Stan Math Library  2.10.0
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 
32  namespace math {
33 
34  // NegBinomial(n|alpha, beta) [alpha > 0; beta > 0; n >= 0]
35  template <bool propto,
36  typename T_n,
37  typename T_shape, typename T_inv_scale>
38  typename return_type<T_shape, T_inv_scale>::type
39  neg_binomial_log(const T_n& n,
40  const T_shape& alpha,
41  const T_inv_scale& beta) {
42  typedef typename stan::partials_return_type<T_n, T_shape,
43  T_inv_scale>::type
44  T_partials_return;
45 
46  static const char* function("stan::math::neg_binomial_log");
47 
53 
54  // check if any vectors are zero length
55  if (!(stan::length(n)
56  && stan::length(alpha)
57  && stan::length(beta)))
58  return 0.0;
59 
60  T_partials_return logp(0.0);
61  check_nonnegative(function, "Failures variable", n);
62  check_positive_finite(function, "Shape parameter", alpha);
63  check_positive_finite(function, "Inverse scale parameter", beta);
64  check_consistent_sizes(function,
65  "Failures variable", n,
66  "Shape parameter", alpha,
67  "Inverse scale parameter", beta);
68 
69  // check if no variables are involved and prop-to
71  return 0.0;
72 
75  using stan::math::digamma;
76  using stan::math::lgamma;
77  using std::log;
78  using std::log;
79 
80  // set up template expressions wrapping scalars into vector views
81  VectorView<const T_n> n_vec(n);
82  VectorView<const T_shape> alpha_vec(alpha);
83  VectorView<const T_inv_scale> beta_vec(beta);
84  size_t size = max_size(n, alpha, beta);
85 
87  operands_and_partials(alpha, beta);
88 
89  size_t len_ab = max_size(alpha, beta);
91  lambda(len_ab);
92  for (size_t i = 0; i < len_ab; ++i)
93  lambda[i] = value_of(alpha_vec[i]) / value_of(beta_vec[i]);
94 
96  log1p_beta(length(beta));
97  for (size_t i = 0; i < length(beta); ++i)
98  log1p_beta[i] = log1p(value_of(beta_vec[i]));
99 
101  log_beta_m_log1p_beta(length(beta));
102  for (size_t i = 0; i < length(beta); ++i)
103  log_beta_m_log1p_beta[i] = log(value_of(beta_vec[i])) - log1p_beta[i];
104 
106  alpha_times_log_beta_over_1p_beta(len_ab);
107  for (size_t i = 0; i < len_ab; ++i)
108  alpha_times_log_beta_over_1p_beta[i]
109  = value_of(alpha_vec[i])
110  * log(value_of(beta_vec[i])
111  / (1.0 + value_of(beta_vec[i])));
112 
114  T_partials_return, T_shape>
115  digamma_alpha(length(alpha));
117  for (size_t i = 0; i < length(alpha); ++i)
118  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
119  }
120 
122  T_partials_return, T_inv_scale> log_beta(length(beta));
124  for (size_t i = 0; i < length(beta); ++i)
125  log_beta[i] = log(value_of(beta_vec[i]));
126  }
127 
129  T_partials_return, T_shape, T_inv_scale>
130  lambda_m_alpha_over_1p_beta(len_ab);
132  for (size_t i = 0; i < len_ab; ++i)
133  lambda_m_alpha_over_1p_beta[i] =
134  lambda[i]
135  - (value_of(alpha_vec[i])
136  / (1.0 + value_of(beta_vec[i])));
137  }
138 
139  for (size_t i = 0; i < size; i++) {
140  if (alpha_vec[i] > 1e10) { // reduces numerically to Poisson
142  logp -= lgamma(n_vec[i] + 1.0);
144  logp += multiply_log(n_vec[i], lambda[i]) - lambda[i];
145 
147  operands_and_partials.d_x1[i]
148  += n_vec[i] / value_of(alpha_vec[i])
149  - 1.0 / value_of(beta_vec[i]);
151  operands_and_partials.d_x2[i]
152  += (lambda[i] - n_vec[i]) / value_of(beta_vec[i]);
153  } else { // standard density definition
155  if (n_vec[i] != 0)
156  logp += binomial_coefficient_log(n_vec[i]
157  + value_of(alpha_vec[i])
158  - 1.0,
159  n_vec[i]);
161  logp +=
162  alpha_times_log_beta_over_1p_beta[i]
163  - n_vec[i] * log1p_beta[i];
164 
166  operands_and_partials.d_x1[i]
167  += digamma(value_of(alpha_vec[i]) + n_vec[i])
168  - digamma_alpha[i]
169  + log_beta_m_log1p_beta[i];
171  operands_and_partials.d_x2[i]
172  += lambda_m_alpha_over_1p_beta[i]
173  - n_vec[i] / (value_of(beta_vec[i]) + 1.0);
174  }
175  }
176  return operands_and_partials.value(logp);
177  }
178 
179  template <typename T_n,
180  typename T_shape, typename T_inv_scale>
181  inline
183  neg_binomial_log(const T_n& n,
184  const T_shape& alpha,
185  const T_inv_scale& beta) {
186  return neg_binomial_log<false>(n, alpha, beta);
187  }
188  }
189 }
190 #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)
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.
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.
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:16
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
return_type< T_shape, T_inv_scale >::type neg_binomial_log(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
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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