I'll take a stab at this one; if I miss the mark, people, please chime in. What's "strange" here is not numpy's behavior but octave's (IMO). Remember that, over R, arctan is used in two different ways: one is simply as a map from (-inf, inf) -> (-pi/2,pi/2) - here, let's call that invtan; the other is as a means to determine "the angle" (conventionally taken to be between -pi and pi) of a point in the plane - but since, for example, tan(pi/4) = tan(-3pi/4) (and in general tan(x) = tan(x-pi)) to uniquely determine said angle, we need to keep track of and take into account the quadrant in which the point lies; this is (the only reason) why arctan2 is a function of two arguments, one representing the abscissa, the other the ordinate of the point. But when the argument is complex (arctan2, as the inverse of the tangent function, *is* a valid function on C), this geometric use no longer makes sense, so there's really no reason to implement arctan2(z,w), z, w complex. If for some reason, e.g., uniformity of algorithmic expression - I don't see any (simple) way to preserve uniformity of code expression - as near as I can tell, you're going to have to implement an if/else if you need to allow for the invtan of two complex arguments - you need to handle arctan2(z,w), implement it as arctan(w/z):
>>> import numpy >>> numpy.arctan(1j/1j) (0.78539816339744828+0j) DG lorenzo bolla wrote: > Weird behaviour with arctan2(complex,complex). > Take a look at this: > > In [11]: numpy.arctan2(1.,1.) > Out[11]: 0.785398163397 > > In [12]: numpy.arctan2(1j,1j) > --------------------------------------------------------------------------- > exceptions.AttributeError Traceback (most > recent call last) > > AttributeError: 'complex' object has no attribute 'arctan2' > > same error for: > > In [13]: numpy.arctan2(1j,1.) > In [14]: numpy.arctan2(1.,1j) > > But arctan2 is defined for complex arguments, as far as Octave knows :-) : > > octave:7> atan2(1,1) > ans = 0.78540 > octave:8> atan2(1j,1j) > ans = 0 > octave:9> atan2(1j,1) > ans = 0 > octave:10> atan2(1,1j) > ans = 1.5708 > > bug or wanted behaviour? > Lorenzo. > ------------------------------------------------------------------------ > > _______________________________________________ > Numpy-discussion mailing list > Numpy-discussion@scipy.org > http://projects.scipy.org/mailman/listinfo/numpy-discussion > _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
