Stan Math Library  2.14.0
reverse mode automatic differentiation
neg_binomial_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CDF_HPP
3 
19 #include <cmath>
20 #include <limits>
21 
22 namespace stan {
23  namespace math {
24 
25  template <typename T_n, typename T_shape,
26  typename T_inv_scale>
28  neg_binomial_cdf(const T_n& n, const T_shape& alpha,
29  const T_inv_scale& beta) {
30  static const char* function("neg_binomial_cdf");
31  typedef typename stan::partials_return_type<T_n, T_shape,
32  T_inv_scale>::type
33  T_partials_return;
34 
35  if (!(stan::length(n) && stan::length(alpha) && stan::length(beta)))
36  return 1.0;
37 
38  T_partials_return P(1.0);
39 
40  check_positive_finite(function, "Shape parameter", alpha);
41  check_positive_finite(function, "Inverse scale parameter", beta);
42  check_consistent_sizes(function,
43  "Failures variable", n,
44  "Shape parameter", alpha,
45  "Inverse scale parameter", beta);
46 
47  VectorView<const T_n> n_vec(n);
48  VectorView<const T_shape> alpha_vec(alpha);
49  VectorView<const T_inv_scale> beta_vec(beta);
50  size_t size = max_size(n, alpha, beta);
51 
53  operands_and_partials(alpha, beta);
54 
55  // Explicit return for extreme values
56  // The gradients are technically ill-defined, but treated as zero
57  for (size_t i = 0; i < stan::length(n); i++) {
58  if (value_of(n_vec[i]) < 0)
59  return operands_and_partials.value(0.0);
60  }
61 
63  T_partials_return, T_shape>
64  digamma_alpha_vec(stan::length(alpha));
65 
67  T_partials_return, T_shape>
68  digamma_sum_vec(stan::length(alpha));
69 
71  for (size_t i = 0; i < stan::length(alpha); i++) {
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 
75  digamma_alpha_vec[i] = digamma(alpha_dbl);
76  digamma_sum_vec[i] = digamma(n_dbl + alpha_dbl + 1);
77  }
78  }
79 
80  for (size_t i = 0; i < size; i++) {
81  // Explicit results for extreme values
82  // The gradients are technically ill-defined, but treated as zero
83  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
84  return operands_and_partials.value(1.0);
85 
86  const T_partials_return n_dbl = value_of(n_vec[i]);
87  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
88  const T_partials_return beta_dbl = value_of(beta_vec[i]);
89 
90  const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
91  const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
92  * (1.0 + beta_dbl) );
93 
94  const T_partials_return P_i =
95  inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
96 
97  P *= P_i;
98 
100  operands_and_partials.d_x1[i]
101  += inc_beta_dda(alpha_dbl, n_dbl + 1, p_dbl,
102  digamma_alpha_vec[i],
103  digamma_sum_vec[i]) / P_i;
104  }
105 
107  operands_and_partials.d_x2[i] +=
108  inc_beta_ddz(alpha_dbl, n_dbl + 1.0, p_dbl) * d_dbl / P_i;
109  }
110 
112  for (size_t i = 0; i < stan::length(alpha); ++i)
113  operands_and_partials.d_x1[i] *= P;
114  }
115 
117  for (size_t i = 0; i < stan::length(beta); ++i)
118  operands_and_partials.d_x2[i] *= P;
119  }
120 
121  return operands_and_partials.value(P);
122  }
123 
124  }
125 }
126 #endif
VectorView< T_return_type, false, true > d_x2
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:16
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.
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
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.
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
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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 max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:22
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
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.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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