Stan Math Library  2.20.0
reverse mode automatic differentiation
inv_chi_square_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_LPDF_HPP
3 
14 #include <cmath>
15 
16 namespace stan {
17 namespace math {
18 
38 template <bool propto, typename T_y, typename T_dof>
40  const T_dof& nu) {
41  static const char* function = "inv_chi_square_lpdf";
42  typedef
43  typename stan::partials_return_type<T_y, T_dof>::type T_partials_return;
44 
45  check_positive_finite(function, "Degrees of freedom parameter", nu);
46  check_not_nan(function, "Random variable", y);
47  check_consistent_sizes(function, "Random variable", y,
48  "Degrees of freedom parameter", nu);
49  if (size_zero(y, nu))
50  return 0;
51 
52  T_partials_return logp(0);
53 
54  scalar_seq_view<T_y> y_vec(y);
55  scalar_seq_view<T_dof> nu_vec(nu);
56  size_t N = max_size(y, nu);
57 
58  for (size_t n = 0; n < length(y); n++)
59  if (value_of(y_vec[n]) <= 0)
60  return LOG_ZERO;
61 
62  using std::log;
63 
65  T_y>
66  log_y(length(y));
67  for (size_t i = 0; i < length(y); i++)
69  log_y[i] = log(value_of(y_vec[i]));
70 
72  inv_y(length(y));
73  for (size_t i = 0; i < length(y); i++)
75  inv_y[i] = 1.0 / value_of(y_vec[i]);
76 
78  lgamma_half_nu(length(nu));
79  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
80  digamma_half_nu_over_two(length(nu));
81  for (size_t i = 0; i < length(nu); i++) {
82  T_partials_return half_nu = 0.5 * value_of(nu_vec[i]);
84  lgamma_half_nu[i] = lgamma(half_nu);
86  digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
87  }
88 
89  operands_and_partials<T_y, T_dof> ops_partials(y, nu);
90  for (size_t n = 0; n < N; n++) {
91  const T_partials_return nu_dbl = value_of(nu_vec[n]);
92  const T_partials_return half_nu = 0.5 * nu_dbl;
93 
95  logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
97  logp -= (half_nu + 1.0) * log_y[n];
99  logp -= 0.5 * inv_y[n];
100 
102  ops_partials.edge1_.partials_[n]
103  += -(half_nu + 1.0) * inv_y[n] + 0.5 * inv_y[n] * inv_y[n];
104  }
106  ops_partials.edge2_.partials_[n] += NEG_LOG_TWO_OVER_TWO
107  - digamma_half_nu_over_two[n]
108  - 0.5 * log_y[n];
109  }
110  }
111  return ops_partials.build(logp);
112 }
113 
114 template <typename T_y, typename T_dof>
116  const T_y& y, const T_dof& nu) {
117  return inv_chi_square_lpdf<false>(y, nu);
118 }
119 
120 } // namespace math
121 } // namespace stan
122 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:21
return_type< T_y, T_dof >::type inv_chi_square_lpdf(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...
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
const double LOG_ZERO
Definition: constants.hpp:150
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
const double NEG_LOG_TWO_OVER_TWO
Definition: constants.hpp:162
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.
internal::ops_partials_edge< double, Op1 > edge1_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23

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