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

[Uwe Ligges]

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




> 
> Regards,
> Iñaki
>