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fixed points piecewise-linear fitting
From: |
Sergei Steshenko |
Subject: |
fixed points piecewise-linear fitting |
Date: |
Sat, 17 Mar 2012 04:43:00 -0700 (PDT) |
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.
- fixed points piecewise-linear fitting,
Sergei Steshenko <=
- Re: fixed points piecewise-linear fitting, Juan Pablo Carbajal, 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, 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