Stan Math Library  2.8.0
reverse mode automatic differentiation
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cauchy_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CCDF_LOG_HPP
3 
4 #include <boost/random/cauchy_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
16 #include <cmath>
17 
18 namespace stan {
19 
20  namespace math {
21 
22  template <typename T_y, typename T_loc, typename T_scale>
23  typename return_type<T_y, T_loc, T_scale>::type
24  cauchy_ccdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
26  T_partials_return;
27 
28  // Size checks
29  if ( !( stan::length(y) && stan::length(mu)
30  && stan::length(sigma) ) )
31  return 0.0;
32 
33  static const char* function("stan::math::cauchy_cdf");
34 
39  using boost::math::tools::promote_args;
41 
42  T_partials_return ccdf_log(0.0);
43 
44  check_not_nan(function, "Random variable", y);
45  check_finite(function, "Location parameter", mu);
46  check_positive_finite(function, "Scale parameter", sigma);
47  check_consistent_sizes(function,
48  "Random variable", y,
49  "Location parameter", mu,
50  "Scale Parameter", sigma);
51 
52  // Wrap arguments in vectors
53  VectorView<const T_y> y_vec(y);
54  VectorView<const T_loc> mu_vec(mu);
55  VectorView<const T_scale> sigma_vec(sigma);
56  size_t N = max_size(y, mu, sigma);
57 
59  operands_and_partials(y, mu, sigma);
60 
61  // Compute CDFLog and its gradients
62  using std::atan;
63  using stan::math::pi;
64  using std::log;
65 
66  // Compute vectorized CDF and gradient
67  for (size_t n = 0; n < N; n++) {
68  // Pull out values
69  const T_partials_return y_dbl = value_of(y_vec[n]);
70  const T_partials_return mu_dbl = value_of(mu_vec[n]);
71  const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
72  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
73  const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
74 
75  // Compute
76  const T_partials_return Pn = 0.5 - atan(z) / pi();
77  ccdf_log += log(Pn);
78 
79  const T_partials_return rep_deriv = 1.0 / (Pn * pi()
80  * (z * z * sigma_dbl
81  + sigma_dbl));
83  operands_and_partials.d_x1[n] -= rep_deriv;
85  operands_and_partials.d_x2[n] += rep_deriv;
87  operands_and_partials.d_x3[n] += rep_deriv * z;
88  }
89  return operands_and_partials.to_var(ccdf_log, y, mu, sigma);
90  }
91  }
92 }
93 #endif
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
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)
fvar< T > atan(const fvar< T > &x)
Definition: atan.hpp:12
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_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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
double pi()
Return the value of pi.
Definition: constants.hpp:86
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.
return_type< T_y, T_loc, T_scale >::type cauchy_ccdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma)

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