Stan Math Library  2.14.0
reverse mode automatic differentiation
cauchy_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LPDF_HPP
3 
17 #include <boost/random/cauchy_distribution.hpp>
18 #include <boost/random/variate_generator.hpp>
19 #include <cmath>
20 
21 namespace stan {
22  namespace math {
23 
41  template <bool propto,
42  typename T_y, typename T_loc, typename T_scale>
44  cauchy_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
45  static const char* function("cauchy_lpdf");
47  T_partials_return;
48 
50 
51  if (!(stan::length(y)
52  && stan::length(mu)
53  && stan::length(sigma)))
54  return 0.0;
55 
56  T_partials_return logp(0.0);
57 
58  check_not_nan(function, "Random variable", y);
59  check_finite(function, "Location parameter", mu);
60  check_positive_finite(function, "Scale parameter", sigma);
61  check_consistent_sizes(function,
62  "Random variable", y,
63  "Location parameter", mu,
64  "Scale parameter", sigma);
65 
67  return 0.0;
68 
69  using std::log;
70 
71  VectorView<const T_y> y_vec(y);
72  VectorView<const T_loc> mu_vec(mu);
73  VectorView<const T_scale> sigma_vec(sigma);
74  size_t N = max_size(y, mu, sigma);
75 
77  VectorBuilder<true, T_partials_return,
78  T_scale> sigma_squared(length(sigma));
80  T_partials_return, T_scale> log_sigma(length(sigma));
81  for (size_t i = 0; i < length(sigma); i++) {
82  const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
83  inv_sigma[i] = 1.0 / sigma_dbl;
84  sigma_squared[i] = sigma_dbl * sigma_dbl;
86  log_sigma[i] = log(sigma_dbl);
87  }
88  }
89 
91  operands_and_partials(y, mu, sigma);
92 
93  for (size_t n = 0; n < N; n++) {
94  const T_partials_return y_dbl = value_of(y_vec[n]);
95  const T_partials_return mu_dbl = value_of(mu_vec[n]);
96 
97  const T_partials_return y_minus_mu
98  = y_dbl - mu_dbl;
99  const T_partials_return y_minus_mu_squared
100  = y_minus_mu * y_minus_mu;
101  const T_partials_return y_minus_mu_over_sigma
102  = y_minus_mu * inv_sigma[n];
103  const T_partials_return y_minus_mu_over_sigma_squared
104  = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
105 
107  logp += NEG_LOG_PI;
109  logp -= log_sigma[n];
111  logp -= log1p(y_minus_mu_over_sigma_squared);
112 
114  operands_and_partials.d_x1[n] -= 2 * y_minus_mu
115  / (sigma_squared[n] + y_minus_mu_squared);
117  operands_and_partials.d_x2[n] += 2 * y_minus_mu
118  / (sigma_squared[n] + y_minus_mu_squared);
120  operands_and_partials.d_x3[n]
121  += (y_minus_mu_squared - sigma_squared[n])
122  * inv_sigma[n] / (sigma_squared[n] + y_minus_mu_squared);
123  }
124  return operands_and_partials.value(logp);
125  }
126 
127  template <typename T_y, typename T_loc, typename T_scale>
128  inline
130  cauchy_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
131  return cauchy_lpdf<false>(y, mu, sigma);
132  }
133 
134  }
135 }
136 #endif
VectorView< T_return_type, false, true > d_x2
const double NEG_LOG_PI
Definition: constants.hpp:183
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
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
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
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.
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:11
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
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
return_type< T_y, T_loc, T_scale >::type cauchy_lpdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) a...
Definition: cauchy_lpdf.hpp:44

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