Stan Math Library  2.14.0
reverse mode automatic differentiation
neg_binomial_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LOG_HPP
3 
25 #include <boost/math/special_functions/digamma.hpp>
26 #include <boost/random/negative_binomial_distribution.hpp>
27 #include <boost/random/variate_generator.hpp>
28 #include <cmath>
29 
30 namespace stan {
31  namespace math {
32 
33  // NegBinomial(n|alpha, beta) [alpha > 0; beta > 0; n >= 0]
34  template <bool propto,
35  typename T_n,
36  typename T_shape, typename T_inv_scale>
38  neg_binomial_log(const T_n& n,
39  const T_shape& alpha,
40  const T_inv_scale& beta) {
41  typedef typename stan::partials_return_type<T_n, T_shape,
42  T_inv_scale>::type
43  T_partials_return;
44 
45  static const char* function("neg_binomial_log");
46 
47  if (!(stan::length(n)
48  && stan::length(alpha)
49  && stan::length(beta)))
50  return 0.0;
51 
52  T_partials_return logp(0.0);
53  check_nonnegative(function, "Failures variable", n);
54  check_positive_finite(function, "Shape parameter", alpha);
55  check_positive_finite(function, "Inverse scale parameter", beta);
56  check_consistent_sizes(function,
57  "Failures variable", n,
58  "Shape parameter", alpha,
59  "Inverse scale parameter", beta);
60 
62  return 0.0;
63 
64  using std::log;
65  using std::log;
66 
67  VectorView<const T_n> n_vec(n);
68  VectorView<const T_shape> alpha_vec(alpha);
69  VectorView<const T_inv_scale> beta_vec(beta);
70  size_t size = max_size(n, alpha, beta);
71 
73  operands_and_partials(alpha, beta);
74 
75  size_t len_ab = max_size(alpha, beta);
77  lambda(len_ab);
78  for (size_t i = 0; i < len_ab; ++i)
79  lambda[i] = value_of(alpha_vec[i]) / value_of(beta_vec[i]);
80 
82  log1p_beta(length(beta));
83  for (size_t i = 0; i < length(beta); ++i)
84  log1p_beta[i] = log1p(value_of(beta_vec[i]));
85 
87  log_beta_m_log1p_beta(length(beta));
88  for (size_t i = 0; i < length(beta); ++i)
89  log_beta_m_log1p_beta[i] = log(value_of(beta_vec[i])) - log1p_beta[i];
90 
92  alpha_times_log_beta_over_1p_beta(len_ab);
93  for (size_t i = 0; i < len_ab; ++i)
94  alpha_times_log_beta_over_1p_beta[i]
95  = value_of(alpha_vec[i])
96  * log(value_of(beta_vec[i])
97  / (1.0 + value_of(beta_vec[i])));
98 
100  T_partials_return, T_shape>
101  digamma_alpha(length(alpha));
103  for (size_t i = 0; i < length(alpha); ++i)
104  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
105  }
106 
108  T_partials_return, T_inv_scale> log_beta(length(beta));
110  for (size_t i = 0; i < length(beta); ++i)
111  log_beta[i] = log(value_of(beta_vec[i]));
112  }
113 
115  T_partials_return, T_shape, T_inv_scale>
116  lambda_m_alpha_over_1p_beta(len_ab);
118  for (size_t i = 0; i < len_ab; ++i)
119  lambda_m_alpha_over_1p_beta[i] =
120  lambda[i]
121  - (value_of(alpha_vec[i])
122  / (1.0 + value_of(beta_vec[i])));
123  }
124 
125  for (size_t i = 0; i < size; i++) {
126  if (alpha_vec[i] > 1e10) { // reduces numerically to Poisson
128  logp -= lgamma(n_vec[i] + 1.0);
130  logp += multiply_log(n_vec[i], lambda[i]) - lambda[i];
131 
133  operands_and_partials.d_x1[i]
134  += n_vec[i] / value_of(alpha_vec[i])
135  - 1.0 / value_of(beta_vec[i]);
137  operands_and_partials.d_x2[i]
138  += (lambda[i] - n_vec[i]) / value_of(beta_vec[i]);
139  } else { // standard density definition
141  if (n_vec[i] != 0)
142  logp += binomial_coefficient_log(n_vec[i]
143  + value_of(alpha_vec[i])
144  - 1.0,
145  n_vec[i]);
147  logp +=
148  alpha_times_log_beta_over_1p_beta[i]
149  - n_vec[i] * log1p_beta[i];
150 
152  operands_and_partials.d_x1[i]
153  += digamma(value_of(alpha_vec[i]) + n_vec[i])
154  - digamma_alpha[i]
155  + log_beta_m_log1p_beta[i];
157  operands_and_partials.d_x2[i]
158  += lambda_m_alpha_over_1p_beta[i]
159  - n_vec[i] / (value_of(beta_vec[i]) + 1.0);
160  }
161  }
162  return operands_and_partials.value(logp);
163  }
164 
165  template <typename T_n,
166  typename T_shape, typename T_inv_scale>
167  inline
169  neg_binomial_log(const T_n& n,
170  const T_shape& alpha,
171  const T_inv_scale& beta) {
172  return neg_binomial_log<false>(n, alpha, beta);
173  }
174 
175  }
176 }
177 #endif
VectorView< T_return_type, false, true > d_x2
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: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
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.
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
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:11
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
return_type< T_shape, T_inv_scale >::type neg_binomial_log(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
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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