1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP 32 template <
typename T_y,
typename T_loc,
typename T_scale>
34 const T_y& y,
const T_loc& mu,
const T_scale& sigma) {
41 static const char*
function =
"cauchy_cdf";
43 T_partials_return P(1.0);
49 mu,
"Scale Parameter", sigma);
61 if (
value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
62 return ops_partials.
build(0.0);
67 for (
size_t n = 0; n < N; n++) {
70 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
74 const T_partials_return y_dbl =
value_of(y_vec[n]);
75 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
76 const T_partials_return sigma_inv_dbl = 1.0 /
value_of(sigma_vec[n]);
78 const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
80 const T_partials_return Pn =
atan(z) /
pi() + 0.5;
85 ops_partials.
edge1_.partials_[n]
86 += sigma_inv_dbl / (
pi() * (1.0 + z * z) * Pn);
88 ops_partials.
edge2_.partials_[n]
89 += -sigma_inv_dbl / (
pi() * (1.0 + z * z) * Pn);
91 ops_partials.
edge3_.partials_[n]
92 += -z * sigma_inv_dbl / (
pi() * (1.0 + z * z) * Pn);
97 ops_partials.
edge1_.partials_[n] *= P;
101 ops_partials.
edge2_.partials_[n] *= P;
105 ops_partials.
edge3_.partials_[n] *= P;
107 return ops_partials.
build(P);
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.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
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.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
fvar< T > atan(const fvar< T > &x)
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
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)
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
return_type< T_y, T_loc, T_scale >::type cauchy_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Returns the cauchy cumulative distribution function for the given location, and scale.
double pi()
Return the value of pi.
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_