JasonGross
commented
3 years ago With #386 and a slight adjustment to the code above, we get
\documentclass{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepackage{gnuplottex}
\usepackage{pgfkeys}
\usepackage{pgfplotstable}
\usepackage{xparse}
\usepackage{xstring}
\makeatletter
% https://tex.stackexchange.com/a/50113/2066
\newcommand*{\IsInteger}[3]{%
\IfStrEq{#1}{ }{%
#3% is a blank string
}{%
\IfInteger{#1}{#2}{#3}%
}%
}%
\newcommand{\pgftognucolumnset}[2]{%
\IsInteger{\pgfkeysvalueof{#1}}{%
% pgf 0-indexes columns, while gnuplot 1-indexes columns, so we add 1 to adjust
\edef#2{\the\numexpr\pgfkeysvalueof{#1}+1\relax}%
}{%
\edef#2{(column("\pgfkeysvalueof{#1}"))}%
}%
}
\makeatletter
% \addplotexponentialregression[params for \addplot][default settings for a and b, also for x and y columns]{table file}
\NewDocumentCommand{\addplotexponentialregression}{ O{no markers} o m}{%
\pgfkeyssetvalue{/addplotexponentialregression/x}{0}
\pgfkeyssetvalue{/addplotexponentialregression/y}{1}
\pgfkeyssetvalue{/addplotexponentialregression/a}{1}
\pgfkeyssetvalue{/addplotexponentialregression/b}{1}
\pgfkeys{/addplotexponentialregression/.cd,#2}
\pgftognucolumnset{/addplotexponentialregression/x}{\@addplotexponentialregression@colx}%
\pgftognucolumnset{/addplotexponentialregression/y}{\@addplotexponentialregression@coly}%
\edef\@addplotexponentialregression@inita{\pgfkeysvalueof{/addplotexponentialregression/a}}%
\edef\@addplotexponentialregression@initb{\pgfkeysvalueof{/addplotexponentialregression/b}}%
\addplot [#1] gnuplot [raw gnuplot] { % allows arbitrary gnuplot commands
f(x) = exp(a*x+b); % Define the function to fit
% Set reasonable starting values here
a=\@addplotexponentialregression@inita;
b=\@addplotexponentialregression@initb;
fit f(x) '#3' u \@addplotexponentialregression@colx:\@addplotexponentialregression@coly\space via a,b; % Select the file
stats '#3' u \@addplotexponentialregression@colx;
plot [x=STATS_min:STATS_max] f(x); % Specify the range to plot
set print "#3-parameters.dat"; % Open a file to save the parameters
print a, b; % Write the parameters to file
};
\pgfplotstableread{#3-parameters.dat}\parameters % Open the file Gnuplot wrote
\pgfplotstablegetelem{0}{0}\of\parameters \xdef\pgfplotstableregressiona{\pgfplotsretval} % Get first element, save into \pgfplotstableregressiona
\pgfplotstablegetelem{0}{1}\of\parameters \xdef\pgfplotstableregressionb{\pgfplotsretval}
}
\makeatother
\begin{document}
%python3 -c 'import math, random; fact0 = (lambda fact0, n: n * fact0(fact0, n - 1) if n > 0 else 1); fact = (lambda n: fact0(fact0, n)); print("\n".join(f"{n:<2} {3*n*n+n+1:<10} {2*math.exp(0.5*n):<20} {2*fact(n):<15} {math.exp(n)+int(random.uniform(0,100)):<15}" for n in range(1, 12)))'
\begin{filecontents*}{data.dat}
n q e f eapprox
1 5 3.2974425414002564 2 97.71828182845904
2 15 5.43656365691809 4 101.38905609893065
3 31 8.963378140676129 12 87.08553692318768
4 53 14.7781121978613 48 92.59815003314424
5 81 24.364987921406946 240 194.4131591025766
6 115 40.171073846375336 1440 410.4287934927351
7 155 66.23090391738462 10080 1174.6331584284585
8 201 109.19630006628847 80640 3032.9579870417283
9 253 180.03426260104362 725760 8198.083927575384
10 311 296.8263182051532 7257600 22124.465794806718
11 375 489.38386452844077 79833600 59973.14171519782
\end{filecontents*}
\begin{tikzpicture}
\begin{axis}[xlabel=$x$,ylabel=$y$,legend pos=north west,axis lines=left]
\addplot[only marks,color=black] table[x=n,y=eapprox]{data.dat};
\addplotexponentialregression[no markers,black][x=n,y=eapprox]{data.dat};
\edef\gnua{\pgfplotstableregressiona}
\edef\gnub{\pgfplotstableregressionb}
\tracingcommands=1\relax
\tracingmacros=1\relax
\addplot[no markers,red,thick,smooth] table [x=n,y={create col/linear regression={y=eapprox,ymode=log}}]
{data.dat};
\edef\ra{\pgfplotstableregressiona}
\edef\rb{\pgfplotstableregressionb}
\addlegendentry{data}
\addlegendentry{
$e^{\pgfmathprintnumber{\gnua}x + \pgfmathprintnumber{\gnub}}$
}
\addlegendentry{
$e^{\pgfmathprintnumber{\ra}x + \pgfmathprintnumber{\rb}}$
}
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[xlabel=$x$,ylabel=$y$,legend pos=north west,axis lines=left,ymode=log]
\addplot[only marks,color=black] table[x=n,y=eapprox]{data.dat};
\addplotexponentialregression[no markers,black][x=n,y=eapprox]{data.dat};
\edef\gnua{\pgfplotstableregressiona}
\edef\gnub{\pgfplotstableregressionb}
\addplot[no markers,red,thick] table [x=n,y={create col/linear regression={y=eapprox,ymode=log}}]
{data.dat};
\edef\ra{\pgfplotstableregressiona}
\edef\rb{\pgfplotstableregressionb}
\addlegendentry{data}
\addlegendentry{
$e^{\pgfmathprintnumber{\gnua}x + \pgfmathprintnumber{\gnub}}$
}
\addlegendentry{
$e^{\pgfmathprintnumber{\ra}x + \pgfmathprintnumber{\rb}}$
}
\end{axis}
\end{tikzpicture}
\end{document}
which is not perfect, but is much, much better
I suspect the issue is that linear regression in log mode doesn't apply log-scaling on the variances (and thus is drastically overweighting points closer to zero), but it should. Here's a test-case: