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Re: residue() confusion
From: |
Henry F. Mollet |
Subject: |
Re: residue() confusion |
Date: |
Mon, 24 Sep 2007 16:37:04 -0700 |
User-agent: |
Microsoft-Entourage/11.1.0.040913 |
I have checked what has become residue4.m at Doug Stewart's URL which agrees
with solution given by Ben Abbot: 2/9 = 0.222222222222222 and 5/54 =
0.0925925925925926.
Is there an easy explanation why the coefficients are so different when I
remove the multiplicity of the poles by using 80.9999 instead of 81.000 in
denominator polynomial?
Henry
octave-2.9.14:26> format long
octave-2.9.14:27> [a,p,k,e] = residue4(num,den)
a =
-7.29060028230561e-27 - 9.25925925925924e-02i
2.22222222690571e-01 - 9.97810470405334e-10i
-1.40225660362292e-25 + 9.25925925925924e-02i
2.22222222690570e-01 + 9.97810470405334e-10i
p =
-0.00000001077635 + 2.99999999494184i
0.00000001077635 + 3.00000000505816i
-0.00000001077635 - 2.99999999494184i
0.00000001077635 - 3.00000000505816i
k = [](0x0)
e =
1
2
1
2
octave-2.9.14:34> den809999=[1 0 18 0 80.9999]
den809999 =
Columns 1 through 3:
1.000000000000000 0.000000000000000 18.000000000000000
Columns 4 and 5:
0.000000000000000 80.999899999999997
octave-2.9.14:35> [a,p,k,e] = residue4(num,den809999)
a =
0.0000000000405 + 66.6203549268702i
-0.0000000000405 - 66.7129475394614i
0.0000000000405 - 66.6203549268781i
-0.0000000000405 + 66.7129475394693i
p =
0.00000000000000 + 2.99833287011296i
-0.00000000000000 + 3.00166620396076i
0.00000000000000 - 2.99833287011296i
-0.00000000000000 - 3.00166620396076i
k = [](0x0)
e =
1
1
1
1
*******************************************************************
on 9/22/07 8:56 PM, Doug Stewart at address@hidden wrote:
> Not yet I was letting some users try it first to make sure that there
> are no more problems before we commit it.
> So give it a try and report back to the list.
> Doug
>
> Ben Abbott wrote:
>> Thanks Doug,
>>
>> Is this fix included in 2.9.14?
>>
>>
>>
>> Doug Stewart wrote:
>>
>>> Here is my results for this question
>>>
>>> num = [1 0 1];
>>> den = [1 0 18 0 81];
>>> [a,p,k,e] = residue(num,den)
>>>
>>> a =
>>>
>>> 1.0e+06 *
>>>
>>> 5.927582766769742 + 2.314767228467131i
>>> 5.927582730209724 - 2.314767214190160i
>>> -5.927582717669299 - 2.314767374340102i
>>> -5.927582681109279 + 2.314767360063129i
>>>
>>> p =
>>>
>>> 0.000000016264485 + 2.999999993648592i
>>> 0.000000016264485 - 2.999999993648592i
>>> -0.000000016264485 + 3.000000006351409i
>>> -0.000000016264485 - 3.000000006351409i
>>>
>>> k = []
>>> e =
>>>
>>> 1
>>> 1
>>> 1
>>> 1
>>>
>>>>> [a,p,k,e] = residue2(num,den)
>>> a =
>>>
>>> -0.000000000000000 - 0.092592592592593i
>>> 0.000000000000000 + 0.092592592592593i
>>> 0.222222222810316 + 0.000000001505971i
>>> 0.222222222810316 - 0.000000001505971i
>>>
>>> p =
>>>
>>> 0.000000016264485 + 2.999999993648592i
>>> 0.000000016264485 - 2.999999993648592i
>>> -0.000000016264485 + 3.000000006351409i
>>> -0.000000016264485 - 3.000000006351409i
>>>
>>> k = []
>>> e =
>>>
>>> 1
>>> 1
>>> 2
>>> 2
>>>
>>>
>>>
>>> the second one is my "fixed" code and this agrees with Matlab.
>>>
>>> You can get my code at:
>>>
>>> www.dougs.homeip.net/octave/residue2.m
>>>
>>> Doug
>>>
>>>
>>>
>>>
>>>
>>> Henry F. Mollet wrote:
>>>
>>>> Your concern is justified. I don't know how to do partial fractions by
>>>> hand
>>>> when there is multiplicity. Therefore I checked results by hand using s =
>>>> linspace (-4i, 4i, 9) as a first check. It appears that Matlab results
>>>> are
>>>> correct if I take into account multiplicity of [1 2 1 2]. Octave results
>>>> appear to be incorrect.
>>>> Henry
>>>> octave-2.9.14:29> s =
>>>> -0 - 4i 0 - 3i 0 - 2i 0 - 1i 0 + 0i 0 + 1i 0 + 2i 0 + 3i
>>>> 0
>>>> + 4i
>>>>
>>>> Using left hand side of equation:
>>>> octave-2.9.14:30> y=(s.^2 + 1)./(s.^4 + 18*s.^2 + 81)
>>>> y =
>>>> Columns 1 through 6:
>>>> -0.30612 + 0.00000i NaN + NaNi -0.12000 - 0.00000i 0.00000
>>>> -
>>>> 0.00000i 0.01235 - 0.00000i 0.00000 - 0.00000i
>>>> Columns 7 through 9:
>>>> -0.12000 + 0.00000i NaN + NaNi -0.30612 + 0.00000i
>>>>
>>>> Using right hand side of equation with partial fraction given by Matlab:
>>>> octave-2.9.14:31> yMatlab= (0 - 0.0926i)./(s-3i) + (0.2222 -
>>>> 0.0000i)./(s-3i).^2 + (0 + 0.0926i)./(s+3i) + (0.2222 +
>>>> 0.0000i)./(s+3i).^2
>>>>
>>>> yMatlab =
>>>> Columns 1 through 6:
>>>> -0.30611 + 0.00000i NaN + NaNi -0.11997 + 0.00000i 0.00001
>>>> +
>>>> 0.00000i 0.01236 + 0.00000i 0.00001 + 0.00000i
>>>> Columns 7 through 9:
>>>> -0.11997 + 0.00000i NaN + NaNi -0.30611 + 0.00000i
>>>>
>>>> Using right hand side of equation with partial fraction given by Octave:
>>>> octave-2.9.14:32> yOctave=(-3.0108e+06 - 1.9734e+06i)./(s-3i) +
>>>> (3.0108e+06
>>>> + 1.9734e+06i)./(s-3i).^2 + (-3.0108e+06 + 1.9734e+06i)./(3+3i) +
>>>> (3.0108e+06 - 1.9734e+06i)./(s+3i).^2
>>>>
>>>> yOctave =
>>>> Columns 1 through 5:
>>>> -2.9632e+06 + 2.3337e+06i NaN + NaNi -2.9095e+06 +
>>>> 2.1230e+06i -6.2042e+05 + 4.4801e+05i -1.8417e+05 - 1.7290e+05i
>>>> Columns 6 through 9:
>>>> -1.2708e+05 - 1.0447e+06i -1.3307e+06 - 4.0746e+06i NaN +
>>>> NaNi -5.2185e+06 + 1.9084e+06i
>>>>
>>>> **********************************
>>>>
>>>> on 9/22/07 2:14 PM, Ben Abbott at address@hidden wrote:
>>>>
>>>>
>>>>
>>>>> I was more concerned about the differences in "a"
>>>>>
>>>>> I suppose I'll need to do a derivation and check the correct answer.
>>>>>
>>>>> On Sep 22, 2007, at 5:05 PM, 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?
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>> _______________________________________________
>>>> Help-octave mailing list
>>>> address@hidden
>>>> https://www.cae.wisc.edu/mailman/listinfo/help-octave
>>>>
>>>>
>>>>
>>> _______________________________________________
>>> Help-octave mailing list
>>> address@hidden
>>> https://www.cae.wisc.edu/mailman/listinfo/help-octave
>>>
>>>
>>>
>>
>>
>
> _______________________________________________
> Help-octave mailing list
> address@hidden
> https://www.cae.wisc.edu/mailman/listinfo/help-octave
- Re: residue() confusion, (continued)
Re: residue() confusion, Henry F. Mollet, 2007/09/22
Re: residue() confusion, Ben Abbott, 2007/09/23
Re: residue() confusion, Doug Stewart, 2007/09/23
Re: residue() confusion, Ben Abbott, 2007/09/23
Re: residue() confusion, Doug Stewart, 2007/09/24
Re: residue() confusion, Ben Abbott, 2007/09/24
Re: residue() confusion, Henry F. Mollet, 2007/09/24
Re: residue() confusion, A. Scottedward Hodel, 2007/09/25