Stan Math Library  2.12.0
reverse mode automatic differentiation
scaled_inv_chi_square_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LOG_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>
50  typename return_type<T_y, T_dof, T_scale>::type
51  scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s) {
52  static const char* function("scaled_inv_chi_square_log");
54  T_partials_return;
55 
56  if (!(stan::length(y)
57  && stan::length(nu)
58  && stan::length(s)))
59  return 0.0;
60 
61  T_partials_return logp(0.0);
62  check_not_nan(function, "Random variable", y);
63  check_positive_finite(function, "Degrees of freedom parameter", nu);
64  check_positive_finite(function, "Scale parameter", s);
65  check_consistent_sizes(function,
66  "Random variable", y,
67  "Degrees of freedom parameter", nu,
68  "Scale parameter", s);
69 
71  return 0.0;
72 
73  VectorView<const T_y> y_vec(y);
74  VectorView<const T_dof> nu_vec(nu);
76  size_t N = max_size(y, nu, s);
77 
78  for (size_t n = 0; n < N; n++) {
79  if (value_of(y_vec[n]) <= 0)
80  return LOG_ZERO;
81  }
82 
83  using std::log;
84 
86  T_partials_return, T_dof> half_nu(length(nu));
87  for (size_t i = 0; i < length(nu); i++)
89  half_nu[i] = 0.5 * value_of(nu_vec[i]);
90 
92  T_partials_return, T_y> log_y(length(y));
93  for (size_t i = 0; i < length(y); i++)
95  log_y[i] = log(value_of(y_vec[i]));
96 
98  T_partials_return, T_y> inv_y(length(y));
99  for (size_t i = 0; i < length(y); i++)
101  inv_y[i] = 1.0 / value_of(y_vec[i]);
102 
104  T_partials_return, T_scale> log_s(length(s));
105  for (size_t i = 0; i < length(s); i++)
107  log_s[i] = log(value_of(s_vec[i]));
108 
110  T_partials_return, T_dof> log_half_nu(length(nu));
112  T_partials_return, T_dof> lgamma_half_nu(length(nu));
114  T_partials_return, T_dof>
115  digamma_half_nu_over_two(length(nu));
116  for (size_t i = 0; i < length(nu); i++) {
118  lgamma_half_nu[i] = lgamma(half_nu[i]);
120  log_half_nu[i] = log(half_nu[i]);
122  digamma_half_nu_over_two[i] = digamma(half_nu[i]) * 0.5;
123  }
124 
126  operands_and_partials(y, nu, s);
127  for (size_t n = 0; n < N; n++) {
128  const T_partials_return s_dbl = value_of(s_vec[n]);
129  const T_partials_return nu_dbl = value_of(nu_vec[n]);
131  logp += half_nu[n] * log_half_nu[n] - lgamma_half_nu[n];
133  logp += nu_dbl * log_s[n];
135  logp -= (half_nu[n]+1.0) * log_y[n];
137  logp -= half_nu[n] * s_dbl*s_dbl * inv_y[n];
138 
140  operands_and_partials.d_x1[n]
141  += -(half_nu[n] + 1.0) * inv_y[n]
142  + half_nu[n] * s_dbl*s_dbl * inv_y[n]*inv_y[n];
143  }
145  operands_and_partials.d_x2[n]
146  += 0.5 * log_half_nu[n] + 0.5
147  - digamma_half_nu_over_two[n]
148  + log_s[n]
149  - 0.5 * log_y[n]
150  - 0.5* s_dbl*s_dbl * inv_y[n];
151  }
153  operands_and_partials.d_x3[n]
154  += nu_dbl / s_dbl - nu_dbl * inv_y[n] * s_dbl;
155  }
156  }
157  return operands_and_partials.value(logp);
158  }
159 
160  template <typename T_y, typename T_dof, typename T_scale>
161  inline
163  scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s) {
164  return scaled_inv_chi_square_log<false>(y, nu, s);
165  }
166 
167  }
168 }
169 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:14
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: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
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_log(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...
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...
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
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.
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 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:15

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