#' Tensor Times Matrix (n-mode tensor matrix product)
#'
#' @param T array of order at least \code{mode}
#' @param M matrix, the right hand side of the mode product such that
#'  \code{ncol(M)} equals \code{dim(T)[mode]} if \code{transposed} is false,
#'  otherwise the dimension matching is \code{nrow(M)} to \code{dim(T)[mode]}.
#' @param mode the mode of the product in the range \code{1:length(dim(T))}
#' @param transposed boolean to multiply with the transposed of \code{M}
#'
#' @returns multi-dimensional array of the same order as \code{T} with
#'  \code{mode} dimension equal to \code{nrow(M)} or \code{ncol(M)} if
#'  \code{transposed} is true.
#'
#' @examples
#' for (mode in 1:4) {
#'     dimA <- sample.int(10, 4, replace = TRUE)
#'     A <- array(rnorm(prod(dimA)), dim = dimA)
#'     nrowB <- sample.int(10, 1)
#'     B <- matrix(rnorm(nrowB * dimA[mode]), nrowB)
#'
#'     C <- ttm(A, B, mode)
#'
#'     dimC <- ifelse(seq_along(dims) != mode, dimA, nrowB)
#'     C.ref <- mat(B %*% mat(A, mode), mode, dims = dimC, inv = TRUE)
#'
#'     stopifnot(all.equal(C, C.ref))
#' }
#'
#' for (mode in 1:4) {
#'     dimA <- sample.int(10, 4, replace = TRUE)
#'     A <- array(rnorm(prod(dimA)), dim = dimA)
#'     ncolB <- sample.int(10, 1)
#'     B <- matrix(rnorm(dimA[mode] * ncolB), dimA[mode])
#'
#'     C <- ttm(A, B, mode, transposed = TRUE)
#'
#'     C.ref <- ttm(A, t(B), mode)
#'
#'     stopifnot(all.equal(C, C.ref))
#' }
#'
#' @export
ttm <- function(T, M, mode = length(dim(T)), transposed = FALSE) {
    storage.mode(T) <- storage.mode(M) <- "double"
    dim(M) <- c(NROW(M), NCOL(M))
    .Call("C_ttm", T, M, as.integer(mode), as.logical(transposed))
}

#' @rdname ttm
#' @export
`%x_1%` <- function(T, M) ttm(T, M, 1L)
#' @rdname ttm
#' @export
`%x_2%` <- function(T, M) ttm(T, M, 2L)
#' @rdname ttm
#' @export
`%x_3%` <- function(T, M) ttm(T, M, 3L)
#' @rdname ttm
#' @export
`%x_4%` <- function(T, M) ttm(T, M, 4L)