Stan Math Library  2.14.0
reverse mode automatic differentiation
neg_binomial_2_lpmf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LPMF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LPMF_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>
26 #include <cmath>
27 
28 namespace stan {
29  namespace math {
30 
31  // NegBinomial(n|mu, phi) [mu >= 0; phi > 0; n >= 0]
32  template <bool propto,
33  typename T_n,
34  typename T_location, typename T_precision>
36  neg_binomial_2_lpmf(const T_n& n,
37  const T_location& mu,
38  const T_precision& phi) {
39  typedef typename stan::partials_return_type<T_n, T_location,
40  T_precision>::type
41  T_partials_return;
42 
43  static const char* function("neg_binomial_2_lpmf");
44 
45  if (!(stan::length(n)
46  && stan::length(mu)
47  && stan::length(phi)))
48  return 0.0;
49 
50  T_partials_return logp(0.0);
51  check_nonnegative(function, "Failures variable", n);
52  check_positive_finite(function, "Location parameter", mu);
53  check_positive_finite(function, "Precision parameter", phi);
54  check_consistent_sizes(function,
55  "Failures variable", n,
56  "Location parameter", mu,
57  "Precision parameter", phi);
58 
60  return 0.0;
61 
62  using std::log;
63  using std::log;
64 
65  VectorView<const T_n> n_vec(n);
67  VectorView<const T_precision> phi_vec(phi);
68  size_t size = max_size(n, mu, phi);
69 
71  operands_and_partials(mu, phi);
72 
73  size_t len_ep = max_size(mu, phi);
74  size_t len_np = max_size(n, phi);
75 
77  for (size_t i = 0, size = length(mu); i < size; ++i)
78  mu__[i] = value_of(mu_vec[i]);
79 
81  for (size_t i = 0, size = length(phi); i < size; ++i)
82  phi__[i] = value_of(phi_vec[i]);
83 
85  for (size_t i = 0, size = length(phi); i < size; ++i)
86  log_phi[i] = log(phi__[i]);
87 
89  log_mu_plus_phi(len_ep);
90  for (size_t i = 0; i < len_ep; ++i)
91  log_mu_plus_phi[i] = log(mu__[i] + phi__[i]);
92 
94  n_plus_phi(len_np);
95  for (size_t i = 0; i < len_np; ++i)
96  n_plus_phi[i] = n_vec[i] + phi__[i];
97 
98  for (size_t i = 0; i < size; i++) {
100  logp -= lgamma(n_vec[i] + 1.0);
102  logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
104  logp -= (n_plus_phi[i])*log_mu_plus_phi[i];
106  logp += multiply_log(n_vec[i], mu__[i]);
108  logp += lgamma(n_plus_phi[i]);
109 
111  operands_and_partials.d_x1[i]
112  += n_vec[i]/mu__[i]
113  - (n_vec[i] + phi__[i])
114  / (mu__[i] + phi__[i]);
116  operands_and_partials.d_x2[i]
117  += 1.0 - n_plus_phi[i]/(mu__[i] + phi__[i])
118  + log_phi[i] - log_mu_plus_phi[i] - digamma(phi__[i])
119  + digamma(n_plus_phi[i]);
120  }
121  return operands_and_partials.value(logp);
122  }
123 
124  template <typename T_n,
125  typename T_location, typename T_precision>
126  inline
128  neg_binomial_2_lpmf(const T_n& n,
129  const T_location& mu,
130  const T_precision& phi) {
131  return neg_binomial_2_lpmf<false>(n, mu, phi);
132  }
133 
134  }
135 }
136 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:20
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
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
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
return_type< T_location, T_precision >::type neg_binomial_2_lpmf(const T_n &n, const T_location &mu, const T_precision &phi)
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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
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
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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