function (X, INDEX, FUN = NULL, ..., simplify = TRUE) 
{
    FUN <- if (!is.null(FUN)) 
        match.fun(FUN)
    if (!is.list(INDEX))           
        INDEX <- list(INDEX)
    nI <- length(INDEX)
    if (!nI) 
        stop("'INDEX' is of length zero")
    namelist <- vector("list", nI)
    names(namelist) <- names(INDEX)
    extent <- integer(nI) 
    nx <- length(X)
    one <- 1L
    group <- rep.int(one, nx)     
    ngroup <- one
    for (i in seq_along(INDEX)) {   
        index <- as.factor(INDEX[[i]])
        if (length(index) != nx) 
            stop("arguments must have same length")
        namelist[[i]] <- levels(index)
        extent[i] <- nlevels(index)
        
        
        group <- group + ngroup * (as.integer(index) - one)
        ngroup <- ngroup * nlevels(index)
    }
    if (is.null(FUN)) 
        return(group)
        
    
    ans <- lapply(X = split(X, group), FUN = FUN, ...)   
    index <- as.integer(names(ans))
    if (simplify && all(unlist(lapply(ans, length)) == 1L)) {
        ansmat <- array(dim = extent, dimnames = namelist)
        ans <- unlist(ans, recursive = FALSE)
    }
    else {
        ansmat <- array(vector("list", prod(extent)), dim = extent, 
            dimnames = namelist)
    }
    if (length(index)) {
        names(ans) <- NULL
        ansmat[index] <- ans
    }
    ansmat
}