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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 
28  namespace math {
29 
49  template <bool propto,
50  typename T_y, typename T_dof>
51  typename return_type<T_y, T_dof>::type
52  inv_chi_square_log(const T_y& y, const T_dof& nu) {
53  static const char* function("stan::math::inv_chi_square_log");
55  T_partials_return;
56 
57  // check if any vectors are zero length
58  if (!(stan::length(y)
59  && stan::length(nu)))
60  return 0.0;
61 
66 
67  T_partials_return logp(0.0);
68  check_positive_finite(function, "Degrees of freedom parameter", nu);
69  check_not_nan(function, "Random variable", y);
70  check_consistent_sizes(function,
71  "Random variable", y,
72  "Degrees of freedom parameter", nu);
73 
74 
75  // set up template expressions wrapping scalars into vector views
76  VectorView<const T_y> y_vec(y);
77  VectorView<const T_dof> nu_vec(nu);
78  size_t N = max_size(y, nu);
79 
80  for (size_t n = 0; n < length(y); n++)
81  if (value_of(y_vec[n]) <= 0)
82  return LOG_ZERO;
83 
85  using boost::math::lgamma;
87  using std::log;
88 
90  T_partials_return, T_y> log_y(length(y));
91  for (size_t i = 0; i < length(y); i++)
93  log_y[i] = log(value_of(y_vec[i]));
94 
96  T_partials_return, T_y> inv_y(length(y));
97  for (size_t i = 0; i < length(y); i++)
99  inv_y[i] = 1.0 / value_of(y_vec[i]);
100 
102  T_partials_return, T_dof> lgamma_half_nu(length(nu));
104  T_partials_return, T_dof>
105  digamma_half_nu_over_two(length(nu));
106  for (size_t i = 0; i < length(nu); i++) {
107  T_partials_return half_nu = 0.5 * value_of(nu_vec[i]);
109  lgamma_half_nu[i] = lgamma(half_nu);
111  digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
112  }
113 
114  OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
115  for (size_t n = 0; n < N; n++) {
116  const T_partials_return nu_dbl = value_of(nu_vec[n]);
117  const T_partials_return half_nu = 0.5 * nu_dbl;
118 
120  logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
122  logp -= (half_nu+1.0) * log_y[n];
124  logp -= 0.5 * inv_y[n];
125 
127  operands_and_partials.d_x1[n]
128  += -(half_nu+1.0) * inv_y[n] + 0.5 * inv_y[n] * inv_y[n];
129  }
131  operands_and_partials.d_x2[n]
132  += NEG_LOG_TWO_OVER_TWO - digamma_half_nu_over_two[n]
133  - 0.5*log_y[n];
134  }
135  }
136  return operands_and_partials.to_var(logp, y, nu);
137  }
138 
139  template <typename T_y, typename T_dof>
140  inline
142  inv_chi_square_log(const T_y& y, const T_dof& nu) {
143  return inv_chi_square_log<false>(y, nu);
144  }
145  }
146 }
147 #endif
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
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
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
A variable implementation that stores operands and derivatives with respect to the variable...
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)
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...
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
const double NEG_LOG_TWO_OVER_TWO
Definition: constants.hpp:191
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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