[Boost-users] Re: ublas and matrix expression

From: Angus Leeming (angus.leeming_at_[hidden])
Date: 2004-04-08 07:27:44

Russell Hind wrote:

> I have an expression
> 
> a = (X^T * X)^-1 * X^T * y
> 
> where x is an n * k matrix
> and   y is an n row vector
> 
> How do I implement this expression in ublas?  I can create and
> populate the matrices and can do the product of matrices and the
> transpose use
> prod and trans, but I'm unsure on the ^-1.  Can I do this with
> ublas?
> 
> (I don't know much about matrices, but have been given the above
> expression as a way of finding a polynomial fit for a set of data).

Hi, Russell.

You are trying to solve a matrix expression.

        A = B^-1 * C*D
is equivalent to
        B*A = B*B^-1 * C*D
which collapses to
        B*A = C*D

So, you can reprase your problem as solve the system
        B*A = E
where B,E are known, E=C*D, to give the unknown A.

Have a look at the (undocumented :-() lu_factorize and lu_substitute 
routines. They should enable you to complete the task.

HTH,

-- 
Angus