Double check atan2 usage

[bmorris3]

Let's double check that we're using atan2 efficiently everywhere.

[LaurentRDC]

Is arctan significantly faster than arctan2?

[bmorris3]

I don't know, @jkentwallace had opinions though.

[jkentwallace]

LaurentRDC and bmorris3, I was concerned not so much about efficiency. Reading through Emilio's original writeup, (in which he used Matlab) he had a comment about using atan(z) vs atan2(y,x). Problem is that atan only goes from -p/2 to +pi/2, whereas atan2 goes from -pi to pi. (That's because in the ratio of x/y = z, not knowing the sign of x and/or y precludes getting the angle in the correct quadrant.)

Quick question: does python support a function called Arg[a + i b]? Arg[] will return the phase angle of a complex number.

[bmorris3]

@jkentwallace I believe what you're looking for is implemented in numpy.angle, which returns

the counterclockwise angle from the positive real axis on the complex plane

[jkentwallace]

Yes! That's it. Basically, this is the same as atan2. However, for those who might be lazy - ahem - you don't need to do atan2[imaginary,real], but just np.angle([]) instead.

Just a thought...