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beta_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_LOG_HPP
3
4 #include <boost/math/special_functions/gamma.hpp>
5 #include <boost/random/gamma_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
7 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
8 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
9 #include <stan/math/prim/scal/err/check_less_or_equal.hpp>
10 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
11 #include <stan/math/prim/scal/err/check_not_nan.hpp>
12 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
13 #include <stan/math/prim/scal/fun/log1m.hpp>
14 #include <stan/math/prim/scal/fun/multiply_log.hpp>
15 #include <stan/math/prim/scal/fun/value_of.hpp>
16 #include <stan/math/prim/scal/fun/digamma.hpp>
17 #include <stan/math/prim/scal/fun/lgamma.hpp>
18 #include <stan/math/prim/scal/fun/lbeta.hpp>
19 #include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
20 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
21 #include <stan/math/prim/scal/fun/constants.hpp>
22 #include <stan/math/prim/scal/meta/include_summand.hpp>
23 #include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
24 #include <stan/math/prim/scal/fun/inc_beta.hpp>
25 #include <cmath>
26
27 namespace stan {
28
29 namespace math {
30
49 template <bool propto,
50 typename T_y, typename T_scale_succ, typename T_scale_fail>
51 typename return_type<T_y, T_scale_succ, T_scale_fail>::type
52 beta_log(const T_y& y,
53 const T_scale_succ& alpha, const T_scale_fail& beta) {
54 static const char* function("stan::math::beta_log");
55
56 typedef typename stan::partials_return_type<T_y,
57 T_scale_succ,
58 T_scale_fail>::type
59 T_partials_return;
60
61 using stan::math::digamma;
62 using stan::math::lgamma;
63
64 using stan::is_constant_struct;
65 using stan::is_vector;
66 using stan::math::check_positive_finite;
67 using stan::math::check_not_nan;
68 using stan::math::check_consistent_sizes;
69 using stan::math::include_summand;
70 using stan::math::log1m;
71 using stan::math::multiply_log;
72 using stan::math::value_of;
73 using stan::math::check_nonnegative;
74 using stan::math::check_less_or_equal;
75 using std::log;
76
77 // check if any vectors are zero length
78 if (!(stan::length(y)
79 && stan::length(alpha)
80 && stan::length(beta)))
81 return 0.0;
82
83 // set up return value accumulator
84 T_partials_return logp(0.0);
85
86 // validate args (here done over var, which should be OK)
87 check_positive_finite(function, "First shape parameter", alpha);
88 check_positive_finite(function, "Second shape parameter", beta);
89 check_not_nan(function, "Random variable", y);
90 check_consistent_sizes(function,
91 "Random variable", y,
92 "First shape parameter", alpha,
93 "Second shape parameter", beta);
94 check_nonnegative(function, "Random variable", y);
95 check_less_or_equal(function, "Random variable", y, 1);
96
97 // check if no variables are involved and prop-to
98 if (!include_summand<propto, T_y, T_scale_succ, T_scale_fail>::value)
99 return 0.0;
100
101 VectorView<const T_y> y_vec(y);
102 VectorView<const T_scale_succ> alpha_vec(alpha);
103 VectorView<const T_scale_fail> beta_vec(beta);
104 size_t N = max_size(y, alpha, beta);
105
106 for (size_t n = 0; n < N; n++) {
107 const T_partials_return y_dbl = value_of(y_vec[n]);
108 if (y_dbl < 0 || y_dbl > 1)
109 return LOG_ZERO;
110 }
111
112 // set up template expressions wrapping scalars into vector views
113 OperandsAndPartials<T_y, T_scale_succ, T_scale_fail>
114 operands_and_partials(y, alpha, beta);
115
116 VectorBuilder<include_summand<propto, T_y, T_scale_succ>::value,
117 T_partials_return, T_y>
118 log_y(length(y));
119 VectorBuilder<include_summand<propto, T_y, T_scale_fail>::value,
120 T_partials_return, T_y>
121 log1m_y(length(y));
122
123 for (size_t n = 0; n < length(y); n++) {
124 if (include_summand<propto, T_y, T_scale_succ>::value)
125 log_y[n] = log(value_of(y_vec[n]));
126 if (include_summand<propto, T_y, T_scale_fail>::value)
127 log1m_y[n] = log1m(value_of(y_vec[n]));
128 }
129
130 VectorBuilder<include_summand<propto, T_scale_succ>::value,
131 T_partials_return, T_scale_succ>
132 lgamma_alpha(length(alpha));
133 VectorBuilder<!is_constant_struct<T_scale_succ>::value,
134 T_partials_return, T_scale_succ>
135 digamma_alpha(length(alpha));
136 for (size_t n = 0; n < length(alpha); n++) {
137 if (include_summand<propto, T_scale_succ>::value)
138 lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
139 if (!is_constant_struct<T_scale_succ>::value)
140 digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
141 }
142
143 VectorBuilder<include_summand<propto, T_scale_fail>::value,
144 T_partials_return, T_scale_fail>
145 lgamma_beta(length(beta));
146 VectorBuilder<!is_constant_struct<T_scale_fail>::value,
147 T_partials_return, T_scale_fail>
148 digamma_beta(length(beta));
149
150 for (size_t n = 0; n < length(beta); n++) {
151 if (include_summand<propto, T_scale_fail>::value)
152 lgamma_beta[n] = lgamma(value_of(beta_vec[n]));
153 if (!is_constant_struct<T_scale_fail>::value)
154 digamma_beta[n] = digamma(value_of(beta_vec[n]));
155 }
156
157 VectorBuilder<include_summand<propto, T_scale_succ, T_scale_fail>::value,
158 T_partials_return, T_scale_succ, T_scale_fail>
159 lgamma_alpha_beta(max_size(alpha, beta));
160
161 VectorBuilder<contains_nonconstant_struct<T_scale_succ,
162 T_scale_fail>::value,
163 T_partials_return, T_scale_succ, T_scale_fail>
164 digamma_alpha_beta(max_size(alpha, beta));
165
166 for (size_t n = 0; n < max_size(alpha, beta); n++) {
167 const T_partials_return alpha_beta = value_of(alpha_vec[n])
168 + value_of(beta_vec[n]);
169 if (include_summand<propto, T_scale_succ, T_scale_fail>::value)
170 lgamma_alpha_beta[n] = lgamma(alpha_beta);
171 if (contains_nonconstant_struct<T_scale_succ, T_scale_fail>::value)
172 digamma_alpha_beta[n] = digamma(alpha_beta);
173 }
174
175 for (size_t n = 0; n < N; n++) {
176 // pull out values of arguments
177 const T_partials_return y_dbl = value_of(y_vec[n]);
178 const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
179 const T_partials_return beta_dbl = value_of(beta_vec[n]);
180
181 // log probability
182 if (include_summand<propto, T_scale_succ, T_scale_fail>::value)
183 logp += lgamma_alpha_beta[n];
184 if (include_summand<propto, T_scale_succ>::value)
185 logp -= lgamma_alpha[n];
186 if (include_summand<propto, T_scale_fail>::value)
187 logp -= lgamma_beta[n];
188 if (include_summand<propto, T_y, T_scale_succ>::value)
189 logp += (alpha_dbl-1.0) * log_y[n];
190 if (include_summand<propto, T_y, T_scale_fail>::value)
191 logp += (beta_dbl-1.0) * log1m_y[n];
192
193 // gradients
194 if (!is_constant_struct<T_y>::value)
195 operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl
196 + (beta_dbl-1)/(y_dbl-1);
197 if (!is_constant_struct<T_scale_succ>::value)
198 operands_and_partials.d_x2[n]
199 += log_y[n] + digamma_alpha_beta[n] - digamma_alpha[n];
200 if (!is_constant_struct<T_scale_fail>::value)
201 operands_and_partials.d_x3[n]
202 += log1m_y[n] + digamma_alpha_beta[n] - digamma_beta[n];
203 }
204 return operands_and_partials.to_var(logp, y, alpha, beta);
205 }
206
207 template <typename T_y, typename T_scale_succ, typename T_scale_fail>
208 inline typename return_type<T_y, T_scale_succ, T_scale_fail>::type
209 beta_log(const T_y& y, const T_scale_succ& alpha,
210 const T_scale_fail& beta) {
211 return beta_log<false>(y, alpha, beta);
212 }
213
214 }
215 }
216 #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
stan::math::beta_log
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_log(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
The log of the beta density for the specified scalar(s) given the specified sample size(s)...
Definition: beta_log.hpp:52
digamma.hpp
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::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::is_vector
Definition: is_vector.hpp:10
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::partials_return_type
Definition: partials_return_type.hpp:16
check_less_or_equal.hpp
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
log1m.hpp
stan::math::check_less_or_equal
bool check_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Return true if y is less or equal to high.
Definition: check_less_or_equal.hpp:81
stan::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
grad_reg_inc_beta.hpp
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
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
inc_beta.hpp
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
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::log1m
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:16
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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