Stan Math Library  2.10.0
reverse mode automatic differentiation
chi_square_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_LOG_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 
28  template <typename T_y, typename T_dof>
29  typename return_type<T_y, T_dof>::type
30  chi_square_cdf_log(const T_y& y, const T_dof& nu) {
31  static const char* function("stan::math::chi_square_cdf_log");
33  T_partials_return;
34 
40 
41  T_partials_return cdf_log(0.0);
42 
43  // Size checks
44  if (!(stan::length(y) && stan::length(nu)))
45  return cdf_log;
46 
47  check_not_nan(function, "Random variable", y);
48  check_nonnegative(function, "Random variable", y);
49  check_positive_finite(function, "Degrees of freedom parameter", nu);
50  check_consistent_sizes(function,
51  "Random variable", y,
52  "Degrees of freedom parameter", nu);
53 
54  // Wrap arguments in vectors
55  VectorView<const T_y> y_vec(y);
56  VectorView<const T_dof> nu_vec(nu);
57  size_t N = max_size(y, nu);
58 
60  operands_and_partials(y, nu);
61 
62  // Explicit return for extreme values
63  // The gradients are technically ill-defined, but treated as zero
64  for (size_t i = 0; i < stan::length(y); i++) {
65  if (value_of(y_vec[i]) == 0)
66  return operands_and_partials.value(stan::math::negative_infinity());
67  }
68 
69  // Compute cdf_log and its gradients
70  using stan::math::gamma_p;
71  using stan::math::digamma;
72  using boost::math::tgamma;
73  using std::exp;
74  using std::pow;
75  using std::log;
76  using std::exp;
77 
78  // Cache a few expensive function calls if nu is a parameter
80  T_partials_return, T_dof> gamma_vec(stan::length(nu));
82  T_partials_return, T_dof> digamma_vec(stan::length(nu));
83 
85  for (size_t i = 0; i < stan::length(nu); i++) {
86  const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
87  gamma_vec[i] = tgamma(alpha_dbl);
88  digamma_vec[i] = digamma(alpha_dbl);
89  }
90  }
91 
92  // Compute vectorized cdf_log and gradient
93  for (size_t n = 0; n < N; n++) {
94  // Explicit results for extreme values
95  // The gradients are technically ill-defined, but treated as zero
96  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
97  return operands_and_partials.value(0.0);
98 
99  // Pull out values
100  const T_partials_return y_dbl = value_of(y_vec[n]);
101  const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
102  const T_partials_return beta_dbl = 0.5;
103 
104  // Compute
105  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
106 
107  cdf_log += log(Pn);
108 
110  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
111  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
113  operands_and_partials.d_x2[n]
114  -= 0.5 * stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
115  * y_dbl, gamma_vec[n],
116  digamma_vec[n]) / Pn;
117  }
118 
119  return operands_and_partials.value(cdf_log);
120  }
121 
122  }
123 }
124 #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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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.
return_type< T_y, T_dof >::type chi_square_cdf_log(const T_y &y, const T_dof &nu)
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.
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
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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