Hi all,

As a follow up to gh-15981, I would like to propose a change to bring complex dtype(s) comparison operators and related functions, in line with respective cpython implementations.

The current state of complex dtype comparisons/ordering as summarised in the issue is as follows:

# In python

>> cnum = 1 + 2j
>> cnum_two = 1 + 3j

# Doing a comparision yields
>> cnum > cnum_two

TypeError: '>' not supported between instances of 'complex' and 'complex'


# Doing the same in Numpy scalar comparision

>> np.array(cnum) > np.array(cnum_two)

# Yields

False

NOTE: only >, <, >= , <= do not work on complex numbers in python , equality (==) does work

similarly sorting uses comparison operators behind to sort complex values. Again this behavior diverges from the default python behavior.

# In native python
>> clist = [cnum, cnum_2]
>> sorted(clist, key=lambda c: (c.real, c.imag))
[(1+2j), (1+3j)]

# In numpy

>> np.sort(clist) #Uses the default comparision order

# Yields same result

# To get a cpython like sorting call we can do the following in numpy
np.take_along_axis(clist, np.lexsort((clist.real, clist.imag), 0), 0)

This proposal aims to bring parity between default python handling of complex numbers and handling complex types in numpy

This is a two-step process

  1. Sort complex numbers in a pythonic way , accepting key arguments, and deprecate usage of sort() on complex numbers without key argument
    1. Possibly extend this to max(), min(), if it makes sense to do so. 
    2. Since sort() is being updated for complex numbers, searchsorted() is also a good candidate for implementing this change.
  2. Once this is done, we can deprecate the usage of comparison operators (>, <, >= , <=) on complex dtypes



Handling sort() for complex numbers
There are two approaches we can take for this 

  1. update sort() method, to have a ‘key’ kwarg. When key value is passed, use lexsort to get indices and continue sorting of it. We could support lambda function keys like python, but that is likely to be very slow.
  2. Create a new wrapper function sort_by() (placeholder name, Requesting name suggestions/feedback)That essentially acts like a syntactic sugar for
    1. np.take_along_axis(clist, np.lexsort((clist.real, clist.imag), 0), 0)
  1. Improve the existing sort_complex() method with the new key search functionality (Though the change will only reflect for complex dtypes).
We could choose either method, both have pros and cons , approach 1 makes the sort function signature, closer to its python counterpart, while using approach 2 provides a better distinction between the two approaches for sorting. The performance on approach 1 function would vary, due to the key being an optional argument. Would love the community’s thoughts on this.

Handling min() and max() for complex numbers


Since min and max are essentially a set of comparisons, in python they are not allowed on complex numbers
>> clist = [cnum, cnum_2]
>>> min(clist)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: '<' not supported between instances of 'complex' and 'complex'

# But using keys argument again works
min(clist, key=lambda c: (c.real, c.imag))
We could use a similar key kwarg for min() and max() in python, but question remains how we handle the keys, in this use case , naive way would be to sort() on keys and take last or first element, which is likely going to be slow. Requesting suggestions on approaching this.

Comments on isclose()
Both python and numpy use the absolute value/magnitude for comparing if two values are close enough. Hence I do not see this change affecting this function.

Requesting feedback and suggestions on the above.

Thank you,

Rakesh