[Rd] prod(numeric(0)) surprise

[Duncan Murdoch]

On 1/9/2006 12:40 PM, Martin Morgan wrote:
> 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,
>

I think the code below works as I'd expect.  Would you really like the 
last answer to be numeric(0)?

 > x <- 1:10
 > sum(x)
[1] 55
 > sum(x[x>5])
[1] 40
 > sum(x[x>10])
[1] 0

Duncan Murdoch

>>     >>>> 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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