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student_t_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LOG_HPP
3
4 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
5 #include <stan/math/prim/scal/meta/partials_return_type.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/lbeta.hpp>
15 #include <stan/math/prim/scal/fun/lgamma.hpp>
16 #include <stan/math/prim/scal/fun/digamma.hpp>
17 #include <stan/math/prim/scal/meta/length.hpp>
18 #include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
19 #include <stan/math/prim/scal/fun/inc_beta.hpp>
20 #include <stan/math/prim/scal/meta/include_summand.hpp>
21 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
22 #include <boost/random/student_t_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25
26 namespace stan {
27 namespace math {
28
54 template <bool propto, typename T_y, typename T_dof,
55 typename T_loc, typename T_scale>
56 typename return_type<T_y, T_dof, T_loc, T_scale>::type
57 student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
58 const T_scale& sigma) {
59 static const char* function("student_t_log");
60 typedef typename stan::partials_return_type<T_y, T_dof, T_loc,
61 T_scale>::type
62 T_partials_return;
63
64 if (!(stan::length(y)
65 && stan::length(nu)
66 && stan::length(mu)
67 && stan::length(sigma)))
68 return 0.0;
69
70 T_partials_return logp(0.0);
71
72 check_not_nan(function, "Random variable", y);
73 check_positive_finite(function, "Degrees of freedom parameter", nu);
74 check_finite(function, "Location parameter", mu);
75 check_positive_finite(function, "Scale parameter", sigma);
76 check_consistent_sizes(function,
77 "Random variable", y,
78 "Degrees of freedom parameter", nu,
79 "Location parameter", mu,
80 "Scale parameter", sigma);
81
82 if (!include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
83 return 0.0;
84
85 VectorView<const T_y> y_vec(y);
86 VectorView<const T_dof> nu_vec(nu);
87 VectorView<const T_loc> mu_vec(mu);
88 VectorView<const T_scale> sigma_vec(sigma);
89 size_t N = max_size(y, nu, mu, sigma);
90
91 using std::log;
92 using std::log;
93
94 VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
95 T_partials_return, T_dof> half_nu(length(nu));
96 for (size_t i = 0; i < length(nu); i++)
97 if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
98 half_nu[i] = 0.5 * value_of(nu_vec[i]);
99
100 VectorBuilder<include_summand<propto, T_dof>::value,
101 T_partials_return, T_dof> lgamma_half_nu(length(nu));
102 VectorBuilder<include_summand<propto, T_dof>::value,
103 T_partials_return, T_dof>
104 lgamma_half_nu_plus_half(length(nu));
105 if (include_summand<propto, T_dof>::value) {
106 for (size_t i = 0; i < length(nu); i++) {
107 lgamma_half_nu[i] = lgamma(half_nu[i]);
108 lgamma_half_nu_plus_half[i] = lgamma(half_nu[i] + 0.5);
109 }
110 }
111
112 VectorBuilder<!is_constant_struct<T_dof>::value,
113 T_partials_return, T_dof> digamma_half_nu(length(nu));
114 VectorBuilder<!is_constant_struct<T_dof>::value,
115 T_partials_return, T_dof>
116 digamma_half_nu_plus_half(length(nu));
117 if (!is_constant_struct<T_dof>::value) {
118 for (size_t i = 0; i < length(nu); i++) {
119 digamma_half_nu[i] = digamma(half_nu[i]);
120 digamma_half_nu_plus_half[i] = digamma(half_nu[i] + 0.5);
121 }
122 }
123
124 VectorBuilder<include_summand<propto, T_dof>::value,
125 T_partials_return, T_dof> log_nu(length(nu));
126 for (size_t i = 0; i < length(nu); i++)
127 if (include_summand<propto, T_dof>::value)
128 log_nu[i] = log(value_of(nu_vec[i]));
129
130 VectorBuilder<include_summand<propto, T_scale>::value,
131 T_partials_return, T_scale> log_sigma(length(sigma));
132 for (size_t i = 0; i < length(sigma); i++)
133 if (include_summand<propto, T_scale>::value)
134 log_sigma[i] = log(value_of(sigma_vec[i]));
135
136 VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
137 T_partials_return, T_y, T_dof, T_loc, T_scale>
138 square_y_minus_mu_over_sigma__over_nu(N);
139
140 VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
141 T_partials_return, T_y, T_dof, T_loc, T_scale>
142 log1p_exp(N);
143
144 for (size_t i = 0; i < N; i++)
145 if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value) {
146 const T_partials_return y_dbl = value_of(y_vec[i]);
147 const T_partials_return mu_dbl = value_of(mu_vec[i]);
148 const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
149 const T_partials_return nu_dbl = value_of(nu_vec[i]);
150 square_y_minus_mu_over_sigma__over_nu[i]
151 = square((y_dbl - mu_dbl) / sigma_dbl) / nu_dbl;
152 log1p_exp[i] = log1p(square_y_minus_mu_over_sigma__over_nu[i]);
153 }
154
155 OperandsAndPartials<T_y, T_dof, T_loc, T_scale>
156 operands_and_partials(y, nu, mu, sigma);
157 for (size_t n = 0; n < N; n++) {
158 const T_partials_return y_dbl = value_of(y_vec[n]);
159 const T_partials_return mu_dbl = value_of(mu_vec[n]);
160 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
161 const T_partials_return nu_dbl = value_of(nu_vec[n]);
162 if (include_summand<propto>::value)
163 logp += NEG_LOG_SQRT_PI;
164 if (include_summand<propto, T_dof>::value)
165 logp += lgamma_half_nu_plus_half[n] - lgamma_half_nu[n]
166 - 0.5 * log_nu[n];
167 if (include_summand<propto, T_scale>::value)
168 logp -= log_sigma[n];
169 if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
170 logp -= (half_nu[n] + 0.5)
171 * log1p_exp[n];
172
173 if (!is_constant_struct<T_y>::value) {
174 operands_and_partials.d_x1[n]
175 += -(half_nu[n]+0.5)
176 * 1.0 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
177 * (2.0 * (y_dbl - mu_dbl) / square(sigma_dbl) / nu_dbl);
178 }
179 if (!is_constant_struct<T_dof>::value) {
180 const T_partials_return inv_nu = 1.0 / nu_dbl;
181 operands_and_partials.d_x2[n]
182 += 0.5*digamma_half_nu_plus_half[n] - 0.5*digamma_half_nu[n]
183 - 0.5 * inv_nu
184 - 0.5*log1p_exp[n]
185 + (half_nu[n] + 0.5)
186 * (1.0/(1.0 + square_y_minus_mu_over_sigma__over_nu[n])
187 * square_y_minus_mu_over_sigma__over_nu[n] * inv_nu);
188 }
189 if (!is_constant_struct<T_loc>::value) {
190 operands_and_partials.d_x3[n]
191 -= (half_nu[n] + 0.5)
192 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
193 * (2.0 * (mu_dbl - y_dbl) / (sigma_dbl*sigma_dbl*nu_dbl));
194 }
195 if (!is_constant_struct<T_scale>::value) {
196 const T_partials_return inv_sigma = 1.0 / sigma_dbl;
197 operands_and_partials.d_x4[n]
198 += -inv_sigma
199 + (nu_dbl + 1.0) / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
200 * (square_y_minus_mu_over_sigma__over_nu[n] * inv_sigma);
201 }
202 }
203 return operands_and_partials.value(logp);
204 }
205
206 template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
207 inline
208 typename return_type<T_y, T_dof, T_loc, T_scale>::type
209 student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
210 const T_scale& sigma) {
211 return student_t_log<false>(y, nu, mu, sigma);
212 }
213
214 }
215 }
216 #endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
lgamma.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:14
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:60
check_positive_finite.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
digamma.hpp
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::math::NEG_LOG_SQRT_PI
const double NEG_LOG_SQRT_PI
Definition: constants.hpp:186
square.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.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
stan::math::square
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:14
include_summand.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::partials_return_type
Definition: partials_return_type.hpp:16
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:40
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
length.hpp
grad_reg_inc_beta.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:60
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
constants.hpp
stan::math::log1p_exp
fvar< T > log1p_exp(const fvar< T > &x)
Definition: log1p_exp.hpp:13
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
lbeta.hpp
stan::math::log1p
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:15
stan::math::student_t_log
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_log(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
The log of the Student-t density for the given y, nu, mean, and scale parameter.
Definition: student_t_log.hpp:57
inc_beta.hpp
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
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
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15
stan::math::OperandsAndPartials::d_x4
VectorView< T_return_type, false, true > d_x4
Definition: OperandsAndPartials.hpp:41

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