Stan Math Library  2.14.0
reverse mode automatic differentiation
chi_square_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LOG_HPP
3 
19 #include <boost/random/chi_squared_distribution.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 
23 namespace stan {
24  namespace math {
25 
45  template <bool propto,
46  typename T_y, typename T_dof>
48  chi_square_log(const T_y& y, const T_dof& nu) {
49  static const char* function("chi_square_log");
51  T_partials_return;
52 
53  if (!(stan::length(y)
54  && stan::length(nu)))
55  return 0.0;
56 
57  T_partials_return logp(0.0);
58  check_not_nan(function, "Random variable", y);
59  check_nonnegative(function, "Random variable", y);
60  check_positive_finite(function, "Degrees of freedom parameter", nu);
61  check_consistent_sizes(function,
62  "Random variable", y,
63  "Degrees of freedom parameter", nu);
64 
65  VectorView<const T_y> y_vec(y);
66  VectorView<const T_dof> nu_vec(nu);
67  size_t N = max_size(y, nu);
68 
69  for (size_t n = 0; n < length(y); n++)
70  if (value_of(y_vec[n]) < 0)
71  return LOG_ZERO;
72 
74  return 0.0;
75 
77  using boost::math::lgamma;
78  using std::log;
79 
81  T_partials_return, T_y> log_y(length(y));
82  for (size_t i = 0; i < length(y); i++)
84  log_y[i] = log(value_of(y_vec[i]));
85 
87  T_partials_return, T_y> inv_y(length(y));
88  for (size_t i = 0; i < length(y); i++)
90  inv_y[i] = 1.0 / value_of(y_vec[i]);
91 
93  T_partials_return, T_dof> lgamma_half_nu(length(nu));
95  T_partials_return, T_dof>
96  digamma_half_nu_over_two(length(nu));
97 
98  for (size_t i = 0; i < length(nu); i++) {
99  T_partials_return half_nu = 0.5 * value_of(nu_vec[i]);
101  lgamma_half_nu[i] = lgamma(half_nu);
103  digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
104  }
105 
106  OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
107 
108  for (size_t n = 0; n < N; n++) {
109  const T_partials_return y_dbl = value_of(y_vec[n]);
110  const T_partials_return half_y = 0.5 * y_dbl;
111  const T_partials_return nu_dbl = value_of(nu_vec[n]);
112  const T_partials_return half_nu = 0.5 * nu_dbl;
114  logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
116  logp += (half_nu-1.0) * log_y[n];
118  logp -= half_y;
119 
121  operands_and_partials.d_x1[n] += (half_nu-1.0)*inv_y[n] - 0.5;
122  }
124  operands_and_partials.d_x2[n] += NEG_LOG_TWO_OVER_TWO
125  - digamma_half_nu_over_two[n] + log_y[n]*0.5;
126  }
127  }
128  return operands_and_partials.value(logp);
129  }
130 
131  template <typename T_y, typename T_dof>
132  inline
134  chi_square_log(const T_y& y, const T_dof& nu) {
135  return chi_square_log<false>(y, nu);
136  }
137 
138  }
139 }
140 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:20
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:14
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
const double LOG_ZERO
Definition: constants.hpp:172
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
return_type< T_y, T_dof >::type chi_square_log(const T_y &y, const T_dof &nu)
The log of a chi-squared density for y with the specified degrees of freedom parameter.
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.
const double NEG_LOG_TWO_OVER_TWO
Definition: constants.hpp:188
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
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
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
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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