1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP
16 #include <boost/random/cauchy_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
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) {
47 static const char*
function(
"stan::math::cauchy_cdf");
53 using boost::math::tools::promote_args;
56 T_partials_return P(1.0);
63 "Location parameter", mu,
64 "Scale Parameter", sigma);
73 operands_and_partials(y, mu, sigma);
78 if (
value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
79 return operands_and_partials.
value(0.0);
87 for (
size_t n = 0; n < N; n++) {
90 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
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]);
99 const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
102 const T_partials_return Pn =
atan(z) /
pi() + 0.5;
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);
119 operands_and_partials.
d_x1[n] *= P;
123 operands_and_partials.
d_x2[n] *= P;
127 operands_and_partials.
d_x3[n] *= P;
130 return operands_and_partials.
value(P);
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.
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)
fvar< T > atan(const fvar< T > &x)
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)
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.
double pi()
Return the value of pi.
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[].
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