Stan Math Library  2.10.0
reverse mode automatic differentiation
binomial_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_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  // Binomial(n|N, theta) [N >= 0; 0 <= n <= N; 0 <= theta <= 1]
33  template <bool propto,
34  typename T_n,
35  typename T_N,
36  typename T_prob>
37  typename return_type<T_prob>::type
38  binomial_log(const T_n& n,
39  const T_N& N,
40  const T_prob& theta) {
42  T_partials_return;
43 
44  static const char* function("stan::math::binomial_log");
45 
52 
53  // check if any vectors are zero length
54  if (!(stan::length(n)
55  && stan::length(N)
56  && stan::length(theta)))
57  return 0.0;
58 
59  T_partials_return logp = 0;
60  check_bounded(function, "Successes variable", n, 0, N);
61  check_nonnegative(function, "Population size parameter", N);
62  check_finite(function, "Probability parameter", theta);
63  check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
64  check_consistent_sizes(function,
65  "Successes variable", n,
66  "Population size parameter", N,
67  "Probability parameter", theta);
68 
69 
70  // check if no variables are involved and prop-to
72  return 0.0;
73 
74  // set up template expressions wrapping scalars into vector views
75  VectorView<const T_n> n_vec(n);
76  VectorView<const T_N> N_vec(N);
77  VectorView<const T_prob> theta_vec(theta);
78  size_t size = max_size(n, N, theta);
79 
80  OperandsAndPartials<T_prob> operands_and_partials(theta);
81 
84  using stan::math::log1m;
85 
87  for (size_t i = 0; i < size; ++i)
88  logp += binomial_coefficient_log(N_vec[i], n_vec[i]);
89  }
90 
92  for (size_t i = 0; i < length(theta); ++i)
93  log1m_theta[i] = log1m(value_of(theta_vec[i]));
94 
95  // no test for include_summand because return if not live
96  for (size_t i = 0; i < size; ++i)
97  logp += multiply_log(n_vec[i], value_of(theta_vec[i]))
98  + (N_vec[i] - n_vec[i]) * log1m_theta[i];
99 
100  if (length(theta) == 1) {
101  T_partials_return temp1 = 0;
102  T_partials_return temp2 = 0;
103  for (size_t i = 0; i < size; ++i) {
104  temp1 += n_vec[i];
105  temp2 += N_vec[i] - n_vec[i];
106  }
108  operands_and_partials.d_x1[0]
109  += temp1 / value_of(theta_vec[0])
110  - temp2 / (1.0 - value_of(theta_vec[0]));
111  }
112  } else {
114  for (size_t i = 0; i < size; ++i)
115  operands_and_partials.d_x1[i]
116  += n_vec[i] / value_of(theta_vec[i])
117  - (N_vec[i] - n_vec[i]) / (1.0 - value_of(theta_vec[i]));
118  }
119  }
120 
121  return operands_and_partials.value(logp);
122  }
123 
124  template <typename T_n,
125  typename T_N,
126  typename T_prob>
127  inline
129  binomial_log(const T_n& n,
130  const T_N& N,
131  const T_prob& theta) {
132  return binomial_log<false>(n, N, theta);
133  }
134 
135  }
136 }
137 #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.
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.
return_type< T_prob >::type binomial_log(const T_n &n, const T_N &N, const T_prob &theta)
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.
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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
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
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:16
VectorView< T_return_type, false, true > d_x1

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