Stan Math Library  2.9.0
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 
4 #include <boost/random/chi_squared_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
22 #include <cmath>
23 
24 
25 namespace stan {
26 
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("stan::math::scaled_inv_chi_square_log");
54  T_partials_return;
55 
60 
61  // check if any vectors are zero length
62  if (!(stan::length(y)
63  && stan::length(nu)
64  && stan::length(s)))
65  return 0.0;
66 
67  T_partials_return logp(0.0);
68  check_not_nan(function, "Random variable", y);
69  check_positive_finite(function, "Degrees of freedom parameter", nu);
70  check_positive_finite(function, "Scale parameter", s);
71  check_consistent_sizes(function,
72  "Random variable", y,
73  "Degrees of freedom parameter", nu,
74  "Scale parameter", s);
75 
76  // check if no variables are involved and prop-to
78  return 0.0;
79 
80  VectorView<const T_y> y_vec(y);
81  VectorView<const T_dof> nu_vec(nu);
83  size_t N = max_size(y, nu, s);
84 
85  for (size_t n = 0; n < N; n++) {
86  if (value_of(y_vec[n]) <= 0)
87  return LOG_ZERO;
88  }
89 
90  using stan::math::lgamma;
91  using stan::math::digamma;
92  using stan::math::square;
93  using std::log;
94 
96  T_partials_return, T_dof> half_nu(length(nu));
97  for (size_t i = 0; i < length(nu); i++)
99  half_nu[i] = 0.5 * value_of(nu_vec[i]);
100 
102  T_partials_return, T_y> log_y(length(y));
103  for (size_t i = 0; i < length(y); i++)
105  log_y[i] = log(value_of(y_vec[i]));
106 
108  T_partials_return, T_y> inv_y(length(y));
109  for (size_t i = 0; i < length(y); i++)
111  inv_y[i] = 1.0 / value_of(y_vec[i]);
112 
114  T_partials_return, T_scale> log_s(length(s));
115  for (size_t i = 0; i < length(s); i++)
117  log_s[i] = log(value_of(s_vec[i]));
118 
120  T_partials_return, T_dof> log_half_nu(length(nu));
122  T_partials_return, T_dof> lgamma_half_nu(length(nu));
124  T_partials_return, T_dof>
125  digamma_half_nu_over_two(length(nu));
126  for (size_t i = 0; i < length(nu); i++) {
128  lgamma_half_nu[i] = lgamma(half_nu[i]);
130  log_half_nu[i] = log(half_nu[i]);
132  digamma_half_nu_over_two[i] = digamma(half_nu[i]) * 0.5;
133  }
134 
136  operands_and_partials(y, nu, s);
137  for (size_t n = 0; n < N; n++) {
138  const T_partials_return s_dbl = value_of(s_vec[n]);
139  const T_partials_return nu_dbl = value_of(nu_vec[n]);
141  logp += half_nu[n] * log_half_nu[n] - lgamma_half_nu[n];
143  logp += nu_dbl * log_s[n];
145  logp -= (half_nu[n]+1.0) * log_y[n];
147  logp -= half_nu[n] * s_dbl*s_dbl * inv_y[n];
148 
150  operands_and_partials.d_x1[n]
151  += -(half_nu[n] + 1.0) * inv_y[n]
152  + half_nu[n] * s_dbl*s_dbl * inv_y[n]*inv_y[n];
153  }
155  operands_and_partials.d_x2[n]
156  += 0.5 * log_half_nu[n] + 0.5
157  - digamma_half_nu_over_two[n]
158  + log_s[n]
159  - 0.5 * log_y[n]
160  - 0.5* s_dbl*s_dbl * inv_y[n];
161  }
163  operands_and_partials.d_x3[n]
164  += nu_dbl / s_dbl - nu_dbl * inv_y[n] * s_dbl;
165  }
166  }
167  return operands_and_partials.to_var(logp, y, nu, s);
168  }
169 
170  template <typename T_y, typename T_dof, typename T_scale>
171  inline
173  scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s) {
174  return scaled_inv_chi_square_log<false>(y, nu, s);
175  }
176  }
177 }
178 #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
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...
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
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
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...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
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
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
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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