Stan Math Library  2.11.0
reverse mode automatic differentiation
inv_chi_square_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_CDF_HPP
3 
4 #include <boost/random/chi_squared_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 #include <limits>
26 
27 namespace stan {
28 
29  namespace math {
30 
31  template <typename T_y, typename T_dof>
32  typename return_type<T_y, T_dof>::type
33  inv_chi_square_cdf(const T_y& y, const T_dof& nu) {
35  T_partials_return;
36 
37  // Size checks
38  if ( !( stan::length(y) && stan::length(nu) ) ) return 1.0;
39 
40  // Error checks
41  static const char* function("stan::math::inv_chi_square_cdf");
42 
47  using boost::math::tools::promote_args;
49  using std::exp;
50 
51  T_partials_return P(1.0);
52 
53  check_positive_finite(function, "Degrees of freedom parameter", nu);
54  check_not_nan(function, "Random variable", y);
55  check_nonnegative(function, "Random variable", y);
56  check_consistent_sizes(function,
57  "Random variable", y,
58  "Degrees of freedom parameter", nu);
59 
60  // Wrap arguments in vectors
61  VectorView<const T_y> y_vec(y);
62  VectorView<const T_dof> nu_vec(nu);
63  size_t N = max_size(y, nu);
64 
65  OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
66 
67  // Explicit return for extreme values
68  // The gradients are technically ill-defined, but treated as zero
69 
70  for (size_t i = 0; i < stan::length(y); i++)
71  if (value_of(y_vec[i]) == 0)
72  return operands_and_partials.value(0.0);
73 
74  // Compute CDF and its gradients
75  using stan::math::gamma_q;
76  using stan::math::digamma;
77  using boost::math::tgamma;
78  using std::exp;
79  using std::pow;
80 
81  // Cache a few expensive function calls if nu is a parameter
83  T_partials_return, T_dof> gamma_vec(stan::length(nu));
85  T_partials_return, T_dof> digamma_vec(stan::length(nu));
86 
88  for (size_t i = 0; i < stan::length(nu); i++) {
89  const T_partials_return nu_dbl = value_of(nu_vec[i]);
90  gamma_vec[i] = tgamma(0.5 * nu_dbl);
91  digamma_vec[i] = digamma(0.5 * nu_dbl);
92  }
93  }
94 
95  // Compute vectorized CDF and gradient
96  for (size_t n = 0; n < N; n++) {
97  // Explicit results for extreme values
98  // The gradients are technically ill-defined, but treated as zero
99  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
100  continue;
101  }
102 
103  // Pull out values
104  const T_partials_return y_dbl = value_of(y_vec[n]);
105  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
106  const T_partials_return nu_dbl = value_of(nu_vec[n]);
107 
108  // Compute
109  const T_partials_return Pn = gamma_q(0.5 * nu_dbl, 0.5 * y_inv_dbl);
110 
111  P *= Pn;
112 
114  operands_and_partials.d_x1[n] += 0.5 * y_inv_dbl * y_inv_dbl
115  * exp(-0.5*y_inv_dbl) * pow(0.5*y_inv_dbl, 0.5*nu_dbl-1)
116  / tgamma(0.5*nu_dbl) / Pn;
118  operands_and_partials.d_x2[n]
119  += 0.5 * stan::math::grad_reg_inc_gamma(0.5 * nu_dbl,
120  0.5 * y_inv_dbl,
121  gamma_vec[n],
122  digamma_vec[n]) / Pn;
123  }
124 
126  for (size_t n = 0; n < stan::length(y); ++n)
127  operands_and_partials.d_x1[n] *= P;
128  }
130  for (size_t n = 0; n < stan::length(nu); ++n)
131  operands_and_partials.d_x2[n] *= P;
132  }
133 
134  return operands_and_partials.value(P);
135  }
136  }
137 }
138 #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.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
return_type< T_y, T_dof >::type inv_chi_square_cdf(const T_y &y, const T_dof &nu)
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
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.
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.
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 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:15
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:16

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