Stan Math Library  2.14.0
reverse mode automatic differentiation
inv_chi_square_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_CDF_HPP
3 
4 #include <boost/random/chi_squared_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 #include <limits>
26 
27 namespace stan {
28  namespace math {
29 
30  template <typename T_y, typename T_dof>
32  inv_chi_square_cdf(const T_y& y, const T_dof& nu) {
34  T_partials_return;
35 
36  if ( !( stan::length(y) && stan::length(nu) ) ) return 1.0;
37 
38  static const char* function("inv_chi_square_cdf");
39 
40  using boost::math::tools::promote_args;
41  using std::exp;
42 
43  T_partials_return P(1.0);
44 
45  check_positive_finite(function, "Degrees of freedom parameter", nu);
46  check_not_nan(function, "Random variable", y);
47  check_nonnegative(function, "Random variable", y);
48  check_consistent_sizes(function,
49  "Random variable", y,
50  "Degrees of freedom parameter", nu);
51 
52  VectorView<const T_y> y_vec(y);
53  VectorView<const T_dof> nu_vec(nu);
54  size_t N = max_size(y, nu);
55 
56  OperandsAndPartials<T_y, T_dof> operands_and_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 operands_and_partials.value(0.0);
63 
64  using boost::math::tgamma;
65  using std::exp;
66  using std::pow;
67 
69  T_partials_return, T_dof> gamma_vec(stan::length(nu));
71  T_partials_return, T_dof> digamma_vec(stan::length(nu));
72 
74  for (size_t i = 0; i < stan::length(nu); i++) {
75  const T_partials_return nu_dbl = value_of(nu_vec[i]);
76  gamma_vec[i] = tgamma(0.5 * nu_dbl);
77  digamma_vec[i] = digamma(0.5 * nu_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 
88  const T_partials_return y_dbl = value_of(y_vec[n]);
89  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
90  const T_partials_return nu_dbl = value_of(nu_vec[n]);
91 
92  const T_partials_return Pn = gamma_q(0.5 * nu_dbl, 0.5 * y_inv_dbl);
93 
94  P *= Pn;
95 
97  operands_and_partials.d_x1[n] += 0.5 * y_inv_dbl * y_inv_dbl
98  * exp(-0.5*y_inv_dbl) * pow(0.5*y_inv_dbl, 0.5*nu_dbl-1)
99  / tgamma(0.5*nu_dbl) / Pn;
101  operands_and_partials.d_x2[n]
102  += 0.5 * grad_reg_inc_gamma(0.5 * nu_dbl,
103  0.5 * y_inv_dbl,
104  gamma_vec[n],
105  digamma_vec[n]) / Pn;
106  }
107 
109  for (size_t n = 0; n < stan::length(y); ++n)
110  operands_and_partials.d_x1[n] *= P;
111  }
113  for (size_t n = 0; n < stan::length(nu); ++n)
114  operands_and_partials.d_x2[n] *= P;
115  }
116  return operands_and_partials.value(P);
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
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
return_type< T_y, T_dof >::type inv_chi_square_cdf(const T_y &y, const T_dof &nu)
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
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
VectorBuilder allocates type T1 values to be used as intermediate values.
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
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
Definition: tgamma.hpp:20
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
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
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:14
VectorView< T_return_type, false, true > d_x1
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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