exp(1i*(an​gle(x)-ang​le(y)))==(​x.*abs(y))​./(abs(x).​*y)，which one is better?

The two expressions seem to be mathematically equal:

exp(1i*(angle(x)-angle(y)))==(x.*abs(y))./(abs(x).*y);

Which one do you think will have a better performance?

[Bruno Luong]

The second one, but you can still do better (I think):

z = x./y;
z = z./abs(z);

or the best one in term of speed

z = x.*conj(y);
z = z./abs(z);

[Tmfu Vh]

@Bruno Luong Really? Unreasonable! How can the combination of .* and conj faster than a single ./ ? Does that mean MATLAB Interpreter does a terrible optimization dealing with ./ ?

[Tmfu Vh]

@Bruno Luong By the way why don't you give your comment as an answer so I can accept it?

[Bruno Luong]

On the processor (old or modern), multiplication operation is serval time faster than division, and conj requires one bit inversion with is pretty fast. This has nothing to do with MATLAB but unitary cost of arithmetic operations.

The angle() is the worse since it requires calling trigonometric function.

[Tmfu Vh]

@Bruno Luong So why doesn't the interpreter just calculate ./ by this way?

[Bruno Luong]

Because x./y is NOT equal to x.*conj(y)

[Tmfu Vh]

@Bruno Luong Magical lesson. Thanks a lot.