Re: Sorting complex values

[Daniel J Sebald]

On 09/27/2014 02:25 PM, Ben Abbott wrote:
> On Sep 27, 2014, at 2:43 PM, Daniel J Sebald<address@hidden>  wrote:
>
> > The one thing that concerns me a bit is that -1 - 0i produces an angle of -pi.
>
> I'm confident this behavior is correct. There is a branch along the negative 
> real axis ... i.e. a phase of +pi and -pi are both correct, but only one of 
> them is proper by IEEE standards.  To determine the phase it is necessary to 
> determine if the imaginary part is positive or negative.  The default is to 
> assume the imaginary part is positive. In the case, of 1 - 0i, the default has 
> been over-ridden.

There's a branch cut in the complex plane for the arc-tangent function. 
 But here it is just numbers represented as modulus and angle

z = |z|e^jTHETA
  = |z|e^jTHETA +- N 2pi

where THETA is the principle argument.  |z|e^jpi and |z|e^-jpi are the 
same number.  Treating the argument as the principle argument or not, 
and sorting on it is basically arbitrary.

I actually prefer to use the principle argument because then the +0/-0 
phenomenon has no bearing on order, in light of sorting of non-complex 
numbers which produces:

octave:70> x = [0 -0 0 -0 0 -0]'
x =

   0
  -0
   0
  -0
   0
  -0

octave:71> [s i] = sort(x)
s =

   0
  -0
   0
  -0
   0
  -0

i =

   1
   2
   3
   4
   5
   6

If the +/-0 is meaningless in non-complex sort, then it probably should 
be meaningless in the complex sort.

Dan