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From: boost (boost_at_[hidden])
Date: 20011121 17:08:06
Hello,
On Wednesday 21 November 2001 11:58, walter_at_[hidden] wrote:
> You've lost me. Could you please explain or give a reference?
Please see below.
> > I'd be happy if I could replace (specialize) a few routines of ublas
> > by ATLAS or vendor supplied BLAS routines in order to perform
>
> benchmarks,
>
> > (mainly _x_gemm).
>
>
> I think, this is one of the next steps as already discussed with Toon
> Knapen. We'll also look at it.
That would be really a good thing for me, since I have to support several
platforms. And on some platforms vendor supplied BLAS might be superior.
Best wishes.
Peter

Outline of my most cpu intensive part

In my application I have to iterativly diagonalize
large sparse matrices which involve the MatrixVector
product of a matrix C with a vector x.
To improve performance one can use a representation
of C where the vector space of C is a tensor product of two
vector spaces V and W.
C is now a sum of operators A_i \otimes B_i, where A_i (B_i) acts on
V (W) only. The total dimension of C is equal the product of the
dimensions of V and W. A basis of the vector space of the product space of
V and W can be represented by a dyadic product of basis states of V and W,
i.e. if v * w^T.
This representation has the advantage that the (sparse) matrix vector
multiplication can be represented by BLAS3 operations instead of BLAS2
operations using dense matrices.
In case you're not lost again, The spaces V and W themselves can
be represented by by direct sums of subspaces V_l (W_k).
The matrices A can now be represente by blocks A_lm, where
A_lm is a mapping from V_l to V_m.
If you're still interested in details you may look at my thesis,
http://www.Physik.UniAugsburg.DE/~peters/thesis/index.html
chapter 5.5 .
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