Re: Matrix decompositions.

Thanks, Nasos that will be great. I am looking forward to it.



Best Regards,
Salman Javaid


On Tue, May 28, 2013 at 8:41 AM, Nasos Iliopoulos <[email protected]>wrote:

>  Yes,
> additionally with the boost transition to github we are planning to make
> contributing to uBlas much easier. We would like though to stress quality
> and find a way to define performance requirements specifications. When the
> github repo (a fork of boostorg/ublas) is ready (I hope I can have it ready
> this weekend) we will include instructions on how to work with pull
> requests (to submit an algorithm or a small bugfix for example), or in
> cases where larger involvement is required maybe give access to the ublas
> development repo to ppl that want to contribute.
>
> -Nasos
>
>
>
> On 05/28/2013 10:59 AM, Salman Javaid wrote:
>
> Are there any plans to integrate Karl's QR Decomposition implementation
> into Boost.uBLAS? I will be grateful for a response.
>
>
>
> Best Regards,
>  Salman Javaid
>
>
> On Thu, May 16, 2013 at 7:06 AM, Karl Rupp <[email protected]> wrote:
>
>> Hi guys,
>>
>> I have a working implementation of QR for uBLAS in ViennaCL for about a
>> year already:
>>
>>
>> https://github.com/viennacl/viennacl-dev/blob/master/viennacl/linalg/qr.hpp
>>
>> Feel free to copy&paste and relicense as needed, I agree to whatever is
>> necessary to integrate into uBLAS if of interest.
>>
>> There is a bit of duplication for the ViennaCL types (requiring
>> host<->GPU transfers) and the uBLAS types (operating in main RAM), yet it
>> gives an idea how things can be implemented. It can certainly be improved
>> here and there (more details on request), yet it addresses most of the
>> points raised by Oswin. And it's faster than a standard LAPACK for sizes
>> above ~1k times 1k.
>>
>> I recommend extracting the Householder reflections into a nice separate
>> interface, since this functionality will also be needed for other
>> algorithms like SVD or GMRES. As a nice side effect, it makes the
>> implementation for QR more compact.
>>
>> Generally, in order to get *any* reasonable performance, one really needs
>> to use matrix-matrix multiplications where possible in order to avoid the
>> memory bandwidth bottleneck.
>>
>> Best regards,
>> Karli
>>
>>
>>
>> On 05/16/2013 01:06 AM, oswin krause wrote:
>>
>>>  Hi,
>>>
>>> These are further good points!
>>>
>>> I also came up with a few new ones(and tips!):
>>>
>>> - QR needs pivoting. It's main usages are SVD and pseudo-inverses. In
>>> both cases the input does not necessary have full rank. Also pivoting
>>> helps for matrices with high condition numbers.
>>>
>>> - For the same reasons H was not formed explicitly, Q should not be
>>> formed. Instead there should be a version of the algorithm which does
>>> only return the reflection vectors forming Q.
>>>
>>> - For dense matrices at least, it is possible to do the QR in-place by
>>> storing the R part as lower triangular and the householder
>>> transformation vectors in the upper triangular. (That is very similar to
>>> how LU is implemented).
>>>
>>> - The best sources for algorithmic information are the LAPACK working
>>> notes.
>>> http://www.netlib.org/lapack/lawns/
>>>
>>> In your case lawn114 sems to be the most relevant, even though it
>>> assumes a fast BLAS3.
>>>
>>> Greetings,
>>> Oswin
>>>
>>>
>>> On 16.05.2013 05:32, Nasos Iliopoulos wrote:
>>>
>>>>  That's not a bad start.
>>>>
>>>> I think Oswin covered a whole lot of items here, but a more complete
>>>> algorithm needs to satisfy some or all of  the following:
>>>>
>>>> - The algortihm should have a dispatch mechanism so that optimized
>>>> versions for various matrix types can be provided. (sparse, banded,
>>>> etc.). You don't necessarily need to provide them all to start with.
>>>> - The algorithm should operate on matrix expressions rather than
>>>> matrices (so it can be applied to for example subranges). Static
>>>> dispatch or overload if for some reason this seems to reduce
>>>> performance.
>>>> - Const correctness is important. Try  using const reference on
>>>> immutable types.
>>>> - Instead of 0.00025 provide a value based on a user choice.If it is
>>>> hard coded by the user, the compiler will  probably convert it into a
>>>> const value.
>>>> - Don't use ints for indexing, use either std::size_t, or
>>>> container::size_type. If you need a signed type (i.e. to count for
>>>> differences on unsigned types) use ptrdiff_t. uBlas containers provide
>>>> a difference_type typedef for that purpose (i.e.
>>>> matrix<double>::difference_type).
>>>> - use noalias(..) =  in every assignment that the lhs is not a part of
>>>> rhs, or when the algebraic operation is mapped 1-1. (i.e. A=2*A+B can
>>>> be written as noalias(A)=2*A+B, but A=prod(B,A)+D cannot atm). This
>>>> provides more benefits than just avoiding temporaries.
>>>>
>>>>
>>>> The QR decomposition of a 100x100 matrix should take no more than a
>>>> few miliseconds (or even less than a milisecond) to run.
>>>> A 1000x1000 should take around 1/3 to 1/10 of a sec.
>>>>
>>>> Compile with:
>>>> g++ -O3 -DNDEBUG Main.cpp -o qrtest
>>>>
>>>> Then you'll see that your code runs pretty fast, but it doesn't scale
>>>> well as Oswin noted.
>>>>
>>>> Best regards,
>>>> -Nasos
>>>>
>>>>
>>>>
>>>>
>>>> On 05/15/2013 10:12 PM, Salman Javaid wrote:
>>>>
>>>>>  Thank you, Oswin for the detailed response. I am going to update the
>>>>> code.
>>>>>
>>>>> David, Nasos, any advise on coding conventions? Or anything else that
>>>>> you can possible suggest? I will stand grateful.
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> Best Regards,
>>>>> Salman Javaid
>>>>>
>>>>>
>>>>> On Tue, May 14, 2013 at 10:53 PM, oswin krause
>>>>> <[email protected]
>>>>>   <mailto:[email protected]>> wrote:
>>>>>
>>>>>     Hi,
>>>>>
>>>>>     in the order I stumbled over the things:
>>>>>
>>>>>     main.cpp
>>>>>     line 44-54: you don't need a copy, instead you should use a
>>>>>     combination of row/subrange.
>>>>>     line 58-60: you should take a look at inner_prod
>>>>>     line 63: 0.00025 is too big.
>>>>>     line 66: You should never create H explicitly.
>>>>>     line 67: because you formed H, this step is O(n^3) which makes
>>>>>     the whole algorithm O(n^4). This can be done in O(n^2)
>>>>>     line 73-79: same applies here.
>>>>>
>>>>>     Greetings,
>>>>>     Oswin
>>>>>
>>>>>     On 14.05.2013 22:12, Salman Javaid wrote:
>>>>>
>>>>>>      Hello uBLAS Contributors:
>>>>>>
>>>>>>                                          I have applied to GSoC 2013
>>>>>>     and pitched implementation of SVD factorization for uBLAS. In
>>>>>>     order to better prepare myself and to get my hands dirty at
>>>>>>     uBLAS, I ended up implementing QR Factorization employing
>>>>>>     Householder Reflections using uBLAS. This is only the first
>>>>>>     draft and will be needing significant improvement, e.g.,
>>>>>>     computation of QR decomposition of 100 * 100 matrix takes around
>>>>>>     30 seconds. But I guess just to get familiar with code base, it
>>>>>>     was a good exercise. Over the next week or two I will be trying
>>>>>>     to optimize the code.
>>>>>>
>>>>>>
>>>>>>                                          I will be absolutely
>>>>>>     grateful if contributors can have a quick glance at the code,
>>>>>>     and point me to any improvements they can suggest. Particularly
>>>>>>     in speeding up matrix multiplication.
>>>>>>
>>>>>>     I used Visual Studio 2010 to compile the code. I will try to get
>>>>>>     the code running on my Ubuntu machine in a couple of days
>>>>>> hopefully.
>>>>>>
>>>>>>     Here the header file:
>>>>>>
>>>>>> https://github.com/salmanjavaid/QR_Decomposition/blob/master/QR_Header.hpp
>>>>>>
>>>>>>
>>>>>>     The main file:
>>>>>>
>>>>>> https://github.com/salmanjavaid/QR_Decomposition/blob/master/Main.cpp
>>>>>>
>>>>>>
>>>>>>     Best Regards,
>>>>>>     Salman Javaid
>>>>>>
>>>>>>
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