Stan Math Library  2.20.0
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 
15 #include <cmath>
16 #include <limits>
17 
18 namespace stan {
19 namespace math {
20 
34 template <typename T_y, typename T_dof>
36  const T_dof& nu) {
37  static const char* function = "chi_square_cdf";
38  typedef
39  typename stan::partials_return_type<T_y, T_dof>::type T_partials_return;
40 
41  T_partials_return cdf(1.0);
42 
43  if (size_zero(y, nu))
44  return cdf;
45 
46  check_not_nan(function, "Random variable", y);
47  check_nonnegative(function, "Random variable", y);
48  check_positive_finite(function, "Degrees of freedom parameter", nu);
49  check_consistent_sizes(function, "Random variable", y,
50  "Degrees of freedom parameter", nu);
51 
52  scalar_seq_view<T_y> y_vec(y);
53  scalar_seq_view<T_dof> nu_vec(nu);
54  size_t N = max_size(y, nu);
55 
56  operands_and_partials<T_y, T_dof> ops_partials(y, nu);
57 
58  // Explicit return for extreme values
59  // The gradients are technically ill-defined, but treated as zero
60  for (size_t i = 0; i < stan::length(y); i++) {
61  if (value_of(y_vec[i]) == 0)
62  return ops_partials.build(0.0);
63  }
64 
65  using std::exp;
66  using std::pow;
67 
68  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
69  gamma_vec(stan::length(nu));
70  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
71  digamma_vec(stan::length(nu));
72 
74  for (size_t i = 0; i < stan::length(nu); i++) {
75  const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
76  gamma_vec[i] = tgamma(alpha_dbl);
77  digamma_vec[i] = digamma(alpha_dbl);
78  }
79  }
80 
81  for (size_t n = 0; n < N; n++) {
82  // Explicit results for extreme values
83  // The gradients are technically ill-defined, but treated as zero
84  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
85  continue;
86 
87  const T_partials_return y_dbl = value_of(y_vec[n]);
88  const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
89  const T_partials_return beta_dbl = 0.5;
90 
91  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
92 
93  cdf *= Pn;
94 
96  ops_partials.edge1_.partials_[n] += beta_dbl * exp(-beta_dbl * y_dbl)
97  * pow(beta_dbl * y_dbl, alpha_dbl - 1)
98  / tgamma(alpha_dbl) / Pn;
100  ops_partials.edge2_.partials_[n]
101  -= 0.5
102  * grad_reg_inc_gamma(alpha_dbl, beta_dbl * y_dbl, gamma_vec[n],
103  digamma_vec[n])
104  / Pn;
105  }
106 
108  for (size_t n = 0; n < stan::length(y); ++n)
109  ops_partials.edge1_.partials_[n] *= cdf;
110  }
112  for (size_t n = 0; n < stan::length(nu); ++n)
113  ops_partials.edge2_.partials_[n] *= cdf;
114  }
115  return ops_partials.build(cdf);
116 }
117 
118 } // namespace math
119 } // namespace stan
120 #endif
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
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
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
return_type< T1, T2 >::type grad_reg_inc_gamma(T1 a, T2 z, T1 g, T1 dig, double precision=1e-6, int max_steps=1e5)
Gradient of the regularized incomplete gamma functions igamma(a, z)
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
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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.
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:15
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
return_type< T_y, T_dof >::type chi_square_cdf(const T_y &y, const T_dof &nu)
Returns the chi square cumulative distribution function for the given variate and degrees of freedom...
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:16
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
Definition: tgamma.hpp:21
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_
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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