Stan Math Library  2.11.0
reverse mode automatic differentiation
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 
24 #include <boost/math/special_functions/gamma.hpp>
25 #include <boost/random/gamma_distribution.hpp>
26 #include <boost/random/variate_generator.hpp>
27 #include <cmath>
28 
29 namespace stan {
30 
31  namespace math {
32 
51  template <bool propto,
52  typename T_y, typename T_scale_succ, typename T_scale_fail>
53  typename return_type<T_y, T_scale_succ, T_scale_fail>::type
54  beta_log(const T_y& y,
55  const T_scale_succ& alpha, const T_scale_fail& beta) {
56  static const char* function("stan::math::beta_log");
57 
58  typedef typename stan::partials_return_type<T_y,
59  T_scale_succ,
60  T_scale_fail>::type
61  T_partials_return;
62 
63  using stan::math::digamma;
64  using stan::math::lgamma;
65 
67  using stan::is_vector;
72  using stan::math::log1m;
77  using std::log;
78 
79  // check if any vectors are zero length
80  if (!(stan::length(y)
81  && stan::length(alpha)
82  && stan::length(beta)))
83  return 0.0;
84 
85  // set up return value accumulator
86  T_partials_return logp(0.0);
87 
88  // validate args (here done over var, which should be OK)
89  check_positive_finite(function, "First shape parameter", alpha);
90  check_positive_finite(function, "Second shape parameter", beta);
91  check_not_nan(function, "Random variable", y);
92  check_consistent_sizes(function,
93  "Random variable", y,
94  "First shape parameter", alpha,
95  "Second shape parameter", beta);
96  check_nonnegative(function, "Random variable", y);
97  check_less_or_equal(function, "Random variable", y, 1);
98 
99  // check if no variables are involved and prop-to
101  return 0.0;
102 
103  VectorView<const T_y> y_vec(y);
104  VectorView<const T_scale_succ> alpha_vec(alpha);
105  VectorView<const T_scale_fail> beta_vec(beta);
106  size_t N = max_size(y, alpha, beta);
107 
108  for (size_t n = 0; n < N; n++) {
109  const T_partials_return y_dbl = value_of(y_vec[n]);
110  if (y_dbl < 0 || y_dbl > 1)
111  return LOG_ZERO;
112  }
113 
114  // set up template expressions wrapping scalars into vector views
116  operands_and_partials(y, alpha, beta);
117 
119  T_partials_return, T_y>
120  log_y(length(y));
122  T_partials_return, T_y>
123  log1m_y(length(y));
124 
125  for (size_t n = 0; n < length(y); n++) {
127  log_y[n] = log(value_of(y_vec[n]));
129  log1m_y[n] = log1m(value_of(y_vec[n]));
130  }
131 
133  T_partials_return, T_scale_succ>
134  lgamma_alpha(length(alpha));
136  T_partials_return, T_scale_succ>
137  digamma_alpha(length(alpha));
138  for (size_t n = 0; n < length(alpha); n++) {
140  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
142  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
143  }
144 
146  T_partials_return, T_scale_fail>
147  lgamma_beta(length(beta));
149  T_partials_return, T_scale_fail>
150  digamma_beta(length(beta));
151 
152  for (size_t n = 0; n < length(beta); n++) {
154  lgamma_beta[n] = lgamma(value_of(beta_vec[n]));
156  digamma_beta[n] = digamma(value_of(beta_vec[n]));
157  }
158 
160  T_partials_return, T_scale_succ, T_scale_fail>
161  lgamma_alpha_beta(max_size(alpha, beta));
162 
164  T_scale_fail>::value,
165  T_partials_return, T_scale_succ, T_scale_fail>
166  digamma_alpha_beta(max_size(alpha, beta));
167 
168  for (size_t n = 0; n < max_size(alpha, beta); n++) {
169  const T_partials_return alpha_beta = value_of(alpha_vec[n])
170  + value_of(beta_vec[n]);
172  lgamma_alpha_beta[n] = lgamma(alpha_beta);
174  digamma_alpha_beta[n] = digamma(alpha_beta);
175  }
176 
177  for (size_t n = 0; n < N; n++) {
178  // pull out values of arguments
179  const T_partials_return y_dbl = value_of(y_vec[n]);
180  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
181  const T_partials_return beta_dbl = value_of(beta_vec[n]);
182 
183  // log probability
185  logp += lgamma_alpha_beta[n];
187  logp -= lgamma_alpha[n];
189  logp -= lgamma_beta[n];
191  logp += (alpha_dbl-1.0) * log_y[n];
193  logp += (beta_dbl-1.0) * log1m_y[n];
194 
195  // gradients
197  operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl
198  + (beta_dbl-1)/(y_dbl-1);
200  operands_and_partials.d_x2[n]
201  += log_y[n] + digamma_alpha_beta[n] - digamma_alpha[n];
203  operands_and_partials.d_x3[n]
204  += log1m_y[n] + digamma_alpha_beta[n] - digamma_beta[n];
205  }
206  return operands_and_partials.value(logp);
207  }
208 
209  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
211  beta_log(const T_y& y, const T_scale_succ& alpha,
212  const T_scale_fail& beta) {
213  return beta_log<false>(y, alpha, beta);
214  }
215 
216  }
217 }
218 #endif
VectorView< T_return_type, false, true > d_x2
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:54
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
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)
VectorBuilder allocates type T1 values to be used as intermediate values.
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.
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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
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
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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