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Re: Problem of polyfit
From: |
Henry F. Mollet |
Subject: |
Re: Problem of polyfit |
Date: |
Thu, 06 Oct 2005 12:53:56 -0700 |
User-agent: |
Microsoft-Entourage/11.1.0.040913 |
Here's a test using N = 1. Polyfit.m gives the expected results as per
least square fit using the hat matrix H.
Henry
octave:29> x'
ans =
1 2 3 4 5 6 7 8 9 10
octave:30> y' % y = 2*x and changed 5th element to 15
ans =
2 4 6 8 15 12 14 16 18 20
octave:31> Onex'
ans =
1 1 1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10
octave:32> yf' % using [P, S] = polyfit (x, y, 1) and saving yf
ans =
Columns 1 through 8:
2.6364 4.6061 6.5758 8.5455 10.5152 12.4848 14.4545 16.4242
Columns 9 and 10:
18.3939 20.3636
octave:33> H = Onex*(Onex'*Onex)^-1*Onex';
octave:34> yhat = H*y;
octave:35> yhat'
ans =
Columns 1 through 8:
2.6364 4.6061 6.5758 8.5455 10.5152 12.4848 14.4545 16.4242
Columns 9 and 10:
18.3939 20.3636
octave:36> (yhat-yf)'
ans =
Columns 1 through 5:
-3.6364e-05 -3.9394e-05 -4.2424e-05 -4.5455e-05 -4.8485e-05
Columns 6 through 10:
4.8485e-05 4.5455e-05 4.2424e-05 3.9394e-05 3.6364e-05
on 10/6/05 2:46 AM, Tetsuro KURITA at address@hidden wrote:
> The following code in "polyfit.m" never give the best fit data in the
> least squares sense as described in document.
>
> X = (x * ones (1, n+1)) .^ (ones (l, 1) * (n : -1 : 0));
> p = X \ y;
>
> This code do nothing to mimimize `sumsq (p(x(i)) - y(i))'.
>
> I think this code should be modified as follows.
>
> X = (x * ones (1, n+1)) .^ (ones (l, 1) * (n: -1 : 0))
> W = X'*X
> z = X'*y
> p = inv(W)*z
>
> I am using Octave 2.1.57 on MacOS X.
>
> =======================================================
> Tetsuro KURITA
> E-mail: address@hidden
> http://homepage.mac.com/tkurita/scriptfactory/
> =======================================================
>
>
>
> -------------------------------------------------------------
> Octave is freely available under the terms of the GNU GPL.
>
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Octave is freely available under the terms of the GNU GPL.
Octave's home on the web: http://www.octave.org
How to fund new projects: http://www.octave.org/funding.html
Subscription information: http://www.octave.org/archive.html
-------------------------------------------------------------
- Re: Problem of polyfit, (continued)
- Re: Problem of polyfit, Tetsuro KURITA, 2005/10/07
- Re: Problem of polyfit, Fredrik Lingvall, 2005/10/07
- Re: Problem of polyfit, Tetsuro KURITA, 2005/10/07
- Re: Problem of polyfit, Paul Kienzle, 2005/10/07
- Re: Problem of polyfit, Fredrik Lingvall, 2005/10/07
- Re: Problem of polyfit, Paul Kienzle, 2005/10/07
Re: Problem of polyfit, Fredrik Lingvall, 2005/10/06
Re: Problem of polyfit, Dmitri A. Sergatskov, 2005/10/07
Re: Problem of polyfit,
Henry F. Mollet <=
- Re: Problem of polyfit, Miroslaw Kwasniak, 2005/10/06
- Re: Problem of polyfit, Henry F. Mollet, 2005/10/06
- Re: Problem of polyfit, Miroslaw Kwasniak, 2005/10/06
- Re: Problem of polyfit, John W. Eaton, 2005/10/06
- Re: Problem of polyfit, Henry F. Mollet, 2005/10/06
- Re: Problem of polyfit, Miroslaw Kwasniak, 2005/10/07
- Re: Problem of polyfit, Henry F. Mollet, 2005/10/07
Re: Problem of polyfit, Tom Holroyd, 2005/10/06