1#ifndef STAN_MATH_PRIM_PROB_MULTI_STUDENT_T_LPDF_HPP
2#define STAN_MATH_PRIM_PROB_MULTI_STUDENT_T_LPDF_HPP
42template <
bool propto,
typename T_y,
typename T_dof,
typename T_loc,
45 const T_y& y,
const T_dof& nu,
const T_loc& mu,
const T_scale& Sigma) {
51 static constexpr const char* function =
"multi_student_t";
54 check_finite(function,
"Degrees of freedom parameter", nu);
65 int num_dims = y_vec[0].size();
70 for (
size_t i = 1, size_mvt_y =
size_mvt(y); i < size_mvt_y; i++) {
72 function,
"Size of one of the vectors of the random variable",
73 y_vec[i].
size(),
"Size of another vector of the random variable",
77 for (
size_t i = 1, size_mvt_mu =
size_mvt(mu); i < size_mvt_mu; i++) {
79 "Size of one of the vectors "
80 "of the location variable",
82 "Size of another vector of "
83 "the location variable",
84 mu_vec[i - 1].
size());
88 "size of location parameter", mu_vec[0].
size());
90 "rows of scale parameter", Sigma.rows());
92 "columns of scale parameter", Sigma.cols());
94 for (
size_t i = 0; i < size_vec; i++) {
98 const auto& Sigma_ref =
to_ref(Sigma);
107 lp +=
lgamma(0.5 * (nu + num_dims)) * size_vec;
108 lp -=
lgamma(0.5 * nu) * size_vec;
109 lp -= (0.5 * num_dims) *
log(nu) * size_vec;
113 lp -= (0.5 * num_dims) *
LOG_PI * size_vec;
123 lp_type sum_lp_vec(0.0);
124 for (
size_t i = 0; i < size_vec; i++) {
130 lp -= 0.5 * (nu + num_dims) * sum_lp_vec;
135template <
typename T_y,
typename T_dof,
typename T_loc,
typename T_scale>
137 const T_y& y,
const T_dof& nu,
const T_loc& mu,
const T_scale& Sigma) {
138 return multi_student_t_lpdf<false>(y, nu, mu, Sigma);
This class provides a low-cost wrapper for situations where you either need an Eigen Vector or RowVec...
void check_symmetric(const char *function, const char *name, const matrix_cl< T > &y)
Check if the matrix_cl is symmetric.
return_type_t< T_y, T_dof, T_loc, T_scale > multi_student_t_lpdf(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
The log of the multivariate student t density for the given y, mu, nu, and scale matrix.
auto as_column_vector_or_scalar(T &&a)
as_column_vector_or_scalar of a kernel generator expression.
size_t size(const T &m)
Returns the size (number of the elements) of a matrix_cl or var_value<matrix_cl<T>>.
size_t size_mvt(const ScalarT &)
Provides the size of a multivariate argument.
typename return_type< Ts... >::type return_type_t
Convenience type for the return type of the specified template parameters.
value_type_t< T > log_determinant_ldlt(LDLT_factor< T > &A)
Returns log(abs(det(A))) given a LDLT_factor of A.
auto make_ldlt_factor(const T &A)
Make an LDLT_factor with matrix type plain_type_t<T>
return_type_t< T, EigMat2 > trace_inv_quad_form_ldlt(LDLT_factor< T > &A, const EigMat2 &B)
Compute the trace of an inverse quadratic form.
void check_consistent_sizes_mvt(const char *)
Trivial no input case, this function is a no-op.
fvar< T > log(const fvar< T > &x)
ref_type_t< T && > to_ref(T &&a)
This evaluates expensive Eigen expressions.
static constexpr double LOG_PI
The natural logarithm of , .
fvar< T > log1p(const fvar< T > &x)
size_t max_size_mvt(const T1 &x1, const Ts &... xs)
Calculate the size of the largest multivariate input.
void check_finite(const char *function, const char *name, const T_y &y)
Return true if all values in y are finite.
void check_ldlt_factor(const char *function, const char *name, LDLT_factor< T > &A)
Raise domain error if the specified LDLT factor is invalid.
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
void check_size_match(const char *function, const char *name_i, T_size1 i, const char *name_j, T_size2 j)
Check if the provided sizes match.
The lgamma implementation in stan-math is based on either the reentrant safe lgamma_r implementation ...
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...