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

[Corrado]

Dear Jaroslav,

thanks for your help.

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:
> On Mon, Sep 7, 2009 at 2:38 PM, Corrado<address@hidden> 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



-- 
Corrado Topi

Global Climate Change & Biodiversity Indicators
Area 18,Department of Biology
University of York, York, YO10 5YW, UK
Phone: + 44 (0) 1904 328645, E-mail: address@hidden