Stan Math Library  2.20.0
reverse mode automatic differentiation
scaled_inv_chi_square_lcdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LCDF_HPP
3 
16 #include <limits>
17 #include <cmath>
18 
19 namespace stan {
20 namespace math {
21 
22 template <typename T_y, typename T_dof, typename T_scale>
24  const T_y& y, const T_dof& nu, const T_scale& s) {
26  T_partials_return;
27 
28  if (size_zero(y, nu, s))
29  return 0.0;
30 
31  static const char* function = "scaled_inv_chi_square_lcdf";
32 
33  T_partials_return P(0.0);
34 
35  check_not_nan(function, "Random variable", y);
36  check_nonnegative(function, "Random variable", y);
37  check_positive_finite(function, "Degrees of freedom parameter", nu);
38  check_positive_finite(function, "Scale parameter", s);
39  check_consistent_sizes(function, "Random variable", y,
40  "Degrees of freedom parameter", nu, "Scale parameter",
41  s);
42 
43  scalar_seq_view<T_y> y_vec(y);
44  scalar_seq_view<T_dof> nu_vec(nu);
45  scalar_seq_view<T_scale> s_vec(s);
46  size_t N = max_size(y, nu, s);
47 
48  operands_and_partials<T_y, T_dof, T_scale> ops_partials(y, nu, s);
49 
50  // Explicit return for extreme values
51  // The gradients are technically ill-defined, but treated as zero
52  for (size_t i = 0; i < stan::length(y); i++) {
53  if (value_of(y_vec[i]) == 0)
54  return ops_partials.build(negative_infinity());
55  }
56 
57  using std::exp;
58  using std::log;
59  using std::pow;
60 
61  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
62  gamma_vec(stan::length(nu));
63  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
64  digamma_vec(stan::length(nu));
65 
67  for (size_t i = 0; i < stan::length(nu); i++) {
68  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
69  gamma_vec[i] = tgamma(half_nu_dbl);
70  digamma_vec[i] = digamma(half_nu_dbl);
71  }
72  }
73 
74  for (size_t n = 0; n < N; n++) {
75  // Explicit results for extreme values
76  // The gradients are technically ill-defined, but treated as zero
77  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
78  continue;
79  }
80 
81  const T_partials_return y_dbl = value_of(y_vec[n]);
82  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
83  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
84  const T_partials_return s_dbl = value_of(s_vec[n]);
85  const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl * y_inv_dbl;
86  const T_partials_return half_nu_s2_overx_dbl
87  = 2.0 * half_nu_dbl * half_s2_overx_dbl;
88 
89  const T_partials_return Pn = gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
90  const T_partials_return gamma_p_deriv
91  = exp(-half_nu_s2_overx_dbl)
92  * pow(half_nu_s2_overx_dbl, half_nu_dbl - 1) / tgamma(half_nu_dbl);
93 
94  P += log(Pn);
95 
97  ops_partials.edge1_.partials_[n]
98  += half_nu_s2_overx_dbl * y_inv_dbl * gamma_p_deriv / Pn;
100  ops_partials.edge2_.partials_[n]
101  += (0.5
102  * grad_reg_inc_gamma(half_nu_dbl, half_nu_s2_overx_dbl,
103  gamma_vec[n], digamma_vec[n])
104  - half_s2_overx_dbl * gamma_p_deriv)
105  / Pn;
107  ops_partials.edge3_.partials_[n]
108  += -2.0 * half_nu_dbl * s_dbl * y_inv_dbl * gamma_p_deriv / 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.
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_lcdf(const T_y &y, const T_dof &nu, const T_scale &s)
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_
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, Op3 > edge3_
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

     [ Stan Home Page ] © 2011–2018, Stan Development Team.