[Rd] Inconsistent rank in qr()

Keith O'Hara keith.ohara at nyu.edu
Mon Jan 22 23:32:26 CET 2018

I agree the result is a little confusing, but the behavior is in line with the documentation and so not ‘unexpected’ as such...

I don’t think this is a matter of semantics, more of a ‘return the rank when we have it for free’ situation—when A is real-valued, qr(A,LAPACK=false) calls a modified version of Linpack’s dqrdc which computes the rank internally; see dqrdc2.f, output ‘k’. Lapack’s dqeqp3 doesn’t return the rank as is.

Just my 2 cents on a potential fix: Matrix::rankMatrix follows the logic of your code, and I think this would be simpler to implement than modifying Lapack.c in two places (around lines 657 and 1175).


> On Jan 22, 2018, at 11:57 AM, Serguei Sokol <sokol at insa-toulouse.fr> wrote:
> Le 22/01/2018 à 17:40, Keith O'Hara a écrit :
>> This behavior is noted in the qr documentation, no?
>> rank - the rank of x as computed by the decomposition(*): always full rank in the LAPACK case.
> For a me a "full rank matrix" is a matrix the rank of which is indeed min(nrow(A), ncol(A))
> but here the meaning of "always is full rank" is somewhat confusing. Does it mean
> that only full rank matrices must be submitted to qr() when LAPACK=TRUE?
> May be there is a jargon where "full rank" is a synonym of min(nrow(A), ncol(A)) for any matrix
> but the fix to stick with commonly admitted rank definition (i.e. the number of linearly independent
> columns in A) is so easy. Why to discard lapack case from it (even properly documented)?
>>> On Jan 22, 2018, at 11:21 AM, Serguei Sokol <sokol at insa-toulouse.fr> wrote:
>>> Hi,
>>> I have noticed different rank values calculated by qr() depending on
>>> LAPACK parameter. When it is FALSE (default) a true rank is estimated and returned.
>>> Unfortunately, when LAPACK is set to TRUE, the min(nrow(A), ncol(A)) is returned
>>> which is only occasionally a true rank.
>>> Would not it be more consistent to replace the rank in the latter case by something
>>> based on the following pseudo code ?
>>> d=abs(diag(qr))
>>> rank=sum(d >= d[1]*tol)
>>> Here, we rely on the fact column pivoting is activated in the called lapack routine (dgeqp3)
>>> and diagonal term in qr matrix are put in decreasing order (according to their absolute values).
>>> Serguei.
>>> How to reproduce:
>>> a=diag(2)
>>> a[2,2]=0
>>> qaf=qr(a, LAPACK=FALSE)
>>> qaf$rank # shows 1. OK it's the true rank value
>>> qat=qr(a, LAPACK=TRUE)
>>> qat$rank #shows 2. Bad, it's not the expected value.
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> -- 
> Serguei Sokol
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> email: sokol at insa-toulouse.fr <mailto:sokol at insa-toulouse.fr>
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