R help - Nov 2009 - unexpected results in comparison (x == y)

Dear readers of the list,

I have a problem a comparison of two data from a vector. The comparison
yields FALSE but should be TRUE. I have checked for mode(), length() and
attributes(). See the following code (R2.10.0):
-----------------------------------------------
# data vector of 66 double data
X
matrix(c(41.41,38.1,39.22,38.1,47.29,46.82,82.46,90.11,45.24,45.74,49.96,53.40,38.20,42.65,45.41,47.92,39.82,42.02,48.17,49.47,39.67,43.89,47.55,50.05,35.75,37.41,46.13,53.64,52.18,56.30,45.15,47.13,41.57,39.08,43.39,44.73,49.38,47.00,45.67,50.53,41.08,44.22,49.28,47.83,49.48,46.04,48.37,47.00,33.96,36.30,49.40,46.44,24.40,24.79,41.55,46.26,37.43,39.88,40.63,38.64,49.92,50.19,47.88,48.61,43.73,44.18),ncol=1)
i = dim(X)

# calculating pairwise differences for each entry in X
Y = matrix(rep(0.0,i[1]*i[1]),ncol=i[1])
for (j in 1:i[1]) {
	Y[j,] = X - X[j,]
}

# getting pairwise absolute differences to vector Z and selecting only (xj -
xk), omitting (xk - xj) 
# and (xj - xj) i.e. diagonal vector
Z = rep(0, ((i[1]*i[1])-i[1])/2)
nn <- 1
for (j in 1:i[1]) {
for (k in 1:i[1]) {
	if (j > k)  {
		Z[nn] <- abs(Y[j,k])
		nn <- nn + 1
	}
}
}
nn <- nn - 1

# sorting Z ascending to ZZ, to determine double entries with same
difference
ii <- 0
ZZ <- sort(Z)

# here the problem occurs:
ZZ[1:10]
ZZ[4]
ZZ[5]
ZZ[4] == ZZ[5]
mode(ZZ[4])
mode(ZZ[5])
length(ZZ[4])
length(ZZ[5])
attributes(ZZ[4])
attributes(ZZ[5])
-----------------------------------------------

I get:
 
> ZZ[1:10]
 [1] 0.00 0.00 0.01 0.02 0.02 0.02 0.04 0.04 0.04 0.05
> ZZ[4]
[1] 0.02
> ZZ[5]
[1] 0.02
> ZZ[4] == ZZ[5]
[1] FALSE
> mode(ZZ[4])
[1] "numeric"
> mode(ZZ[5])
[1] "numeric"
> length(ZZ[4])
[1] 1
> length(ZZ[5])
[1] 1
> attributes(ZZ[4])
NULL
> attributes(ZZ[5])
NULL

Which is ok, except for ZZ[4] == ZZ[5].

Can someone please give me an advice where to look?
In real world situations the original vector (X) will contain upto 100
entries. 



-- 
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I'm guessing that it's in the FAQ, although I have not committed its  
number to memory.

Try using all.equal() instead of "=="

-- 
David


On Nov 4, 2009, at 7:49 AM, Peter Tillmann wrote:
>
> Dear readers of the list,
>
> I have a problem a comparison of two data from a vector. The  
> comparison
> yields FALSE but should be TRUE. I have checked for mode(), length()  
> and
> attributes(). See the following code (R2.10.0):
> -----------------------------------------------
> # data vector of 66 double data
> X >
matrix(c(41.41,38.1,39.22,38.1,47.29,46.82,82.46,90.11,45.24,45.74,49.96,53.40,38.20,42.65,45.41,47.92,39.82,42.02,48.17,49.47,39.67,43.89,47.55,50.05,35.75,37.41,46.13,53.64,52.18,56.30,45.15,47.13,41.57,39.08,43.39,44.73,49.38,47.00,45.67,50.53,41.08,44.22,49.28,47.83,49.48,46.04,48.37,47.00,33.96,36.30,49.40,46.44,24.40,24.79,41.55,46.26,37.43,39.88,40.63,38.64,49.92,50.19,47.88,48.61,43.73,44.18),ncol=1)
> i = dim(X)
>
> # calculating pairwise differences for each entry in X
> Y = matrix(rep(0.0,i[1]*i[1]),ncol=i[1])
> for (j in 1:i[1]) {
> 	Y[j,] = X - X[j,]
> }
>
> # getting pairwise absolute differences to vector Z and selecting  
> only (xj -
> xk), omitting (xk - xj)
> # and (xj - xj) i.e. diagonal vector
> Z = rep(0, ((i[1]*i[1])-i[1])/2)
> nn <- 1
> for (j in 1:i[1]) {
> for (k in 1:i[1]) {
> 	if (j > k)  {
> 		Z[nn] <- abs(Y[j,k])
> 		nn <- nn + 1
> 	}
> }
> }
> nn <- nn - 1
>
> # sorting Z ascending to ZZ, to determine double entries with same
> difference
> ii <- 0
> ZZ <- sort(Z)
>
> # here the problem occurs:
> ZZ[1:10]
> ZZ[4]
> ZZ[5]
> ZZ[4] == ZZ[5]
> mode(ZZ[4])
> mode(ZZ[5])
> length(ZZ[4])
> length(ZZ[5])
> attributes(ZZ[4])
> attributes(ZZ[5])
> -----------------------------------------------
>
> I get:
>
>> ZZ[1:10]
> [1] 0.00 0.00 0.01 0.02 0.02 0.02 0.04 0.04 0.04 0.05
>> ZZ[4]
> [1] 0.02
>> ZZ[5]
> [1] 0.02
>> ZZ[4] == ZZ[5]
> [1] FALSE
>> mode(ZZ[4])
> [1] "numeric"
>> mode(ZZ[5])
> [1] "numeric"
>> length(ZZ[4])
> [1] 1
>> length(ZZ[5])
> [1] 1
>> attributes(ZZ[4])
> NULL
>> attributes(ZZ[5])
> NULL
>
> Which is ok, except for ZZ[4] == ZZ[5].
>
> Can someone please give me an advice where to look?
> In real world situations the original vector (X) will contain upto 100
> entries.
>
>
>
> -- 
> View this message in context:
http://old.nabble.com/unexpected-results-in-comparison-%28x-%3D%3D-y%29-tp26195749p26195749.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius, MD
Heritage Laboratories
West Hartford, CT

FAQ 7.31:
http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-the
se-numbers-are-equal_003f 
> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Peter Tillmann
> Sent: Mittwoch, 4. November 2009 13:50
> To: r-help at r-project.org
> Subject: [R] unexpected results in comparison (x == y)
> 
> 
> Dear readers of the list,
> 
> I have a problem a comparison of two data from a vector. The 
> comparison yields FALSE but should be TRUE. I have checked 
> for mode(), length() and attributes(). See the following code 
> (R2.10.0):
> -----------------------------------------------
> # data vector of 66 double data
> X > matrix(c(41.41,38.1,39.22,38.1,47.29,46.82,82.46,90.11,45.24,4
> 5.74,49.96,53.40,38.20,42.65,45.41,47.92,39.82,42.02,48.17,49.
> 47,39.67,43.89,47.55,50.05,35.75,37.41,46.13,53.64,52.18,56.30
> ,45.15,47.13,41.57,39.08,43.39,44.73,49.38,47.00,45.67,50.53,4
> 1.08,44.22,49.28,47.83,49.48,46.04,48.37,47.00,33.96,36.30,49.
> 40,46.44,24.40,24.79,41.55,46.26,37.43,39.88,40.63,38.64,49.92
> ,50.19,47.88,48.61,43.73,44.18),ncol=1)
> i = dim(X)
> 
> # calculating pairwise differences for each entry in X Y = 
> matrix(rep(0.0,i[1]*i[1]),ncol=i[1])
> for (j in 1:i[1]) {
> 	Y[j,] = X - X[j,]
> }
> 
> # getting pairwise absolute differences to vector Z and 
> selecting only (xj - xk), omitting (xk - xj) # and (xj - xj) 
> i.e. diagonal vector Z = rep(0, ((i[1]*i[1])-i[1])/2) nn <- 1 
> for (j in 1:i[1]) { for (k in 1:i[1]) {
> 	if (j > k)  {
> 		Z[nn] <- abs(Y[j,k])
> 		nn <- nn + 1
> 	}
> }
> }
> nn <- nn - 1
> 
> # sorting Z ascending to ZZ, to determine double entries with 
> same difference ii <- 0 ZZ <- sort(Z)
> 
> # here the problem occurs:
> ZZ[1:10]
> ZZ[4]
> ZZ[5]
> ZZ[4] == ZZ[5]
> mode(ZZ[4])
> mode(ZZ[5])
> length(ZZ[4])
> length(ZZ[5])
> attributes(ZZ[4])
> attributes(ZZ[5])
> -----------------------------------------------
> 
> I get:
>  
> > ZZ[1:10]
>  [1] 0.00 0.00 0.01 0.02 0.02 0.02 0.04 0.04 0.04 0.05
> > ZZ[4]
> [1] 0.02
> > ZZ[5]
> [1] 0.02
> > ZZ[4] == ZZ[5]
> [1] FALSE
> > mode(ZZ[4])
> [1] "numeric"
> > mode(ZZ[5])
> [1] "numeric"
> > length(ZZ[4])
> [1] 1
> > length(ZZ[5])
> [1] 1
> > attributes(ZZ[4])
> NULL
> > attributes(ZZ[5])
> NULL
> 
> Which is ok, except for ZZ[4] == ZZ[5].
> 
> Can someone please give me an advice where to look?
> In real world situations the original vector (X) will contain 
> upto 100 entries. 
> 
> 
> 
> --
> View this message in context: 
> http://old.nabble.com/unexpected-results-in-comparison-%28x-%3
D%3D-y%29-tp26195749p26195749.html
> Sent from the R help mailing list archive at Nabble.com.
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

On 11/04/2009 11:49 PM, Peter Tillmann wrote:
> Dear readers of the list,
> ...
> Which is ok, except for ZZ[4] == ZZ[5].
>
> Can someone please give me an advice where to look?
> In real world situations the original vector (X) will contain upto 100
> entries.
>
>    
Hi Peter,
This looks like there is a small difference in the two values that is 
not appearing when printed.

zz[4]-zz[5]
[1] -7.105427e-15

Jim

Peter Tillmann wrote:
> 
> Dear readers of the list,
> 
> I have a problem a comparison of two data from a vector. The comparison
> yields FALSE but should be TRUE. I have checked for mode(), length() and
> attributes(). See the following code (R2.10.0):
> 
> *SNIP*
> 
>> ZZ[4]
> [1] 0.02
>> ZZ[5]
> [1] 0.02
>> ZZ[4] == ZZ[5]
> [1] FALSE
> 
> *SNIP*
> 
> 
This looks like a side effect of roundoff error due to the finite precision
of numbers stored by a computer.  There was a large discussion of this issue
on the list about two weeks ago, you could read the posts at: 

  http://old.nabble.com/Rounding-error-in-seq%28...%29-ts25686630.html

They may provide some insight.  The punchline is that:

  0.2 = 2 * (1/10)

And 1/10 is not representable as a form of:

  2^n

For some integer n. Therefore the number 0.2 cannot be represented exactly
in floating point arithmetic and so inconsistencies will occur-- as you just
observed.  It's one of those realities of computer science that always
catches us non-computer scientists by surprise.

Hope this helps!

-Charlie

-----
Charlie Sharpsteen
Undergraduate
Environmental Resources Engineering
Humboldt State University
-- 
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