__lt__ and arange for complex numbers #11505
Description
I tried to find any kind of documentation on how numpy implements inequality comparison between complex numbers, but I found none.
It seems like __lt__ is implemented as (lhs.real, lhs.imag) < (rhs.real, rhs.imag), or in other words
if lhs.real < rhs.real:
return True
if lhs.real > rhs.real:
return False
return lhs.imag < rhs.imag
Tests that brought me to this conclusion:
>>> numpy.array(9+999j) < numpy.array(10+10j)
True
>>> numpy.array(11+1j) < numpy.array(10+10j)
False
>>> numpy.array(10+1j) < numpy.array(10+10j)
True
>>> numpy.array(10+11j) < numpy.array(10+10j)
False
Is this correct? If so it would at the bare minimum require some formal documentation, as another perfectly valid implementation could have been abs(lhs) < abs(rhs).
Also, arange behaves weirdly and I can't put any sense in it. I would have expected it to be coherent with __lt__, that is
i = start
while (i < stop if step > 0 else i > stop):
yield i
i += step
but it isn't:
>>> numpy.arange(0+1j, 4+1j, 1)
array([], dtype=complex128)
>>> numpy.arange(0+1j, 4+4j, 1)
array([0.+1.j, 1.+1.j, 2.+1.j])
>>> numpy.arange(0, 4j, 1j)
array([], dtype=complex128)
>>> numpy.arange(0, 8+4j, 1)
array([0.+0.j, 1.+0.j, 2.+0.j, 3.+0.j])