Re: [ublas] Efficiently standardizing covariance matrix

From: Michael Stevens (mail_at_[hidden])
Date: 2006-08-29 00:08:46

On Friday, 18. August 2006 20:03, Jerry Swan wrote:
> Given a matrix D with dimensions nvars by ncases and a vector m containing
> the mean values of each row of D, I wish to calculate the standardized
> covariance of D, i.e. to form a covariance matrix with zero mean.
>
> If I were merely concerned with the unstandardized covariance matrix, I
> understand that I could efficiently calculate it as follows:
>
> matrix<real> covar = prod(D,trans(D))/ncases;
>
> The code for explicitly calculating the standardized variant appears below.
> Is there some variant of the above that would allow this to be more
> efficiently calculated using ublas?

Hi Jerry,

You should use the function outer_product to calculate covariances

Converting from my own code (see Bayes++ in my signature). 
My S is your data matrix.

   typedef matrix,real> Matrix;
    typedef matrix_column<Matrix> Column;
    X.clear();              // Covariance

    const Matrix::size_type nSamples = S.size2();
    for (Matrix::size_type i = 0; i != nSamples; ++i) {
        Column Si(S,i);
        X.plus_assign (outer_prod(Si-x, Si-x));
    }

   X.plus_assign (trans(X));
   X /= real(nSamples*2);

Hopefully this compiles, I just hand converted it!

Regards,
        Michael

-- 
___________________________________
Michael Stevens Systems Engineering
34128 Kassel, Germany
Phone/Fax: [phone]
Navigation Systems, Estimation  and
                 Bayesian Filtering
    http://bayesclasses.sf.net
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