Re: uBLAS Observation: terrible execution speed for prod(matrix,prod(matrix,prod(matrix,matrix)))

From: Matthias Kronenberger (mkronen_at_[hidden])
Date: 2002-07-30 05:57:01

The problem is that expression templates avoid temporary objects by
evaluating expressions as they are needed.
By nesting too many matrix products, the inner products have to be computed
many times.

----- Original Message -----
From: "Terje Slettebų" <terje.s_at_[hidden]>
Newsgroups: gmane.comp.lib.boost.user
Sent: Monday, July 29, 2002 8:44 PM
Subject: Re: uBLAS Observation: terrible execution speed for
prod(matrix,prod(matrix,prod(matrix,matrix)))

> >From: Walter Bowen
>
> >Observation 1)  For matrix products of two small (~3-by-3) matrices (
> >i.e., prod(smallMat1, smallMat2) ) uBLAS executes MUCH FASTER than
> >Math.h++.
>
> >Observation 2) For matrix produces of two large matrices (100 by 100)
> >uBLAS and Math.h++ give similar execuation speed.
>
> >Obervation 3) (This is the kicker...) for strung-together matrix
> >products like "Mat1 * Mat2 * Mat3 * Mat4 * Mat5", which I am
> >implementing as
> >"prod(Mat1, prod(Mat2, prod( Mat3, prod(Mat4,Mat5) )  ) ) Math.h++ is
> >MUCH MUCH FASTER than uBLAS.   -- by ~2 orders OF MAGNITUDE!  I believe
> >that this is a characteristic of the scalability of template
> >expressions.
>
> >My question is this:  Is there a way I an instruct uBLAS not to use
> >template expressions when for  strung-together matrix products?
>
> I'm not familiar with uBLAS, but I thought this was one of the _strengths_
> of expression templates (if that's what you mean), that it may be used to
> e.g. unroll loops (especially useful for smaller matrices), and also fuse
> loops together, avoiding temporary matrices, such as your expression above
> here, involving several matrices being multiplied together (especially
> useful for larger matrices, where several matrices are multiplied
together).
>
> At least, that's the approach taken in libraries such as Blitz++, where
they
> have achieved performance comparable to Fortran, both for small and large
> matrices. It performs especially good on expressions with several large
> matrices, as loop-unrolling is not enough for that. You also need to
> eliminate temporary matrices, and fuse the loops to one set of loops.
>
>
> Regards,
>
> Terje
>
>
>