[R] Finding a basis in a set of vectors

[Peter Dalgaard]

Zhou Fang wrote:
> Ah ha, that does work.
> 
> What do you mean it isn't robust, though? I mean, obviously linear
> dependency structures in general are not stable under small
> perturbations...?
> 
> Or is it that it's platform dependent?

The former. In particular there is an issue with columns that have all 
entries near-zero. There were a couple of gotchas in its main 
application of thinning projection matrices within anova.mlm (the 2.8.1 
version has a zapsmall() kludge for that reason).

(This can of course also make things platform dependent, since roundoff 
accumulates differently depending on compilers and such.)

> 
> Zhou
> 
> On Fri, Feb 6, 2009 at 2:28 PM, Peter Dalgaard <P.Dalgaard at biostat.ku.dk> wrote:
>> Zhou Fang wrote:
>>> Hi,
>>>
>>> Okay, I have a n x p matrix X, which I know is not full rank. In
>>> particular, there may be linear dependencies amongst the columns (but
>>> not that many). What is a fast way of finding a linearly independent
>>> subset of the columns of X that will span the column space of X, in R?
>>> If it helps, I have the QR decomposition of the original X 'for free'.
>>>
>>> I know that it's possible to do this directly by looping over the
>>> columns and adding them, but at the very least, a solution without
>>> horrible slow loops would be nice.
>> Have a look at stats:::Thin.col(), but beware that it isn't terribly robust.
>>
>>> Any ideas welcome.
>>>
>>> Zhou Fang
>>>
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>>
>> --
>>   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>>  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
>>  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
>> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907
>>
>>


-- 
    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907