I have recently asked a question about introducing an asinh scale in pgfplots. While the solution given in there does implement an asinh scale, when I tried to implement it in my particular case I've ran into issues with TeX's arithmetic capabilities. Here is the MWE for the plots I'm trying to make, with some sample data:
\documentclass[tikz]{standalone}
\RequirePackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepgfplotslibrary{groupplots}
\begin{filecontents*}{test.csv}
omega,fourier,taylor,difference
0.005,4.987077148249813,4.987091800330847,-0.000014652081034682851
0.01,2.462786454121935,2.4627864738907936,-1.976885855015098e-8
0.015,1.6235281489052666,1.6235281572784597,-8.373193027821912e-9
0.02,1.204952393476056,1.2049523992339104,-5.7578544154779365e-9
0.025,0.9544299006551121,0.9544299005892345,6.58776366790903e-11
0.030000000000000002,0.7878264002353925,0.7878263086975342,9.153785829330019e-8
0.034999999999999996,0.6691154984701168,0.6691154463463513,5.212376541496866e-8
0.04,0.5802997343493119,0.5802996961894273,3.815988458555353e-8
0.045,0.5113889297067079,0.5113889018372114,2.786949648836412e-8
0.049999999999999996,0.45639407396299425,0.45639405187333804,2.208965621530723e-8
0.055,0.4115071911027988,0.41150717820418004,1.2898618784173976e-8
0.06,0.37419179301714756,0.37419177612374904,1.6893398513406765e-8
0.065,0.3426932893639227,0.342693282313883,7.050039663170082e-9
0.07,0.3157594850539202,0.31575949114955054,-6.095630333824431e-9
0.07500000000000001,0.2924728846807708,0.2924728900462833,-5.3655124787610475e-9
0.08,0.27214592099214724,0.27214592236660834,-1.3744611004895546e-9
0.085,0.25425324713739395,0.2542532507717706,-3.6343766329771654e-9
0.09000000000000001,0.2383866203253262,0.23838662235094785,-2.025621642642861e-9
0.095,0.22422400057497033,0.22422400250542995,-1.930459625487657e-9
0.1,0.21150797773036173,0.21150797959795256,-1.867590831983179e-9
\end{filecontents*}
\begin{document}
\begin{tikzpicture}
\begin{groupplot}[group style={group size=1 by 2, x descriptions at=edge bottom, vertical sep=2.5ex},
axis lines = left,
minor tick num = 1,
xmajorgrids=true,
ymajorgrids=true,
legend pos=north east,
xlabel = \(\Omega\),
width = 0.9\textwidth,
xticklabel style={
/pgf/number format/fixed,
/pgf/number format/precision=5
},
scaled x ticks=false]
\nextgroupplot[height= 0.4\textwidth,ymode=log]
\addplot+[mark=none] table [x=omega,y=fourier,col sep=comma] {test.csv};
\addlegendentry{Fourier}
\addplot+[mark=none] table [x=omega,y=taylor,col sep=comma] {test.csv};
\addlegendentry{Taylor}
\nextgroupplot[height= 0.25\textwidth,]
\addplot+[mark=none] table [x=omega,y=difference,col sep=comma] {test.csv};
\addlegendentry{difference}
\end{groupplot}
\end{tikzpicture}
\end{document}
Notice that the difference column has considerable variations, both in the powers of ten associated to it and in the signs. Hence, the asinh scale seems appropriate. When I tried to implement the solution given in the question I mentioned before I did this:
\documentclass[tikz]{standalone}
\RequirePackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepgfplotslibrary{groupplots}
\usetikzlibrary{math}
\tikzmath{
function asinhinv(\x,\a){
\xa = \x / \a ;
return \a * ln(\xa + sqrt(\xa*\xa + 1)) ;
};
function asinh(\y,\a){
return \a * sinh(\y/\a) ;
};
}
\pgfplotsset{
ymode asinh/.style = {
y coord trafo/.code={\pgfmathparse{asinhinv(##1,#1)}},
y coord inv trafo/.code={\pgfmathparse{asinh(##1,#1)}},
},
ymode asinh/.default = 1
}
\begin{filecontents*}{test.csv}
omega,fourier,taylor,difference
0.005,4.987077148249813,4.987091800330847,-0.000014652081034682851
0.01,2.462786454121935,2.4627864738907936,-1.976885855015098e-8
0.015,1.6235281489052666,1.6235281572784597,-8.373193027821912e-9
0.02,1.204952393476056,1.2049523992339104,-5.7578544154779365e-9
0.025,0.9544299006551121,0.9544299005892345,6.58776366790903e-11
0.030000000000000002,0.7878264002353925,0.7878263086975342,9.153785829330019e-8
0.034999999999999996,0.6691154984701168,0.6691154463463513,5.212376541496866e-8
0.04,0.5802997343493119,0.5802996961894273,3.815988458555353e-8
0.045,0.5113889297067079,0.5113889018372114,2.786949648836412e-8
0.049999999999999996,0.45639407396299425,0.45639405187333804,2.208965621530723e-8
0.055,0.4115071911027988,0.41150717820418004,1.2898618784173976e-8
0.06,0.37419179301714756,0.37419177612374904,1.6893398513406765e-8
0.065,0.3426932893639227,0.342693282313883,7.050039663170082e-9
0.07,0.3157594850539202,0.31575949114955054,-6.095630333824431e-9
0.07500000000000001,0.2924728846807708,0.2924728900462833,-5.3655124787610475e-9
0.08,0.27214592099214724,0.27214592236660834,-1.3744611004895546e-9
0.085,0.25425324713739395,0.2542532507717706,-3.6343766329771654e-9
0.09000000000000001,0.2383866203253262,0.23838662235094785,-2.025621642642861e-9
0.095,0.22422400057497033,0.22422400250542995,-1.930459625487657e-9
0.1,0.21150797773036173,0.21150797959795256,-1.867590831983179e-9
\end{filecontents*}
\begin{document}
\begin{tikzpicture}
\begin{groupplot}[group style={group size=1 by 2, x descriptions at=edge bottom, vertical sep=2.5ex},
axis lines = left,
minor tick num = 1,
xmajorgrids=true,
ymajorgrids=true,
legend pos=north east,
xlabel = \(\Omega\),
width = 0.9\textwidth,
xticklabel style={
/pgf/number format/fixed,
/pgf/number format/precision=5
},
scaled x ticks=false]
\nextgroupplot[height= 0.4\textwidth,ymode=log]
\addplot+[mark=none] table [x=omega,y=fourier,col sep=comma] {test.csv};
\addlegendentry{Fourier}
\addplot+[mark=none] table [x=omega,y=taylor,col sep=comma] {test.csv};
\addlegendentry{Taylor}
\nextgroupplot[height= 0.25\textwidth,ymode asinh=1e-9]
\addplot+[mark=none] table [x=omega,y=difference,col sep=comma] {test.csv};
\addlegendentry{difference}
\end{groupplot}
\end{tikzpicture}
\end{document}
which gave the result
alongside some complaints from LaTeX about arithmetic overflow. I guess 1e-9 might be quite a small number for TeX's capabilities. Is there any way of bypassing this issue?
I'm running TeX Live 2019 (hence the compat=1.16 in pgfplots) and compiling with LuaTeX, so solutions that exploit lua are welcome.
