Stan Math Library  2.10.0
reverse mode automatic differentiation
cauchy_cdf.hpp
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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 
22  namespace math {
23 
36  template <typename T_y, typename T_loc, typename T_scale>
37  typename return_type<T_y, T_loc, T_scale>::type
38  cauchy_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
40  T_partials_return;
41 
42  // Size checks
43  if ( !( stan::length(y) && stan::length(mu)
44  && stan::length(sigma) ) )
45  return 1.0;
46 
47  static const char* function("stan::math::cauchy_cdf");
48 
53  using boost::math::tools::promote_args;
55 
56  T_partials_return P(1.0);
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 
66  // Wrap arguments in vectors
67  VectorView<const T_y> y_vec(y);
68  VectorView<const T_loc> mu_vec(mu);
69  VectorView<const T_scale> sigma_vec(sigma);
70  size_t N = max_size(y, mu, sigma);
71 
73  operands_and_partials(y, mu, sigma);
74 
75  // Explicit return for extreme values
76  // The gradients are technically ill-defined, but treated as zero
77  for (size_t i = 0; i < stan::length(y); i++) {
78  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
79  return operands_and_partials.value(0.0);
80  }
81 
82  // Compute CDF and its gradients
83  using std::atan;
84  using stan::math::pi;
85 
86  // Compute vectorized CDF and gradient
87  for (size_t n = 0; n < N; n++) {
88  // Explicit results for extreme values
89  // The gradients are technically ill-defined, but treated as zero
90  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
91  continue;
92  }
93 
94  // Pull out values
95  const T_partials_return y_dbl = value_of(y_vec[n]);
96  const T_partials_return mu_dbl = value_of(mu_vec[n]);
97  const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
98 
99  const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
100 
101  // Compute
102  const T_partials_return Pn = atan(z) / pi() + 0.5;
103 
104  P *= Pn;
105 
107  operands_and_partials.d_x1[n]
108  += sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
110  operands_and_partials.d_x2[n]
111  += - sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
113  operands_and_partials.d_x3[n]
114  += - z * sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
115  }
116 
118  for (size_t n = 0; n < stan::length(y); ++n)
119  operands_and_partials.d_x1[n] *= P;
120  }
122  for (size_t n = 0; n < stan::length(mu); ++n)
123  operands_and_partials.d_x2[n] *= P;
124  }
126  for (size_t n = 0; n < stan::length(sigma); ++n)
127  operands_and_partials.d_x3[n] *= P;
128  }
129 
130  return operands_and_partials.value(P);
131  }
132  }
133 }
134 #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:38
double pi()
Return the value of pi.
Definition: constants.hpp:86
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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