########################################################################
    # When R adds a number or vector to an array it adds it columnwise
    # Thus if the 1x3 column mean of a n x 3 array is added to the array
    # it is added to the 1st 3 entries in col. 1, then the next 3 and so on.
    # To add to (subtract from) the rows, we need to take the transpose
    # of the array, add the vector to it, then take the transpose of the result.
    # The next few functions do this.
    ########################################################################
add.arr.vec <- function (arr, vec) {
       # Add a point to an array
   t(t(arr) + vec)
}

mult.arr.vec <- function (arr, vec) {
       # Mult. a point to an array
   t(t(arr)*vec)
}

div.arr.vec <- function (arr, vec) {
       # Divide an array by a point
   t(t(arr)/vec)
}

pt.arr.dist <- function(pt, array) {
       # Compute the Euclidean distance from a point to an array
   sqrt(apply((t(t(array)-as.vector(pt,mode="numeric")))^2, 1, sum))
}