On Sep 8, 2011, at 4:41 PM, Marc Schwartz wrote:
On Sep 8, 2011, at 3:09 PM, David Winsemius wrote:
On Sep 8, 2011, at 3:54 PM, Marc Schwartz wrote:
On Sep 8, 2011, at 2:42 PM, David Winsemius wrote:
On Sep 8, 2011, at 3:35 PM, Alexander Engelhardt wrote:
Am 08.09.2011 20:48, schrieb Marc Schwartz:
There was a post from Martin Maechler some years ago and I had
to search a bit to find it. For these sorts of issues, I
typically trust his judgement.
The post is here:
https://stat.ethz.ch/pipermail/r-help/2003-April/032471.html
His solution also handles complex numbers.
For those too lazy to follow
He is basically creating the function is.whole:
is.whole <- function(x)
is.numeric(x) && floor(x)==x
Are you sure? I thought the test would have been all.equal(x,
round(x,0) )
My reasoning was that 1.999999999999 should be considered 2 but
floor would make it 1.
David, I am confuzzled. Why would that be equal to 2?
So that sqrt(3) * sqrt(3) would be a "whole number". (It is true
the the floor based wholeness criterion would make sqrt(2)*sqrt(2)
Somehow it doesn't see "right" that only half of square roots of
integers that have been squared should pass the wholeness test:
is.whole <- function(a, tol = 1e-7) {
+ is.eq <- function(x,y) {
+ r <- all.equal(x,y, tol=tol)
+ is.logical(r) && r
+ }
+ (is.numeric(a) && is.eq(a, floor(a))) ||
+ (is.complex(a) && {ri <- c(Re(a),Im(a)); is.eq(ri, floor(ri))})
+ }
is.whole( sqrt(2)^2 )
[1] TRUE
is.whole( sqrt(3)^2 )
[1] FALSE
<snip content>
OK. I suspect it may down to what assumptions one is willing to
make, including the level of tolerance used for the comparison.
Out of interest I tested whether my guess that half of the squared-
sqrt's would fail and it was not even close to 50%. So I took the
testing further and cannot explain the results:
> sum(sapply(sqrt(2:10000)^2, is.whole))
[1] 7577
> sum(sapply(((2:10000)^(1/3) )^3, is.whole))
[1] 49 # No that _is_ strange.
> sum(sapply(((2:10000)^(1/4) )^4, is.whole))
[1] 6207
> sum(sapply(((2:10000)^(1/5) )^5, is.whole))
[1] 9946
> sum(sapply(((2:10000)^(1/6) )^6, is.whole))
[1] 1324
Pondering the irregular pattern of results above is probably entirely
tangential. I think that if a number "should" have been an integer it
should have been defined as an integer and otherwise being close
enough on either side of an integer value should be enough.
is.whole2 <- function(a, tol = 1e-7) {
is.eq <- function(x,y) {
r <- all.equal(x,y, tol=tol)
is.logical(r) && r
}
(is.numeric(a) && is.eq(a, round(a,0))) ||
(is.complex(a) && {ri <- c(Re(a),Im(a)); is.eq(ri, floor(ri))})
}
> sum(sapply(((2:10000)^(1/3) )^3, is.whole2))
[1] 9999
> sum(sapply(((2:10000)^(1/5) )^5, is.whole2))
[1] 9999
is.whole() of course works for 2 because:
print(sqrt(2) ^ 2, 20)
[1] 2.0000000000000004441
is slightly larger than 2, so:
floor(sqrt(2) ^ 2)
[1] 2
works, as does:
round(sqrt(2) ^ 2, 0)
[1] 2
On the other hand:
print(sqrt(3) ^ 2, 20)
[1] 2.9999999999999995559
is slightly smaller than 3, so:
floor(sqrt(3) ^ 2)
[1] 2
versus:
round(sqrt(3) ^ 2, 0)
[1] 3
Not sure if Martin (cc'd now) might have any comments 8 plus years
later relative to this issue, as I would again defer to his
judgement here.
The other solution proposed, using modulo division, would logically
fail in both cases:
(sqrt(3) ^ 2) %% 1 == 0
[1] FALSE
(sqrt(2) ^ 2) %% 1 == 0
[1] FALSE
Regards,
Marc
David Winsemius, MD
West Hartford, CT
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