[R] The behavior of match function

[Marc Schwartz]

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