Stan Math Library  2.10.0
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 
24 #include <boost/random/binomial_distribution.hpp>
25 #include <boost/random/variate_generator.hpp>
26 
27 
28 namespace stan {
29 
30  namespace math {
31 
32  // BinomialLogit(n|N, alpha) [N >= 0; 0 <= n <= N]
33  // BinomialLogit(n|N, alpha) = Binomial(n|N, inv_logit(alpha))
34  template <bool propto,
35  typename T_n,
36  typename T_N,
37  typename T_prob>
38  typename return_type<T_prob>::type
39  binomial_logit_log(const T_n& n,
40  const T_N& N,
41  const T_prob& alpha) {
43  T_partials_return;
44 
45  static const char* function("stan::math::binomial_logit_log");
46 
53 
54  // check if any vectors are zero length
55  if (!(stan::length(n)
56  && stan::length(N)
57  && stan::length(alpha)))
58  return 0.0;
59 
60  T_partials_return logp = 0;
61  check_bounded(function, "Successes variable", n, 0, N);
62  check_nonnegative(function, "Population size parameter", N);
63  check_finite(function, "Probability parameter", alpha);
64  check_consistent_sizes(function,
65  "Successes variable", n,
66  "Population size parameter", N,
67  "Probability parameter", alpha);
68 
69  // check if no variables are involved and prop-to
71  return 0.0;
72 
73  // set up template expressions wrapping scalars into vector views
74  VectorView<const T_n> n_vec(n);
75  VectorView<const T_N> N_vec(N);
76  VectorView<const T_prob> alpha_vec(alpha);
77  size_t size = max_size(n, N, alpha);
78 
79  OperandsAndPartials<T_prob> operands_and_partials(alpha);
80 
84 
86  for (size_t i = 0; i < size; ++i)
87  logp += binomial_coefficient_log(N_vec[i], n_vec[i]);
88  }
89 
91  log_inv_logit_alpha(length(alpha));
92  for (size_t i = 0; i < length(alpha); ++i)
93  log_inv_logit_alpha[i] = log_inv_logit(value_of(alpha_vec[i]));
94 
96  log_inv_logit_neg_alpha(length(alpha));
97  for (size_t i = 0; i < length(alpha); ++i)
98  log_inv_logit_neg_alpha[i] = log_inv_logit(-value_of(alpha_vec[i]));
99 
100  for (size_t i = 0; i < size; ++i)
101  logp += n_vec[i] * log_inv_logit_alpha[i]
102  + (N_vec[i] - n_vec[i]) * log_inv_logit_neg_alpha[i];
103 
104  if (length(alpha) == 1) {
105  T_partials_return temp1 = 0;
106  T_partials_return temp2 = 0;
107  for (size_t i = 0; i < size; ++i) {
108  temp1 += n_vec[i];
109  temp2 += N_vec[i] - n_vec[i];
110  }
112  operands_and_partials.d_x1[0]
113  += temp1 * inv_logit(-value_of(alpha_vec[0]))
114  - temp2 * inv_logit(value_of(alpha_vec[0]));
115  }
116  } else {
118  for (size_t i = 0; i < size; ++i)
119  operands_and_partials.d_x1[i]
120  += n_vec[i] * inv_logit(-value_of(alpha_vec[i]))
121  - (N_vec[i] - n_vec[i]) * inv_logit(value_of(alpha_vec[i]));
122  }
123  }
124 
125  return operands_and_partials.value(logp);
126  }
127 
128  template <typename T_n,
129  typename T_N,
130  typename T_prob>
131  inline
133  binomial_logit_log(const T_n& n,
134  const T_N& N,
135  const T_prob& alpha) {
136  return binomial_logit_log<false>(n, N, alpha);
137  }
138  }
139 }
140 #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
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
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.
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.
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.
VectorBuilder allocates type T1 values to be used as intermediate values.
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 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
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)
VectorView< T_return_type, false, true > d_x1

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