Stan Math Library  2.9.0
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 
8 
12 
19 #include <cmath>
20 #include <limits>
21 
22 namespace stan {
23  namespace math {
24 
25  // Negative Binomial CDF
26  template <typename T_n, typename T_shape,
27  typename T_inv_scale>
28  typename return_type<T_shape, T_inv_scale>::type
29  neg_binomial_cdf(const T_n& n, const T_shape& alpha,
30  const T_inv_scale& beta) {
31  static const char* function("stan::math::neg_binomial_cdf");
32  typedef typename stan::partials_return_type<T_n, T_shape,
33  T_inv_scale>::type
34  T_partials_return;
35 
38 
39  // Ensure non-zero arugment lengths
40  if (!(stan::length(n) && stan::length(alpha) && stan::length(beta)))
41  return 1.0;
42 
43  T_partials_return P(1.0);
44 
45  // Validate arguments
46  check_positive_finite(function, "Shape parameter", alpha);
47  check_positive_finite(function, "Inverse scale parameter", beta);
48  check_consistent_sizes(function,
49  "Failures variable", n,
50  "Shape parameter", alpha,
51  "Inverse scale parameter", beta);
52 
53  // Wrap arguments in vector views
54  VectorView<const T_n> n_vec(n);
55  VectorView<const T_shape> alpha_vec(alpha);
56  VectorView<const T_inv_scale> beta_vec(beta);
57  size_t size = max_size(n, alpha, beta);
58 
59  // Compute vectorized CDF and gradient
64  using stan::math::digamma;
65 
67  operands_and_partials(alpha, beta);
68 
69  // Explicit return for extreme values
70  // The gradients are technically ill-defined, but treated as zero
71  for (size_t i = 0; i < stan::length(n); i++) {
72  if (value_of(n_vec[i]) < 0)
73  return operands_and_partials.to_var(0.0, alpha, beta);
74  }
75 
76  // Cache a few expensive function calls if alpha is a parameter
78  T_partials_return, T_shape>
79  digamma_alpha_vec(stan::length(alpha));
80 
82  T_partials_return, T_shape>
83  digamma_sum_vec(stan::length(alpha));
84 
86  for (size_t i = 0; i < stan::length(alpha); i++) {
87  const T_partials_return n_dbl = value_of(n_vec[i]);
88  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
89 
90  digamma_alpha_vec[i] = digamma(alpha_dbl);
91  digamma_sum_vec[i] = digamma(n_dbl + alpha_dbl + 1);
92  }
93  }
94 
95  for (size_t i = 0; i < size; i++) {
96  // Explicit results for extreme values
97  // The gradients are technically ill-defined, but treated as zero
98  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
99  return operands_and_partials.to_var(1.0, alpha, beta);
100 
101  const T_partials_return n_dbl = value_of(n_vec[i]);
102  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
103  const T_partials_return beta_dbl = value_of(beta_vec[i]);
104 
105  const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
106  const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
107  * (1.0 + beta_dbl) );
108 
109  const T_partials_return P_i =
110  inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
111 
112  P *= P_i;
113 
115  operands_and_partials.d_x1[i]
116  += inc_beta_dda(alpha_dbl, n_dbl + 1, p_dbl,
117  digamma_alpha_vec[i],
118  digamma_sum_vec[i]) / P_i;
119  }
120 
122  operands_and_partials.d_x2[i] +=
123  inc_beta_ddz(alpha_dbl, n_dbl + 1.0, p_dbl) * d_dbl / P_i;
124  }
125 
127  for (size_t i = 0; i < stan::length(alpha); ++i)
128  operands_and_partials.d_x1[i] *= P;
129  }
130 
132  for (size_t i = 0; i < stan::length(beta); ++i)
133  operands_and_partials.d_x2[i] *= P;
134  }
135 
136  return operands_and_partials.to_var(P, alpha, beta);
137  }
138 
139  } // prob
140 } // stan
141 #endif
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.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
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.
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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:20
A variable implementation that stores operands and derivatives with respect to the variable...
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:21
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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