Re: [Boost-Users] uBLAS Observation: terrible execution speed for prod(matrix,prod(matrix,prod(matrix,matrix)))

From: Terje Slettebų (terje.s_at_[hidden])
Date: 2002-07-29 13:44:45

>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