Re: I think I have found another problem in residue.

[Doug Stewart]

Ben Abbott wrote:
> On Dec 9, 2007, at 12:23 PM, Doug Stewart wrote:
>
> > I would like Ben Abbott to try the following code
> >
> > n=poly([ -11 -10 ])*1000
> >
> > d=poly([ -3-3j -3+3j -3-3j -3+3j -3-3j -3+3j -5.6 -1 ])
> >
> > roots(d)
> >
> > residue(n,d)
> >
> >
> > I get
> >
> > p =
> >
> > -5.60000 + 0.00000i
> >
> > -3.00010 + 3.00003i
> >
> > -3.00010 - 3.00003i
> >
> > -2.99992 + 3.00007i
> >
> > -2.99992 - 3.00007i
> >
> > -2.99998 + 2.99990i
> >
> > -2.99998 - 2.99990i
> >
> > -1.00000 + 0.00000i
> >
> > ans =
> >
> > -1.3195 - 0.0000i
> >
> > -3.7935 + 8.3944i
> >
> > 14.5612 + 10.6427i
> >
> > 16.3548 - 13.2580i
> >
> > -3.7935 - 8.3944i
> >
> > 14.5612 - 10.6427i
> >
> > 16.3548 + 13.2580i
> >
> > 8.9065 - 0.0000i
> >
> >
> > but it should be:
> >
> > p =
> >
> > -5.60000 + 0.00000i
> >
> > -3.00010 + 3.00003i
> >
> > -3.00010 - 3.00003i
> >
> > -2.99992 + 3.00007i
> >
> > -2.99992 - 3.00007i
> >
> > -2.99998 + 2.99990i
> >
> > -2.99998 - 2.99990i
> >
> > -1.00000 + 0.00000i
> >
> > ans =
> >
> > -1.3195 - 0.0000i
> >
> > -3.7935 + 8.3944i
> > -3.7935 - 8.3944i
> >
> > 14.5612 + 10.6427i
> >
> > 14.5612 - 10.6427i
> >
> > 16.3548 - 13.2580i
> > 16.3548 + 13.2580i
> >
> > 8.9065 - 0.0000i
> >
> >
> > Could you verify what I am getting please.?
> > Doug Stewart
>
> Doug, I took your example and modified it slightly. Please see the 
> attached test script. The script displays [r, p]
>
> I've run the script from Octave on Tiger/PPC and Leopard/Intel, as 
> well as on Matlab 7.3b. In each case I get the same results (except 
> that matlab appears to refine the roots a bit better).
>
> ---------------------------
> octave:30> test
> ans =
>
>    -1.31921 +  0.00000i   -5.60000 +  0.00000i
>    -3.79336 +  8.39318i   -2.99998 +  3.00009i
>    14.55944 + 10.64154i   -3.00008 +  2.99997i
>    16.35697 - 13.24746i   -2.99994 +  2.99994i
>    -3.79336 -  8.39318i   -2.99998 -  3.00009i
>    14.55944 - 10.64154i   -3.00008 -  2.99997i
>    16.35697 + 13.24746i   -2.99994 -  2.99994i
>     8.90592 -  0.00000i   -1.00000 +  0.00000i
> ---------------------------
>
> The Matlab result is
>
> ---------------------------
> >> test
> ans =
>  -1.3195            -5.6000
>  -3.7929 + 8.3933i  -3.0000 + 3.0000i
>  14.5590 +10.6397i  -3.0000 + 3.0000i
>  16.3510 -13.2508i  -3.0000 + 3.0000i
>  -3.7929 - 8.3933i  -3.0000 - 3.0000i
>  14.5590 -10.6397i  -3.0000 - 3.0000i
>  16.3510 +13.2508i  -3.0000 - 3.0000i
>   8.9054            -1.0000 
> ---------------------------
>
> It appears to me that Octave and Matlab's residue.m script work in 
> compatible/consistent ways ... hmmm, perhaps I've misinterpreted your 
> point?
>
> I'm on a tight schedule today, so I don't have time for doing a 
> derivation by hand to verify the results. My presence online will be 
> spotty for the next few days, but will check back when I can.
>
> Ben
>
>
> ------------------------------------------------------------------------
OK!  Then the problem is at my end.

I agree that this is a good answer from residue.
Doug Stewart