[R] Decimal Accuracy Loss?

[Petr Savicky]

On Wed, Apr 06, 2011 at 11:33:48AM -0400, Brigid Mooney wrote:
> This is hopefully a quick question on decimal accuracy.  Is any
> decimal accuracy lost when casting a numeric vector as a matrix?  And
> then again casting the result back to a numeric?
> 
> I'm finding that my calculation values are different when I run for
> loops that manually calculate matrix multiplication as compared to
> when I cast the vectors as matrices and multiply them using "%*%".
> (The errors are very small, but the process is run iteratively
> thousands of times, at which point the error between the two
> differences becomes noticeable.)
> 
> I've read FAQ # 7.31 "Why doesn't R think these numbers are equal?",
> but just want to confirm that the differences in values are due to
> differences in the matrix multiplication operator and manual
> calculation via for loops, rather than information that is lost when
> casting a numeric as a matrix and back again.

Others already confirmed that casting a numeric as a matrix and back
again does not change the numbers. It is likely that the library
operator "%*%" is more accurate than a straightforward for loop.
For example, sum(x) uses a more accurate algorithm than iteration
of s <- s + x[i] in double precision.

Petr Savicky.