From maechler at stat.math.ethz.ch  Tue Dec 28 20:06:07 2010
From: maechler at stat.math.ethz.ch (Martin Maechler)
Date: Tue, 28 Dec 2010 20:06:07 +0100
Subject: [Rd] RFC: sapply() limitation from vector to matrix,
	but not further
In-Reply-To: <4D1A290C.8040205@acm.org>
References: <19702.2469.739772.13707@lynne.math.ethz.ch>
	<AANLkTin6pbS_99RjSje12Zr7M9mwLy0oKNX7H8gz1Zgh@mail.gmail.com>
	<19738.1821.84824.284589@cmath-6.math.ethz.ch>
	<4D1A290C.8040205@acm.org>
Message-ID: <AANLkTikeGUT5yCLrhg7kA-8=QQsWcr6B8s1w5weoEbvO@mail.gmail.com>

On Tue, Dec 28, 2010 at 19:14, Tony Plate <tplate at acm.org> wrote:
> The abind() function from the abind package is an alternative here -- it can
> take a list argument, which makes it easy to use with the result of
> lapply(). ?It's also able take direction about which dimension to join on.
>
>> x <- list(a=1,b=2,c=3)
>> f <- function(v) matrix(v, nrow=2, ncol=4)
>> sapply(x, f)
> ? ? a b c
> [1,] 1 2 3
> [2,] 1 2 3
> [3,] 1 2 3
> [4,] 1 2 3
> [5,] 1 2 3
> [6,] 1 2 3
> [7,] 1 2 3
> [8,] 1 2 3
>>
>> # The 'along=' argument to abind() determines on which dimension
>> # the list elements are joined. ?Use a fractional value to put the new
>> # dimension between existing ones.
>>
>> dim(abind(lapply(x, f), along=0))
> [1] 3 2 4
>> dim(abind(lapply(x, f), along=1.5))
> [1] 2 3 4
>> dim(abind(lapply(x, f), along=3))
> [1] 2 4 3
>> abind(lapply(x, f), along=3)
> , , a
>
> ? ? [,1] [,2] [,3] [,4]
> [1,] ? ?1 ? ?1 ? ?1 ? ?1
> [2,] ? ?1 ? ?1 ? ?1 ? ?1
>
> , , b
>
> ? ? [,1] [,2] [,3] [,4]
> [1,] ? ?2 ? ?2 ? ?2 ? ?2
> [2,] ? ?2 ? ?2 ? ?2 ? ?2
>
> , , c
>
> ? ? [,1] [,2] [,3] [,4]
> [1,] ? ?3 ? ?3 ? ?3 ? ?3
> [2,] ? ?3 ? ?3 ? ?3 ? ?3
>

Thank you, Tony.
Indeed, yes,  abind() is nice here (and in the good ol' APL spirit !)

Wanting to keep things both simple *and* fast here, of course,
hence I currently contemplate the following code,
where the new  simplify2array()  is  considerably simpler than  abind():

##' "Simplify" a list of commonly structured components into an array.
##'
##' @title simplify list() to an array if the list elements are
structurally equal
##' @param x a list, typically resulting from lapply()
##' @param higher logical indicating if an array() of "higher rank"
##'  should be returned when appropriate, namely when all elements of
##' \code{x} have the same \code{\link{dim}()}ension.
##' @return x itself, or an array if the simplification "is sensible"
simplify2array <- function(x, higher = TRUE)
{
    if(length(common.len <- unique(unlist(lapply(x, length)))) > 1L)
        return(x)
    if(common.len == 1L)
        unlist(x, recursive = FALSE)
    else if(common.len > 1L) {
        n <- length(x)
        ## make sure that array(*) will not call rep() {e.g. for 'call's}:
        r <- as.vector(unlist(x, recursive = FALSE))
        if(higher && length(c.dim <- unique(lapply(x, dim))) == 1 &&
           is.numeric(c.dim <- c.dim[[1L]]) &&
           prod(d <- c(c.dim, n)) == length(r)) {

            iN1 <- is.null(n1 <- dimnames(x[[1L]]))
            n2 <- names(x)
            dnam <-
                if(!(iN1 && is.null(n2)))
                    c(if(iN1) rep.int(list(n1), length(c.dim)) else n1,
                      list(n2)) ## else NULL
            array(r, dim = d, dimnames = dnam)

        } else if(prod(d <- c(common.len, n)) == length(r))
            array(r, dim = d,
                  dimnames= if(!(is.null(n1 <- names(x[[1L]])) &
                  is.null(n2 <- names(x)))) list(n1,n2))
        else x
    }
    else x
}

sapply <- function(X, FUN, ..., simplify = TRUE, USE.NAMES = TRUE)
{
    FUN <- match.fun(FUN)
    answer <- lapply(X, FUN, ...)
    if(USE.NAMES && is.character(X) && is.null(names(answer)))
	names(answer) <- X
    if(!identical(simplify, FALSE) && length(answer))
	simplify2array(answer, higher = (simplify == "array"))
    else answer
}



[Rd] RFC: sapply() limitation from vector to matrix, but not further
Martin Maechler