Stan Math Library  2.15.0
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 
19 #include <limits>
20 
21 namespace stan {
22  namespace math {
23 
24  template <typename T_n, typename T_location,
25  typename T_precision>
27  neg_binomial_2_cdf(const T_n& n,
28  const T_location& mu,
29  const T_precision& phi) {
30  static const char* function("neg_binomial_2_cdf");
31  typedef typename stan::partials_return_type<T_n, T_location,
32  T_precision>::type
33  T_partials_return;
34 
35  T_partials_return P(1.0);
36  if (!(stan::length(n)
37  && stan::length(mu)
38  && stan::length(phi)))
39  return P;
40 
41  check_positive_finite(function, "Location parameter", mu);
42  check_positive_finite(function, "Precision parameter", phi);
43  check_not_nan(function, "Random variable", n);
44  check_consistent_sizes(function,
45  "Random variable", n,
46  "Location parameter", mu,
47  "Precision Parameter", phi);
48 
52  size_t size = max_size(n, mu, phi);
53 
55  operands_and_partials(mu, phi);
56 
57  // Explicit return for extreme values
58  // The gradients are technically ill-defined, but treated as zero
59  for (size_t i = 0; i < stan::length(n); i++) {
60  if (value_of(n_vec[i]) < 0)
61  return operands_and_partials.value(0.0);
62  }
63 
65  T_partials_return, T_precision>
66  digamma_phi_vec(stan::length(phi));
67 
69  T_partials_return, T_precision>
70  digamma_sum_vec(stan::length(phi));
71 
73  for (size_t i = 0; i < stan::length(phi); i++) {
74  const T_partials_return n_dbl = value_of(n_vec[i]);
75  const T_partials_return phi_dbl = value_of(phi_vec[i]);
76 
77  digamma_phi_vec[i] = digamma(phi_dbl);
78  digamma_sum_vec[i] = digamma(n_dbl + phi_dbl + 1);
79  }
80  }
81 
82  for (size_t i = 0; i < size; i++) {
83  // Explicit results for extreme values
84  // The gradients are technically ill-defined, but treated as zero
85  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
86  return operands_and_partials.value(1.0);
87 
88  const T_partials_return n_dbl = value_of(n_vec[i]);
89  const T_partials_return mu_dbl = value_of(mu_vec[i]);
90  const T_partials_return phi_dbl = value_of(phi_vec[i]);
91 
92  const T_partials_return p_dbl = phi_dbl / (mu_dbl + phi_dbl);
93  const T_partials_return d_dbl = 1.0 / ((mu_dbl + phi_dbl)
94  * (mu_dbl + phi_dbl));
95 
96  const T_partials_return P_i =
97  inc_beta(phi_dbl, n_dbl + 1.0, p_dbl);
98 
99  P *= P_i;
100 
102  operands_and_partials.d_x1[i] +=
103  - inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl) * phi_dbl * d_dbl / P_i;
104 
106  operands_and_partials.d_x2[i]
107  += inc_beta_dda(phi_dbl, n_dbl + 1, p_dbl,
108  digamma_phi_vec[i],
109  digamma_sum_vec[i]) / P_i
110  + inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl)
111  * mu_dbl * d_dbl / P_i;
112  }
113  }
114 
116  for (size_t i = 0; i < stan::length(mu); ++i)
117  operands_and_partials.d_x1[i] *= P;
118  }
119 
121  for (size_t i = 0; i < stan::length(phi); ++i)
122  operands_and_partials.d_x2[i] *= P;
123  }
124 
125  return operands_and_partials.value(P);
126  }
127 
128  }
129 }
130 #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)
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
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.
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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
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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