Stan Math Library  2.20.0
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 
16 #include <cmath>
17 #include <limits>
18 
19 namespace stan {
20 namespace math {
21 
35 template <typename T_y, typename T_dof>
37  const T_dof& nu) {
38  typedef
39  typename stan::partials_return_type<T_y, T_dof>::type T_partials_return;
40 
41  if (size_zero(y, nu))
42  return 0.0;
43 
44  static const char* function = "inv_chi_square_lcdf";
45 
46  T_partials_return P(0.0);
47 
48  check_positive_finite(function, "Degrees of freedom parameter", nu);
49  check_not_nan(function, "Random variable", y);
50  check_nonnegative(function, "Random variable", y);
51  check_consistent_sizes(function, "Random variable", y,
52  "Degrees of freedom parameter", nu);
53 
54  scalar_seq_view<T_y> y_vec(y);
55  scalar_seq_view<T_dof> nu_vec(nu);
56  size_t N = max_size(y, nu);
57 
58  operands_and_partials<T_y, T_dof> ops_partials(y, nu);
59 
60  // Explicit return for extreme values
61  // The gradients are technically ill-defined, but treated as zero
62  for (size_t i = 0; i < stan::length(y); i++)
63  if (value_of(y_vec[i]) == 0)
64  return ops_partials.build(negative_infinity());
65 
66  using std::exp;
67  using std::log;
68  using std::pow;
69 
70  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
71  gamma_vec(stan::length(nu));
72  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
73  digamma_vec(stan::length(nu));
74 
76  for (size_t i = 0; i < stan::length(nu); i++) {
77  const T_partials_return nu_dbl = value_of(nu_vec[i]);
78  gamma_vec[i] = tgamma(0.5 * nu_dbl);
79  digamma_vec[i] = digamma(0.5 * nu_dbl);
80  }
81  }
82 
83  for (size_t n = 0; n < N; n++) {
84  // Explicit results for extreme values
85  // The gradients are technically ill-defined, but treated as zero
86  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
87  continue;
88  }
89 
90  const T_partials_return y_dbl = value_of(y_vec[n]);
91  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
92  const T_partials_return nu_dbl = value_of(nu_vec[n]);
93 
94  const T_partials_return Pn = gamma_q(0.5 * nu_dbl, 0.5 * y_inv_dbl);
95 
96  P += log(Pn);
97 
99  ops_partials.edge1_.partials_[n]
100  += 0.5 * y_inv_dbl * y_inv_dbl * exp(-0.5 * y_inv_dbl)
101  * pow(0.5 * y_inv_dbl, 0.5 * nu_dbl - 1) / tgamma(0.5 * nu_dbl)
102  / Pn;
104  ops_partials.edge2_.partials_[n]
105  += 0.5
106  * grad_reg_inc_gamma(0.5 * nu_dbl, 0.5 * y_inv_dbl, gamma_vec[n],
107  digamma_vec[n])
108  / Pn;
109  }
110  return ops_partials.build(P);
111 }
112 
113 } // namespace math
114 } // namespace stan
115 #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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
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.
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 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: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.
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:13
internal::ops_partials_edge< double, Op1 > edge1_
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:115
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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