Stan Math Library  2.20.0
reverse mode automatic differentiation
neg_binomial_2_log_lpmf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_LPMF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_LPMF_HPP
3 
14 #include <cmath>
15 
16 namespace stan {
17 namespace math {
18 
19 // NegBinomial(n|eta, phi) [phi > 0; n >= 0]
20 template <bool propto, typename T_n, typename T_log_location,
21  typename T_precision>
23  const T_n& n, const T_log_location& eta, const T_precision& phi) {
24  typedef
25  typename stan::partials_return_type<T_n, T_log_location,
26  T_precision>::type T_partials_return;
27 
28  static const char* function = "neg_binomial_2_log_lpmf";
29 
30  if (size_zero(n, eta, phi))
31  return 0.0;
32 
33  T_partials_return logp(0.0);
34  check_nonnegative(function, "Failures variable", n);
35  check_finite(function, "Log location parameter", eta);
36  check_positive_finite(function, "Precision parameter", phi);
37  check_consistent_sizes(function, "Failures variable", n,
38  "Log location parameter", eta, "Precision parameter",
39  phi);
40 
42  return 0.0;
43 
44  using std::exp;
45  using std::log;
46 
47  scalar_seq_view<T_n> n_vec(n);
49  scalar_seq_view<T_precision> phi_vec(phi);
50  size_t size = max_size(n, eta, phi);
51 
53 
54  size_t len_ep = max_size(eta, phi);
55  size_t len_np = max_size(n, phi);
56 
58  for (size_t i = 0, size = length(eta); i < size; ++i)
59  eta__[i] = value_of(eta_vec[i]);
60 
62  for (size_t i = 0, size = length(phi); i < size; ++i)
63  phi__[i] = value_of(phi_vec[i]);
64 
66  for (size_t i = 0, size = length(phi); i < size; ++i)
67  log_phi[i] = log(phi__[i]);
68 
70  logsumexp_eta_logphi(len_ep);
71  for (size_t i = 0; i < len_ep; ++i)
72  logsumexp_eta_logphi[i] = log_sum_exp(eta__[i], log_phi[i]);
73 
75  for (size_t i = 0; i < len_np; ++i)
76  n_plus_phi[i] = n_vec[i] + phi__[i];
77 
78  for (size_t i = 0; i < size; i++) {
80  logp -= lgamma(n_vec[i] + 1.0);
82  logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
84  logp -= (n_plus_phi[i]) * logsumexp_eta_logphi[i];
86  logp += n_vec[i] * eta__[i];
88  logp += lgamma(n_plus_phi[i]);
89 
91  ops_partials.edge1_.partials_[i]
92  += n_vec[i] - n_plus_phi[i] / (phi__[i] / exp(eta__[i]) + 1.0);
94  ops_partials.edge2_.partials_[i]
95  += 1.0 - n_plus_phi[i] / (exp(eta__[i]) + phi__[i]) + log_phi[i]
96  - logsumexp_eta_logphi[i] - digamma(phi__[i])
97  + digamma(n_plus_phi[i]);
98  }
99  return ops_partials.build(logp);
100 }
101 
102 template <typename T_n, typename T_log_location, typename T_precision>
104 neg_binomial_2_log_lpmf(const T_n& n, const T_log_location& eta,
105  const T_precision& phi) {
106  return neg_binomial_2_log_lpmf<false>(n, eta, phi);
107 }
108 } // namespace math
109 } // namespace stan
110 #endif
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: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
fvar< T > log_sum_exp(const std::vector< fvar< T > > &v)
Definition: log_sum_exp.hpp:12
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.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
Template metaprogram to calculate the partial derivative type resulting from promoting all the scalar...
return_type< T_log_location, T_precision >::type neg_binomial_2_log_lpmf(const T_n &n, const T_log_location &eta, const T_precision &phi)
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
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.
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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