Stan Math Library  2.12.0
reverse mode automatic differentiation
chi_square_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_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 
36  template <typename T_y, typename T_dof>
37  typename return_type<T_y, T_dof>::type
38  chi_square_cdf(const T_y& y, const T_dof& nu) {
39  static const char* function("chi_square_cdf");
41  T_partials_return;
42 
43  T_partials_return cdf(1.0);
44 
45  if (!(stan::length(y) && stan::length(nu)))
46  return cdf;
47 
48  check_not_nan(function, "Random variable", y);
49  check_nonnegative(function, "Random variable", y);
50  check_positive_finite(function, "Degrees of freedom parameter", nu);
51  check_consistent_sizes(function,
52  "Random variable", y,
53  "Degrees of freedom parameter", nu);
54 
55  VectorView<const T_y> y_vec(y);
56  VectorView<const T_dof> nu_vec(nu);
57  size_t N = max_size(y, nu);
58 
60  operands_and_partials(y, nu);
61 
62  // Explicit return for extreme values
63  // The gradients are technically ill-defined, but treated as zero
64  for (size_t i = 0; i < stan::length(y); i++) {
65  if (value_of(y_vec[i]) == 0)
66  return operands_and_partials.value(0.0);
67  }
68 
69  using boost::math::tgamma;
70  using std::exp;
71  using std::pow;
72  using std::exp;
73 
75  T_partials_return, T_dof> gamma_vec(stan::length(nu));
77  T_partials_return, T_dof> digamma_vec(stan::length(nu));
78 
80  for (size_t i = 0; i < stan::length(nu); i++) {
81  const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
82  gamma_vec[i] = tgamma(alpha_dbl);
83  digamma_vec[i] = digamma(alpha_dbl);
84  }
85  }
86 
87  for (size_t n = 0; n < N; n++) {
88  // Explicit results for extreme values
89  // The gradients are technically ill-defined, but treated as zero
90  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
91  continue;
92 
93  const T_partials_return y_dbl = value_of(y_vec[n]);
94  const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
95  const T_partials_return beta_dbl = 0.5;
96 
97  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
98 
99  cdf *= Pn;
100 
102  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
103  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
105  operands_and_partials.d_x2[n]
106  -= 0.5 * grad_reg_inc_gamma(alpha_dbl, beta_dbl
107  * y_dbl, gamma_vec[n],
108  digamma_vec[n]) / Pn;
109  }
110 
112  for (size_t n = 0; n < stan::length(y); ++n)
113  operands_and_partials.d_x1[n] *= cdf;
114  }
116  for (size_t n = 0; n < stan::length(nu); ++n)
117  operands_and_partials.d_x2[n] *= cdf;
118  }
119  return operands_and_partials.value(cdf);
120  }
121 
122  }
123 }
124 #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
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.
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)
return_type< T_y, T_dof >::type chi_square_cdf(const T_y &y, const T_dof &nu)
Calculates the chi square cumulative distribution function for the given variate and degrees of freed...
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
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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