R devel - Jan 2018 - Inconsistent rank in qr()

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.

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.


> 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.
> 
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

Le 22/01/2018 ? 17:40, Keith O'Hara a ?crit?:
> 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.
>>
>> ______________________________________________
>> R-devel at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>
-- 
Serguei Sokol
Ingenieur de recherche INRA

Cellule math?matique
LISBP, INSA/INRA UMR 792, INSA/CNRS UMR 5504
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tel: +33 5 6155 9849
email: sokol at insa-toulouse.fr
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