[R] Precision in R

[David Winsemius]

On Jan 15, 2009, at 12:25 PM, Charles C. Berry wrote:
>
>
> This is what I get on windows XP:
>
>> tcp1-tcp2
>              [,1]          [,2]          [,3]
> [1,] -2.861023e-06 -4.768372e-07 -4.768372e-07
> [2,] -4.768372e-07 -3.814697e-06  2.622604e-06
> [3,] -4.768372e-07  2.622604e-06 -5.960464e-08
>>
>
> but on my Gentoo Linux Intel Core 2 Duo:
>
> print(tcp1-tcp2,digits=20)
>     [,1] [,2] [,3]
> [1,]    0    0    0
> [2,]    0    0    0
> [3,]    0    0    0
>>
>
> So, it would seem to be that the floating point calcs on my Windows
> box, David's Mac, and whatever system you are using are not as
> accurate as they might be.

For the record; on an Intel Mac (Leopard) with Urbanek's compilation  
of R 2.8.1

 >  print(tcp1-tcp2,digits=20)
      [,1] [,2] [,3]
[1,]    0    0    0
[2,]    0    0    0
[3,]    0    0    0

-- 
David Winsemius

>
>
> It is well known that rounding error can play havoc with  
> crossproducts (particularly when the range of magnitudes of the  
> numbers is wide as it is here), which is why matrix decompositions  
> are generally used for solving least squares problems.
>
> The internal code for crossprod and tcrossprod is different, so the
> computations are likely done in a different order, which would account
> for the difference in tcp1 and tcp2 . Ultimately, array.c and blas.f  
> SUBROUTINE
> DSYRK have the code if you want to dig into it.
>
> So to summarize: the difference is not due to R per se, but in the
> limited accuracy of floating point calcs on the system used.
>
> HTH,
>
> Chuck


snip