Re: Patch to residue.m

[Ben Abbott]

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.

Ben

residue.patch
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ChangeLog
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residue.m
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