Stan Math Library  2.15.0
reverse mode automatic differentiation
inv_chi_square_lcdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_LCDF_HPP
3 
22 #include <boost/random/chi_squared_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 #include <limits>
26 
27 namespace stan {
28  namespace math {
29 
43  template <typename T_y, typename T_dof>
45  inv_chi_square_lcdf(const T_y& y, const T_dof& nu) {
47  T_partials_return;
48 
49  if ( !( stan::length(y) && stan::length(nu) ) ) return 0.0;
50 
51  static const char* function("inv_chi_square_lcdf");
52 
53  using boost::math::tools::promote_args;
54  using std::exp;
55 
56  T_partials_return P(0.0);
57 
58  check_positive_finite(function, "Degrees of freedom parameter", nu);
59  check_not_nan(function, "Random variable", y);
60  check_nonnegative(function, "Random variable", y);
61  check_consistent_sizes(function,
62  "Random variable", y,
63  "Degrees of freedom parameter", nu);
64 
67  size_t N = max_size(y, nu);
68 
69  OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
70 
71  // Explicit return for extreme values
72  // The gradients are technically ill-defined, but treated as zero
73  for (size_t i = 0; i < stan::length(y); i++)
74  if (value_of(y_vec[i]) == 0)
75  return operands_and_partials.value(negative_infinity());
76 
77  using boost::math::tgamma;
78  using std::exp;
79  using std::pow;
80  using std::log;
81 
83  T_partials_return, T_dof> gamma_vec(stan::length(nu));
85  T_partials_return, T_dof> digamma_vec(stan::length(nu));
86 
88  for (size_t i = 0; i < stan::length(nu); i++) {
89  const T_partials_return nu_dbl = value_of(nu_vec[i]);
90  gamma_vec[i] = tgamma(0.5 * nu_dbl);
91  digamma_vec[i] = digamma(0.5 * nu_dbl);
92  }
93  }
94 
95  for (size_t n = 0; n < N; n++) {
96  // Explicit results for extreme values
97  // The gradients are technically ill-defined, but treated as zero
98  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
99  continue;
100  }
101 
102  const T_partials_return y_dbl = value_of(y_vec[n]);
103  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
104  const T_partials_return nu_dbl = value_of(nu_vec[n]);
105 
106  const T_partials_return Pn = gamma_q(0.5 * nu_dbl, 0.5 * y_inv_dbl);
107 
108  P += log(Pn);
109 
111  operands_and_partials.d_x1[n] += 0.5 * y_inv_dbl * y_inv_dbl
112  * exp(-0.5*y_inv_dbl) * pow(0.5*y_inv_dbl, 0.5*nu_dbl-1)
113  / tgamma(0.5*nu_dbl) / Pn;
115  operands_and_partials.d_x2[n]
116  += 0.5 * grad_reg_inc_gamma(0.5 * nu_dbl,
117  0.5 * y_inv_dbl,
118  gamma_vec[n],
119  digamma_vec[n]) / Pn;
120  }
121  return operands_and_partials.value(P);
122  }
123 
124  }
125 }
126 #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
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
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.
return_type< T_y, T_dof >::type inv_chi_square_lcdf(const T_y &y, const T_dof &nu)
Returns the inverse chi square log cumulative distribution function for the given variate and degrees...
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
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
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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