Stan Math Library  2.9.0
reverse mode automatic differentiation
binomial_logit_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LOGIT_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LOGIT_LOG_HPP
3 
4 #include <boost/random/binomial_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
24 
25 
26 namespace stan {
27 
28  namespace math {
29 
30  // BinomialLogit(n|N, alpha) [N >= 0; 0 <= n <= N]
31  // BinomialLogit(n|N, alpha) = Binomial(n|N, inv_logit(alpha))
32  template <bool propto,
33  typename T_n,
34  typename T_N,
35  typename T_prob>
36  typename return_type<T_prob>::type
37  binomial_logit_log(const T_n& n,
38  const T_N& N,
39  const T_prob& alpha) {
41  T_partials_return;
42 
43  static const char* function("stan::math::binomial_logit_log");
44 
51 
52  // check if any vectors are zero length
53  if (!(stan::length(n)
54  && stan::length(N)
55  && stan::length(alpha)))
56  return 0.0;
57 
58  T_partials_return logp = 0;
59  check_bounded(function, "Successes variable", n, 0, N);
60  check_nonnegative(function, "Population size parameter", N);
61  check_finite(function, "Probability parameter", alpha);
62  check_consistent_sizes(function,
63  "Successes variable", n,
64  "Population size parameter", N,
65  "Probability parameter", alpha);
66 
67  // check if no variables are involved and prop-to
69  return 0.0;
70 
71  // set up template expressions wrapping scalars into vector views
72  VectorView<const T_n> n_vec(n);
73  VectorView<const T_N> N_vec(N);
74  VectorView<const T_prob> alpha_vec(alpha);
75  size_t size = max_size(n, N, alpha);
76 
77  OperandsAndPartials<T_prob> operands_and_partials(alpha);
78 
82 
84  for (size_t i = 0; i < size; ++i)
85  logp += binomial_coefficient_log(N_vec[i], n_vec[i]);
86  }
87 
89  log_inv_logit_alpha(length(alpha));
90  for (size_t i = 0; i < length(alpha); ++i)
91  log_inv_logit_alpha[i] = log_inv_logit(value_of(alpha_vec[i]));
92 
94  log_inv_logit_neg_alpha(length(alpha));
95  for (size_t i = 0; i < length(alpha); ++i)
96  log_inv_logit_neg_alpha[i] = log_inv_logit(-value_of(alpha_vec[i]));
97 
98  for (size_t i = 0; i < size; ++i)
99  logp += n_vec[i] * log_inv_logit_alpha[i]
100  + (N_vec[i] - n_vec[i]) * log_inv_logit_neg_alpha[i];
101 
102  if (length(alpha) == 1) {
103  T_partials_return temp1 = 0;
104  T_partials_return temp2 = 0;
105  for (size_t i = 0; i < size; ++i) {
106  temp1 += n_vec[i];
107  temp2 += N_vec[i] - n_vec[i];
108  }
110  operands_and_partials.d_x1[0]
111  += temp1 * inv_logit(-value_of(alpha_vec[0]))
112  - temp2 * inv_logit(value_of(alpha_vec[0]));
113  }
114  } else {
116  for (size_t i = 0; i < size; ++i)
117  operands_and_partials.d_x1[i]
118  += n_vec[i] * inv_logit(-value_of(alpha_vec[i]))
119  - (N_vec[i] - n_vec[i]) * inv_logit(value_of(alpha_vec[i]));
120  }
121  }
122 
123  return operands_and_partials.to_var(logp, alpha);
124  }
125 
126  template <typename T_n,
127  typename T_N,
128  typename T_prob>
129  inline
131  binomial_logit_log(const T_n& n,
132  const T_N& N,
133  const T_prob& alpha) {
134  return binomial_logit_log<false>(n, N, alpha);
135  }
136  }
137 }
138 #endif
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > inv_logit(const fvar< T > &x)
Definition: inv_logit.hpp:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
bool check_bounded(const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high)
Return true if the value is between the low and high values, inclusively.
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)
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...
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_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
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 metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
fvar< T > log_inv_logit(const fvar< T > &x)
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
return_type< T_prob >::type binomial_logit_log(const T_n &n, const T_N &N, const T_prob &alpha)

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