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#' @title Calculate matrix W
#' @description Calculate observed matrix W for all G variables and G-E interactions. Denote Wj as the n x (q+1) sub-matrix of W corresponding the jth G variable.
#' The first column of Wj is the observation vector of the jth G variable, and the rest q columns of Wj are observations of G-E interactions.
#' @param E Observed matrix of E variables, of dimension n x q.
#' @param G Observed matrix of G variables, of dimensions n x p.
#' @return A matrix of dimension n x [p(q+1)].
#' @export
#' @examples
#' n <- 30; q <- 3; p <- 5;
#' E <- MASS::mvrnorm (n, rep (0, q), diag (q))
#' G <- MASS::mvrnorm (n, rep (0, p), diag (p))
#' W <- matW (E, G)
matW <- function(E, G)
{
Estar <- cbind(1, E)
p <- ncol(G)
q <- ncol(E)
n <- nrow(E)
W <- matrix(0, n, p * (q + 1))
for (j in 1:p) {
ind <- ((q + 1) * (j - 1) + 1):((q + 1) * j)
Gj <- G[, j]
Wj <- Gj * Estar
W[, ind] <- Wj
}
return(W = W)
}
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