Re: fixed points piecewise-linear fitting

[Ben Abbott]

On Mar 20, 2012, at 6:33 PM, Ben Abbott wrote:

> On Mar 20, 2012, at 6:14 PM, Martin Helm wrote:
> 
>> Am 20.03.2012 22:31, schrieb Ben Abbott:
>>> After more testing I concluded the problem isn't a linear one. Meaning
>>> that your linear solution isn't working as I'd hoped. For my example
>>> the RMSE was about 70 for your solution and about 10 for my fsolve()
>>> approach. I did find that your linear approach provided a reasonable
>>> initial guess, so I am using that. I'll clean things up and attach the
>>> script later. Ben 
>> Ben, not sure what you exactly tested, I rewrote my function slightly to
>> match yours (giving back the pp structure) and compared
>> 
>> x = 0:39;
>> y = [8.8500 32.0775 74.7375 107.6775 132.0975 156.6675 ...
>> 169.0650 187.5375 202.2575 198.0750 225.9600 204.3550 ...
>> 233.8125 204.5925 232.3625 204.7550 220.1925 199.5875 ...
>> 197.3025 175.3050 218.6325 163.0775 170.6625 148.2850 ...
>> 154.5950 135.4050 138.8600 125.6750 118.8450 99.2675 ...
>> 129.1675 91.1925 89.7000 76.8825 83.6625 74.1950 ...
>>   73.9125 55.8750 59.8675 48.1900];
>> xi = linspace (min (x), max (x), ceil (numel (x) / 5));
>> pp = ppolyfit (x, y, xi, "spline");
>> yi = ppval (pp, xi);
>> clf
>> plot (x, y, "s", xi, yi, "o", x, ppval (pp, x));
>> xlabel ("Dependent Variable")
>> ylabel ("Fitted Function")
>> legend ("data", "interval bounds", "fit")
>> xlabel ("Dependent Variable")
>> ylabel ("Fitted Function")
>> legend ("data", "interval bounds", "fit")
>> pp2 = ppfit2 (xi, x, y, "spline");
>> hold on
>> plot (x, ppval (pp2, x), "b--");
>> disp (max(abs(ppval (pp2, x) - ppval (pp, x))))
>> 
>> which returns as max difference in the function values 6.7130e-08
>> 
>> attached the slightly modified ppfit2
>> 
>> <ppfit2.m>
> 
> Ok. Thanks for updated version.
> 
> I'll take another look.
> 
> Ben

I did make another mistake.

Using methods "linear" or "spline" give the same result. However, using your 
approach "cubic"/"pchip" doesn't produce a minimum least squares solution.

I've attached a test script (go_ppfit.m) and both ppfit.m (mine) and ppfit2.m 
(yours). I modified yours to support weighted least squares.

Ben

go_ppfit.m
Description: Binary data

ppfit.m
Description: Binary data

ppfit2.m
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