Stan Math Library  2.14.0
reverse mode automatic differentiation
inv_chi_square_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_LOG_HPP
3 
4 #include <boost/random/chi_squared_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 
26 namespace stan {
27  namespace math {
28 
48  template <bool propto,
49  typename T_y, typename T_dof>
51  inv_chi_square_log(const T_y& y, const T_dof& nu) {
52  static const char* function("inv_chi_square_log");
54  T_partials_return;
55 
56  if (!(stan::length(y)
57  && stan::length(nu)))
58  return 0.0;
59 
60  T_partials_return logp(0.0);
61  check_positive_finite(function, "Degrees of freedom parameter", nu);
62  check_not_nan(function, "Random variable", y);
63  check_consistent_sizes(function,
64  "Random variable", y,
65  "Degrees of freedom parameter", nu);
66 
67  VectorView<const T_y> y_vec(y);
68  VectorView<const T_dof> nu_vec(nu);
69  size_t N = max_size(y, nu);
70 
71  for (size_t n = 0; n < length(y); n++)
72  if (value_of(y_vec[n]) <= 0)
73  return LOG_ZERO;
74 
76  using boost::math::lgamma;
77  using std::log;
78 
80  T_partials_return, T_y> log_y(length(y));
81  for (size_t i = 0; i < length(y); i++)
83  log_y[i] = log(value_of(y_vec[i]));
84 
86  T_partials_return, T_y> inv_y(length(y));
87  for (size_t i = 0; i < length(y); i++)
89  inv_y[i] = 1.0 / value_of(y_vec[i]);
90 
92  T_partials_return, T_dof> lgamma_half_nu(length(nu));
94  T_partials_return, T_dof>
95  digamma_half_nu_over_two(length(nu));
96  for (size_t i = 0; i < length(nu); i++) {
97  T_partials_return half_nu = 0.5 * value_of(nu_vec[i]);
99  lgamma_half_nu[i] = lgamma(half_nu);
101  digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
102  }
103 
104  OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
105  for (size_t n = 0; n < N; n++) {
106  const T_partials_return nu_dbl = value_of(nu_vec[n]);
107  const T_partials_return half_nu = 0.5 * nu_dbl;
108 
110  logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
112  logp -= (half_nu+1.0) * log_y[n];
114  logp -= 0.5 * inv_y[n];
115 
117  operands_and_partials.d_x1[n]
118  += -(half_nu+1.0) * inv_y[n] + 0.5 * inv_y[n] * inv_y[n];
119  }
121  operands_and_partials.d_x2[n]
122  += NEG_LOG_TWO_OVER_TWO - digamma_half_nu_over_two[n]
123  - 0.5*log_y[n];
124  }
125  }
126  return operands_and_partials.value(logp);
127  }
128 
129  template <typename T_y, typename T_dof>
130  inline
132  inv_chi_square_log(const T_y& y, const T_dof& nu) {
133  return inv_chi_square_log<false>(y, nu);
134  }
135 
136  }
137 }
138 #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...
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.
return_type< T_y, T_dof >::type inv_chi_square_log(const T_y &y, const T_dof &nu)
The log of an inverse chi-squared density for y with the specified degrees of freedom parameter...
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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