Stan Math Library  2.15.0
reverse mode automatic differentiation
chi_square_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LPDF_HPP
3 
20 #include <boost/random/chi_squared_distribution.hpp>
21 #include <boost/random/variate_generator.hpp>
22 #include <cmath>
23 
24 namespace stan {
25  namespace math {
26 
46  template <bool propto,
47  typename T_y, typename T_dof>
49  chi_square_lpdf(const T_y& y, const T_dof& nu) {
50  static const char* function("chi_square_lpdf");
52  T_partials_return;
53 
54  if (!(stan::length(y)
55  && stan::length(nu)))
56  return 0.0;
57 
58  T_partials_return logp(0.0);
59  check_not_nan(function, "Random variable", y);
60  check_nonnegative(function, "Random variable", y);
61  check_positive_finite(function, "Degrees of freedom parameter", nu);
62  check_consistent_sizes(function,
63  "Random variable", y,
64  "Degrees of freedom parameter", nu);
65 
68  size_t N = max_size(y, nu);
69 
70  for (size_t n = 0; n < length(y); n++)
71  if (value_of(y_vec[n]) < 0)
72  return LOG_ZERO;
73 
75  return 0.0;
76 
78  using boost::math::lgamma;
79  using std::log;
80 
82  T_partials_return, T_y> log_y(length(y));
83  for (size_t i = 0; i < length(y); i++)
85  log_y[i] = log(value_of(y_vec[i]));
86 
88  T_partials_return, T_y> inv_y(length(y));
89  for (size_t i = 0; i < length(y); i++)
91  inv_y[i] = 1.0 / value_of(y_vec[i]);
92 
94  T_partials_return, T_dof> lgamma_half_nu(length(nu));
96  T_partials_return, T_dof>
97  digamma_half_nu_over_two(length(nu));
98 
99  for (size_t i = 0; i < length(nu); i++) {
100  T_partials_return half_nu = 0.5 * value_of(nu_vec[i]);
102  lgamma_half_nu[i] = lgamma(half_nu);
104  digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
105  }
106 
107  OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
108 
109  for (size_t n = 0; n < N; n++) {
110  const T_partials_return y_dbl = value_of(y_vec[n]);
111  const T_partials_return half_y = 0.5 * y_dbl;
112  const T_partials_return nu_dbl = value_of(nu_vec[n]);
113  const T_partials_return half_nu = 0.5 * nu_dbl;
115  logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
117  logp += (half_nu-1.0) * log_y[n];
119  logp -= half_y;
120 
122  operands_and_partials.d_x1[n] += (half_nu-1.0)*inv_y[n] - 0.5;
123  }
125  operands_and_partials.d_x2[n] += NEG_LOG_TWO_OVER_TWO
126  - digamma_half_nu_over_two[n] + log_y[n]*0.5;
127  }
128  }
129  return operands_and_partials.value(logp);
130  }
131 
132  template <typename T_y, typename T_dof>
133  inline
135  chi_square_lpdf(const T_y& y, const T_dof& nu) {
136  return chi_square_lpdf<false>(y, nu);
137  }
138 
139  }
140 }
141 #endif
VectorView< T_return_type, false, true > d_x2
return_type< T_y, T_dof >::type chi_square_lpdf(const T_y &y, const T_dof &nu)
The log of a chi-squared density for y with the specified degrees of freedom parameter.
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
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.
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
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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