Stan Math Library  2.9.0
reverse mode automatic differentiation
chi_square_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CCDF_LOG_HPP
3 
4 #include <boost/random/chi_squared_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
19 #include <cmath>
20 #include <limits>
21 
22 namespace stan {
23 
24  namespace math {
25 
26  template <typename T_y, typename T_dof>
27  typename return_type<T_y, T_dof>::type
28  chi_square_ccdf_log(const T_y& y, const T_dof& nu) {
29  static const char* function("stan::math::chi_square_ccdf_log");
31  T_partials_return;
32 
38 
39  T_partials_return ccdf_log(0.0);
40 
41  // Size checks
42  if (!(stan::length(y) && stan::length(nu)))
43  return ccdf_log;
44 
45  check_not_nan(function, "Random variable", y);
46  check_nonnegative(function, "Random variable", y);
47  check_positive_finite(function, "Degrees of freedom parameter", nu);
48  check_consistent_sizes(function,
49  "Random variable", y,
50  "Degrees of freedom parameter", nu);
51 
52  // Wrap arguments in vectors
53  VectorView<const T_y> y_vec(y);
54  VectorView<const T_dof> nu_vec(nu);
55  size_t N = max_size(y, nu);
56 
58  operands_and_partials(y, nu);
59 
60  // Explicit return for extreme values
61  // The gradients are technically ill-defined, but treated as zero
62  for (size_t i = 0; i < stan::length(y); i++) {
63  if (value_of(y_vec[i]) == 0)
64  return operands_and_partials.to_var(0.0, y, nu);
65  }
66 
67  // Compute ccdf_log and its gradients
68  using stan::math::gamma_p;
69  using stan::math::digamma;
70  using boost::math::tgamma;
71  using std::exp;
72  using std::pow;
73  using std::log;
74  using std::exp;
75 
76  // Cache a few expensive function calls if nu is a parameter
78  T_partials_return, T_dof> gamma_vec(stan::length(nu));
80  T_partials_return, T_dof> digamma_vec(stan::length(nu));
81 
83  for (size_t i = 0; i < stan::length(nu); i++) {
84  const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
85  gamma_vec[i] = tgamma(alpha_dbl);
86  digamma_vec[i] = digamma(alpha_dbl);
87  }
88  }
89 
90  // Compute vectorized ccdf_log and gradient
91  for (size_t n = 0; n < N; n++) {
92  // Explicit results for extreme values
93  // The gradients are technically ill-defined, but treated as zero
94  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
95  return operands_and_partials.to_var(stan::math::negative_infinity(),
96  y, nu);
97 
98  // Pull out values
99  const T_partials_return y_dbl = value_of(y_vec[n]);
100  const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
101  const T_partials_return beta_dbl = 0.5;
102 
103  // Compute
104  const T_partials_return Pn = 1.0 - gamma_p(alpha_dbl, beta_dbl * y_dbl);
105 
106  ccdf_log += log(Pn);
107 
109  operands_and_partials.d_x1[n] -= beta_dbl * exp(-beta_dbl * y_dbl)
110  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
112  operands_and_partials.d_x2[n]
113  += 0.5 * stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
114  * y_dbl, gamma_vec[n],
115  digamma_vec[n]) / Pn;
116  }
117 
118  return operands_and_partials.to_var(ccdf_log, y, nu);
119  }
120  }
121 }
122 #endif
return_type< T_y, T_dof >::type chi_square_ccdf_log(const T_y &y, const T_dof &nu)
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:15
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
fvar< T > tgamma(const fvar< T > &x)
Definition: tgamma.hpp:15
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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