Stan Math Library  2.11.0
reverse mode automatic differentiation
chi_square_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_HPP
3 
19 #include <boost/random/chi_squared_distribution.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 #include <limits>
23 
24 namespace stan {
25 
26  namespace math {
27 
37  template <typename T_y, typename T_dof>
38  typename return_type<T_y, T_dof>::type
39  chi_square_cdf(const T_y& y, const T_dof& nu) {
40  static const char* function("stan::math::chi_square_cdf");
42  T_partials_return;
43 
49 
50  T_partials_return cdf(1.0);
51 
52  // Size checks
53  if (!(stan::length(y) && stan::length(nu)))
54  return cdf;
55 
56  check_not_nan(function, "Random variable", y);
57  check_nonnegative(function, "Random variable", y);
58  check_positive_finite(function, "Degrees of freedom parameter", nu);
59  check_consistent_sizes(function,
60  "Random variable", y,
61  "Degrees of freedom parameter", nu);
62 
63  // Wrap arguments in vectors
64  VectorView<const T_y> y_vec(y);
65  VectorView<const T_dof> nu_vec(nu);
66  size_t N = max_size(y, nu);
67 
69  operands_and_partials(y, nu);
70 
71  // Explicit return for extreme values
72  // The gradients are technically ill-defined, but treated as zero
73  for (size_t i = 0; i < stan::length(y); i++) {
74  if (value_of(y_vec[i]) == 0)
75  return operands_and_partials.value(0.0);
76  }
77 
78  // Compute CDF and its gradients
79  using stan::math::gamma_p;
80  using stan::math::digamma;
81  using boost::math::tgamma;
82  using std::exp;
83  using std::pow;
84  using std::exp;
85 
86  // Cache a few expensive function calls if nu is a parameter
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 alpha_dbl = value_of(nu_vec[i]) * 0.5;
95  gamma_vec[i] = tgamma(alpha_dbl);
96  digamma_vec[i] = digamma(alpha_dbl);
97  }
98  }
99 
100  // Compute vectorized CDF and gradient
101  for (size_t n = 0; n < N; n++) {
102  // Explicit results for extreme values
103  // The gradients are technically ill-defined, but treated as zero
104  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
105  continue;
106 
107  // Pull out values
108  const T_partials_return y_dbl = value_of(y_vec[n]);
109  const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
110  const T_partials_return beta_dbl = 0.5;
111 
112  // Compute
113  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
114 
115  cdf *= Pn;
116 
118  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
119  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
121  operands_and_partials.d_x2[n]
122  -= 0.5 * stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
123  * y_dbl, gamma_vec[n],
124  digamma_vec[n]) / Pn;
125  }
126 
128  for (size_t n = 0; n < stan::length(y); ++n)
129  operands_and_partials.d_x1[n] *= cdf;
130  }
132  for (size_t n = 0; n < stan::length(nu); ++n)
133  operands_and_partials.d_x2[n] *= cdf;
134  }
135 
136  return operands_and_partials.value(cdf);
137  }
138  }
139 }
140 #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
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
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:15
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.
return_type< T_y, T_dof >::type chi_square_cdf(const T_y &y, const T_dof &nu)
Calculates the chi square cumulative distribution function for the given variate and degrees of freed...
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
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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