Stan Math Library  2.20.0
reverse mode automatic differentiation
chi_square_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_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 = "chi_square_lpdf";
42  typedef
43  typename stan::partials_return_type<T_y, T_dof>::type T_partials_return;
44 
45  check_not_nan(function, "Random variable", y);
46  check_nonnegative(function, "Random variable", y);
47  check_positive_finite(function, "Degrees of freedom parameter", nu);
48  check_consistent_sizes(function, "Random variable", y,
49  "Degrees of freedom parameter", nu);
50  if (size_zero(y, nu))
51  return 0;
52 
53  T_partials_return logp(0);
54 
55  scalar_seq_view<T_y> y_vec(y);
56  scalar_seq_view<T_dof> nu_vec(nu);
57  size_t N = max_size(y, nu);
58 
59  for (size_t n = 0; n < length(y); n++)
60  if (value_of(y_vec[n]) < 0)
61  return LOG_ZERO;
62 
64  return 0.0;
65 
66  using std::log;
67 
69  T_y>
70  log_y(length(y));
71  for (size_t i = 0; i < length(y); i++)
73  log_y[i] = log(value_of(y_vec[i]));
74 
76  inv_y(length(y));
77  for (size_t i = 0; i < length(y); i++)
79  inv_y[i] = 1.0 / value_of(y_vec[i]);
80 
82  lgamma_half_nu(length(nu));
83  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
84  digamma_half_nu_over_two(length(nu));
85 
86  for (size_t i = 0; i < length(nu); i++) {
87  T_partials_return half_nu = 0.5 * value_of(nu_vec[i]);
89  lgamma_half_nu[i] = lgamma(half_nu);
91  digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
92  }
93 
94  operands_and_partials<T_y, T_dof> ops_partials(y, nu);
95 
96  for (size_t n = 0; n < N; n++) {
97  const T_partials_return y_dbl = value_of(y_vec[n]);
98  const T_partials_return half_y = 0.5 * y_dbl;
99  const T_partials_return nu_dbl = value_of(nu_vec[n]);
100  const T_partials_return half_nu = 0.5 * nu_dbl;
102  logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
104  logp += (half_nu - 1.0) * log_y[n];
106  logp -= half_y;
107 
109  ops_partials.edge1_.partials_[n] += (half_nu - 1.0) * inv_y[n] - 0.5;
110  }
112  ops_partials.edge2_.partials_[n] += NEG_LOG_TWO_OVER_TWO
113  - digamma_half_nu_over_two[n]
114  + log_y[n] * 0.5;
115  }
116  }
117  return ops_partials.build(logp);
118 }
119 
120 template <typename T_y, typename T_dof>
121 inline typename return_type<T_y, T_dof>::type chi_square_lpdf(const T_y& y,
122  const T_dof& nu) {
123  return chi_square_lpdf<false>(y, nu);
124 }
125 
126 } // namespace math
127 } // namespace stan
128 #endif
return_type< T_y, T_dof >::type chi_square_lpdf(const T_y &y, const T_dof &nu)
The log of a chi-squared density for y with the specified degrees of freedom parameter.
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
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_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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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