Patch to residue.m

[Ben Abbott]

On Jan 18, 2008, at 12:58 AM, John W. Eaton wrote:

> On 11-Jan-2008, Ben Abbott wrote:
>
> | I believe this patch is ready to be committed.
> |
> | In the event of pole multiplicity, the committed version of  
> residue.m
> | does not use a single pole to represent a group of multiplicity.
> | Instead the expansion of residues is done with the poles returned by
> | roots . The attached patch changes the pole value associated with a
> | group of multiplicity to be that of the mean of then entire group.
> |
> | For example, if the poles were given by
> |
> | octave:1> p = [3 3 3 3 3];
> | octave:2> p = roots(poly(p))
> | p =
> |
> |     3.0026 + 0.0000i
> |     3.0008 + 0.0024i
> |     3.0008 - 0.0024i
> |     2.9979 + 0.0015i
> |     2.9979 - 0.0015i
> |
> | The current committed version expands to residues as
> |
> | r(1)/(x-p(1)) + r(2)/(x-p(2)).^2 + r(3)/(x-p(3)).^3 + r(4)/(x- 
> p(4)).^4
> | + r(5)/(x-p(5)).^5
> |
> | With each element of p(:) being different. However, the expansion of
> | residues  should use a single value for the poles of a multiplicity
> | group.
> |
> | octave:3> p = mean(p)*ones(size(p))
> | p =
> |
> |     3.0000
> |     3.0000
> |     3.0000
> |     3.0000
> |     3.0000
> |
> | This patch makes this change.
> |
> | In addition the checks for poles of zero value, pure real values,  
> and
> | pure imaginary values is done *after* consideration of pole
> | multiplicity.
> |
> | The attached patch and ChangeLog are identical to that submitted on
> | Dec 31.
>
> OK, sorry for the delay.  I checked this in to CVS head and the 3.0
> branch.
>
> Thanks,
>
> jwe

Thanks John
Ben