Stan Math Library  2.14.0
reverse mode automatic differentiation
binomial_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CDF_HPP
3 
23 #include <boost/random/binomial_distribution.hpp>
24 #include <boost/random/variate_generator.hpp>
25 #include <cmath>
26 
27 namespace stan {
28  namespace math {
29 
30  template <typename T_n, typename T_N, typename T_prob>
32  binomial_cdf(const T_n& n, const T_N& N, const T_prob& theta) {
33  static const char* function("binomial_cdf");
35  T_partials_return;
36 
37  if (!(stan::length(n) && stan::length(N) && stan::length(theta)))
38  return 1.0;
39 
40  T_partials_return P(1.0);
41 
42  check_nonnegative(function, "Population size parameter", N);
43  check_finite(function, "Probability parameter", theta);
44  check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
45  check_consistent_sizes(function,
46  "Successes variable", n,
47  "Population size parameter", N,
48  "Probability parameter", theta);
49 
50  VectorView<const T_n> n_vec(n);
51  VectorView<const T_N> N_vec(N);
52  VectorView<const T_prob> theta_vec(theta);
53  size_t size = max_size(n, N, theta);
54 
55  using std::exp;
56  using std::pow;
57  using std::exp;
58 
59  OperandsAndPartials<T_prob> operands_and_partials(theta);
60 
61  // Explicit return for extreme values
62  // The gradients are technically ill-defined, but treated as zero
63  for (size_t i = 0; i < stan::length(n); i++) {
64  if (value_of(n_vec[i]) < 0)
65  return operands_and_partials.value(0.0);
66  }
67 
68  for (size_t i = 0; i < size; i++) {
69  // Explicit results for extreme values
70  // The gradients are technically ill-defined, but treated as zero
71  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
72  continue;
73  }
74 
75  const T_partials_return n_dbl = value_of(n_vec[i]);
76  const T_partials_return N_dbl = value_of(N_vec[i]);
77  const T_partials_return theta_dbl = value_of(theta_vec[i]);
78  const T_partials_return betafunc = exp(lbeta(N_dbl-n_dbl, n_dbl+1));
79  const T_partials_return Pi = inc_beta(N_dbl - n_dbl, n_dbl + 1,
80  1 - theta_dbl);
81 
82  P *= Pi;
83 
85  operands_and_partials.d_x1[i] -= pow(theta_dbl, n_dbl)
86  * pow(1-theta_dbl, N_dbl-n_dbl-1) / betafunc / Pi;
87  }
88 
90  for (size_t i = 0; i < stan::length(theta); ++i)
91  operands_and_partials.d_x1[i] *= P;
92  }
93 
94  return operands_and_partials.value(P);
95  }
96 
97  }
98 }
99 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
return_type< T_prob >::type binomial_cdf(const T_n &n, const T_N &N, const T_prob &theta)
void check_bounded(const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high)
Check if the value is between the low and high values, inclusively.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.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
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
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
VectorView< T_return_type, false, true > d_x1

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