1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LPDF_HPP 35 template <
bool propto,
typename T_y,
typename T_loc,
typename T_scale>
37 const T_y& y,
const T_loc& mu,
const T_scale& sigma) {
38 static const char*
function =
"cauchy_lpdf";
45 T_partials_return logp(0.0);
51 mu,
"Scale parameter", sigma);
68 for (
size_t i = 0; i <
length(sigma); i++) {
69 const T_partials_return sigma_dbl =
value_of(sigma_vec[i]);
70 inv_sigma[i] = 1.0 / sigma_dbl;
71 sigma_squared[i] = sigma_dbl * sigma_dbl;
73 log_sigma[i] =
log(sigma_dbl);
79 for (
size_t n = 0; n < N; n++) {
80 const T_partials_return y_dbl =
value_of(y_vec[n]);
81 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
83 const T_partials_return y_minus_mu = y_dbl - mu_dbl;
84 const T_partials_return y_minus_mu_squared = y_minus_mu * y_minus_mu;
85 const T_partials_return y_minus_mu_over_sigma = y_minus_mu * inv_sigma[n];
86 const T_partials_return y_minus_mu_over_sigma_squared
87 = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
94 logp -=
log1p(y_minus_mu_over_sigma_squared);
97 ops_partials.
edge1_.partials_[n]
98 -= 2 * y_minus_mu / (sigma_squared[n] + y_minus_mu_squared);
100 ops_partials.
edge2_.partials_[n]
101 += 2 * y_minus_mu / (sigma_squared[n] + y_minus_mu_squared);
103 ops_partials.
edge3_.partials_[n]
104 += (y_minus_mu_squared - sigma_squared[n]) * inv_sigma[n]
105 / (sigma_squared[n] + y_minus_mu_squared);
107 return ops_partials.
build(logp);
110 template <
typename T_y,
typename T_loc,
typename T_scale>
112 const T_y& y,
const T_loc& mu,
const T_scale& sigma) {
113 return cauchy_lpdf<false>(y, mu, sigma);
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...
fvar< T > log(const fvar< T > &x)
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.
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > log1p(const fvar< T > &x)
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_
return_type< T_y, T_loc, T_scale >::type cauchy_lpdf(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...