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neg_binomial_2_log_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_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 
24 namespace stan {
25 
26  namespace math {
27 
28  // NegBinomial(n|eta, phi) [phi > 0; n >= 0]
29  template <bool propto,
30  typename T_n,
31  typename T_log_location, typename T_precision>
32  typename return_type<T_log_location, T_precision>::type
33  neg_binomial_2_log_log(const T_n& n,
34  const T_log_location& eta,
35  const T_precision& phi) {
36  typedef typename stan::partials_return_type<T_n, T_log_location,
37  T_precision>::type
38  T_partials_return;
39 
40  static const char* function("stan::prob::neg_binomial_2_log_log");
41 
48 
49  // check if any vectors are zero length
50  if (!(stan::length(n)
51  && stan::length(eta)
52  && stan::length(phi)))
53  return 0.0;
54 
55  T_partials_return logp(0.0);
56  check_nonnegative(function, "Failures variable", n);
57  check_finite(function, "Log location parameter", eta);
58  check_positive_finite(function, "Precision parameter", phi);
59  check_consistent_sizes(function,
60  "Failures variable", n,
61  "Log location parameter", eta,
62  "Precision parameter", phi);
63 
64  // check if no variables are involved and prop-to
66  return 0.0;
67 
70  using stan::math::digamma;
71  using stan::math::lgamma;
72  using std::exp;
73  using std::log;
74 
75  // set up template expressions wrapping scalars into vector views
76  VectorView<const T_n> n_vec(n);
78  VectorView<const T_precision> phi_vec(phi);
79  size_t size = max_size(n, eta, phi);
80 
82  operands_and_partials(eta, phi);
83 
84  size_t len_ep = max_size(eta, phi);
85  size_t len_np = max_size(n, phi);
86 
88  for (size_t i = 0, size = length(eta); i < size; ++i)
89  eta__[i] = value_of(eta_vec[i]);
90 
92  for (size_t i = 0, size = length(phi); i < size; ++i)
93  phi__[i] = value_of(phi_vec[i]);
94 
95 
97  log_phi(length(phi));
98  for (size_t i = 0, size = length(phi); i < size; ++i)
99  log_phi[i] = log(phi__[i]);
100 
102  logsumexp_eta_logphi(len_ep);
103  for (size_t i = 0; i < len_ep; ++i)
104  logsumexp_eta_logphi[i] = log_sum_exp(eta__[i], log_phi[i]);
105 
107  n_plus_phi(len_np);
108  for (size_t i = 0; i < len_np; ++i)
109  n_plus_phi[i] = n_vec[i] + phi__[i];
110 
111  for (size_t i = 0; i < size; i++) {
113  logp -= lgamma(n_vec[i] + 1.0);
115  logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
117  logp -= (n_plus_phi[i])*logsumexp_eta_logphi[i];
119  logp += n_vec[i]*eta__[i];
121  logp += lgamma(n_plus_phi[i]);
122 
124  operands_and_partials.d_x1[i]
125  += n_vec[i] - n_plus_phi[i]
126  / (phi__[i]/exp(eta__[i]) + 1.0);
128  operands_and_partials.d_x2[i]
129  += 1.0 - n_plus_phi[i]/(exp(eta__[i]) + phi__[i])
130  + log_phi[i] - logsumexp_eta_logphi[i] - digamma(phi__[i])
131  + digamma(n_plus_phi[i]);
132  }
133  return operands_and_partials.to_var(logp, eta, phi);
134  }
135 
136  template <typename T_n,
137  typename T_log_location, typename T_precision>
138  inline
141  const T_log_location& eta,
142  const T_precision& phi) {
143  return neg_binomial_2_log_log<false>(n, eta, phi);
144  }
145  }
146 }
147 #endif
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
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:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
return_type< T_log_location, T_precision >::type neg_binomial_2_log_log(const T_n &n, const T_log_location &eta, const T_precision &phi)
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)
fvar< T > log_sum_exp(const std::vector< fvar< T > > &v)
Definition: log_sum_exp.hpp:14
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
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 > 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
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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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