#' Multi Linear Multiplication
#'
#'     C = A x { B1, ..., Br }
#'
#' @param A tensor (multi-linear array)
#' @param B matrix or list of matrices
#' @param ... further matrices, concatenated with \code{B}
#' @param modes integer sequence of the same length as number of matrices
#'  supplied (in \code{B} and \code{...})
#'
#' @examples
#' # general usage
#' dimA <- c(3, 17, 19, 2)
#' dimC <- c(7, 11, 13, 5)
#' A <- array(rnorm(prod(dimA)), dim = dimA)
#' B <- Map(function(p, q) matrix(rnorm(p * q), p, q), dimC, dimA)
#' C1 <- mlm(A, B)
#' C2 <- mlm(A, B[[1]], B[[2]], B[[3]], B[[4]])
#' C3 <- mlm(A, B[[3]], B[[1]], B[[2]], B[[4]], modes = c(3, 1, 2, 4))
#' C4 <- mlm(A, B[1:3], B[[4]])
#' stopifnot(all.equal(C1, C2))
#' stopifnot(all.equal(C1, C3))
#' stopifnot(all.equal(C1, C4))
#'
#' # selected modes
#' C1 <- mlm(A, B, modes = 2:3)
#' C2 <- mlm(A, B[[2]], B[[3]], modes = 2:3)
#' C3 <- ttm(ttm(A, B[[2]], 2), B[[3]], 3)
#' stopifnot(all.equal(C1, C2))
#' stopifnot(all.equal(C1, C3))
#'
#' # analog to matrix multiplication
#' A <- matrix(rnorm( 6), 2, 3)
#' B <- matrix(rnorm(12), 3, 4)
#' C <- matrix(rnorm(20), 4, 5)
#' stopifnot(all.equal(
#'     A %*% B %*% t(C),
#'     mlm(B, list(A, C))
#' ))
#'
#' # usage with repeated modes (non commutative)
#' dimA <- c(3, 17, 19, 2)
#' A <- array(rnorm(prod(dimA)), dim = dimA)
#' B1 <- matrix(rnorm(9), 3, 3)
#' B2 <- matrix(rnorm(9), 3, 3)
#' C <- matrix(rnorm(4), 2, 2)
#' # same modes do NOT commute
#' all.equal(
#'     mlm(A, B1, B2, C, modes = c(1, 1, 4)),  # NOT equal!
#'     mlm(A, B2, B1, C, modes = c(1, 1, 4))
#' )
#' # but different modes do commute
#' P1 <- mlm(A, C, B1, B2, modes = c(4, 1, 1))
#' P2 <- mlm(A, B1, C, B2, modes = c(1, 4, 1))
#' P3 <- mlm(A, B1, B2, C, modes = c(1, 1, 4))
#' stopifnot(all.equal(P1, P2))
#' stopifnot(all.equal(P1, P3))
#'
#' @export
mlm <- function(A, B, ..., modes = seq_along(B)) {
    # Collect all matrices in `B`
    B <- c(if (is.matrix(B)) list(B) else B, list(...))

    # iteratively apply Tensor Times Matrix multiplication over modes
    for (i in seq_along(modes)) {
        A <- ttm(A, B[[i]], modes[i])
    }

    # return result tensor
    A
}