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Re: fixed points piecewise-linear fitting
From: |
Juan Pablo Carbajal |
Subject: |
Re: fixed points piecewise-linear fitting |
Date: |
Sat, 17 Mar 2012 13:17:59 +0100 |
On Sat, Mar 17, 2012 at 12:43 PM, Sergei Steshenko <address@hidden> wrote:
> Hello,
>
> strictly speaking, it's not an Octave-specific question, but an algorithmic
> one.
>
> Suppose there is a measured function Y(X). In Octave terms X is a vector with
> N elements.
>
> Suppose there are fixed points Xf such that
>
> X(1) <= Xf(1)
> Xf(end) <= X(end).
>
> The Xf points are more sparse than X.
>
>
> The Xf points are fixed, i.e. one can't change them as he/she pleases.
>
> The goal is to find piecewise-linear function Yf(Xf) which best fits Y(X).
>
> I.e. for each two Xf(k), Xf(k+1) pair of points to find a piece of straight
> line defined by Yf(k), Yf(k+1)pair of points such that the whole Yf fits Y
> pretty well.
>
> Best fitting I'm interested in is according to minimum of sum(abs(Y -
> Yf_interpolated)). The Yf_interpolated is linear interpolated Yf on X, so
> dimensions of Y and Yf_interpolated match.
>
>
> I did some quick web searching and my impression is that there is no
> universally adopted algorithm for this task, but there is a number solutions,
> including some for R-language.
>
> I myself wrote a straightforward brute force implementation which works
> pretty well and acceptably fast for me.
>
> Anyway, I'm writing this Email in the hope to be educated by the community -
> maybe there are already more elegant wheels than the one I've invented.
>
> Thanks,
> Sergei.
>
> _______________________________________________
> Help-octave mailing list
> address@hidden
> https://mailman.cae.wisc.edu/listinfo/help-octave
Hi,
What you describe is also known as Langrange (or linear)
interpolation. You can use interp1 with the option linear
an example
t=linspace(0,2*pi,100);
ts=linspace(0,2*pi,10);
ys=sin(ts);
y=interp1(ts,ys,t,'linear');
plot(t,y,'.',ts,ys,'o',t,sin(t),'-')
I hope this is what you were asking (to restrict the inteprolation to
a subinterval, you could use lookup function before the
interpolation).
--
M. Sc. Juan Pablo Carbajal
-----
PhD Student
University of Zürich
http://ailab.ifi.uzh.ch/carbajal/
- fixed points piecewise-linear fitting, Sergei Steshenko, 2012/03/17
- Re: fixed points piecewise-linear fitting,
Juan Pablo Carbajal <=
- Re: fixed points piecewise-linear fitting, Ben Abbott, 2012/03/17
- Re: fixed points piecewise-linear fitting, Sergei Steshenko, 2012/03/17
- Re: fixed points piecewise-linear fitting, Ben Abbott, 2012/03/17
- Re: fixed points piecewise-linear fitting, Sergei Steshenko, 2012/03/17
- Re: fixed points piecewise-linear fitting, Ben Abbott, 2012/03/17
- Re: fixed points piecewise-linear fitting, Juan Pablo Carbajal, 2012/03/17
- Re: fixed points piecewise-linear fitting, c., 2012/03/18
- Re: fixed points piecewise-linear fitting, Sergei Steshenko, 2012/03/18