[Rd] prod(numeric(0)) surprise

[Martin Morgan]

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
>
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