Stan Math Library  2.14.0
reverse mode automatic differentiation
neg_binomial_lcdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LCDF_HPP
3 
21 #include <boost/math/special_functions/digamma.hpp>
22 #include <boost/random/negative_binomial_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 #include <limits>
26 
27 namespace stan {
28  namespace math {
29 
30  template <typename T_n, typename T_shape,
31  typename T_inv_scale>
33  neg_binomial_lcdf(const T_n& n, const T_shape& alpha,
34  const T_inv_scale& beta) {
35  static const char* function("neg_binomial_lcdf");
36  typedef typename stan::partials_return_type<T_n, T_shape,
37  T_inv_scale>::type
38  T_partials_return;
39 
40  if (!(stan::length(n) && stan::length(alpha) && stan::length(beta)))
41  return 0.0;
42 
43  T_partials_return P(0.0);
44 
45  check_positive_finite(function, "Shape parameter", alpha);
46  check_positive_finite(function, "Inverse scale parameter", beta);
47  check_consistent_sizes(function,
48  "Failures variable", n,
49  "Shape parameter", alpha,
50  "Inverse scale parameter", beta);
51 
52  VectorView<const T_n> n_vec(n);
53  VectorView<const T_shape> alpha_vec(alpha);
54  VectorView<const T_inv_scale> beta_vec(beta);
55  size_t size = max_size(n, alpha, beta);
56 
57  using std::exp;
58  using std::pow;
59  using std::log;
60  using std::exp;
61 
63  operands_and_partials(alpha, beta);
64 
65  // Explicit return for extreme values
66  // The gradients are technically ill-defined, but treated as zero
67  for (size_t i = 0; i < stan::length(n); i++) {
68  if (value_of(n_vec[i]) < 0)
69  return operands_and_partials.value(negative_infinity());
70  }
71 
73  T_partials_return, T_shape>
74  digammaN_vec(stan::length(alpha));
76  T_partials_return, T_shape>
77  digammaAlpha_vec(stan::length(alpha));
79  T_partials_return, T_shape>
80  digammaSum_vec(stan::length(alpha));
81 
83  for (size_t i = 0; i < stan::length(alpha); i++) {
84  const T_partials_return n_dbl = value_of(n_vec[i]);
85  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
86 
87  digammaN_vec[i] = digamma(n_dbl + 1);
88  digammaAlpha_vec[i] = digamma(alpha_dbl);
89  digammaSum_vec[i] = digamma(n_dbl + alpha_dbl + 1);
90  }
91  }
92 
93  for (size_t i = 0; i < size; i++) {
94  // Explicit results for extreme values
95  // The gradients are technically ill-defined, but treated as zero
96  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
97  return operands_and_partials.value(0.0);
98 
99  const T_partials_return n_dbl = value_of(n_vec[i]);
100  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
101  const T_partials_return beta_dbl = value_of(beta_vec[i]);
102  const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
103  const T_partials_return d_dbl = 1.0 / ( (1.0 + beta_dbl)
104  * (1.0 + beta_dbl) );
105  const T_partials_return Pi = inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
106  const T_partials_return beta_func = exp(lbeta(n_dbl + 1, alpha_dbl));
107 
108  P += log(Pi);
109 
111  T_partials_return g1 = 0;
112  T_partials_return g2 = 0;
113 
114  grad_reg_inc_beta(g1, g2, alpha_dbl,
115  n_dbl + 1, p_dbl,
116  digammaAlpha_vec[i],
117  digammaN_vec[i],
118  digammaSum_vec[i],
119  beta_func);
120  operands_and_partials.d_x1[i] += g1 / Pi;
121  }
123  operands_and_partials.d_x2[i] += d_dbl * pow(1-p_dbl, n_dbl)
124  * pow(p_dbl, alpha_dbl-1) / beta_func / Pi;
125  }
126 
127  return operands_and_partials.value(P);
128  }
129 
130  }
131 }
132 #endif
VectorView< T_return_type, false, true > d_x2
return_type< T_shape, T_inv_scale >::type neg_binomial_lcdf(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
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
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...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void grad_reg_inc_beta(T &g1, T &g2, const T &a, const T &b, const T &z, const T &digammaA, const T &digammaB, const T &digammaSum, const T &betaAB)
Computes the gradients of the regularized incomplete beta function.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:22
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 > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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
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
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
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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