Stan Math Library  2.15.0
reverse mode automatic differentiation
chi_square_lcdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LCDF_HPP
3 
20 #include <boost/random/chi_squared_distribution.hpp>
21 #include <boost/random/variate_generator.hpp>
22 #include <cmath>
23 #include <limits>
24 
25 namespace stan {
26  namespace math {
27 
41  template <typename T_y, typename T_dof>
43  chi_square_lcdf(const T_y& y, const T_dof& nu) {
44  static const char* function("chi_square_lcdf");
46  T_partials_return;
47 
48  T_partials_return cdf_log(0.0);
49 
50  if (!(stan::length(y) && stan::length(nu)))
51  return cdf_log;
52 
53  check_not_nan(function, "Random variable", y);
54  check_nonnegative(function, "Random variable", y);
55  check_positive_finite(function, "Degrees of freedom parameter", nu);
56  check_consistent_sizes(function,
57  "Random variable", y,
58  "Degrees of freedom parameter", nu);
59 
62  size_t N = max_size(y, nu);
63 
65  operands_and_partials(y, nu);
66 
67  // Explicit return for extreme values
68  // The gradients are technically ill-defined, but treated as zero
69  for (size_t i = 0; i < stan::length(y); i++) {
70  if (value_of(y_vec[i]) == 0)
71  return operands_and_partials.value(negative_infinity());
72  }
73 
74  using boost::math::tgamma;
75  using std::exp;
76  using std::pow;
77  using std::log;
78  using std::exp;
79 
81  T_partials_return, T_dof> gamma_vec(stan::length(nu));
83  T_partials_return, T_dof> digamma_vec(stan::length(nu));
84 
86  for (size_t i = 0; i < stan::length(nu); i++) {
87  const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
88  gamma_vec[i] = tgamma(alpha_dbl);
89  digamma_vec[i] = digamma(alpha_dbl);
90  }
91  }
92 
93  for (size_t n = 0; n < N; n++) {
94  // Explicit results for extreme values
95  // The gradients are technically ill-defined, but treated as zero
96  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
97  return operands_and_partials.value(0.0);
98 
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  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
104 
105  cdf_log += log(Pn);
106 
108  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
109  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
111  operands_and_partials.d_x2[n]
112  -= 0.5 * grad_reg_inc_gamma(alpha_dbl, beta_dbl
113  * y_dbl, gamma_vec[n],
114  digamma_vec[n]) / Pn;
115  }
116  return operands_and_partials.value(cdf_log);
117  }
118 
119  }
120 }
121 #endif
VectorView< T_return_type, false, true > d_x2
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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
return_type< T_y, T_dof >::type chi_square_lcdf(const T_y &y, const T_dof &nu)
Returns the chi square log cumulative distribution function for the given variate and degrees of free...
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6, int max_steps=1e5)
Gradient of the regularized incomplete gamma functions igamma(a, z)
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
Definition: tgamma.hpp:20
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.
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
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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