Stan Math Library  2.12.0
reverse mode automatic differentiation
cauchy_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_LOG_HPP
3 
16 #include <boost/random/cauchy_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 namespace stan {
21  namespace math {
22 
23  template <typename T_y, typename T_loc, typename T_scale>
24  typename return_type<T_y, T_loc, T_scale>::type
25  cauchy_cdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
27  T_partials_return;
28 
29  if ( !( stan::length(y) && stan::length(mu)
30  && stan::length(sigma) ) )
31  return 0.0;
32 
33  static const char* function("cauchy_cdf");
34 
35  using boost::math::tools::promote_args;
36 
37  T_partials_return cdf_log(0.0);
38 
39  check_not_nan(function, "Random variable", y);
40  check_finite(function, "Location parameter", mu);
41  check_positive_finite(function, "Scale parameter", sigma);
42  check_consistent_sizes(function,
43  "Random variable", y,
44  "Location parameter", mu,
45  "Scale Parameter", sigma);
46 
47  VectorView<const T_y> y_vec(y);
48  VectorView<const T_loc> mu_vec(mu);
49  VectorView<const T_scale> sigma_vec(sigma);
50  size_t N = max_size(y, mu, sigma);
51 
53  operands_and_partials(y, mu, sigma);
54 
55  using std::atan;
56  using std::log;
57 
58  for (size_t n = 0; n < N; n++) {
59  const T_partials_return y_dbl = value_of(y_vec[n]);
60  const T_partials_return mu_dbl = value_of(mu_vec[n]);
61  const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
62  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
63 
64  const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
65 
66  const T_partials_return Pn = atan(z) / pi() + 0.5;
67  cdf_log += log(Pn);
68 
69  const T_partials_return rep_deriv
70  = 1.0 / (pi() * Pn * (z * z * sigma_dbl + sigma_dbl));
72  operands_and_partials.d_x1[n] += rep_deriv;
74  operands_and_partials.d_x2[n] -= rep_deriv;
76  operands_and_partials.d_x3[n] -= rep_deriv * z;
77  }
78  return operands_and_partials.value(cdf_log);
79  }
80 
81  }
82 }
83 #endif
VectorView< T_return_type, false, true > d_x2
return_type< T_y, T_loc, T_scale >::type cauchy_cdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
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
fvar< T > atan(const fvar< T > &x)
Definition: atan.hpp:12
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
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
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.
double pi()
Return the value of pi.
Definition: constants.hpp:85
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

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