Stan Math Library  2.12.0
reverse mode automatic differentiation
scaled_inv_chi_square_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CCDF_LOG_HPP
3 
22 #include <boost/random/chi_squared_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <limits>
25 #include <cmath>
26 
27 namespace stan {
28  namespace math {
29 
30  template <typename T_y, typename T_dof, typename T_scale>
31  typename return_type<T_y, T_dof, T_scale>::type
32  scaled_inv_chi_square_ccdf_log(const T_y& y, const T_dof& nu,
33  const T_scale& s) {
35  T_partials_return;
36 
37  if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
38  return 0.0;
39 
40  static const char* function("scaled_inv_chi_square_ccdf_log");
41 
42  using std::exp;
43 
44  T_partials_return P(0.0);
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_positive_finite(function, "Scale parameter", s);
50  check_consistent_sizes(function,
51  "Random variable", y,
52  "Degrees of freedom parameter", nu,
53  "Scale parameter", s);
54 
55  VectorView<const T_y> y_vec(y);
56  VectorView<const T_dof> nu_vec(nu);
58  size_t N = max_size(y, nu, s);
59 
61  operands_and_partials(y, nu, s);
62 
63  // Explicit return for extreme values
64  // The gradients are technically ill-defined, but treated as zero
65  for (size_t i = 0; i < stan::length(y); i++) {
66  if (value_of(y_vec[i]) == 0)
67  return operands_and_partials.value(0.0);
68  }
69 
70  using boost::math::tgamma;
71  using std::exp;
72  using std::pow;
73  using std::log;
74 
76  T_partials_return, T_dof> gamma_vec(stan::length(nu));
78  T_partials_return, T_dof> digamma_vec(stan::length(nu));
79 
81  for (size_t i = 0; i < stan::length(nu); i++) {
82  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
83  gamma_vec[i] = tgamma(half_nu_dbl);
84  digamma_vec[i] = digamma(half_nu_dbl);
85  }
86  }
87 
88  for (size_t n = 0; n < N; n++) {
89  // Explicit results for extreme values
90  // The gradients are technically ill-defined, but treated as zero
91  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
92  return operands_and_partials.value(negative_infinity());
93  }
94 
95  const T_partials_return y_dbl = value_of(y_vec[n]);
96  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
97  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
98  const T_partials_return s_dbl = value_of(s_vec[n]);
99  const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
100  * y_inv_dbl;
101  const T_partials_return half_nu_s2_overx_dbl
102  = 2.0 * half_nu_dbl * half_s2_overx_dbl;
103 
104  const T_partials_return Pn = gamma_p(half_nu_dbl,
105  half_nu_s2_overx_dbl);
106  const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
107  * pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
108 
109  P += log(Pn);
110 
112  operands_and_partials.d_x1[n] -= half_nu_s2_overx_dbl * y_inv_dbl
113  * gamma_p_deriv / Pn;
115  operands_and_partials.d_x2[n]
116  -= (0.5 * grad_reg_inc_gamma(half_nu_dbl,
117  half_nu_s2_overx_dbl,
118  gamma_vec[n],
119  digamma_vec[n])
120  - half_s2_overx_dbl * gamma_p_deriv)
121  / Pn;
123  operands_and_partials.d_x3[n] += 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
124  * gamma_p_deriv / Pn;
125  }
126  return operands_and_partials.value(P);
127  }
128 
129  }
130 }
131 #endif
VectorView< T_return_type, false, true > d_x2
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
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.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_ccdf_log(const T_y &y, const T_dof &nu, const T_scale &s)
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:14
VectorBuilder allocates type T1 values to be used as intermediate values.
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
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
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
fvar< T > tgamma(const fvar< T > &x)
Definition: tgamma.hpp:14
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
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
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)
Definition: digamma.hpp:15

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