Angle between consecutive gradients computation

[Niccolo-Ajroldi]

I am trying to reproduce the results of this work, and I encountered a methodological issue regarding angles computation.

The tangent of the angle between consecutive gradients is here computed as abs((previous_grad - grad) / (1 + previous_grad * grad)):

AngularGrad/myoptims/tanangulargrad.py

Line 80 in cd8cbec

tan_theta = abs((previous_grad - grad) / (1 + previous_grad * grad))

However, the result of this operation is not a scalar, but a vector with the same shape as grad. What is the interpretation of such quantity? The paper states that this is the tangent of the angle between consecutive gradients, but it does not seem to be the case.

Thank you in advance!