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Loopin Matrix Multiplication Performance Improvement

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Tommaso Belluzzo
Tommaso Belluzzo on 3 May 2020
Hi all! I'm struggling to reduce computation time on a function I created:
function [beta,covariance,residuals] = hac_regression(y,x,ratio)
t = length(y);
[beta,~,residuals] = regress(y,x);
h = diag(residuals) * x;
q_hat = (x.' * x) / t;
o_hat = (h.' * h) / t;
l = round(ratio * t,0);
for i = 1:(l - 1)
o_tmp = (h(1:(t-i),:).' * h((1+i):t,:)) / (t - i);
o_hat = o_hat + (((l - i) / l) * (o_tmp + o_tmp.'));
end
covariance = (q_hat \ o_hat) / q_hat;
end
Below, a result of a profiling run:
I think nothing can be done with respect to built-in "regress" call.
But I'm wondering if the loop can somehow be optimized in order to reduce the overhead. On computations performed on very large datasets, even a small 5% improvement may dramatically reduce the overall computation time.
Below a reproducible example:
y = rand(100,1);
x = rand(100,3)
[beta,covariance,residuals] = hac_regression(y,x,0.1);
Thanks for your help!

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