[Octave-bug-tracker] [bug #60384] `mpoles` incorrectly classifies distinct poles as unique ones

[Markus Mützel]

Update of bug #60384 (project octave):

        Operating System:               GNU/Linux => Any                    
                 Summary: Residue function produces incorrect results when
multiplicity of poles > 1 => `mpoles` incorrectly classifies distinct poles as
unique ones

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Follow-up Comment #4:

I believe, the root of the issue is that `mpoles` incorrectly classifies the
two distinct roots in the original example as a single root with multiplicity
2:

A = [1, 1.100000536842105e+04, 1.703789473684211e+03, 0];
poles1 = roots (A);
[e, idx] = mpoles (poles1, 0.001, 1)


In Octave:

>> [e, idx] = mpoles (poles1, 0.001, 1)
e =

   1
   2
   1

idx =

   3
   2
   1


I'd guess that this might be because one of the poles differs in orders of
magnitude from the other ones.

Re-titling report.

Fwiw, in Matlab:

>> A = [1, 1.100000536842105e+04, 1.703789473684211e+03, 0];
poles1 = roots (A);
[e, idx] = mpoles (poles1, 0.001, 1)

e =

     1
     1
     1


idx =

     2
     3
     1


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