MATLAB: Fast computation of an equation.

parallel computing

Given two matrices:
We want a the fastest way to compute the vector \phi…. (j=1 to m).
Is there a way to use parallel computation, any trick?

Best Answer

The efficientcy of the bellow method depend on m, n, s
% Generate dummy test data
m = 1000;
n = 1000;
s = 1000;
W = rand(m,n);
V = rand(m,n);
X = rand(n,s);
% Walter method
tic
Xp = permute(X,[3 1 2]);
Z1 = sum((Xp-W).*(V-Xp),2);
Z1 = reshape(Z1,[m s]).';
toc % Elapsed time is 2.816333 seconds.
% My new method
tic
Z2 = -sum(X.^2,1)+(W+V)*X-sum(W.*V,2);
Z2 = Z2.';
toc % Elapsed time is 0.040274 seconds.
% Check correctness
norm(Z1-Z2,'fro')/norm(Z1,'fro') % 4.6622e-15
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