Stan Math Library  2.12.0
reverse mode automatic differentiation
scaled_inv_chi_square_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_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 
43  template <typename T_y, typename T_dof, typename T_scale>
44  typename return_type<T_y, T_dof, T_scale>::type
45  scaled_inv_chi_square_cdf(const T_y& y, const T_dof& nu,
46  const T_scale& s) {
48  T_partials_return;
49 
50  if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
51  return 1.0;
52 
53  static const char* function("scaled_inv_chi_square_cdf");
54 
55  using std::exp;
56 
57  T_partials_return P(1.0);
58 
59  check_not_nan(function, "Random variable", y);
60  check_nonnegative(function, "Random variable", y);
61  check_positive_finite(function, "Degrees of freedom parameter", nu);
62  check_positive_finite(function, "Scale parameter", s);
63  check_consistent_sizes(function,
64  "Random variable", y,
65  "Degrees of freedom parameter", nu,
66  "Scale parameter", s);
67 
68  VectorView<const T_y> y_vec(y);
69  VectorView<const T_dof> nu_vec(nu);
71  size_t N = max_size(y, nu, s);
72 
74  operands_and_partials(y, nu, s);
75 
76  // Explicit return for extreme values
77  // The gradients are technically ill-defined, but treated as zero
78  for (size_t i = 0; i < stan::length(y); i++) {
79  if (value_of(y_vec[i]) == 0)
80  return operands_and_partials.value(0.0);
81  }
82 
83  using boost::math::tgamma;
84  using std::exp;
85  using std::pow;
86 
88  T_partials_return, T_dof> gamma_vec(stan::length(nu));
90  T_partials_return, T_dof> digamma_vec(stan::length(nu));
91 
93  for (size_t i = 0; i < stan::length(nu); i++) {
94  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
95  gamma_vec[i] = tgamma(half_nu_dbl);
96  digamma_vec[i] = digamma(half_nu_dbl);
97  }
98  }
99 
100  for (size_t n = 0; n < N; n++) {
101  // Explicit results for extreme values
102  // The gradients are technically ill-defined, but treated as zero
103  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
104  continue;
105  }
106 
107  const T_partials_return y_dbl = value_of(y_vec[n]);
108  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
109  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
110  const T_partials_return s_dbl = value_of(s_vec[n]);
111  const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
112  * y_inv_dbl;
113  const T_partials_return half_nu_s2_overx_dbl
114  = 2.0 * half_nu_dbl * half_s2_overx_dbl;
115 
116  const T_partials_return Pn = gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
117  const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
118  * pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
119 
120  P *= Pn;
121 
123  operands_and_partials.d_x1[n] += half_nu_s2_overx_dbl * y_inv_dbl
124  * gamma_p_deriv / Pn;
125 
127  operands_and_partials.d_x2[n]
128  += (0.5 * grad_reg_inc_gamma(half_nu_dbl,
129  half_nu_s2_overx_dbl,
130  gamma_vec[n],
131  digamma_vec[n])
132  - half_s2_overx_dbl * gamma_p_deriv)
133  / Pn;
134 
136  operands_and_partials.d_x3[n]
137  += - 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
138  * gamma_p_deriv / Pn;
139  }
140 
142  for (size_t n = 0; n < stan::length(y); ++n)
143  operands_and_partials.d_x1[n] *= P;
144  }
146  for (size_t n = 0; n < stan::length(nu); ++n)
147  operands_and_partials.d_x2[n] *= P;
148  }
150  for (size_t n = 0; n < stan::length(s); ++n)
151  operands_and_partials.d_x3[n] *= P;
152  }
153  return operands_and_partials.value(P);
154  }
155 
156  }
157 }
158 #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
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_cdf(const T_y &y, const T_dof &nu, const T_scale &s)
The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter...
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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
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
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:14
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
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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