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Is this correct?

4 messages · Joe, ecatchpole, vincent@7d4.com +1 more

Original
Joe
# 
Dear userR,

With the following results, are they correct or acceptable?
[1] 5.4
[1] FALSE
[1] -8.881784e-16
[1] -4.440892e-16
[1] 0
_
platform i386-pc-mingw32
arch     i386
os       mingw32
system   i386, mingw32
status
major    2
minor    2.0
year     2005
month    10
day      06
svn rev  35749
language R

What can I do to correct them if they are not correct?
Thanks!
--
C. Joseph Lu
Department of Statistics
National Cheng-Kung University
Tainan, Taiwan, ROC
ecatchpole
# 
See the R FAQ list, section 7. Why doesn't R think these numbers are equal?

Ted.

On 11/10/05 15:42,  Joe wrote,:

  
    

      
      
    

  


  


      

    

    

      
      

        
      

    

    

      
      

        


  

        

      Duncan Murdoch
    

    

      
      #
    

  


  

      
Joe wrote:

            

      
      
      
    

        
Yes.  See the FAQ:

7.31 Why doesn't R think these numbers are equal?

The only numbers that can be represented exactly in R's numeric type are 
integers and fractions whose denominator is a power of 2. Other numbers 
have to be rounded to (typically) 53 binary digits accuracy. As a 
result, two floating point numbers will not reliably be equal unless 
they have been computed by the same algorithm, and not always even then. 
For example

      R> a <- sqrt(2)
      R> a * a == 2
      [1] FALSE
      R> a * a - 2
      [1] 4.440892e-16

The function all.equal() compares two objects using a numeric tolerance 
of .Machine$double.eps ^ 0.5. If you want much greater accuracy than 
this you will need to consider error propagation carefully.

For more information, see e.g. David Goldberg (1991), ?What Every 
Computer Scientist Should Know About Floating-Point Arithmetic?, ACM 
Computing Surveys, 23/1, 5?48, also available via 
http://docs.sun.com/source/806-3568/ncg_goldberg.html.