Re: fixed points piecewise-linear fitting

[Martin Helm]

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
Description: Text Data