);
126
127 // gradients
128 if (!is_constant_struct<T_y>::value)
129 operands_and_partials.d_x1[n] -= 2 * y_minus_mu
130 / (sigma_squared[n] + y_minus_mu_squared);
131 if (!is_constant_struct<T_loc>::value)
132 operands_and_partials.d_x2[n] += 2 * y_minus_mu
133 / (sigma_squared[n] + y_minus_mu_squared);
134 if (!is_constant_struct<T_scale>::value)
135 operands_and_partials.d_x3[n]
136 += (y_minus_mu_squared - sigma_squared[n])
137 * inv_sigma[n] / (sigma_squared[n] + y_minus_mu_squared);
138 }
139 return operands_and_partials.to_var(logp, y, mu, sigma);
140 }
141
142 template <typename T_y, typename T_loc, typename T_scale>
143 inline
144 typename return_type<T_y, T_loc, T_scale>::type
145 cauchy_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
146 return cauchy_log<false>(y, mu, sigma);
147 }
148
149
150 }
151 }
152 #endif
check_not_nan.hpp
stan::math::NEG_LOG_PI
const double NEG_LOG_PI
Definition: constants.hpp:186
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
square.hpp
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
stan::math::square
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
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
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::math::cauchy_log
return_type< T_y, T_loc, T_scale >::type cauchy_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) a...
Definition: cauchy_log.hpp:43
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
log1p.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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