prod(numeric(0)) surprise

I'm a little confused. I understand that numeric(0) means an empty
numeric vector, not the number 0 expressed as numeric. As it is now,
prod(numeric(0)) generates something -- a vector of length 1
containing the number 1 -- from nothing. I would have expected

prod(numeric(0)) ==> numeric(0)

this is consistent with

numeric(0) ==> numeric(0)
numeric(0) * 1 ==> numeric(0)
cumprod(numeric(0)) ==> numeric(0)

and, because concatenation occus before function evaluation,

prod(c(numeric(0),1)) ==> prod( c(1) ) ==> 1

I would expect sum() to behave the same way, e.g., sum(numeric(0)) ==>
numeric(0). From below,

    >>>> consider exp(sum(log(numeric(0)))) ... ?)

    >>
    >> That's a fairly standard mathematical convention, which
    >> is presumably why sum and prod work that way.
    >>
    >> Duncan Murdoch

I would have expected numeric(0) as the result (numeric(0) is the
result from log(numeric(0)), etc).

Martin (Morgan)


Martin Maechler <maechler at stat.math.ethz.ch> writes:

"Ben" == Ben Bolker <bolker at zoo.ufl.edu>
    on Sun, 08 Jan 2006 21:40:05 -0500 writes:

    Ben> Duncan Murdoch wrote:

    >> On 1/8/2006 9:24 PM, Ben Bolker wrote:
    >>

    >>> It surprised me that prod(numeric(0)) is 1.  I guess if
    >>> you say (operation(nothing) == identity element) this
    >>> makes sense, but ??

    >>
    >>
    >> What value were you expecting, or were you expecting an
    >> error?  I can't think how any other value could be
    >> justified, and throwing an error would make a lot of
    >> formulas more complicated.
    >>

    >>>

    >>

    >>>> consider exp(sum(log(numeric(0)))) ... ?)

    >>
    >> That's a fairly standard mathematical convention, which
    >> is presumably why sum and prod work that way.
    >>
    >> Duncan Murdoch

    Ben>    OK.  I guess I was expecting NaN/NA (as opposed to
    Ben> an error), but I take the "this makes everything else
    Ben> more complicated" point.  Should this be documented or
    Ben> is it just too obvious ... ?  (Funny -- I'm willing to
    Ben> take gamma(1)==1 without any argument or suggestion
    Ben> that it should be documented ...)

see?  so it looks to me as if you have finally convinced
yourself that '1' is the most reasonable result.. ;-)

Anyway, I've added a sentence to help(prod)  {which matches
the sentence in help(sum), BTW}.

Martin