Stan Math Library  2.14.0
reverse mode automatic differentiation
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 
21 #include <boost/math/special_functions/digamma.hpp>
22 #include <boost/random/negative_binomial_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 
26 namespace stan {
27  namespace math {
28 
29  // NegBinomial(n|eta, phi) [phi > 0; n >= 0]
30  template <bool propto,
31  typename T_n,
32  typename T_log_location, typename T_precision>
34  neg_binomial_2_log_log(const T_n& n,
35  const T_log_location& eta,
36  const T_precision& phi) {
37  typedef typename stan::partials_return_type<T_n, T_log_location,
38  T_precision>::type
39  T_partials_return;
40 
41  static const char* function("neg_binomial_2_log_log");
42 
43  if (!(stan::length(n)
44  && stan::length(eta)
45  && stan::length(phi)))
46  return 0.0;
47 
48  T_partials_return logp(0.0);
49  check_nonnegative(function, "Failures variable", n);
50  check_finite(function, "Log location parameter", eta);
51  check_positive_finite(function, "Precision parameter", phi);
52  check_consistent_sizes(function,
53  "Failures variable", n,
54  "Log location parameter", eta,
55  "Precision parameter", phi);
56 
58  return 0.0;
59 
60  using std::exp;
61  using std::log;
62 
63  VectorView<const T_n> n_vec(n);
65  VectorView<const T_precision> phi_vec(phi);
66  size_t size = max_size(n, eta, phi);
67 
69  operands_and_partials(eta, phi);
70 
71  size_t len_ep = max_size(eta, phi);
72  size_t len_np = max_size(n, phi);
73 
75  for (size_t i = 0, size = length(eta); i < size; ++i)
76  eta__[i] = value_of(eta_vec[i]);
77 
79  for (size_t i = 0, size = length(phi); i < size; ++i)
80  phi__[i] = value_of(phi_vec[i]);
81 
83  log_phi(length(phi));
84  for (size_t i = 0, size = length(phi); i < size; ++i)
85  log_phi[i] = log(phi__[i]);
86 
88  logsumexp_eta_logphi(len_ep);
89  for (size_t i = 0; i < len_ep; ++i)
90  logsumexp_eta_logphi[i] = log_sum_exp(eta__[i], log_phi[i]);
91 
93  n_plus_phi(len_np);
94  for (size_t i = 0; i < len_np; ++i)
95  n_plus_phi[i] = n_vec[i] + phi__[i];
96 
97  for (size_t i = 0; i < size; i++) {
99  logp -= lgamma(n_vec[i] + 1.0);
101  logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
103  logp -= (n_plus_phi[i])*logsumexp_eta_logphi[i];
105  logp += n_vec[i]*eta__[i];
107  logp += lgamma(n_plus_phi[i]);
108 
110  operands_and_partials.d_x1[i]
111  += n_vec[i] - n_plus_phi[i]
112  / (phi__[i]/exp(eta__[i]) + 1.0);
114  operands_and_partials.d_x2[i]
115  += 1.0 - n_plus_phi[i]/(exp(eta__[i]) + phi__[i])
116  + log_phi[i] - logsumexp_eta_logphi[i] - digamma(phi__[i])
117  + digamma(n_plus_phi[i]);
118  }
119  return operands_and_partials.value(logp);
120  }
121 
122  template <typename T_n,
123  typename T_log_location, typename T_precision>
124  inline
127  const T_log_location& eta,
128  const T_precision& phi) {
129  return neg_binomial_2_log_log<false>(n, eta, phi);
130  }
131  }
132 }
133 #endif
VectorView< T_return_type, false, true > d_x2
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
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
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)
fvar< T > log_sum_exp(const std::vector< fvar< T > > &v)
Definition: log_sum_exp.hpp:13
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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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