Randomness not due to seed

On 20 July 2011 at 14:03, Jeroen Ooms wrote:
| >> I think Bill Dunlap's answer addressed it:  the claim appears to be false.
| 
| Here is another example where there is randomness that is not due to
| the seed. On the same machine, the same R binary, but through another
| interface. First directly in the shell:
| 
| > sessionInfo()
| R version 2.13.1 (2011-07-08)
| Platform: i686-pc-linux-gnu (32-bit)
| 
| locale:
|  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
|  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
|  [5] LC_MONETARY=C              LC_MESSAGES=en_US.UTF-8
|  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
|  [9] LC_ADDRESS=C               LC_TELEPHONE=C
| [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
| 
| attached base packages:
| [1] stats     graphics  grDevices utils     datasets  methods   base
| 
| > set.seed(123)
| > print(coef(lm(dist~speed, data=cars)),digits=22)
|               (Intercept)                     speed
| -17.579094890510951643137   3.932408759124087715975

That's PBKAC --- even double precision does NOT get you 22 digits precision.

 

You may want to read up on 'what every computer scientist should know about
floating point arithmetic' by Goldberg (which is both a true internet classic)
and ponder why a common setting for the various 'epsilon' settings of general
convergence is set to of the constants supplied by the OS and/or its C
library. R has

 #define SINGLE_EPS     FLT_EPSILON
 [...]
 #define DOUBLE_EPS     DBL_EPSILON

in Constants.h. You can then chase the definition of FLT_EPSILON and
DBL_EPSILON through your system headers (which is a good exercise).

One place you may end up in the manual -- the following from the GNU libc
documentationon :Floating Point Parameters"

FLT_EPSILON
    This is the minimum positive floating point number of type float such that
    1.0 + FLT_EPSILON != 1.0 is true. It's supposed to be no greater than 1E-5. 

DBL_EPSILON
LDBL_EPSILON
    These are similar to FLT_EPSILON, but for the data types double and long
    double, respectively. The type of the macro's value is the same as the type
    it describes. The values are not supposed to be greater than 1E-9.

So there -- nine digits. 

Dirk 


| # And this is through eclipse (java)
| 
| > sessionInfo()
| R version 2.13.1 (2011-07-08)
| Platform: i686-pc-linux-gnu (32-bit)
| 
| locale:
|  [1] LC_CTYPE=en_US.UTF-8          LC_NUMERIC=C
|  [3] LC_TIME=en_US.UTF-8           LC_COLLATE=en_US.UTF-8
|  [5] LC_MONETARY=en_US.UTF-8       LC_MESSAGES=en_US.UTF-8
|  [7] LC_PAPER=en_US.UTF-8          LC_NAME=en_US.UTF-8
|  [9] LC_ADDRESS=en_US.UTF-8        LC_TELEPHONE=en_US.UTF-8
| [11] LC_MEASUREMENT=en_US.UTF-8    LC_IDENTIFICATION=en_US.UTF-8
| 
| attached base packages:
| [1] stats     graphics  grDevices utils     datasets  methods   base
| 
| other attached packages:
| [1] rj_0.5.2-1
| 
| loaded via a namespace (and not attached):
| [1] rJava_0.9-1  tools_2.13.1
| 
| > set.seed(123)
| > print(coef(lm(dist~speed, data=cars)),digits=22)
|              (Intercept)                    speed
| 

| 
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