Re: residue() confusion

[Ben Abbott]

ok, I did some quick math

(x^2+1)/(x^4+18*x^2+81) = (2/9)/(x-3i) + (2/9)/(x+3i) + (1/54i)/(x-3i)^2 -
(1/54i)/(x+3i)^2

Thus,

a = [1/54i 2/9 -1/54i 2/9]
p = [3i 3i -3i -3i]
k = []
e = [2 1 2 1]

Can someone confirm they are able to get the correct answer from their
installation of Octave? 

I'm running 2.9.13 on both PPC and Intel based Macs


Ben Abbott wrote:
> 
> Regarding the various results, I was more concerned about the differences
> in "a" ... the pole locations are consistent but their residues are
> different.
> 
> 
> Henry F. Mollet wrote:
>> 
>> The result for e should be [1 2 1 2] (multiplicity for both poles). Note
>> that Matlab does not even give e.  My mis-understanding of the problem
>> was
>> pointed out by Doug Stewart. Doug posted new code yesterday, which I've
>> tried unsuccessfully, but I cannot be sure that I've implemented
>> residual.m
>> correctly. The corrected code still produced e = [1 1 1 1] for me.
>> Henry
>> 
>> 
>> on 9/22/07 1:31 PM, Ben Abbott at address@hidden wrote:
>> 
>>> 
>>> As a result of reading through Hodel's
>>> http://www.nabble.com/bug-in-residue.m-tf4475396.html post  I decided to
>>> check to see how my Octave installation and my Matlab installation
>>> responded
>>> to the example
>>> 
>>> Using Matlab v7.3
>>> --------------------------
>>>  num = [1 0 1];
>>>  den = [1 0 18 0 81];
>>>  [a,p,k] = residue(num,den)
>>> 
>>> a =
>>> 
>>>         0 - 0.0926i
>>>    0.2222 - 0.0000i
>>>         0 + 0.0926i
>>>    0.2222 + 0.0000i
>>> 
>>> 
>>> p =
>>> 
>>>    0.0000 + 3.0000i
>>>    0.0000 + 3.0000i
>>>    0.0000 - 3.0000i
>>>    0.0000 - 3.0000i
>>> 
>>> 
>>> k =
>>> 
>>>      []
>>> --------------------------
>>> 
>>> Using Octave 2.9.13 (via Fink) on Mac OSX
>>> --------------------------
>>>  num = [1 0 1];
>>>  den = [1 0 18 0 81];
>>>  [a,p,k] = residue(num,den)
>>> 
>>> a =
>>> 
>>>   -3.0108e+06 - 1.9734e+06i
>>>   -3.0108e+06 + 1.9734e+06i
>>>   3.0108e+06 + 1.9734e+06i
>>>   3.0108e+06 - 1.9734e+06i
>>> 
>>> p =
>>> 
>>>   -0.0000 + 3.0000i
>>>   -0.0000 - 3.0000i
>>>    0.0000 + 3.0000i
>>>    0.0000 - 3.0000i
>>> 
>>> k = [](0x0)
>>> e =
>>> 
>>>    1
>>>    1
>>>    1
>>>    1
>>> --------------------------
>>> 
>>> These are different from both the result that
>>> http://www.nabble.com/bug-in-residue.m-tf4475396.html Hodel obtained ,
>>> as
>>> well as different from
>>> http://www.nabble.com/bug-in-residue.m-tf4475396.html Mollet's
>>> 
>>> Thoughts anyone?
>>> 
>> 
>> 
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>> 
>> 
> 
> 

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