How can I compute linear correlation coefficient for my input faster than CORR using Statistics Toolbox 7.3 (R2010a)?

I am executing a code which makes hundreds of calls to CORR. I call CORR once on a large matrix to compute Pearson's linear correlation coefficient (default) as follows:

load returns

tic

ret_corr1 = corr(returns,'type','Pearson');

toc

Elapsed time is 0.081229 seconds.

When I execute the function hundreds of times, the overall time taken is extremely large.

Answer 1

[MathWorks Support Team]

This enhancement has been incorporated in Release 2011a (R2011a). For previous product releases, read below for any possible workarounds:

The following two workarounds allow you to compute the Pearson's linear correlation coefficient faster than CORR.

Workaround 1:

tic

ret_cov = cov(returns);

[~,ret_corr2] = cov2corr(ret_cov);

toc

Elapsed time is 0.009861 seconds.

Workaround 2:

tic

n = size(returns,2);

N = size(returns,1);

ret_corr3 = zeros(n,n);

for ix = 2:n

      for iy = 1:ix-1

          xm  = returns(:,ix);

          xmsx = (xm-mean(xm))./std(xm);

          ym = returns(:,iy);

          ymsy = (ym-mean(ym))./std(ym);

          ret_corr3(ix,iy) = (1/(N-1))*sum(xmsx.*ymsy);

      end

end

ret_corr3 = ret_corr3 + ret_corr3' + eye(n);

toc

Elapsed time is 0.016819 seconds.