[Octave-bug-tracker] [bug #53880] (x<1)(1) depends on x(2):

[Dave Goel]

URL:
  <http://savannah.gnu.org/bugs/?53880>

                 Summary: (x<1)(1) depends on x(2): 
                 Project: GNU Octave
            Submitted by: deego
            Submitted on: Fri 11 May 2018 08:09:43 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Matlab Compatibility
                  Status: None
             Assigned to: None
         Originator Name: DAVE GOEL
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 4.2.2
        Operating System: GNU/Linux

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Details:

QUIZ:  Think of a strange scenario where the result of (x<1)(1)  depends on
the value of x(2) (!)

Yes, there's such an a possible:  

x=[-2 -1] and x = [-2 i] return different answers for (x<1)(1).


That's because octave switches to abs() if it encounters complex numbers. 

The problems with this, in my opinion, are:

(1) Strange logic above of result(1) depending on x(2).

(2) A strange discontinuity in y<1 between y = -2 and x = -2 + eps i 

(3) Matlab, see below. 

(4) As it stands, < is therefore useless and unreliable when using complex
numbers. You cannot consistently rely on it to use abs, since you never know
when x will be interpreted as real.  

----

A more consistent approach seems to be to use Re() instead of Abs() when
comparing complex numbers.  Instead of any strange behaviors as above, that
transitions smoothly when x becomes real. 

Finally, matlab seems to use the behavior I recommended:
https://www.mathworks.com/help/matlab/ref/lt.html#bt297ps-5





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