[ublas] Efficiently standardizing covariance matrix

From: Jerry Swan (pmxjs_at_[hidden])
Date: 2006-08-18 14:03:00

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?

    for( icase=0; icase<ncases; ++icase )
    { 
        // Cumulate covariances
        for( var=0 ; var<nvars; ++var ) 
        {
            diff1 = data( icase, var ) - means[var];
            
            for( var2=var; var2<nvars; ++var2 )
            {
                diff2 = data( icase, var2 ) - means[var2];
                covar( var2, var ) += diff1 * diff2;
            }
        }
    }

    for( var=0; var<nvars; ++var )
    {         
        // Divide sums by n
        for( var2=var; var2<nvars; ++var2 )
        { 
            covar( var2, var ) /= ncases;

            // symmetrically duplicate            
            if( var != var2 )
                covar( var, var2 ) = covar( var2, var );
        }
    }

Regards,

Jerry.


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