modified residues() for matlab compatibility

[Ben Abbott]

I've made some rather significant modifications to residue.m and  
added a companion function, mpoles.m, in order to produce a matlab  
compatible version of the former.

The basic change was to add the reciprocal operation.

[r, p, k] = residues (b, a);

and

[b, a] = residues (r, p, k);

I choose to significantly rewrite the residues function. My motive  
was to reduce the opportunity for bugs.

Matlab uses the support function mpoles.m to ensure a consistent  
treatment of pole multiplicity in each of these operations. So I  
decided it made sense to write an equivalent support function for  
Octave.

The tests I've run on this implementation were successful. For  
example, I compared the patched versions from Hodel and Stewart to my  
new implementation.

b = [1 0 1];
a = [1 0 18 0 81];
[r,p,k] = residue(b,a);
disp(num2str(r,'%14.12f'))

My implementation gives

0.000000000000-0.092592591339i
0.222222224416+0.000000000000i
0.000000000000+0.092592591339i
0.222222224416-0.000000000000i

residue from 2.9.14 with Hodel' s patch gives

-0.000000000000+0.092592591966i
0.222222222536-0.000000004302i
-0.000000000000-0.092592591966i
0.222222222536+0.000000004302i

residue from 2.9.14 with Stewart's patch gives

-0.000000000000-0.092592592593i
0.222222223789+0.000000002390i
-0.000000000000+0.092592592593i
0.222222223789-0.000000002390i

I plan to run more test, and see if I can improve the agreement  
(differs in the 9th decimal place). However, I thought it a good time  
to solicit feedback, and participation in testing.

If anyone has an application that puts residue.m through its paces,  
I'd appreciate you taking a look.

Also if anyone is up to checking the scripts for adherence to the  
common coding practices of the Octave contributers, I'd appreciate  
any feedback.

rresidue_bpa.m
Description: Binary data

mpoles.m
Description: Binary data