# Ublas :

Subject: Re: [ublas] LU decomposition: how can I get a unique solution?
From: Alfredo Correa (correaa_at_[hidden])
Date: 2009-10-15 22:33:20

Pietro,

this is because LU decomposition is not unique. ublas (or blas) makes
it unique by imposing that the diagonal or L are ones. You can do the
same in your manual calculation to make sure.

On Thu, Oct 15, 2009 at 4:38 AM, <Pietro.Mele_at_[hidden]> wrote:
> I have a problem finding the LU decomposition of a matrix. I want to impose
> the L diagonal elements to be equal to 1. I included the code, and this is
> the (wrong?) result:
>
> Initial matrix:
> 4 3
> 6 3
>
> *** Expected result (found with pen and paper): ***
>
> L matrix:
> 1    0
> 1.5  1
>
> U matrix:
> 4   3
> 0  -1.5
>
> Inverse matrix:
>  -0.5  0.5
>   1   -2/3
>
> *** Matrices returned by ublas/lu.hpp: ***
>
> lu_factorize A:
> 4   3/4
> 6   -3/2
>
> L matrix:
> 1  0
> 6  1
>
> U matrix:
> 4   3/4
> 0  -3/2
>
> Inverse matrix:
>  -0.5  0.5
>   1   -2/3
>
> So the inverse matrices are the same, but the L and U matrices used to find
> them are different (I got them from the lu factorized initial matrix). Who's
> right? Ublas or my pen?
>
> With "ublas/lu.hpp" how can I specify the values of the diagonal elements
> needed to obtain a unique solution (i.e. unique L and U matrices)?
>
> Thank you for any help.
>
> Pietro
>
>
> Boost 1.40.0
> O.S.:  Linux (RedHat)
> gcc:  3.4.6
> kernel:  2.6.9-55.ELsmp
>
> Tags: ublas, lu.hpp, lu decomposition, boost, matrix
>
>
>
>
> Pietro Mele
> CFD Software Developer
> T. +44 1235 777700
> F. +44 1235 764705
> attwilliams.com
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