Re: [Boost-users] Re: ublas and matrix expression

From: Lorenzo Bolla (bolla_at_[hidden])
Date: 2004-04-08 11:28:15

seeing the dimension of your matrix, the easiest way to do that is:
1. compute z = X^T y: z is 5 x 1
2. compute A = X^T X with prod (trans (X), X): A is 5 x 5
3. use LAPACK to solve: A a = z (5 x 5 linear system)

ublas::solve only works for particular types of matrices (for example,
triangular matrices - upper or lower... - like the tag...).

regards,
lorenzo.

On Thu, Apr 08, 2004 at 04:36:17PM +0100, Russell Hind wrote:
> Angus Leeming wrote:
> >
> >X is 500x5
> >trans(X) is 5x500
> >prod(trans(X),X) is 5x5, which is a square matrix. So, yes, it can be 
> >inverted (all other requirements assumed satisfied...). And if it's 
> >5x5 the lu_ functions are perfect. In fact, you could probably invert 
> >it by hand ;-)
> >
> 
> Is there no method in ublas that can invert it?  I haven't done matrices 
> for years, and don't have any docs on doing it.
> 
> The initial problem I'm trying to solve is
> 
> a = (X^T X)^-1 X^T y
> 
> where y is a 500 row vector and X is the 500 x 5 matrix.  But I can't 
> use lu_* with the compiler/boost version I have.
> 
> ublas::solve says it does A^-1 * b but what is the tag parameter passed 
> to it?   It can be lower_tag or upper_tag but I can't find what these 
> mean in the docs, or the difference between them or which I should be using.
> 
> Thanks
> 
> Russell
> 
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