Stan Math Library  2.20.0
reverse mode automatic differentiation
neg_binomial_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP
3 
13 #include <cmath>
14 #include <limits>
15 
16 namespace stan {
17 namespace math {
18 
19 template <typename T_n, typename T_shape, typename T_inv_scale>
21  const T_n& n, const T_shape& alpha, const T_inv_scale& beta) {
22  static const char* function = "neg_binomial_cdf";
24  T_partials_return;
25 
26  if (size_zero(n, alpha, beta))
27  return 1.0;
28 
29  T_partials_return P(1.0);
30 
31  check_positive_finite(function, "Shape parameter", alpha);
32  check_positive_finite(function, "Inverse scale parameter", beta);
33  check_consistent_sizes(function, "Failures variable", n, "Shape parameter",
34  alpha, "Inverse scale parameter", beta);
35 
36  scalar_seq_view<T_n> n_vec(n);
37  scalar_seq_view<T_shape> alpha_vec(alpha);
38  scalar_seq_view<T_inv_scale> beta_vec(beta);
39  size_t size = max_size(n, alpha, beta);
40 
41  operands_and_partials<T_shape, T_inv_scale> ops_partials(alpha, beta);
42 
43  // Explicit return for extreme values
44  // The gradients are technically ill-defined, but treated as zero
45  for (size_t i = 0; i < stan::length(n); i++) {
46  if (value_of(n_vec[i]) < 0)
47  return ops_partials.build(0.0);
48  }
49 
50  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
51  digamma_alpha_vec(stan::length(alpha));
52 
53  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
54  digamma_sum_vec(stan::length(alpha));
55 
57  for (size_t i = 0; i < stan::length(alpha); i++) {
58  const T_partials_return n_dbl = value_of(n_vec[i]);
59  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
60 
61  digamma_alpha_vec[i] = digamma(alpha_dbl);
62  digamma_sum_vec[i] = digamma(n_dbl + alpha_dbl + 1);
63  }
64  }
65 
66  for (size_t i = 0; i < size; i++) {
67  // Explicit results for extreme values
68  // The gradients are technically ill-defined, but treated as zero
69  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
70  return ops_partials.build(1.0);
71 
72  const T_partials_return n_dbl = value_of(n_vec[i]);
73  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
74  const T_partials_return beta_dbl = value_of(beta_vec[i]);
75 
76  const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
77  const T_partials_return d_dbl = 1.0 / ((1.0 + beta_dbl) * (1.0 + beta_dbl));
78 
79  const T_partials_return P_i = inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
80 
81  P *= P_i;
82 
84  ops_partials.edge1_.partials_[i]
85  += inc_beta_dda(alpha_dbl, n_dbl + 1, p_dbl, digamma_alpha_vec[i],
86  digamma_sum_vec[i])
87  / P_i;
88  }
89 
91  ops_partials.edge2_.partials_[i]
92  += inc_beta_ddz(alpha_dbl, n_dbl + 1.0, p_dbl) * d_dbl / P_i;
93  }
94 
96  for (size_t i = 0; i < stan::length(alpha); ++i)
97  ops_partials.edge1_.partials_[i] *= P;
98  }
99 
101  for (size_t i = 0; i < stan::length(beta); ++i)
102  ops_partials.edge2_.partials_[i] *= P;
103  }
104 
105  return ops_partials.build(P);
106 }
107 
108 } // namespace math
109 } // namespace stan
110 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
return_type< T_shape, T_inv_scale >::type neg_binomial_cdf(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
T inc_beta_dda(T a, T b, T z, T digamma_a, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a.
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
T inc_beta_ddz(T a, T b, T z)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z.
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
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
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 max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:21
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
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_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23

     [ Stan Home Page ] © 2011–2018, Stan Development Team.