Re: [ublas] Fast small matrices / homogeneous matrices with uBlas

Subject: Re: [ublas] Fast small matrices / homogeneous matrices with uBlas
From: Riccardo Rossi (rrossi_at_[hidden])
Date: 2010-08-09 09:42:01

Dear List,

        i work in Finite Elements and in there it is very typical that
the matrix is structured in blocks of constant size (typically 3*3 or
4*4)

the point is that the graph of a block matrix is much reduced with
respect to the original CSR matrix so for example ILU type
preconditioners could be constructed in a very efficient way.
This is also the case for AMG precondtioners.

furthermore the multiplication operator should be much more efficient
than the scalar versions since the data locality can be fully exploited.

To make an example the Trilinos Tpetra package allows for this sort of
construction.

In any case i understand that adding such capability is no
priority...nevertheless i think it would be important to think about
before better than eventually retrofitting the design later on.

greetings
riccardo

-- 
________________________________________________________________
Riccardo Rossi, Ph.D, Civil Engineer
member of the Kratos Group: kratos.cimne.upc.es
Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE)
Universidad Politécnica de Cataluña (UPC)
Edificio C-1, campus Norte UPC
Gran Capitan, s/n
08034 Barcelona, España
Tel. [phone]
________________________________________________________________
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On Mon, 2010-08-09 at 08:21 -0400, Nasos Iliopoulos wrote:
> Riccardo,
> Excluding product (*) and division (/) operators I suppose it would
> work, as it already does. If matrix product is implemented with
> operator * overloading, this would be working also.
> 
> 
> 
> 
> I don't know though how this can be interpreted, and atm I doubt it
> can be cast to a full matrix (it can be converted though). I think the
> fixed matrix container should allow a cast to a block matrix.What do
> you have in mind, some kind of algebra, or block matrix construction
> of some sort? 
> 
> 
> 
> #include <boost/numeric/ublas/matrix.hpp>
> 
> #include <boost/numeric/ublas/io.hpp>
> 
> using namespace boost::numeric::ublas;
> 
> int main(int argc, char *argv[])
> 
> {
> 
> matrix<matrix<double> > AA(3,3), BB(3,3); // or matrix<matrix<double>
> > AA(3,3,0), BB(3,3,0);
> 
> 
> matrix<double> CC(3,3);
> 
> for (unsigned int i=0; i!=3; i++)
> 
> for (unsigned int j=0; j!=3; j++)
> 
> CC(i,j) = i + j + 1 + i*j;
> 
> std::cout << CC << std::endl;
> 
> 
> AA(0,0)=CC;
> 
> AA(1,1)=CC;
> 
> AA(2,2)=CC;
> 
> std::cout << AA << std::endl;
> 
> for (unsigned int i=0; i!=3; i++)
> 
> for (unsigned int j=0; j!=3; j++)
> 
> CC(i,j) = 2*i + 0.1*j + 0.75 + i*j*i*0.22;
> 
> 
> BB(0,0)=CC;
> 
> BB(1,1)=CC;
> 
> BB(2,2)=CC;
> 
> std::cout << BB << std::endl;
> 
> std::cout << AA+BB << std::endl;
> 
> return 0;
> 
> }
> 
> 
> 
> Best
> Nasos
> 
> > From: rrossi_at_[hidden]
> > To: ublas_at_[hidden]
> > Date: Mon, 9 Aug 2010 13:24:04 +0200
> > Subject: Re: [ublas] Fast small matrices / homogeneous matrices with
> uBlas
> > 
> > Dear Nasos,
> > 
> > just to add my cent to the discussion ... do you believe there is
> > any hope that the tiny matrix and vectors can be used as "scalar
> types"
> > in the construction of matrices and vectors?
> > 
> > for example
> > matrix < TinyMatrix<3,3> > 
> > 
> > i know there was long ago a discussion on this issue, but i guess
> the
> > new design would give the right opportunity to think about this
> > possibility...
> > 
> > anyway
> > thank you for the attention
> > Riccardo
> > 
> > -- 
> > ________________________________________________________________
> > Riccardo Rossi, Ph.D, Civil Engineer
> > member of the Kratos Group: kratos.cimne.upc.es
> > Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE)
> > Universidad Politécnica de Cataluña (UPC)
> > Edificio C-1, campus Norte UPC
> > Gran Capitan, s/n
> > 08034 Barcelona, España
> > Tel. [phone]
> > ________________________________________________________________
> > 
> > AVISO IMPORTANTE
> > 
> > Los datos de carácter personal contenidos en el mensaje, se
> registrarán
> > en un fichero para facilitar la gestión de las comunicaciones de
> CIMNE.
> > Se pueden ejercitar los derechos de acceso, rectificación,
> cancelación y
> > oposición por escrito, dirigiéndose a nuestras oficinas de CIMNE,
> Gran
> > Capitán s/n, Edificio C1 - Campus Norte UPC, 08034 Barcelona,
> España.
> > 
> > AVÍS IMPORTANT
> > 
> > Les dades de carà cter personal contingudes en aquest missatge es
> > registraran en un fitxer per facilitar la gestió de les
> comunicacions
> > del CIMNE. Es poden exercir els drets d'accés, rectificació,
> > cancel·lació i oposició, per escrit a les nostres oficines del
> CIMNE,
> > Gran Capità s/n, Edifici C1, Campus Nord UPC, 08034 Barcelona,
> Espanya.
> > 
> > IMPORTANT NOTICE
> > 
> > All personal data contained in this mail will be processed
> > confidentially and stored in a file property of CIMNE in order to
> manage
> > corporate communications. You may exercise the right of access,
> > rectification, deletion and objection by letter sent to CIMNE, Gran
> > Capitán, Edificio C1 - Campus Norte UPC, 08034 Barcelona, Spain.
> > 
> > 
> > 
> > 
> > 
> > On Mon, 2010-08-09 at 07:20 -0400, Nasos Iliopoulos wrote:
> > > Thomas,
> > > There is an active discussion and a proposal that will bring fixed
> > > vector and fixed matrices (appropriate for small containers) into
> > > uBlas. My feeling is that it is getting to a good shape and will
> > > probably make it into the next release. Follow this post for some
> > > code:
> > > 
> > > http://lists.boost.org/MailArchives/ublas/2010/07/4500.php
> > > 
> > > > And secondly, it cannot use the matrices structure such as the
> fact
> > > > that the last line of an homogenous
> > > > matrix never changes.
> > > 
> > > Although this is the case with some applications (and even some
> > > graphics API providers, like AMD), there are applications that
> fixing
> > > the last row is not desirable (i.e. when you do projections and
> expect
> > > to use the w component of your 4 vector prior to perspective
> > > division). I suppose uBlas will support fixed containers in the
> > > future, but I find unlikely that it will make any assumptions like
> > > homogeneity (in which case you just need to divide by the last
> > > element, if you mean to retrieve 3D points).
> > > 
> > > Best
> > > Nasos
> > > 
> > > 
> > > > Date: Mon, 9 Aug 2010 11:32:27 +0900
> > > > From: thomas.moulard_at_[hidden]
> > > > To: ublas_at_[hidden]
> > > > CC: fbleibel_at_[hidden]; florent_at_[hidden]
> > > > Subject: [ublas] Fast small matrices / homogeneous matrices with
> > > uBlas
> > > > 
> > > > Hello everyone,
> > > > I am currently evaluating the possibility for uBlas to have a
> better
> > > > support for small matrices.
> > > > In particular, 3d transformation matrices represented by
> homogenous
> > > matrices.
> > > > 
> > > > First, I have seen that uBlas is slower than libraries
> specifically
> > > > targeted for small matrices like tvmet.
> > > > And secondly, it cannot use the matrices structure such as the
> fact
> > > > that the last line of an homogenous
> > > > matrix never changes.
> > > > 
> > > > I was wondering if anyone here would have tried to tackle these
> > > problems?
> > > > 
> > > > Any advice would be greatly appreciated,
> > > > --
> > > > Thomas Moulard
> > > > _______________________________________________
> > > > ublas mailing list
> > > > ublas_at_[hidden]
> > > > http://lists.boost.org/mailman/listinfo.cgi/ublas
> > > > Sent to: nasos_i_at_[hidden]
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> > 
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