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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 <boost/random/student_t_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/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 <cmath>
23
24 namespace stan {
25
26 namespace math {
27
53 template <bool propto, typename T_y, typename T_dof,
54 typename T_loc, typename T_scale>
55 typename return_type<T_y, T_dof, T_loc, T_scale>::type
56 student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
57 const T_scale& sigma) {
58 static const char* function("stan::math::student_t_log");
59 typedef typename stan::partials_return_type<T_y, T_dof, T_loc,
60 T_scale>::type
61 T_partials_return;
62
63 using stan::math::check_positive_finite;
64 using stan::math::check_finite;
65 using stan::math::check_not_nan;
66 using stan::math::check_consistent_sizes;
67
68 // check if any vectors are zero length
69 if (!(stan::length(y)
70 && stan::length(nu)
71 && stan::length(mu)
72 && stan::length(sigma)))
73 return 0.0;
74
75 T_partials_return logp(0.0);
76
77 // validate args (here done over var, which should be OK)
78 check_not_nan(function, "Random variable", y);
79 check_positive_finite(function, "Degrees of freedom parameter", nu);
80 check_finite(function, "Location parameter", mu);
81 check_positive_finite(function, "Scale parameter", sigma);
82 check_consistent_sizes(function,
83 "Random variable", y,
84 "Degrees of freedom parameter", nu,
85 "Location parameter", mu,
86 "Scale parameter", sigma);
87
88 // check if no variables are involved and prop-to
89 if (!include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
90 return 0.0;
91
92 VectorView<const T_y> y_vec(y);
93 VectorView<const T_dof> nu_vec(nu);
94 VectorView<const T_loc> mu_vec(mu);
95 VectorView<const T_scale> sigma_vec(sigma);
96 size_t N = max_size(y, nu, mu, sigma);
97
98 using std::log;
99 using stan::math::digamma;
100 using stan::math::lgamma;
101 using stan::math::square;
102 using stan::math::value_of;
103 using std::log;
104
105 VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
106 T_partials_return, T_dof> half_nu(length(nu));
107 for (size_t i = 0; i < length(nu); i++)
108 if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
109 half_nu[i] = 0.5 * value_of(nu_vec[i]);
110
111 VectorBuilder<include_summand<propto, T_dof>::value,
112 T_partials_return, T_dof> lgamma_half_nu(length(nu));
113 VectorBuilder<include_summand<propto, T_dof>::value,
114 T_partials_return, T_dof>
115 lgamma_half_nu_plus_half(length(nu));
116 if (include_summand<propto, T_dof>::value) {
117 for (size_t i = 0; i < length(nu); i++) {
118 lgamma_half_nu[i] = lgamma(half_nu[i]);
119 lgamma_half_nu_plus_half[i] = lgamma(half_nu[i] + 0.5);
120 }
121 }
122
123 VectorBuilder<!is_constant_struct<T_dof>::value,
124 T_partials_return, T_dof> digamma_half_nu(length(nu));
125 VectorBuilder<!is_constant_struct<T_dof>::value,
126 T_partials_return, T_dof>
127 digamma_half_nu_plus_half(length(nu));
128 if (!is_constant_struct<T_dof>::value) {
129 for (size_t i = 0; i < length(nu); i++) {
130 digamma_half_nu[i] = digamma(half_nu[i]);
131 digamma_half_nu_plus_half[i] = digamma(half_nu[i] + 0.5);
132 }
133 }
134
135 VectorBuilder<include_summand<propto, T_dof>::value,
136 T_partials_return, T_dof> log_nu(length(nu));
137 for (size_t i = 0; i < length(nu); i++)
138 if (include_summand<propto, T_dof>::value)
139 log_nu[i] = log(value_of(nu_vec[i]));
140
141 VectorBuilder<include_summand<propto, T_scale>::value,
142 T_partials_return, T_scale> log_sigma(length(sigma));
143 for (size_t i = 0; i < length(sigma); i++)
144 if (include_summand<propto, T_scale>::value)
145 log_sigma[i] = log(value_of(sigma_vec[i]));
146
147 VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
148 T_partials_return, T_y, T_dof, T_loc, T_scale>
149 square_y_minus_mu_over_sigma__over_nu(N);
150
151 VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
152 T_partials_return, T_y, T_dof, T_loc, T_scale>
153 log1p_exp(N);
154
155 for (size_t i = 0; i < N; i++)
156 if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value) {
157 const T_partials_return y_dbl = value_of(y_vec[i]);
158 const T_partials_return mu_dbl = value_of(mu_vec[i]);
159 const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
160 const T_partials_return nu_dbl = value_of(nu_vec[i]);
161 square_y_minus_mu_over_sigma__over_nu[i]
162 = square((y_dbl - mu_dbl) / sigma_dbl) / nu_dbl;
163 log1p_exp[i] = log1p(square_y_minus_mu_over_sigma__over_nu[i]);
164 }
165
166 OperandsAndPartials<T_y, T_dof, T_loc, T_scale>
167 operands_and_partials(y, nu, mu, sigma);
168 for (size_t n = 0; n < N; n++) {
169 const T_partials_return y_dbl = value_of(y_vec[n]);
170 const T_partials_return mu_dbl = value_of(mu_vec[n]);
171 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
172 const T_partials_return nu_dbl = value_of(nu_vec[n]);
173 if (include_summand<propto>::value)
174 logp += NEG_LOG_SQRT_PI;
175 if (include_summand<propto, T_dof>::value)
176 logp += lgamma_half_nu_plus_half[n] - lgamma_half_nu[n]
177 - 0.5 * log_nu[n];
178 if (include_summand<propto, T_scale>::value)
179 logp -= log_sigma[n];
180 if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
181 logp -= (half_nu[n] + 0.5)
182 * log1p_exp[n];
183
184 if (!is_constant_struct<T_y>::value) {
185 operands_and_partials.d_x1[n]
186 += -(half_nu[n]+0.5)
187 * 1.0 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
188 * (2.0 * (y_dbl - mu_dbl) / square(sigma_dbl) / nu_dbl);
189 }
190 if (!is_constant_struct<T_dof>::value) {
191 const T_partials_return inv_nu = 1.0 / nu_dbl;
192 operands_and_partials.d_x2[n]
193 += 0.5*digamma_half_nu_plus_half[n] - 0.5*digamma_half_nu[n]
194 - 0.5 * inv_nu
195 - 0.5*log1p_exp[n]
196 + (half_nu[n] + 0.5)
197 * (1.0/(1.0 + square_y_minus_mu_over_sigma__over_nu[n])
198 * square_y_minus_mu_over_sigma__over_nu[n] * inv_nu);
199 }
200 if (!is_constant_struct<T_loc>::value) {
201 operands_and_partials.d_x3[n]
202 -= (half_nu[n] + 0.5)
203 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
204 * (2.0 * (mu_dbl - y_dbl) / (sigma_dbl*sigma_dbl*nu_dbl));
205 }
206 if (!is_constant_struct<T_scale>::value) {
207 const T_partials_return inv_sigma = 1.0 / sigma_dbl;
208 operands_and_partials.d_x4[n]
209 += -inv_sigma
210 + (nu_dbl + 1.0) / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
211 * (square_y_minus_mu_over_sigma__over_nu[n] * inv_sigma);
212 }
213 }
214 return operands_and_partials.to_var(logp, y, nu, mu, sigma);
215 }
216
217 template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
218 inline
219 typename return_type<T_y, T_dof, T_loc, T_scale>::type
220 student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
221 const T_scale& sigma) {
222 return student_t_log<false>(y, nu, mu, sigma);
223 }
224 }
225 }
226 #endif
check_not_nan.hpp
lgamma.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
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
digamma.hpp
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::math::NEG_LOG_SQRT_PI
const double NEG_LOG_SQRT_PI
Definition: constants.hpp:189
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::partials_return_type
Definition: partials_return_type.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
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:62
stan::VectorBuilder
Definition: VectorBuilder.hpp:61
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::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::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:56
inc_beta.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
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::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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