Stan Math Library  2.10.0
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 
25  namespace math {
26 
46  template <bool propto,
47  typename T_y, typename T_dof>
48  typename return_type<T_y, T_dof>::type
49  chi_square_log(const T_y& y, const T_dof& nu) {
50  static const char* function("stan::math::chi_square_log");
52  T_partials_return;
53 
54  // check if any vectors are zero length
55  if (!(stan::length(y)
56  && stan::length(nu)))
57  return 0.0;
58 
64 
65  T_partials_return logp(0.0);
66  check_not_nan(function, "Random variable", y);
67  check_nonnegative(function, "Random variable", y);
68  check_positive_finite(function, "Degrees of freedom parameter", nu);
69  check_consistent_sizes(function,
70  "Random variable", y,
71  "Degrees of freedom parameter", nu);
72 
73 
74  // set up template expressions wrapping scalars into vector views
75  VectorView<const T_y> y_vec(y);
76  VectorView<const T_dof> nu_vec(nu);
77  size_t N = max_size(y, nu);
78 
79  for (size_t n = 0; n < length(y); n++)
80  if (value_of(y_vec[n]) < 0)
81  return LOG_ZERO;
82 
83  // check if no variables are involved and prop-to
85  return 0.0;
86 
88  using boost::math::lgamma;
90  using std::log;
91 
93  T_partials_return, T_y> log_y(length(y));
94  for (size_t i = 0; i < length(y); i++)
96  log_y[i] = log(value_of(y_vec[i]));
97 
99  T_partials_return, T_y> inv_y(length(y));
100  for (size_t i = 0; i < length(y); i++)
102  inv_y[i] = 1.0 / value_of(y_vec[i]);
103 
105  T_partials_return, T_dof> lgamma_half_nu(length(nu));
107  T_partials_return, T_dof>
108  digamma_half_nu_over_two(length(nu));
109 
110  for (size_t i = 0; i < length(nu); i++) {
111  T_partials_return half_nu = 0.5 * value_of(nu_vec[i]);
113  lgamma_half_nu[i] = lgamma(half_nu);
115  digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
116  }
117 
118  OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
119 
120  for (size_t n = 0; n < N; n++) {
121  const T_partials_return y_dbl = value_of(y_vec[n]);
122  const T_partials_return half_y = 0.5 * y_dbl;
123  const T_partials_return nu_dbl = value_of(nu_vec[n]);
124  const T_partials_return half_nu = 0.5 * nu_dbl;
126  logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
128  logp += (half_nu-1.0) * log_y[n];
130  logp -= half_y;
131 
133  operands_and_partials.d_x1[n] += (half_nu-1.0)*inv_y[n] - 0.5;
134  }
136  operands_and_partials.d_x2[n] += NEG_LOG_TWO_OVER_TWO
137  - digamma_half_nu_over_two[n] + log_y[n]*0.5;
138  }
139  }
140  return operands_and_partials.value(logp);
141  }
142 
143  template <typename T_y, typename T_dof>
144  inline
146  chi_square_log(const T_y& y, const T_dof& nu) {
147  return chi_square_log<false>(y, nu);
148  }
149 
150  }
151 }
152 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
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
const double LOG_ZERO
Definition: constants.hpp:175
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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...
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
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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.
const double NEG_LOG_TWO_OVER_TWO
Definition: constants.hpp:191
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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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