Stan Math Library  2.20.0
reverse mode automatic differentiation
neg_binomial_lpmf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LPMF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LPMF_HPP
3 
15 #include <cmath>
16 
17 namespace stan {
18 namespace math {
19 
20 // NegBinomial(n|alpha, beta) [alpha > 0; beta > 0; n >= 0]
21 template <bool propto, typename T_n, typename T_shape, typename T_inv_scale>
23  const T_n& n, const T_shape& alpha, const T_inv_scale& beta) {
25  T_partials_return;
26 
27  static const char* function = "neg_binomial_lpmf";
28 
29  if (size_zero(n, alpha, beta))
30  return 0.0;
31 
32  T_partials_return logp(0.0);
33  check_nonnegative(function, "Failures variable", n);
34  check_positive_finite(function, "Shape parameter", alpha);
35  check_positive_finite(function, "Inverse scale parameter", beta);
36  check_consistent_sizes(function, "Failures variable", n, "Shape parameter",
37  alpha, "Inverse scale parameter", beta);
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_shape> alpha_vec(alpha);
46  scalar_seq_view<T_inv_scale> beta_vec(beta);
47  size_t size = max_size(n, alpha, beta);
48 
49  operands_and_partials<T_shape, T_inv_scale> ops_partials(alpha, beta);
50 
51  size_t len_ab = max_size(alpha, beta);
53  for (size_t i = 0; i < len_ab; ++i)
54  lambda[i] = value_of(alpha_vec[i]) / value_of(beta_vec[i]);
55 
57  for (size_t i = 0; i < length(beta); ++i)
58  log1p_beta[i] = log1p(value_of(beta_vec[i]));
59 
61  length(beta));
62  for (size_t i = 0; i < length(beta); ++i)
63  log_beta_m_log1p_beta[i] = log(value_of(beta_vec[i])) - log1p_beta[i];
64 
66  alpha_times_log_beta_over_1p_beta(len_ab);
67  for (size_t i = 0; i < len_ab; ++i)
68  alpha_times_log_beta_over_1p_beta[i]
69  = value_of(alpha_vec[i])
70  * log(value_of(beta_vec[i]) / (1.0 + value_of(beta_vec[i])));
71 
72  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
73  digamma_alpha(length(alpha));
75  for (size_t i = 0; i < length(alpha); ++i)
76  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
77  }
78 
80  T_inv_scale>
81  log_beta(length(beta));
83  for (size_t i = 0; i < length(beta); ++i)
84  log_beta[i] = log(value_of(beta_vec[i]));
85  }
86 
88  T_shape, T_inv_scale>
89  lambda_m_alpha_over_1p_beta(len_ab);
91  for (size_t i = 0; i < len_ab; ++i)
92  lambda_m_alpha_over_1p_beta[i]
93  = lambda[i]
94  - (value_of(alpha_vec[i]) / (1.0 + value_of(beta_vec[i])));
95  }
96 
97  for (size_t i = 0; i < size; i++) {
98  if (alpha_vec[i] > 1e10) { // reduces numerically to Poisson
100  logp -= lgamma(n_vec[i] + 1.0);
102  logp += multiply_log(n_vec[i], lambda[i]) - lambda[i];
103 
105  ops_partials.edge1_.partials_[i]
106  += n_vec[i] / value_of(alpha_vec[i]) - 1.0 / value_of(beta_vec[i]);
108  ops_partials.edge2_.partials_[i]
109  += (lambda[i] - n_vec[i]) / value_of(beta_vec[i]);
110  } else { // standard density definition
112  if (n_vec[i] != 0)
113  logp += binomial_coefficient_log(
114  n_vec[i] + value_of(alpha_vec[i]) - 1.0, n_vec[i]);
116  logp += alpha_times_log_beta_over_1p_beta[i] - n_vec[i] * log1p_beta[i];
117 
119  ops_partials.edge1_.partials_[i]
120  += digamma(value_of(alpha_vec[i]) + n_vec[i]) - digamma_alpha[i]
121  + log_beta_m_log1p_beta[i];
123  ops_partials.edge2_.partials_[i]
124  += lambda_m_alpha_over_1p_beta[i]
125  - n_vec[i] / (value_of(beta_vec[i]) + 1.0);
126  }
127  }
128  return ops_partials.build(logp);
129 }
130 
131 template <typename T_n, typename T_shape, typename T_inv_scale>
133  const T_n& n, const T_shape& alpha, const T_inv_scale& beta) {
134  return neg_binomial_lpmf<false>(n, alpha, beta);
135 }
136 
137 } // namespace math
138 } // namespace stan
139 #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 > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
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...
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
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
return_type< T_shape, T_inv_scale >::type neg_binomial_lpmf(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
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
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:12
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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