Stan Math Library  2.20.0
reverse mode automatic differentiation
cauchy_lccdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LCCDF_HPP
3 
12 #include <cmath>
13 
14 namespace stan {
15 namespace math {
16 
32 template <typename T_y, typename T_loc, typename T_scale>
34  const T_y& y, const T_loc& mu, const T_scale& sigma) {
36  T_partials_return;
37 
38  if (size_zero(y, mu, sigma))
39  return 0.0;
40 
41  static const char* function = "cauchy_lccdf";
42 
43  T_partials_return ccdf_log(0.0);
44 
45  check_not_nan(function, "Random variable", y);
46  check_finite(function, "Location parameter", mu);
47  check_positive_finite(function, "Scale parameter", sigma);
48  check_consistent_sizes(function, "Random variable", y, "Location parameter",
49  mu, "Scale Parameter", sigma);
50 
51  scalar_seq_view<T_y> y_vec(y);
52  scalar_seq_view<T_loc> mu_vec(mu);
53  scalar_seq_view<T_scale> sigma_vec(sigma);
54  size_t N = max_size(y, mu, sigma);
55 
56  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
57 
58  using std::atan;
59  using std::log;
60 
61  for (size_t n = 0; n < N; n++) {
62  const T_partials_return y_dbl = value_of(y_vec[n]);
63  const T_partials_return mu_dbl = value_of(mu_vec[n]);
64  const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
65  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
66  const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
67 
68  const T_partials_return Pn = 0.5 - atan(z) / pi();
69  ccdf_log += log(Pn);
70 
71  const T_partials_return rep_deriv
72  = 1.0 / (Pn * pi() * (z * z * sigma_dbl + sigma_dbl));
74  ops_partials.edge1_.partials_[n] -= rep_deriv;
76  ops_partials.edge2_.partials_[n] += rep_deriv;
78  ops_partials.edge3_.partials_[n] += rep_deriv * z;
79  }
80  return ops_partials.build(ccdf_log);
81 }
82 
83 } // namespace math
84 } // namespace stan
85 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
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.
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
fvar< T > atan(const fvar< T > &x)
Definition: atan.hpp:13
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.
return_type< T_y, T_loc, T_scale >::type cauchy_lccdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Returns the cauchy log complementary cumulative distribution function for the given location...
internal::ops_partials_edge< double, Op2 > edge2_
double pi()
Return the value of pi.
Definition: constants.hpp:80
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, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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