Stan Math Library  2.20.0
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 
14 #include <cmath>
15 
16 namespace stan {
17 namespace math {
18 
19 // NegBinomial(n|mu, phi) [mu >= 0; phi > 0; n >= 0]
20 template <bool propto, typename T_n, typename T_location, typename T_precision>
22  const T_n& n, const T_location& mu, const T_precision& phi) {
23  typedef
25  T_partials_return;
26 
27  static const char* function = "neg_binomial_2_lpmf";
28 
29  if (size_zero(n, mu, phi))
30  return 0.0;
31 
32  T_partials_return logp(0.0);
33  check_nonnegative(function, "Failures variable", n);
34  check_positive_finite(function, "Location parameter", mu);
35  check_positive_finite(function, "Precision parameter", phi);
36  check_consistent_sizes(function, "Failures variable", n, "Location parameter",
37  mu, "Precision parameter", phi);
38 
40  return 0.0;
41 
42  using std::log;
43 
44  scalar_seq_view<T_n> n_vec(n);
45  scalar_seq_view<T_location> mu_vec(mu);
46  scalar_seq_view<T_precision> phi_vec(phi);
47  size_t size = max_size(n, mu, phi);
48 
50 
51  size_t len_ep = max_size(mu, phi);
52  size_t len_np = max_size(n, phi);
53 
55  for (size_t i = 0, size = length(mu); i < size; ++i)
56  mu__[i] = value_of(mu_vec[i]);
57 
59  for (size_t i = 0, size = length(phi); i < size; ++i)
60  phi__[i] = value_of(phi_vec[i]);
61 
63  for (size_t i = 0, size = length(phi); i < size; ++i)
64  log_phi[i] = log(phi__[i]);
65 
67  log_mu_plus_phi(len_ep);
68  for (size_t i = 0; i < len_ep; ++i)
69  log_mu_plus_phi[i] = log(mu__[i] + phi__[i]);
70 
72  for (size_t i = 0; i < len_np; ++i)
73  n_plus_phi[i] = n_vec[i] + phi__[i];
74 
75  for (size_t i = 0; i < size; i++) {
77  logp -= lgamma(n_vec[i] + 1.0);
79  logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
81  logp -= (n_plus_phi[i]) * log_mu_plus_phi[i];
83  logp += multiply_log(n_vec[i], mu__[i]);
85  logp += lgamma(n_plus_phi[i]);
86 
87  // if phi is large we probably overflow, defer to Poisson:
88  if (phi__[i] > 1e5) {
89  logp = poisson_lpmf(n_vec[i], mu__[i]);
90  }
91 
93  ops_partials.edge1_.partials_[i]
94  += n_vec[i] / mu__[i] - (n_vec[i] + phi__[i]) / (mu__[i] + phi__[i]);
96  ops_partials.edge2_.partials_[i]
97  += 1.0 - n_plus_phi[i] / (mu__[i] + phi__[i]) + log_phi[i]
98  - log_mu_plus_phi[i] - digamma(phi__[i]) + digamma(n_plus_phi[i]);
99  }
100  return ops_partials.build(logp);
101 }
102 
103 template <typename T_n, typename T_location, typename T_precision>
105  const T_n& n, const T_location& mu, const T_precision& phi) {
106  return neg_binomial_2_lpmf<false>(n, mu, phi);
107 }
108 
109 } // namespace math
110 } // namespace stan
111 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:21
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
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.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
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.
return_type< T_rate >::type poisson_lpmf(const T_n &n, const T_rate &lambda)
internal::ops_partials_edge< double, Op1 > edge1_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23

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