[Octave-bug-tracker] [bug #47865] cplxpair(array, tol) uses wrong units for tol

[Rik]

Follow-up Comment #1, bug #47865 (project octave):

This looks related to bug #45810 which was marked as fixed.

The Matlab documentation string for cplxpair is here
(http://www.mathworks.com/help/matlab/ref/cplxpair.html) and it doesn't
mention anything about the tolerance being in the range 0 to 1.

However, the description of tolerance is ambiguous.


A default tolerance of 100*eps relative to abs(A(i)) determines which numbers
are real and which elements are paired complex conjugates.


I'm not sure exactly how to interpret that.  Octave has chosen to interpret it
as


100 * eps (abs (A(i)))


But it would be quicker if we could calculate


100 * eps * abs (A(i))


It's not quite the same thing as you can see below


octave:1> eps (1000)
ans =    1.1369e-13
octave:2> eps*1000
ans =    2.2204e-13


In any case, Octave may have the correct default tolerance, but Matlab uses an
entirely different method of determining the tolerance when a value is
specified.

The only way to go about this is to test different inputs to the cplxpair
function and see what happens.

Try the test case from bug #45810


z2 = [2000 * (1+eps) + 4j; 2000 * (1-eps) - 4j];


What do the following do under Matlab?


cplxpair (z2, -0.1)
cplxpair (z2, 0)
cplxpair (z2, 0.99)
cplxpair (z2, 1)
cplxpair (z2, 2)


If you are right that tolerance is in the range [0,1) then three of the
statements should produce an error.


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