Dirk Eddelbuettel — written Dec 9, 2013 — source
The ubiquitous LAPACK library provides several implementations for the singular-value decomposition (SVD). We will illustrate possible speed gains from using the divide-and-conquer method by comparing it to the base case.
Having the two implementations, which differ only in the
argument (added recently in Armadillo 3.930), we are ready to do a
simple timing comparison.
Unit: milliseconds expr min lq median uq max neval baseSVD(X) 421.2 422.6 424.2 426.2 442.1 100 dcSVD(X) 111.0 111.5 111.9 113.6 126.1 100
The speed gain is noticeable which a ratio of about 3.9 at the median. However, we can also look at complex-valued matrices.
Unit: milliseconds expr min lq median uq max neval cxBaseSVD(X) 1248.7 1253.7 1257.5 1262.3 1311.7 100 cxDcSVD(X) 259.2 259.8 260.5 263.2 327.9 100
Here the difference is even more pronounced at about 4.8. However,
it is precisely this complex-value divide-and-conquer method which
is missing in R’s own Lapack. So R built with the default
configuration can not currently take advantage of the
complex-valued divide-and-conquer algorithm. Only builds which use
an external Lapack library (as for example the Debian and Ubuntu
builds) can. Let’s hope that R will add this functionality to its
next release R 3.1.0. Update: And the underlying
routine has now been added to the upcoming R 3.1.0 release. Nice.