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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>
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 
65  using stan::is_vector;
70  using stan::math::log1m;
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
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
114  operands_and_partials(y, alpha, beta);
115 
117  T_partials_return, T_y>
118  log_y(length(y));
120  T_partials_return, T_y>
121  log1m_y(length(y));
122 
123  for (size_t n = 0; n < length(y); n++) {
125  log_y[n] = log(value_of(y_vec[n]));
127  log1m_y[n] = log1m(value_of(y_vec[n]));
128  }
129 
131  T_partials_return, T_scale_succ>
132  lgamma_alpha(length(alpha));
134  T_partials_return, T_scale_succ>
135  digamma_alpha(length(alpha));
136  for (size_t n = 0; n < length(alpha); n++) {
138  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
140  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
141  }
142 
144  T_partials_return, T_scale_fail>
145  lgamma_beta(length(beta));
147  T_partials_return, T_scale_fail>
148  digamma_beta(length(beta));
149 
150  for (size_t n = 0; n < length(beta); n++) {
152  lgamma_beta[n] = lgamma(value_of(beta_vec[n]));
154  digamma_beta[n] = digamma(value_of(beta_vec[n]));
155  }
156 
158  T_partials_return, T_scale_succ, T_scale_fail>
159  lgamma_alpha_beta(max_size(alpha, beta));
160 
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]);
170  lgamma_alpha_beta[n] = lgamma(alpha_beta);
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
183  logp += lgamma_alpha_beta[n];
185  logp -= lgamma_alpha[n];
187  logp -= lgamma_beta[n];
189  logp += (alpha_dbl-1.0) * log_y[n];
191  logp += (beta_dbl-1.0) * log1m_y[n];
192 
193  // gradients
195  operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl
196  + (beta_dbl-1)/(y_dbl-1);
198  operands_and_partials.d_x2[n]
199  += log_y[n] + digamma_alpha_beta[n] - digamma_alpha[n];
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>
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
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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)
const double LOG_ZERO
Definition: constants.hpp:175
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
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.
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:16
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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