Stan Math Library  2.12.0
reverse mode automatic differentiation
cauchy_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP
3 
16 #include <boost/random/cauchy_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <limits>
19 
20 namespace stan {
21  namespace math {
22 
35  template <typename T_y, typename T_loc, typename T_scale>
36  typename return_type<T_y, T_loc, T_scale>::type
37  cauchy_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
39  T_partials_return;
40 
41  if ( !( stan::length(y) && stan::length(mu)
42  && stan::length(sigma) ) )
43  return 1.0;
44 
45  static const char* function("cauchy_cdf");
46 
47  using boost::math::tools::promote_args;
48 
49  T_partials_return P(1.0);
50 
51  check_not_nan(function, "Random variable", y);
52  check_finite(function, "Location parameter", mu);
53  check_positive_finite(function, "Scale parameter", sigma);
54  check_consistent_sizes(function,
55  "Random variable", y,
56  "Location parameter", mu,
57  "Scale Parameter", sigma);
58 
59  VectorView<const T_y> y_vec(y);
60  VectorView<const T_loc> mu_vec(mu);
61  VectorView<const T_scale> sigma_vec(sigma);
62  size_t N = max_size(y, mu, sigma);
63 
65  operands_and_partials(y, mu, sigma);
66 
67  // Explicit return for extreme values
68  // The gradients are technically ill-defined, but treated as zero
69  for (size_t i = 0; i < stan::length(y); i++) {
70  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
71  return operands_and_partials.value(0.0);
72  }
73 
74  using std::atan;
75 
76  for (size_t n = 0; n < N; n++) {
77  // Explicit results for extreme values
78  // The gradients are technically ill-defined, but treated as zero
79  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
80  continue;
81  }
82 
83  const T_partials_return y_dbl = value_of(y_vec[n]);
84  const T_partials_return mu_dbl = value_of(mu_vec[n]);
85  const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
86 
87  const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
88 
89  const T_partials_return Pn = atan(z) / pi() + 0.5;
90 
91  P *= Pn;
92 
94  operands_and_partials.d_x1[n]
95  += sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
97  operands_and_partials.d_x2[n]
98  += - sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
100  operands_and_partials.d_x3[n]
101  += - z * sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
102  }
103 
105  for (size_t n = 0; n < stan::length(y); ++n)
106  operands_and_partials.d_x1[n] *= P;
107  }
109  for (size_t n = 0; n < stan::length(mu); ++n)
110  operands_and_partials.d_x2[n] *= P;
111  }
113  for (size_t n = 0; n < stan::length(sigma); ++n)
114  operands_and_partials.d_x3[n] *= P;
115  }
116  return operands_and_partials.value(P);
117  }
118 
119  }
120 }
121 #endif
VectorView< T_return_type, false, true > d_x2
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
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.
return_type< T_y, T_loc, T_scale >::type cauchy_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Calculates the cauchy cumulative distribution function for the given variate, location, and scale.
Definition: cauchy_cdf.hpp:37
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

     [ Stan Home Page ] © 2011–2016, Stan Development Team.