[Rd] Reason for difference in singular value decomposition produced by function La.svd (via prcomp)?

peter dalgaard pdalgd at gmail.com
Mon Aug 12 14:57:10 CEST 2013

On Aug 12, 2013, at 10:26 , Ulrike Grömping wrote:

> Dear expeRts,
> I previously posted this message to R-help and did not get a response, therefore I now try here, with a few additional system details added.
> I have run some simulations under R 2.15.1 on a Mac (OS X, 10.6.8), and I have rerun a sample of them under R 3.0.1 on Windows 7 (and also for comparison under R2.14.1 on Windows XP). For most cases, I get exactly the same results in all three runs. However, for those cases that depend on principal components computed with prcomp, where the particular choice of the orthogonalization is arbitrary because of several identical singular values, I get different results between the two Windows versions on the one hand and the Mac version on the other hand. I did not find anything documented about the difference; maybe I didn't know where to look. Can someone help me understand the reason?

What did you expect? There is nothing in the SVD algorithm to select a solution which satisfies some auxiliary criterion that makes it unique.

When the orthogonalization is arbitrary, the particular solution that you get may depend on rounding error and other low-level details of the algorithm. A change of machine/os/compiler/etc. may give you a different result. 

> Best, Ulrike
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Peter Dalgaard, Professor
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

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