1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LOG_HPP
17 #include <boost/random/cauchy_distribution.hpp>
18 #include <boost/random/variate_generator.hpp>
42 template <
bool propto,
43 typename T_y,
typename T_loc,
typename T_scale>
44 typename return_type<T_y, T_loc, T_scale>::type
45 cauchy_log(
const T_y& y,
const T_loc& mu,
const T_scale& sigma) {
46 static const char*
function(
"stan::math::cauchy_log");
64 T_partials_return logp(0.0);
72 "Location parameter", mu,
73 "Scale parameter", sigma);
91 T_scale> sigma_squared(
length(sigma));
93 T_partials_return, T_scale> log_sigma(
length(sigma));
94 for (
size_t i = 0; i <
length(sigma); i++) {
95 const T_partials_return sigma_dbl =
value_of(sigma_vec[i]);
96 inv_sigma[i] = 1.0 / sigma_dbl;
97 sigma_squared[i] = sigma_dbl * sigma_dbl;
99 log_sigma[i] =
log(sigma_dbl);
104 operands_and_partials(y, mu, sigma);
106 for (
size_t n = 0; n < N; n++) {
108 const T_partials_return y_dbl =
value_of(y_vec[n]);
109 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
112 const T_partials_return y_minus_mu
114 const T_partials_return y_minus_mu_squared
115 = y_minus_mu * y_minus_mu;
116 const T_partials_return y_minus_mu_over_sigma
117 = y_minus_mu * inv_sigma[n];
118 const T_partials_return y_minus_mu_over_sigma_squared
119 = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
125 logp -= log_sigma[n];
127 logp -=
log1p(y_minus_mu_over_sigma_squared);
131 operands_and_partials.
d_x1[n] -= 2 * y_minus_mu
132 / (sigma_squared[n] + y_minus_mu_squared);
134 operands_and_partials.
d_x2[n] += 2 * y_minus_mu
135 / (sigma_squared[n] + y_minus_mu_squared);
137 operands_and_partials.
d_x3[n]
138 += (y_minus_mu_squared - sigma_squared[n])
139 * inv_sigma[n] / (sigma_squared[n] + y_minus_mu_squared);
141 return operands_and_partials.
value(logp);
144 template <
typename T_y,
typename T_loc,
typename T_scale>
147 cauchy_log(
const T_y& y,
const T_loc& mu,
const T_scale& sigma) {
148 return cauchy_log<false>(y, mu, sigma);
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.
fvar< T > log(const fvar< T > &x)
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)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
fvar< T > square(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)
return_type< T_y, T_loc, T_scale >::type cauchy_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) a...
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
VectorBuilder allocates type T1 values to be used as intermediate values.
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.
fvar< T > log1p(const fvar< T > &x)
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