Re: Patch to residue.m

[John W. Eaton]

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