Re: bug in residue.m

> Octave 2.9.13 on Mac OS X:
> The m-file below reveals a problem in residue.m,  in Octave's
> polynomial scripts.  I started to debug it, but the
> code is fairly intricate.  The problem is that the code fails to
> detect multiple roots.
> Consider the case:
>
> octave:7> num = [1,0,1];
> octave:7> den =  [1,0,18,0,81];
> octave:8> [a,p,k,e] = residue(num,den)
>
> fails to detect the multiple poles at +/- j3 on my machine.  The
> problem appears to be that residue expects the roots to be returned in
> a specific order.  The problem in this case is resolved by sorting the
> poles by their imaginary parts.
>
> octave:9> %sort poles by imaginary part
> octave:9> [a,p,k,e] = residue(num,den)
> a =
>
>   7.3527e-25 + 9.2593e-02i
>   2.2222e-01 + 2.3902e-09i
>   -3.6764e-25 - 9.2593e-02i
>   2.2222e-01 + 2.3902e-09i
>
> p =
>
>   -0.0000 - 3.0000i
>    0.0000 - 3.0000i
>    0.0000 + 3.0000i
>   -0.0000 + 3.0000i
>
> k = [](0x0)
> e =
>
>    1
>    2
>    1
>    2
>
> The change to residue.m is in the following diff:  *Note* This will
> fix my problem, but it can still break if two pairs of complex poles
> have the same imaginary part, e.g., if you have poles at
> 1+j, 1-j, -1+j, and -1-j,
> if they are sorted in  order of imaginary part
> -1+j,1+j,-1-j, 1-j,
> then the code will still fail to detect the multiplicity.  The details
> of the code are complicated enough that I can't propose a proper fix
> right now, but this patch will fix the problem cited above.
>
> *** /sw/share/octave/2.9.13/m/polynomial/residue.m      Fri Sep  7
> 09:44:44 2007
> --- residue.m   Tue Sep 18 10:38:20 2007
> ***************
> *** 201,207 ****
>  
>     ## Find the poles.
>  
> !   p = roots (a);
>     lp = length (p);
>  
>     ## Determine if the poles are (effectively) zero.
> --- 201,207 ----
>  
>     ## Find the poles.
>  
> !   p = sortcom(roots (a), "im");
>     lp = length (p);
>  
>     ## Determine if the poles are (effectively) zero.
>
>
> A. Scottedward Hodel hodelas@... <mailto:hodelas@...>
> http://homepage.mac.com/hodelas/tar
>
>
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