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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 
17 #include <boost/random/chi_squared_distribution.hpp>
18 #include <boost/random/variate_generator.hpp>
19 #include <cmath>
20 #include <limits>
21 
22 namespace stan {
23 
24  namespace math {
25 
35  template <typename T_y, typename T_dof>
36  typename return_type<T_y, T_dof>::type
37  chi_square_cdf(const T_y& y, const T_dof& nu) {
38  static const char* function("stan::math::chi_square_cdf");
40  T_partials_return;
41 
47 
48  T_partials_return cdf(1.0);
49 
50  // Size checks
51  if (!(stan::length(y) && stan::length(nu)))
52  return cdf;
53 
54  check_not_nan(function, "Random variable", y);
55  check_nonnegative(function, "Random variable", y);
56  check_positive_finite(function, "Degrees of freedom parameter", nu);
57  check_consistent_sizes(function,
58  "Random variable", y,
59  "Degrees of freedom parameter", nu);
60 
61  // Wrap arguments in vectors
62  VectorView<const T_y> y_vec(y);
63  VectorView<const T_dof> nu_vec(nu);
64  size_t N = max_size(y, nu);
65 
67  operands_and_partials(y, nu);
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);
74  }
75 
76  // Compute CDF and its gradients
77  using stan::math::gamma_p;
78  using stan::math::digamma;
79  using boost::math::tgamma;
80  using std::exp;
81  using std::pow;
82  using std::exp;
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 alpha_dbl = value_of(nu_vec[i]) * 0.5;
93  gamma_vec[i] = tgamma(alpha_dbl);
94  digamma_vec[i] = digamma(alpha_dbl);
95  }
96  }
97 
98  // Compute vectorized CDF 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  continue;
104 
105  // Pull out values
106  const T_partials_return y_dbl = value_of(y_vec[n]);
107  const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
108  const T_partials_return beta_dbl = 0.5;
109 
110  // Compute
111  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
112 
113  cdf *= Pn;
114 
116  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
117  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
119  operands_and_partials.d_x2[n]
120  -= 0.5 * stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
121  * y_dbl, 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] *= cdf;
128  }
130  for (size_t n = 0; n < stan::length(nu); ++n)
131  operands_and_partials.d_x2[n] *= cdf;
132  }
133 
134  return operands_and_partials.to_var(cdf, y, nu);
135  }
136  }
137 }
138 #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
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)
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
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
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:15
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
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 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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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