Stan Math Library  2.11.0
reverse mode automatic differentiation
neg_binomial_2_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_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>
26 #include <cmath>
27 
28 namespace stan {
29 
30  namespace math {
31 
32  // NegBinomial(n|mu, phi) [mu >= 0; phi > 0; n >= 0]
33  template <bool propto,
34  typename T_n,
35  typename T_location, typename T_precision>
36  typename return_type<T_location, T_precision>::type
37  neg_binomial_2_log(const T_n& n,
38  const T_location& mu,
39  const T_precision& phi) {
40  typedef typename stan::partials_return_type<T_n, T_location,
41  T_precision>::type
42  T_partials_return;
43 
44  static const char* function("stan::math::neg_binomial_2_log");
45 
51 
52  // check if any vectors are zero length
53  if (!(stan::length(n)
54  && stan::length(mu)
55  && stan::length(phi)))
56  return 0.0;
57 
58  T_partials_return logp(0.0);
59  check_nonnegative(function, "Failures variable", n);
60  check_positive_finite(function, "Location parameter", mu);
61  check_positive_finite(function, "Precision parameter", phi);
62  check_consistent_sizes(function,
63  "Failures variable", n,
64  "Location parameter", mu,
65  "Precision parameter", phi);
66 
67  // check if no variables are involved and prop-to
69  return 0.0;
70 
72  using stan::math::digamma;
73  using stan::math::lgamma;
74  using std::log;
75  using std::log;
76 
77  // set up template expressions wrapping scalars into vector views
78  VectorView<const T_n> n_vec(n);
80  VectorView<const T_precision> phi_vec(phi);
81  size_t size = max_size(n, mu, phi);
82 
84  operands_and_partials(mu, phi);
85 
86  size_t len_ep = max_size(mu, phi);
87  size_t len_np = max_size(n, phi);
88 
90  for (size_t i = 0, size = length(mu); i < size; ++i)
91  mu__[i] = value_of(mu_vec[i]);
92 
94  for (size_t i = 0, size = length(phi); i < size; ++i)
95  phi__[i] = value_of(phi_vec[i]);
96 
98  for (size_t i = 0, size = length(phi); i < size; ++i)
99  log_phi[i] = log(phi__[i]);
100 
102  log_mu_plus_phi(len_ep);
103  for (size_t i = 0; i < len_ep; ++i)
104  log_mu_plus_phi[i] = log(mu__[i] + 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])*log_mu_plus_phi[i];
119  logp += multiply_log(n_vec[i], mu__[i]);
121  logp += lgamma(n_plus_phi[i]);
122 
124  operands_and_partials.d_x1[i]
125  += n_vec[i]/mu__[i]
126  - (n_vec[i] + phi__[i])
127  / (mu__[i] + phi__[i]);
129  operands_and_partials.d_x2[i]
130  += 1.0 - n_plus_phi[i]/(mu__[i] + phi__[i])
131  + log_phi[i] - log_mu_plus_phi[i] - digamma(phi__[i])
132  + digamma(n_plus_phi[i]);
133  }
134  return operands_and_partials.value(logp);
135  }
136 
137  template <typename T_n,
138  typename T_location, typename T_precision>
139  inline
141  neg_binomial_2_log(const T_n& n,
142  const T_location& mu,
143  const T_precision& phi) {
144  return neg_binomial_2_log<false>(n, mu, phi);
145  }
146  }
147 }
148 #endif
VectorView< T_return_type, false, true > d_x2
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
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...
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...
This class builds partial derivatives with respect to a set of operands.
return_type< T_location, T_precision >::type neg_binomial_2_log(const T_n &n, const T_location &mu, const T_precision &phi)
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
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.
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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