Re: [R] The behavior of match function

From: Marc Schwartz <MSchwartz_at_mn.rr.com>
Date: Fri 21 Oct 2005 - 14:42:35 EST

On Fri, 2005-10-21 at 11:19 +0800, ronggui wrote:
> > x<-1:10
> > y<-x+1e-20
> > x
> [1] 1 2 3 4 5 6 7 8 9 10
> > y
> [1] 1 2 3 4 5 6 7 8 9 10
> > identical(x,y)
> [1] FALSE
> > match(x,y)
> [1] 1 2 3 4 5 6 7 8 9 10
>
> What's the principle the function use to determine if x match y?
>
> Thank you!

In this case, you are comparing x (an integer) with y (a numeric):

> x <- 1:10
> y <- x + 1e-20

> class(x)

[1] "integer"
> class(y)

[1] "numeric"

Now:

> x == y

 [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE works element-wise, because the differences between the values (1e-20) are less than:

> .Machine$double.eps

[1] 2.220446e-16

which is the smallest positive float such that 1 plus that value != 1. See ?.Machine for more information on that.

For the same reason:

> match(x, y)
 [1] 1 2 3 4 5 6 7 8 9 10

> x %in% y

 [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE both work element-wise.

However, if you used the following for 'y':

> y <- x + 1e-15

Note the results now:

> x == y

 [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE because you are now have differences that are greater than .Machine $double.eps.

In general however, when comparing floats, you will want to use all.equal():

> all.equal(x, y)
[1] TRUE which compares the values within a specified level of tolerance. See ?all.equal for more information and importantly note the use of isTRUE() as well:

> isTRUE(all.equal(x, y))
[1] TRUE Using isTRUE() in this way will result in a single TRUE or FALSE result depending upon the comparison. If the differences happen to be outside the tolerance level, you get something like the following:

> y <- x + 1e-5

> all.equal(x, y)
[1] "Mean relative difference: 1.818182e-06"

which does not help if all you want is a single boolean result. Thus the use of isTRUE() helps here:

> isTRUE(all.equal(x, y))
[1] FALSE You should also read R FAQ 7.31 "Why doesn't R think these numbers are equal?".

HTH, Marc Schwartz



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