Stan Math Library  2.12.0
reverse mode automatic differentiation
chi_square_cdf_log.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_LOG_HPP
3 
19 #include <boost/random/chi_squared_distribution.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 #include <limits>
23 
24 namespace stan {
25  namespace math {
26 
27  template <typename T_y, typename T_dof>
28  typename return_type<T_y, T_dof>::type
29  chi_square_cdf_log(const T_y& y, const T_dof& nu) {
30  static const char* function("chi_square_cdf_log");
32  T_partials_return;
33 
34  T_partials_return cdf_log(0.0);
35 
36  if (!(stan::length(y) && stan::length(nu)))
37  return cdf_log;
38 
39  check_not_nan(function, "Random variable", y);
40  check_nonnegative(function, "Random variable", y);
41  check_positive_finite(function, "Degrees of freedom parameter", nu);
42  check_consistent_sizes(function,
43  "Random variable", y,
44  "Degrees of freedom parameter", nu);
45 
46  VectorView<const T_y> y_vec(y);
47  VectorView<const T_dof> nu_vec(nu);
48  size_t N = max_size(y, nu);
49 
51  operands_and_partials(y, nu);
52 
53  // Explicit return for extreme values
54  // The gradients are technically ill-defined, but treated as zero
55  for (size_t i = 0; i < stan::length(y); i++) {
56  if (value_of(y_vec[i]) == 0)
57  return operands_and_partials.value(negative_infinity());
58  }
59 
60  using boost::math::tgamma;
61  using std::exp;
62  using std::pow;
63  using std::log;
64  using std::exp;
65 
67  T_partials_return, T_dof> gamma_vec(stan::length(nu));
69  T_partials_return, T_dof> digamma_vec(stan::length(nu));
70 
72  for (size_t i = 0; i < stan::length(nu); i++) {
73  const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
74  gamma_vec[i] = tgamma(alpha_dbl);
75  digamma_vec[i] = digamma(alpha_dbl);
76  }
77  }
78 
79  for (size_t n = 0; n < N; n++) {
80  // Explicit results for extreme values
81  // The gradients are technically ill-defined, but treated as zero
82  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
83  return operands_and_partials.value(0.0);
84 
85  const T_partials_return y_dbl = value_of(y_vec[n]);
86  const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
87  const T_partials_return beta_dbl = 0.5;
88 
89  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
90 
91  cdf_log += log(Pn);
92 
94  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
95  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
97  operands_and_partials.d_x2[n]
98  -= 0.5 * grad_reg_inc_gamma(alpha_dbl, beta_dbl
99  * y_dbl, gamma_vec[n],
100  digamma_vec[n]) / Pn;
101  }
102  return operands_and_partials.value(cdf_log);
103  }
104 
105  }
106 }
107 #endif
VectorView< T_return_type, false, true > d_x2
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: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
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
This class builds partial derivatives with respect to a set of operands.
return_type< T_y, T_dof >::type chi_square_cdf_log(const T_y &y, const T_dof &nu)
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:14
VectorBuilder allocates type T1 values to be used as intermediate values.
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.
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6)
Gradient of the regularized incomplete gamma functions igamma(a, z)
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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:14
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
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.
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)
Definition: digamma.hpp:15

     [ Stan Home Page ] © 2011–2016, Stan Development Team.