# logdens_simultanee
#' logdens_simultanee calculates Gaussian log-densities for a bivariate signal
#' under a mixture model with P components
#' @param xk the bivariate signal
#' @param phi parameters of the mixture, P components
#' @return the value of the log density
logdens_simultanee <- function(xk, phi) {
P <- length(phi$prop)
m <- phi$mu
s <- phi$sigma
nk <- dim(xk)[2]
tmp <- matrix(ncol = P, nrow = 1)
tmp <- vapply(seq_len(P), function(p) {
-nk * log(sqrt(2 * pi) * s[1, p]) - 0.5 *
sum((xk[1, ] - m[1, p])^2) / s[1, p]^2 -
nk * log(sqrt(2 * pi) * s[2, p]) -
0.5 * sum((xk[2, ] - m[2, p])^2) / s[2, p]^2
})
invisible(tmp)
}
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