pgfplots memory error due to specific xmax limit

Question

I am facing a problem with setting the limits of my plot in pgfplots. The following script (from an answer here )

\documentclass[border=5mm]{standalone}
\usepackage{pgfplotstable}

\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro{\XMax}{1.1e-3} %changing this to 1.05e-3 gives error
\pgfmathsetmacro{\XMin}{0.95e-3}
\begin{axis}[
  xmin=\XMin,
  xmax=\XMax
]
\pgfplotstableread{
x y dydx
0.96e-3 2 1
0.98e-3 1 -1
0.99e-3 3 0.5
}\mydata
% get number of rows in table
% subtract 1 because row indexing starts at zero
\pgfplotstablegetrowsof{\mydata}
\pgfmathtruncatemacro{\NumRows}{\pgfplotsretval-1}
\pgfmathsetmacro{\AxRange}{\XMax-\XMin}

\pgfplotsinvokeforeach{0,...,\NumRows}{ % loop over rows

  % extract the data from the table
  \pgfplotstablegetelem{#1}{x}\of\mydata
  \pgfmathsetmacro{\X}{\pgfplotsretval}
  \pgfplotstablegetelem{#1}{y}\of\mydata
  \pgfmathsetmacro{\Y}{\pgfplotsretval}
  \pgfplotstablegetelem{#1}{dydx}\of\mydata
  \pgfmathsetmacro{\DYDX}{\pgfplotsretval}

  % calculate start and end of domain for line
  \pgfmathsetmacro{\DomainStart}{\X-\AxRange*0.1}
  \pgfmathsetmacro{\DomainEnd}{\X+\AxRange*0.1}

  % plot
  \addplot +[domain=\DomainStart:\DomainEnd,mark=none,thick,samples=2] {\Y + \DYDX * (x-\X)};
}

\end{axis}
\end{tikzpicture}
\end{document}

creates the following figure.

But changing the value of Xmax to 1.05e-3 gives the following error.

Package pgfplots Warning: running in backwards compatibility mode (unsuitable tick labels; missing features). Consider writing \pgfplotsset{compat=1.14} into your preamble.
 on input line 4.

Runaway definition?
->
./a.tex:40: TeX capacity exceeded, sorry [main memory size=5000000].
\pgfplotsapplistXXpushback@smallbufoverfl ...toka 
                                                  \the \t@pgfplots@tokb \the...
l.40 }

./a.tex:40:  ==> Fatal error occurred, no output PDF file produced!
Transcript written on /Users/manav/Desktop/.texpadtmp/a.log.

Why would the output be so sensitive to the xmax limit? Is there anything that can be done to force this limit without running into the error?

Answer 1

It happens that one runs into such problems with pgf, as the numerical capabilities are a bit limited. Just like in Why tikz fail at computation?, it seems that using \fpeval from the xfp package to do the calculations works here as well. I used that also to calculate the y-values of the endpoints of the lines, and used \addplot coordinates to plot the lines. This works with a smaller range as well, here with xmax=1.0e-3.

%%%%%%%%
%% the following only for example
\RequirePackage{filecontents}
% the filecontents environment writes its content to the specified file
\begin{filecontents*}{data.dat}
x y dydx
0.96e-3 2 1
0.98e-3 1 -1
0.99e-3 3 0.5
\end{filecontents*}
%%%%%%%

\documentclass[border=5mm]{standalone}
\usepackage{pgfplotstable}
\usepackage{xfp}
\begin{document}
\begin{tikzpicture}
\pgfplotstableread{data.dat}\mydata
% get number of rows in table
% subtract 1 because row indexing starts at zero
\pgfplotstablegetrowsof{\mydata}
\pgfmathtruncatemacro{\NumRows}{\pgfplotsretval-1}

\begin{axis}[
  xmin=0.95e-3,
  xmax=1.0e-3,
  samples=2
]

\edef\AxRange{\fpeval{\pgfkeysvalueof{/pgfplots/xmax}-\pgfkeysvalueof{/pgfplots/xmin}}}

\pgfplotsinvokeforeach{0,...,\NumRows}{ % loop over rows

  % extract the data from the table
  \pgfplotstablegetelem{#1}{x}\of\mydata
  \pgfmathsetmacro{\X}{\pgfplotsretval}
  \pgfplotstablegetelem{#1}{y}\of\mydata
  \pgfmathsetmacro{\Y}{\pgfplotsretval}
  \pgfplotstablegetelem{#1}{dydx}\of\mydata
  \pgfmathsetmacro{\DYDX}{\pgfplotsretval}

  % calculate start and end of domain for line
  \edef\XStart{\fpeval{\X-\AxRange*0.1}}
  \edef\XEnd{\fpeval{\X+\AxRange*0.1}}
  % calculate start and end y-values of line
  \edef\YStart{\fpeval{\Y + \DYDX * (\XStart-\X)}}
  \edef\YEnd{\fpeval{\Y + \DYDX * (\XEnd-\X)}}

  % plot
  \addplot +[mark=none,thick] coordinates {(\XStart, \YStart) (\XEnd, \YEnd)};
}

\end{axis}
\end{tikzpicture}
\end{document}