hypot is smart with avoiding overflows. But for limited values sqrt(a^2+b^2) is much faster:
for k = 1:length(x)
H(:,:,k) = sqrt((X-x(k)).^2 + (Y-y(k)).^2);
end
I get a speedup of factor 3, much more than the bsxfun tricks.
The power operator is expensive, so it is worth to try to reduce the squaring by using the identity: (a-b)^2 == a^2 - 2*a*b + b^2:
X2 = X .^ 2;
Y2 = Y .^ 2;
for k = 1:length(x)
H(:,:,k) = sqrt(X2 - X*(2*x(k)) + x(k)^2 + Y2 - Y*(2*y(k)) + y(k)^2);
end
2*X*x(k) is less efficient than X*(2*x(k)), because in the first case you have two multiplications of a scalar with a matrix, but in the second one one matrix operation only.
But this is slower than the first method. It seems like Matlab smartly performs a multiplikation for .^2 and not a power operation.
