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## Re: Matrix regression of distnce matrices + non negative least square

 From: Corrado Subject: Re: Matrix regression of distnce matrices + non negative least square Date: Mon, 7 Sep 2009 15:21:39 +0100 User-agent: KMail/1.11.4 (Linux/2.6.28-13-generic; KDE/4.2.4; x86_64; ; )

```Dear Jaroslav,

I actually do not understand what you are suggesting:

1) The data would be stored in matrices, which I can easily dump into csv files
2) The distance matrices are up to 5000 x 5000 (but they symmetric, so only
n(n-1)/2 are important), but the ones I am using now are just 1500 x 1500.
3) I thought lsqnonneg only worked on linear system in the form y=ax
4) The terms are matrices, how do you write a canonical form???? the x1 ....
xn are matrices (e.g. 1500 x 1500) .... the ci are coefficients in R ....

Regards

On Monday 07 September 2009 14:39:04 you wrote:
> > Dear friends,
> >
> > I would like to solve the following regression problem:
> >
> > y=c1 x1 + c2 x2 + .... + cn xn
> >
> > where the y, xi are all matrices and the ci are constants that need to be
> > determined. The y, xi are distance matrices (symmetric). Obviously ci
> > should be forced to positive or null (i.e. non negative).
> >
> > Any suggestion?
>
> First convert the linear system into canonical form (matrix of
> coefficients and vector of rhs), then use lsqnonneg.
> Since the matrices are symmetric, extracting just lower/upper
> triangular parts will suffice. The best way how to do the first will
> depend on the dimensionality of your problem and how your data is
> stored.
>
> regards

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