Re: uBLAS Matrix Multiplication

From: jhrwalter (jhr.walter_at_[hidden])
Date: 2002-11-10 14:43:24

--- In Boost-Users_at_y..., John Lloyd <yg-boost-users_at_m...> wrote:
> Hickman, Greg wrote:
> 
> > Why isn't there an overloaded
> > 
> > matrix_expression
> > operator* (const matrix_expression&, const matrix_expression&);
> > 
> > for peforming matrix multiplication?
> > 
> > Greg Hickman
> > 
> > Info: <http://www.boost.org>
> > Wiki: <http://www.crystalclearsoftware.com/cgi-
bin/boost_wiki/wiki.pl>
> > Unsubscribe: <mailto:boost-users-unsubscribe_at_y...>
> >  
> > 
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> 
> I think it has something to do with the fact that expression 
templates can 
> be very inefficient for certain chained operations, e.g., A * B * 
v, where 
> A and B are matrices and v is a vector.
> 
> Suppose you have a  matrix expression like A = B * C * D.  Using 
expression 
> templates, this could result in an order n^5 time complexity as 
opposed to 
> order n^3 complexity.

Exactly. I believe the theoretically more important signature is
prod<matrix_type> (A, B), although prod (A, B) will be more 
frequently used practically (BTW: the complexity of prod (A, B) (i, 
j) is O(n) as opposed to O(n^3) for prod<matrix_type> (A, B) (i, j)).

Best regards

Joerg