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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 
20 #include <boost/random/chi_squared_distribution.hpp>
21 #include <boost/random/variate_generator.hpp>
22 #include <limits>
23 #include <cmath>
24 
25 namespace stan {
26 
27  namespace math {
28 
29  template <typename T_y, typename T_dof, typename T_scale>
30  typename return_type<T_y, T_dof, T_scale>::type
31  scaled_inv_chi_square_ccdf_log(const T_y& y, const T_dof& nu,
32  const T_scale& s) {
34  T_partials_return;
35 
36  // Size checks
37  if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
38  return 0.0;
39 
40  static const char* function("stan::math::scaled_inv_chi_square_ccdf_log");
41 
47  using std::exp;
48 
49  T_partials_return P(0.0);
50 
51  check_not_nan(function, "Random variable", y);
52  check_nonnegative(function, "Random variable", y);
53  check_positive_finite(function, "Degrees of freedom parameter", nu);
54  check_positive_finite(function, "Scale parameter", s);
55  check_consistent_sizes(function,
56  "Random variable", y,
57  "Degrees of freedom parameter", nu,
58  "Scale parameter", s);
59 
60  // Wrap arguments in vectors
61  VectorView<const T_y> y_vec(y);
62  VectorView<const T_dof> nu_vec(nu);
64  size_t N = max_size(y, nu, s);
65 
67  operands_and_partials(y, nu, s);
68 
69  // Explicit return for extreme values
70  // The gradients are technically ill-defined, but treated as zero
71  for (size_t i = 0; i < stan::length(y); i++) {
72  if (value_of(y_vec[i]) == 0)
73  return operands_and_partials.to_var(0.0, y, nu, s);
74  }
75 
76  // Compute cdf_log and its gradients
77  using stan::math::gamma_q;
78  using stan::math::digamma;
79  using boost::math::tgamma;
80  using std::exp;
81  using std::pow;
82  using std::log;
83 
84  // Cache a few expensive function calls if nu is a parameter
86  T_partials_return, T_dof> gamma_vec(stan::length(nu));
88  T_partials_return, T_dof> digamma_vec(stan::length(nu));
89 
91  for (size_t i = 0; i < stan::length(nu); i++) {
92  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
93  gamma_vec[i] = tgamma(half_nu_dbl);
94  digamma_vec[i] = digamma(half_nu_dbl);
95  }
96  }
97 
98  // Compute vectorized cdf_log and gradient
99  for (size_t n = 0; n < N; n++) {
100  // Explicit results for extreme values
101  // The gradients are technically ill-defined, but treated as zero
102  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
103  return operands_and_partials.to_var(stan::math::negative_infinity(),
104  y, nu, s);
105  }
106 
107  // Pull out values
108  const T_partials_return y_dbl = value_of(y_vec[n]);
109  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
110  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
111  const T_partials_return s_dbl = value_of(s_vec[n]);
112  const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
113  * y_inv_dbl;
114  const T_partials_return half_nu_s2_overx_dbl
115  = 2.0 * half_nu_dbl * half_s2_overx_dbl;
116 
117  // Compute
118  const T_partials_return Pn = 1.0 - gamma_q(half_nu_dbl,
119  half_nu_s2_overx_dbl);
120  const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
121  * pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
122 
123  P += log(Pn);
124 
126  operands_and_partials.d_x1[n] -= half_nu_s2_overx_dbl * y_inv_dbl
127  * gamma_p_deriv / Pn;
129  operands_and_partials.d_x2[n]
130  -= (0.5 * stan::math::grad_reg_inc_gamma(half_nu_dbl,
131  half_nu_s2_overx_dbl,
132  gamma_vec[n],
133  digamma_vec[n])
134  - half_s2_overx_dbl * gamma_p_deriv)
135  / Pn;
137  operands_and_partials.d_x3[n] += 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
138  * gamma_p_deriv / Pn;
139  }
140 
141  return operands_and_partials.to_var(P, y, nu, s);
142  }
143  }
144 }
145 #endif
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:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
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)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
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:15
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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:15
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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