# Transform x coords, then set x limits

I'm trying to reproduce the following pyplot figure with pgfplots:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 1)
plt.plot(np.log(x)-np.log(1-x), np.log(x / (x + (1-x))))
plt.xlim(-3, 3)
plt.show()


My attempt so far with pgfplots, using x coord trafo:

\documentclass[tikz,12pt,preview]{standalone}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=1.13}

\begin{document}

\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
mark=none,domain=0:1,samples=200},
x coord trafo/.code={\pgfmathparse{log10(#1) - log10(1-#1)}},
]
\addplot {log10(x / (x + (1-x)))};
\end{axis}
\end{tikzpicture}

\end{document}


I think I'm close, but am unable to set xlim to (-3, 3). I think I'm thinking too much in a pyplot manner! Is there an elegant way to achieve this?

• I don't know pyplot, but are you searching for xmin and xmax? – Stefan Pinnow Jul 29 at 18:36

Hopefully everything is stated in the comments of the code ...

% used PGFPlots v1.16
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
% set the x axis limits
% (for details see also the comment before \addplot)
xmin=-3,xmax=3,
%        % commented no markers to show that default sample rate is
%        % sufficient when the domain is adapted accordingly
%        no markers,
% because at x = 0 and x = 1 the values are not defined
% I adopted the values a bit
domain=0.001:0.999,
%        % because after adopting the domain the first and last point
%        % aren't "skipped" there should be no need for such a high sample rate
%        samples=51,
% added smooth just in case the samples are to less
smooth,
]
% instead of using x coord trafo just plot a parametric plot
% (as I assume you did in pyplot)
% this allows to easily set xmin and xmax
% (if you would stick to x coord trafo you would need to know
%  the *untransformed* x values which correspond to the
%  transformed values of -3 and 3 and state them in xmin and xmax)
{log10(x) - log10(1-x)},
{log10(x / (x + (1-x)))}
);
\end{axis}
\end{tikzpicture}
\end{document} • Thanks Stefan! Oddly I did not realise I could do a parametric plot...! Thanks very much for the comments in the code. – jodles Jul 29 at 19:43

Why don't you use a parametric plot?

\documentclass[tikz,12pt,preview]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}

\begin{document}

\begin{tikzpicture}
\begin{axis}[domain=0.0:1,samples=200,]
\addplot[thick, blue] ({log10(x)-log10(1-x)}, {log10(x / (x + (1-x)))});
\end{axis}
\end{tikzpicture}

\end{document} • Thanks Rmano! It baffles me that I did not realise I could use a parametric plot... – jodles Jul 29 at 19:45