Re: [Help-gsl] Complex QR decomposition

[Patrick Alken]

Dear Christian,

  Thank you for following up, and I apologize for taking so long to get
back to you. I have looked at your patch and added the complex QR
routines, with some modifications. The main one is I have deprecated the
complex_householder_hm function because it is based on Level-1 BLAS
operations which are quite slow. I have made a new function
complex_householder_left() which uses Level-2 BLAS, at the cost of
requiring extra workspace. The end result is that the tau parameter to
QR_decomp must be length N, instead of MIN(M,N) now.

I have made a similar change to the real QR_decomp function, in a way
which is backward compatible with the current interface.

I updated the docs and put everything on the git now.

Ultimately, I would like to implement the Level-3 BLAS QR algorithm from
Elmroth and Gustavson (which is already implemented for the real case),
since the current Level-2 code is quite slow for larger matrices which
are routinely encountered in research. I hope to get around to this
soon, or if you are interested, please go ahead and try to implement it.

Thanks again for the delay,
Patrick

On 6/3/20 4:52 AM, Christian Krueger wrote:
> Hi Patrick,
>
> I don't want to insist on getting my patches introduced. But as I have,
> meanwhile, learned a bit more about git and such, I thought I would make
> my patch more easily accessible. I've merged my changes onto the current
> git commit (as of today -- bb7f532c) and attach two clean patches (one
> for the Householder fix and one for the complex QR) that could be applied.
>
> Cheers,
> Christian
>
>
> On 11/27/17 10:34 PM, Patrick Alken wrote:
>> Hi Christian,
>>
>>   This should be very useful. I will take a look at your code as soon
>> as I can, though it may be a while as I am very busy with other things
>> at the moment. I will add this to the bug tracker so it isn't lost.
>>
>> Thanks,
>> Patrick
>>
>> On 11/27/2017 08:34 AM, Christian Krueger wrote:
>>> Hi,
>>>
>>> I was looking for the QR decomposition for complex-valued matrices. As
>>> GSL does not provide this yet, I have copied the code for the
>>> real-valued QR and modified it to handle complex-valued matrices.
>>>
>>> As I've seen in the archive that this feature has been requested a few
>>> times already, I am happy to share it with everyone who wants to use it.
>>> My github repository can be found at:
>>> https://github.com/mangroveck/gsl-qr-complex-devel.git
>>>
>>> The file linalg/qrc.c is essentially a copy of the file linalg/qr.c and
>>> provides a bunch of gsl_linalg_complex_QR_* functions. I've had to add
>>> "_complex" to the function calls and sometimes take the conjugate of tau
>>> when calling the householder-functions but the whole process was fairly
>>> straight-forward and the decomposition works.
>>>
>>> * My repository also includes my patch for the
>>> gsl_linalg_complex_householder_hv() function to handle the N=1 case.
>>> (I've just reported the bug on the bug-list).
>>> * I've added various tests to the file linalg/test.c to test the new
>>> gsl_linalg_complex_QR_* functions (in the same style as the tests for
>>> the real-valued QR decomp).
>>> * I've also adjusted the header file linalg/gsl_linalg.h and the file
>>> Makefile.am
>>>
>>> The only exception is the function gsl_linalg_complex_QR_update() which
>>> I haven't adjusted yet as it requires Givens rotations and they don't
>>> take complex values yet (within GSL). All other functionality from qr.c
>>> is now available for complex values, too.
>>>
>>> If it helps, I'm happy for this code to be included in GSL.
>>>
>>> Christian
>>>
>>>
>>
>>
>>
>>