Stan Math Library  2.15.0
reverse mode automatic differentiation
scaled_inv_chi_square_lcdf.hpp
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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 
23 #include <boost/random/chi_squared_distribution.hpp>
24 #include <boost/random/variate_generator.hpp>
25 #include <limits>
26 #include <cmath>
27 
28 namespace stan {
29  namespace math {
30 
31  template <typename T_y, typename T_dof, typename T_scale>
33  scaled_inv_chi_square_lcdf(const T_y& y, const T_dof& nu,
34  const T_scale& s) {
36  T_partials_return;
37 
38  if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
39  return 0.0;
40 
41  static const char* function("scaled_inv_chi_square_lcdf");
42 
43  using std::exp;
44 
45  T_partials_return P(0.0);
46 
47  check_not_nan(function, "Random variable", y);
48  check_nonnegative(function, "Random variable", y);
49  check_positive_finite(function, "Degrees of freedom parameter", nu);
50  check_positive_finite(function, "Scale parameter", s);
51  check_consistent_sizes(function,
52  "Random variable", y,
53  "Degrees of freedom parameter", nu,
54  "Scale parameter", s);
55 
59  size_t N = max_size(y, nu, s);
60 
62  operands_and_partials(y, nu, s);
63 
64  // Explicit return for extreme values
65  // The gradients are technically ill-defined, but treated as zero
66  for (size_t i = 0; i < stan::length(y); i++) {
67  if (value_of(y_vec[i]) == 0)
68  return operands_and_partials.value(negative_infinity());
69  }
70 
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  continue;
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_q(half_nu_dbl, half_nu_s2_overx_dbl);
105  const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
106  * pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
107 
108  P += log(Pn);
109 
111  operands_and_partials.d_x1[n] += half_nu_s2_overx_dbl * y_inv_dbl
112  * gamma_p_deriv / Pn;
114  operands_and_partials.d_x2[n]
115  += (0.5 * grad_reg_inc_gamma(half_nu_dbl,
116  half_nu_s2_overx_dbl,
117  gamma_vec[n],
118  digamma_vec[n])
119  - half_s2_overx_dbl * gamma_p_deriv)
120  / Pn;
122  operands_and_partials.d_x3[n] += - 2.0 * half_nu_dbl * s_dbl
123  * y_inv_dbl * gamma_p_deriv / Pn;
124  }
125  return operands_and_partials.value(P);
126  }
127 
128  }
129 }
130 #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
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)
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.
VectorView< T_return_type, false, true > d_x3
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.
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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