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Re: residue() confusion
From: |
Ben Abbott |
Subject: |
Re: residue() confusion |
Date: |
Sat, 22 Sep 2007 20:25:09 -0700 (PDT) |
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
>>
>>
>
> _______________________________________________
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>
--
View this message in context:
http://www.nabble.com/residue%28%29-confusion-tf4502015.html#a12842532
Sent from the Octave - General mailing list archive at Nabble.com.
- 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