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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 
8 
13 
17 
23 
24 #include <boost/math/special_functions/digamma.hpp>
25 #include <boost/random/negative_binomial_distribution.hpp>
26 #include <boost/random/variate_generator.hpp>
27 
28 #include <limits>
29 #include <vector>
30 
31 namespace stan {
32  namespace math {
33 
34  template <typename T_n, typename T_location,
35  typename T_precision>
36  typename return_type<T_location, T_precision>::type
37  neg_binomial_2_cdf(const T_n& n,
38  const T_location& mu,
39  const T_precision& phi) {
40  static const char* function("stan::prob::neg_binomial_2_cdf");
41  typedef typename stan::partials_return_type<T_n, T_location,
42  T_precision>::type
43  T_partials_return;
44 
49 
50  // Ensure non-zero arugment lengths
51  if (!(stan::length(n) && stan::length(mu) && stan::length(phi)))
52  return 1.0;
53 
54  T_partials_return P(1.0);
55 
56  // Validate arguments
57  check_positive_finite(function, "Location parameter", mu);
58  check_positive_finite(function, "Precision parameter", phi);
59  check_not_nan(function, "Random variable", n);
60  check_consistent_sizes(function,
61  "Random variable", n,
62  "Location parameter", mu,
63  "Precision Parameter", phi);
64 
65  // Wrap arguments in vector views
66  VectorView<const T_n> n_vec(n);
68  VectorView<const T_precision> phi_vec(phi);
69  size_t size = max_size(n, mu, phi);
70 
71  // Compute vectorized CDF and gradient
76  using stan::math::digamma;
77 
79  operands_and_partials(mu, phi);
80 
81  // Explicit return for extreme values
82  // The gradients are technically ill-defined, but treated as zero
83  for (size_t i = 0; i < stan::length(n); i++) {
84  if (value_of(n_vec[i]) < 0)
85  return operands_and_partials.to_var(0.0, mu, phi);
86  }
87 
88  // Cache a few expensive function calls if phi is a parameter
90  T_partials_return, T_precision>
91  digamma_phi_vec(stan::length(phi));
92 
94  T_partials_return, T_precision>
95  digamma_sum_vec(stan::length(phi));
96 
98  for (size_t i = 0; i < stan::length(phi); i++) {
99  const T_partials_return n_dbl = value_of(n_vec[i]);
100  const T_partials_return phi_dbl = value_of(phi_vec[i]);
101 
102  digamma_phi_vec[i] = digamma(phi_dbl);
103  digamma_sum_vec[i] = digamma(n_dbl + phi_dbl + 1);
104  }
105  }
106 
107  for (size_t i = 0; i < size; i++) {
108  // Explicit results for extreme values
109  // The gradients are technically ill-defined, but treated as zero
110  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
111  return operands_and_partials.to_var(1.0, mu, phi);
112 
113  const T_partials_return n_dbl = value_of(n_vec[i]);
114  const T_partials_return mu_dbl = value_of(mu_vec[i]);
115  const T_partials_return phi_dbl = value_of(phi_vec[i]);
116 
117  const T_partials_return p_dbl = phi_dbl / (mu_dbl + phi_dbl);
118  const T_partials_return d_dbl = 1.0 / ((mu_dbl + phi_dbl)
119  * (mu_dbl + phi_dbl));
120 
121  const T_partials_return P_i =
122  inc_beta(phi_dbl, n_dbl + 1.0, p_dbl);
123 
124  P *= P_i;
125 
127  operands_and_partials.d_x1[i] +=
128  - inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl) * phi_dbl * d_dbl / P_i;
129 
131  operands_and_partials.d_x2[i]
132  += inc_beta_dda(phi_dbl, n_dbl + 1, p_dbl,
133  digamma_phi_vec[i],
134  digamma_sum_vec[i]) / P_i
135  + inc_beta_ddz(phi_dbl, n_dbl + 1.0, p_dbl)
136  * mu_dbl * d_dbl / P_i;
137  }
138  }
139 
141  for (size_t i = 0; i < stan::length(mu); ++i)
142  operands_and_partials.d_x1[i] *= P;
143  }
144 
146  for (size_t i = 0; i < stan::length(phi); ++i)
147  operands_and_partials.d_x2[i] *= P;
148  }
149 
150  return operands_and_partials.to_var(P, mu, phi);
151  }
152 
153  } // math
154 } // stan
155 #endif
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.
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)
Definition: size.hpp:11
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
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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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