fitting polynomial function
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fitting polynomial function
by Becker, Martin
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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 ------------------------------------------------------------------------------ Come build with us! The BlackBerry(R) Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9 - 12, 2009. Register now! http://p.sf.net/sfu/devconference _______________________________________________ Gnuplot-info mailing list Gnuplot-info@... https://lists.sourceforge.net/lists/listinfo/gnuplot-info |
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Re: fitting polynomial function
by Hans-Bernhard Bröker-2
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Becker, Martin wrote:
> But when I try to evaluate the polynomial function (typing in the > "final set of parameters" I get from gnuplot manually), Why on earth would you do that? The results have all been stored into the respective user-defined variables under the names you gave them. Try "show var" after you fit and you'll see. You'll also want to re-read the "help fit" pages. > a = -20719.6 +/- 4.261e+04 (205.6%) > b = 186386 +/- 3.689e+05 (197.9%) [...] That's not a good fit by any stretch of the imagination. All resulting parameters are completely dominated by error. > 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. That's exactly the problem. It would be utterly pointless to print all 15 decimals in each of those parameters in a fit result summary. Especially in a fit like this, where not even the first digit is actually significant! ------------------------------------------------------------------------------ Come build with us! The BlackBerry(R) Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9 - 12, 2009. Register now! http://p.sf.net/sfu/devconference _______________________________________________ Gnuplot-info mailing list Gnuplot-info@... https://lists.sourceforge.net/lists/listinfo/gnuplot-info |
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Re: fitting polynomial function
by Thomas Sefzick
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show variables
or print a,b,c,d,e,f,g,h,j,k will give you the precise values of the variables.
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