Stan Math Library  2.15.0
reverse mode automatic differentiation
scaled_inv_chi_square_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LPDF_HPP
3 
22 #include <boost/random/chi_squared_distribution.hpp>
23 #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, typename T_scale>
52  const T_dof& nu, const T_scale& s) {
53  static const char* function("scaled_inv_chi_square_lpdf");
55  T_partials_return;
56 
57  if (!(stan::length(y)
58  && stan::length(nu)
59  && stan::length(s)))
60  return 0.0;
61 
62  T_partials_return logp(0.0);
63  check_not_nan(function, "Random variable", y);
64  check_positive_finite(function, "Degrees of freedom parameter", nu);
65  check_positive_finite(function, "Scale parameter", s);
66  check_consistent_sizes(function,
67  "Random variable", y,
68  "Degrees of freedom parameter", nu,
69  "Scale parameter", s);
70 
72  return 0.0;
73 
77  size_t N = max_size(y, nu, s);
78 
79  for (size_t n = 0; n < N; n++) {
80  if (value_of(y_vec[n]) <= 0)
81  return LOG_ZERO;
82  }
83 
84  using std::log;
85 
87  T_partials_return, T_dof> half_nu(length(nu));
88  for (size_t i = 0; i < length(nu); i++)
90  half_nu[i] = 0.5 * value_of(nu_vec[i]);
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_scale> log_s(length(s));
106  for (size_t i = 0; i < length(s); i++)
108  log_s[i] = log(value_of(s_vec[i]));
109 
111  T_partials_return, T_dof> log_half_nu(length(nu));
113  T_partials_return, T_dof> lgamma_half_nu(length(nu));
115  T_partials_return, T_dof>
116  digamma_half_nu_over_two(length(nu));
117  for (size_t i = 0; i < length(nu); i++) {
119  lgamma_half_nu[i] = lgamma(half_nu[i]);
121  log_half_nu[i] = log(half_nu[i]);
123  digamma_half_nu_over_two[i] = digamma(half_nu[i]) * 0.5;
124  }
125 
127  operands_and_partials(y, nu, s);
128  for (size_t n = 0; n < N; n++) {
129  const T_partials_return s_dbl = value_of(s_vec[n]);
130  const T_partials_return nu_dbl = value_of(nu_vec[n]);
132  logp += half_nu[n] * log_half_nu[n] - lgamma_half_nu[n];
134  logp += nu_dbl * log_s[n];
136  logp -= (half_nu[n]+1.0) * log_y[n];
138  logp -= half_nu[n] * s_dbl*s_dbl * inv_y[n];
139 
141  operands_and_partials.d_x1[n]
142  += -(half_nu[n] + 1.0) * inv_y[n]
143  + half_nu[n] * s_dbl*s_dbl * inv_y[n]*inv_y[n];
144  }
146  operands_and_partials.d_x2[n]
147  += 0.5 * log_half_nu[n] + 0.5
148  - digamma_half_nu_over_two[n]
149  + log_s[n]
150  - 0.5 * log_y[n]
151  - 0.5* s_dbl*s_dbl * inv_y[n];
152  }
154  operands_and_partials.d_x3[n]
155  += nu_dbl / s_dbl - nu_dbl * inv_y[n] * s_dbl;
156  }
157  }
158  return operands_and_partials.value(logp);
159  }
160 
161  template <typename T_y, typename T_dof, typename T_scale>
162  inline
164  scaled_inv_chi_square_lpdf(const T_y& y, const T_dof& nu,
165  const T_scale& s) {
166  return scaled_inv_chi_square_lpdf<false>(y, nu, s);
167  }
168 
169  }
170 }
171 #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.
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...
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.
VectorView< T_return_type, false, true > d_x3
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_lpdf(const T_y &y, const T_dof &nu, const T_scale &s)
The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter...
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.
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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