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neg_binomial_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_CCDF_LOG_HPP
3 
4 #include <boost/math/special_functions/digamma.hpp>
5 #include <boost/random/negative_binomial_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
22 #include <cmath>
23 #include <limits>
24 
25 namespace stan {
26 
27  namespace math {
28 
29  template <typename T_n, typename T_shape,
30  typename T_inv_scale>
31  typename return_type<T_shape, T_inv_scale>::type
32  neg_binomial_ccdf_log(const T_n& n, const T_shape& alpha,
33  const T_inv_scale& beta) {
34  static const char* function("stan::math::neg_binomial_ccdf_log");
35  typedef typename stan::partials_return_type<T_n, T_shape,
36  T_inv_scale>::type
37  T_partials_return;
38 
43 
44  // Ensure non-zero arugment lengths
45  if (!(stan::length(n) && stan::length(alpha) && stan::length(beta)))
46  return 0.0;
47 
48  T_partials_return P(0.0);
49 
50  // Validate arguments
51  check_positive_finite(function, "Shape parameter", alpha);
52  check_positive_finite(function, "Inverse scale parameter", beta);
53  check_consistent_sizes(function,
54  "Failures variable", n,
55  "Shape parameter", alpha,
56  "Inverse scale parameter", beta);
57 
58  // Wrap arguments in vector views
59  VectorView<const T_n> n_vec(n);
60  VectorView<const T_shape> alpha_vec(alpha);
61  VectorView<const T_inv_scale> beta_vec(beta);
62  size_t size = max_size(n, alpha, beta);
63 
64  // Compute vectorized cdf_log and gradient
67  using stan::math::digamma;
68  using stan::math::lbeta;
69  using std::exp;
70  using std::pow;
71  using std::log;
72  using std::exp;
73 
75  operands_and_partials(alpha, beta);
76 
77  // Explicit return for extreme values
78  // The gradients are technically ill-defined, but treated as zero
79  for (size_t i = 0; i < stan::length(n); i++) {
80  if (value_of(n_vec[i]) < 0)
81  return operands_and_partials.to_var(0.0, alpha, beta);
82  }
83 
84  // Cache a few expensive function calls if alpha is a parameter
86  T_partials_return, T_shape>
87  digammaN_vec(stan::length(alpha));
89  T_partials_return, T_shape>
90  digammaAlpha_vec(stan::length(alpha));
92  T_partials_return, T_shape>
93  digammaSum_vec(stan::length(alpha));
94 
96  for (size_t i = 0; i < stan::length(alpha); i++) {
97  const T_partials_return n_dbl = value_of(n_vec[i]);
98  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
99 
100  digammaN_vec[i] = digamma(n_dbl + 1);
101  digammaAlpha_vec[i] = digamma(alpha_dbl);
102  digammaSum_vec[i] = digamma(n_dbl + alpha_dbl + 1);
103  }
104  }
105 
106  for (size_t i = 0; i < size; i++) {
107  // Explicit results for extreme values
108  // The gradients are technically ill-defined, but treated as zero
109  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
110  return operands_and_partials.to_var(stan::math::negative_infinity(),
111  alpha, beta);
112 
113  const T_partials_return n_dbl = value_of(n_vec[i]);
114  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
115  const T_partials_return beta_dbl = value_of(beta_vec[i]);
116  const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
117  const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
118  * (1.0 + beta_dbl) );
119  const T_partials_return Pi = 1.0 - inc_beta(alpha_dbl, n_dbl + 1.0,
120  p_dbl);
121  const T_partials_return beta_func = exp(lbeta(n_dbl + 1, alpha_dbl));
122 
123  P += log(Pi);
124 
126  T_partials_return g1 = 0;
127  T_partials_return g2 = 0;
128 
129  stan::math::grad_reg_inc_beta(g1, g2, alpha_dbl,
130  n_dbl + 1, p_dbl,
131  digammaAlpha_vec[i],
132  digammaN_vec[i],
133  digammaSum_vec[i],
134  beta_func);
135  operands_and_partials.d_x1[i] -= g1 / Pi;
136  }
138  operands_and_partials.d_x2[i] -= d_dbl * pow(1-p_dbl, n_dbl)
139  * pow(p_dbl, alpha_dbl-1) / beta_func / Pi;
140  }
141 
142  return operands_and_partials.to_var(P, alpha, beta);
143  }
144  }
145 }
146 #endif
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
return_type< T_shape, T_inv_scale >::type neg_binomial_ccdf_log(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
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
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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