[Numpy-discussion] Question about numpy.max(<complex matrix>)

[Stuart Brorson]

On Fri, 21 Sep 2007, Robert Kern wrote:
> Stuart Brorson wrote:
>>>> Is it NumPy's goal to be as compatible with Matlab as possible?
>>> No.
>>
>> OK, so that's fair enough.  But how about self-consistency?
>> I was thinking about this issue as I was biking home this evening.
>>
>> To review my question:
>>
>>   >>> a
>>    array([[ 1. +1.j ,  1. +2.j ],
>>           [ 2. +1.j ,  1.9+1.9j]])
>>   >>> numpy.max(a)
>>    (2+1j)
>>
>> Why does NumPy return 2+1j, which is the element with the largest real
>> part?  Why not return the element with the largest *magnitude*?
>> Here's an answer from the list:
>>
>>> There isn't a single, well-defined (partial) ordering of complex numbers. Both
>>> the lexicographical ordering (numpy) and the magnitude (Matlab) are useful, but
>>> the lexicographical ordering has the feature that
>>>
>>>   (not (a < b)) and (not (b < a)) implies (a == b)
>> [snip]
>>
>> Sounds good, but actually NumPy is a little schizophrenic when it
>> comes to defining an order for complex numbers. Here's another NumPy
>> session log:
>>
>>   >>> a = 2+1j
>>   >>> b = 2+2j
>>   >>> a>b
>>    Traceback (most recent call last):
>>      File "<stdin>", line 1, in <module>
>>    TypeError: no ordering relation is defined for complex numbers
>>   >>> a<b
>>    Traceback (most recent call last):
>>      File "<stdin>", line 1, in <module>
>>    TypeError: no ordering relation is defined for complex numbers
>
> No, that's a Python session log and the objects you are comparing are Python
> complex objects. No numpy in sight. Here is what numpy does for its complex
> scalar objects:
>
>>>> from numpy import *
>>>> a = complex64(2+1j)
>>>> b = complex64(2+2j)
>>>> a < b
> True

OK, fair enough.  I was wrong.  But, ummmmm, in my example above, when
you find the max of a complex array, you compare based upon the *real*
part of each element.  Here, you compare based upon complex
*magnitude*.

Again, I wonder about self-consistency.

I guess the thing which bothers me is that finding the max of a
complex array by finding the element with the largest *real* part
seems..... well..... ummmm, like a bug.   Or at least rather
non-intuitive.  Yes, you can use any ordering relationship for complex
numbers you want, but, gee, it seems to me that once you choose one
then you should stick to it.

>> Or are NumPy behaviors --
>> once defined -- never changed?
>
> We do try to keep backwards compatibility.

Great! Thank you!

Stuart