Stan Math Library  2.20.0
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 
14 #include <cmath>
15 #include <limits>
16 
17 namespace stan {
18 namespace math {
19 
20 template <typename T_n, typename T_shape, typename T_inv_scale>
22  const T_n& n, const T_shape& alpha, const T_inv_scale& beta) {
23  static const char* function = "neg_binomial_lcdf";
25  T_partials_return;
26 
27  if (size_zero(n, alpha, beta))
28  return 0.0;
29 
30  T_partials_return P(0.0);
31 
32  check_positive_finite(function, "Shape parameter", alpha);
33  check_positive_finite(function, "Inverse scale parameter", beta);
34  check_consistent_sizes(function, "Failures variable", n, "Shape parameter",
35  alpha, "Inverse scale parameter", beta);
36 
37  scalar_seq_view<T_n> n_vec(n);
38  scalar_seq_view<T_shape> alpha_vec(alpha);
39  scalar_seq_view<T_inv_scale> beta_vec(beta);
40  size_t size = max_size(n, alpha, beta);
41 
42  using std::exp;
43  using std::log;
44  using std::pow;
45 
46  operands_and_partials<T_shape, T_inv_scale> ops_partials(alpha, beta);
47 
48  // Explicit return for extreme values
49  // The gradients are technically ill-defined, but treated as zero
50  for (size_t i = 0; i < stan::length(n); i++) {
51  if (value_of(n_vec[i]) < 0)
52  return ops_partials.build(negative_infinity());
53  }
54 
55  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
56  digammaN_vec(stan::length(alpha));
57  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
58  digammaAlpha_vec(stan::length(alpha));
59  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
60  digammaSum_vec(stan::length(alpha));
61 
63  for (size_t i = 0; i < stan::length(alpha); i++) {
64  const T_partials_return n_dbl = value_of(n_vec[i]);
65  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
66 
67  digammaN_vec[i] = digamma(n_dbl + 1);
68  digammaAlpha_vec[i] = digamma(alpha_dbl);
69  digammaSum_vec[i] = digamma(n_dbl + alpha_dbl + 1);
70  }
71  }
72 
73  for (size_t i = 0; i < size; i++) {
74  // Explicit results for extreme values
75  // The gradients are technically ill-defined, but treated as zero
76  if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
77  return ops_partials.build(0.0);
78 
79  const T_partials_return n_dbl = value_of(n_vec[i]);
80  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
81  const T_partials_return beta_dbl = value_of(beta_vec[i]);
82  const T_partials_return p_dbl = beta_dbl / (1.0 + beta_dbl);
83  const T_partials_return d_dbl = 1.0 / ((1.0 + beta_dbl) * (1.0 + beta_dbl));
84  const T_partials_return Pi = inc_beta(alpha_dbl, n_dbl + 1.0, p_dbl);
85  const T_partials_return beta_func = stan::math::beta(n_dbl + 1, alpha_dbl);
86 
87  P += log(Pi);
88 
90  T_partials_return g1 = 0;
91  T_partials_return g2 = 0;
92 
93  grad_reg_inc_beta(g1, g2, alpha_dbl, n_dbl + 1, p_dbl,
94  digammaAlpha_vec[i], digammaN_vec[i], digammaSum_vec[i],
95  beta_func);
96  ops_partials.edge1_.partials_[i] += g1 / Pi;
97  }
99  ops_partials.edge2_.partials_[i] += d_dbl * pow(1 - p_dbl, n_dbl)
100  * pow(p_dbl, alpha_dbl - 1)
101  / beta_func / Pi;
102  }
103 
104  return ops_partials.build(P);
105 }
106 
107 } // namespace math
108 } // namespace stan
109 #endif
return_type< T_shape, T_inv_scale >::type neg_binomial_lcdf(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
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 > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:18
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.
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.
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.
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:21
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 > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:16
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_
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:115
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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