Re: Sorting complex values

[Rik]

On 09/27/2014 02:05 PM, Ben Abbott wrote:
> On Sep 27, 2014, at 4:29 PM, Daniel J Sebald <address@hidden> wrote:
>
>> 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
> Ok.  I get the point now.  I happy to run some examples in Matlab if that 
> would be useful.
>
> x = [ [1 -1 i -i].' [1 -1 i -i]' ];
>
> sort (x)
>
> ans =
>
>    0.0000 - 1.0000i   0.0000 - 1.0000i
>    1.0000 + 0.0000i   1.0000 + 0.0000i
>    0.0000 + 1.0000i   0.0000 + 1.0000i
>   -1.0000 + 0.0000i  -1.0000 + 0.0000i

I have to say that this ordering by Matlab makes the most sense to me.

--Rik