[Rd] Unexpected behaviour of base::qr()$rank

[Bernd Funovits]

Thanks for the fast replies. There was a bug in 
Matrix::rankMatrix(matrix(0)) which returned 1 (fixed by Martin Maechler 
in the development version of Matrix) and I thought here is an issue 
here too. Sorry for asking too quickly...

Best,
Bernd

Am 22.06.2017 um 21:41 schrieb Iñaki Úcar:
> 2017-06-22 20:31 GMT+02:00 Uwe Ligges <ligges at statistik.tu-dortmund.de>:
>>
>> On 22.06.2017 20:09, Iñaki Úcar wrote:
>>> 2017-06-22 19:49 GMT+02:00 Uwe Ligges <ligges at statistik.tu-dortmund.de>:
>>>> On 22.06.2017 17:11, Bernd Funovits wrote:
>>>>>
>>>>> Hello,
>>>>>
>>>>> I experienced some unexpected behaviour while determining the rank of
>>>>> matrices (sometimes 1x1 matrices):
>>>>> base::qr(matrix(1e-20))$rank returns 1 (incorrect)
>>>>> base::qr(diag(c(1, 1e-20)))$rank returns 2 (incorrect)
>>>>
>>>>
>>>> Why do you believe this is incorrect?
>>>>
>>>> 0 != 1e-20
>>>>
>>>> and 1e-20 is well representable without significant rounding errors given
>>>>
>>>>> .Machine$double.xmin
>>>> [1] 2.225074e-308
>>>>
>>>>
>>>> Best,
>>>> Uwe Ligges
>>>
>>> qr() has a tolerance argument which by default is tol=1e-07.
>>
>> But the tolerance is not about the size of the values! It is about the
>> reduction of the norm during the householder transformation. From the
>> sources <https://svn.r-project.org/R/trunk/src/appl/dqrdc2.f>
>>
>>
>> c     cycle the columns from l to p left-to-right until one
>> c     with non-negligible norm is located.  a column is considered
>> c     to have become negligible if its norm has fallen below
>> c     tol times its original norm....
>>
>> Best,
>> Uwe Ligges
> Oh, I apologise, I read the arguments section in the help page, but
> not the asterisk down below. Then the result is ok. Sorry for the
> noise.
>
> Regards,
> Iñaki