Stan Math Library  2.12.0
reverse mode automatic differentiation
neg_binomial_2_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_CDF_HPP
3 
18 #include <limits>
19 
20 namespace stan {
21  namespace math {
22 
23  template <typename T_n, typename T_location,
24  typename T_precision>
25  typename return_type<T_location, T_precision>::type
26  neg_binomial_2_cdf(const T_n& n,
27  const T_location& mu,
28  const T_precision& phi) {
29  static const char* function("stan::prob::neg_binomial_2_cdf");
30  typedef typename stan::partials_return_type<T_n, T_location,
31  T_precision>::type
32  T_partials_return;
33 
34  T_partials_return P(1.0);
35  if (!(stan::length(n)
36  && stan::length(mu)
37  && stan::length(phi)))
38  return P;
39 
40  check_positive_finite(function, "Location parameter", mu);
41  check_positive_finite(function, "Precision parameter", phi);
42  check_not_nan(function, "Random variable", n);
43  check_consistent_sizes(function,
44  "Random variable", n,
45  "Location parameter", mu,
46  "Precision Parameter", phi);
47 
48  VectorView<const T_n> n_vec(n);
50  VectorView<const T_precision> phi_vec(phi);
51  size_t size = max_size(n, mu, phi);
52 
54  operands_and_partials(mu, phi);
55 
56  // Explicit return for extreme values
57  // The gradients are technically ill-defined, but treated as zero
58  for (size_t i = 0; i < stan::length(n); i++) {
59  if (value_of(n_vec[i]) < 0)
60  return operands_and_partials.value(0.0);
61  }
62 
64  T_partials_return, T_precision>
65  digamma_phi_vec(stan::length(phi));
66 
68  T_partials_return, T_precision>
69  digamma_sum_vec(stan::length(phi));
70 
72  for (size_t i = 0; i < stan::length(phi); i++) {
73  const T_partials_return n_dbl = value_of(n_vec[i]);
74  const T_partials_return phi_dbl = value_of(phi_vec[i]);
75 
76  digamma_phi_vec[i] = digamma(phi_dbl);
77  digamma_sum_vec[i] = digamma(n_dbl + phi_dbl + 1);
78  }
79  }
80 
81  for (size_t i = 0; i < size; i++) {
82  // Explicit results for extreme values
83  // The gradients are technically ill-defined, but treated as zero
84  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
85  return operands_and_partials.value(1.0);
86 
87  const T_partials_return n_dbl = value_of(n_vec[i]);
88  const T_partials_return mu_dbl = value_of(mu_vec[i]);
89  const T_partials_return phi_dbl = value_of(phi_vec[i]);
90 
91  const T_partials_return p_dbl = phi_dbl / (mu_dbl + phi_dbl);
92  const T_partials_return d_dbl = 1.0 / ((mu_dbl + phi_dbl)
93  * (mu_dbl + phi_dbl));
94 
95  const T_partials_return P_i =
96  inc_beta(phi_dbl, n_dbl + 1.0, p_dbl);
97 
98  P *= P_i;
99 
101  operands_and_partials.d_x1[i] +=
102  - inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl) * phi_dbl * d_dbl / P_i;
103 
105  operands_and_partials.d_x2[i]
106  += inc_beta_dda(phi_dbl, n_dbl + 1, p_dbl,
107  digamma_phi_vec[i],
108  digamma_sum_vec[i]) / P_i
109  + inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl)
110  * mu_dbl * d_dbl / P_i;
111  }
112  }
113 
115  for (size_t i = 0; i < stan::length(mu); ++i)
116  operands_and_partials.d_x1[i] *= P;
117  }
118 
120  for (size_t i = 0; i < stan::length(phi); ++i)
121  operands_and_partials.d_x2[i] *= P;
122  }
123 
124  return operands_and_partials.value(P);
125  }
126 
127  }
128 }
129 #endif
VectorView< T_return_type, false, true > d_x2
return_type< T_location, T_precision >::type neg_binomial_2_cdf(const T_n &n, const T_location &mu, const T_precision &phi)
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
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.
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
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
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 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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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