Re: fixed points piecewise-linear fitting

[Sergei Steshenko]

----- Original Message -----
> From: Juan Pablo Carbajal <address@hidden>
> To: Sergei Steshenko <address@hidden>
> Cc: "address@hidden" <address@hidden>
> Sent: Saturday, March 17, 2012 2:17 PM
> Subject: Re: fixed points piecewise-linear fitting
> 
> 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


No, it is _not_ what i am asking, even though I am using a 'interp1' a lot in 
my code.

This is _not_ interpolation. I am not interested in my "curve" going through 
certain points, I am interested in _fitting_, i.e. most likely the resulting Yf 
will _not_ go through any of Y points.

I suggest to enter the subject of this Email into any web search engine - there 
will be quite a few matches.

Regards,
  Sergei.