Re: [Gnuplot-info] fitting polynomial function

[Thomas S. <t.s...@fz...>]

show variables
or
print a,b,c,d,e,f,g,h,j,k
will give you the precise values of the variables.


Becker, Martin wrote:
> 
> Hi,
> 
> I am using the "fit" function in Gnuplot.
> The results are very good, even when fitting polynomials with large
> exponents.
> 
> But when I try to evaluate the polynomial function (typing in the "final
> set of parameters" I get from gnuplot manually), the resulting curve is
> not the same as when plotting the function via f(x).
> 
> Here's how you can reproduce that issue:
> 
> testfit.txt:
> 0.703046801 6.148059
> 0.741713434 6.234822
> 0.773950468 6.266732
> 0.834634823 6.349324
> 0.858792937 6.367429
> 0.945874445 6.455779
> 1.018601748 6.493238
> 1.056631087 6.515271
> 1.132619496 6.561212
> 1.208396235 6.623743
> 1.273432446 6.626688
> 1.322841114 6.661144
> 1.361994398 6.699116
> 1.419894331 6.703436
> 1.449532378 6.745392
> 1.495365168 6.799023
> 1.535109234 6.797992
> 1.551450853 6.892794
> 1.591150493 7.062142
> 1.609838136 7.056377
> 1.644491435 7.110281
> 1.664403966 6.909729
> 1.693825512 7.008516
> 1.719950161 6.966135
> 1.73447221  7.010832
> 1.750159151 7.056173
> 1.757950486 7.011614
> 1.769690372 7.051956
> 1.776861121 7.299418
> 1.784387803 7.534082
> 1.793996571 7.368413
> 1.799427481 6.789878
> 1.809187046 6.787986
> 1.815111552 7.235731
> 1.820633772 6.987372
> 1.830313952 6.4942
> 1.839906457 6.455258
> 1.849030092 6.912105
> 1.857638041 5.93482
> 
> gnuplot> plot "testfit.txt"
> gnuplot>
> f(x)=a+b*x+c*x**2+d*x**3+e*x**4+f*x**5+g*x**6+h*x**7+i*x**8+j*x**9+k*x**10
> gnuplot> fit f(x) "testfit.txt" via a,b,c,d,e,f,g,h,i,j,k
> 
> ...
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
> 
> a               = -20719.6         +/- 4.261e+04    (205.6%)
> b               = 186386           +/- 3.689e+05    (197.9%)
> c               = -744986          +/- 1.419e+06    (190.4%)
> d               = 1.74269e+06      +/- 3.191e+06    (183.1%)
> e               = -2.64203e+06     +/- 4.648e+06    (175.9%)
> f               = 2.71275e+06      +/- 4.585e+06    (169%)
> g               = -1.91066e+06     +/- 3.102e+06    (162.3%)
> h               = 911686           +/- 1.422e+06    (155.9%)
> i               = -282112          +/- 4.227e+05    (149.8%)
> j               = 51135.2          +/- 7.364e+04    (144%)
> k               = -4124.11         +/- 5711         (138.5%)
> ...
> 
> gnuplot> set multi
> gnuplot> plot "testfit.txt", f(x)  -> fits perfectly!
> gnuplot> set xrange[0.6:2]
> gnuplot> set yrange[5.8:7.6]
> gnuplot> plot
> -20719.6+186386*x-744986*x**2+1.74269e+06*x**3-2.64203e+06*x**4+2.71275e+06*x**5-1.91066e+06*x**6+911686*x**7-282112*x**8+51135.2*x**9-4124.11*x**10
> -> that seems to be a completely different curve!
> 
> What can I do to get the correct fitting function (which is used
> internally by gnuplot - otherwise it wouldn't be able to show the correct
> fitting curve)?
> 
> The problem might be that the coefficients I get from gnuplot's fit
> function are lacking some decimals, but I'm not sure about that.
> 
> Any ideas?
> 
> Thanks,
> Martin
> 
> 
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