Stan Math Library  2.20.0
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 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
34 template <typename T_n, typename T_N, typename T_prob>
35 typename return_type<T_prob>::type binomial_cdf(const T_n& n, const T_N& N,
36  const T_prob& theta) {
37  static const char* function = "binomial_cdf";
39  T_partials_return;
40 
41  if (size_zero(n, N, theta))
42  return 1.0;
43 
44  T_partials_return P(1.0);
45 
46  check_nonnegative(function, "Population size parameter", N);
47  check_finite(function, "Probability parameter", theta);
48  check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
49  check_consistent_sizes(function, "Successes variable", n,
50  "Population size parameter", N,
51  "Probability parameter", theta);
52 
53  scalar_seq_view<T_n> n_vec(n);
54  scalar_seq_view<T_N> N_vec(N);
55  scalar_seq_view<T_prob> theta_vec(theta);
56  size_t size = max_size(n, N, theta);
57 
58  using std::exp;
59  using std::pow;
60 
61  operands_and_partials<T_prob> ops_partials(theta);
62 
63  // Explicit return for extreme values
64  // The gradients are technically ill-defined, but treated as zero
65  for (size_t i = 0; i < stan::length(n); i++) {
66  if (value_of(n_vec[i]) < 0)
67  return ops_partials.build(0.0);
68  }
69 
70  for (size_t i = 0; i < size; i++) {
71  // Explicit results for extreme values
72  // The gradients are technically ill-defined, but treated as zero
73  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
74  continue;
75  }
76 
77  const T_partials_return n_dbl = value_of(n_vec[i]);
78  const T_partials_return N_dbl = value_of(N_vec[i]);
79  const T_partials_return theta_dbl = value_of(theta_vec[i]);
80  const T_partials_return betafunc = beta(N_dbl - n_dbl, n_dbl + 1);
81  const T_partials_return Pi
82  = inc_beta(N_dbl - n_dbl, n_dbl + 1, 1 - theta_dbl);
83 
84  P *= Pi;
85 
87  ops_partials.edge1_.partials_[i]
88  -= pow(theta_dbl, n_dbl) * pow(1 - theta_dbl, N_dbl - n_dbl - 1)
89  / betafunc / Pi;
90  }
91 
93  for (size_t i = 0; i < stan::length(theta); ++i)
94  ops_partials.edge1_.partials_[i] *= P;
95  }
96 
97  return ops_partials.build(P);
98 }
99 
100 } // namespace math
101 } // namespace stan
102 #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)
Returns the CDF for the binomial distribution evaluated at the specified success, population size...
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
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:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:18
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
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:16
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.
internal::ops_partials_edge< double, Op1 > edge1_

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