Error message: Dimension too large

Question

I am graphing the restriction of a cubic function on the domain [0, 20]. The function has a maximum value of about 3,079 at about 11.5. To get some view of it, I use the specification unit vector ratio={1 100}. PgfPlots gives me the error message "Dimension too large." How do I get this to plot?

\documentclass[10pt]{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}

\begin{tikzpicture}
\begin{axis}[width=6in,axis equal image,unit vector ratio={1 100},clip=false,
    axis lines=middle,
    xmin=-2,xmax=20,
    domain=-2:0.5,
    xlabel=$x$,ylabel=$y$,
    ymin=-100,ymax=3000,
    restrict y to domain=-100:3000,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={},ytick={},
    extra x ticks={11.547},
    extra x tick labels={$20/\sqrt{3}$},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]
\addplot[samples=501,domain=-2:20,blue] {400*x - x^3};
\end{axis}
\end{tikzpicture}


\end{document}

Answer 1

Using all three of these:

• width=6in
• axis equal image
• unit vector ratio={1 100}

makes no sense. Most of what axis equal image does is to set unit vector ratio={1 1} which you immediately override with the other setting. The only other thing it does is to shrink the axis box to fit the axis min and max values at the specified unit vector ratio, which renders the width key setting totally impossible to reach because of the selected unit vector ratio.

Just let pgfplots do its job (use the width and height keys) and everything works fine. Here's a truly minimal example of that at work¹:

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    samples=100,
    width=6in,
    height=4in, % or whatever height you want
%    axis equal image,
%    unit vector ratio={1 250},
  ]
    \addplot[domain=-2:20] {400*x - x^3};
  \end{axis}
\end{tikzpicture}
\end{document}

¹: I've said this before, and I'll say it again: putting all of the excess styling code in all of your questions just makes them harder to read and understand what you're after. Please, make some effort to determine what is actually needed to show the problem you want to solve, before just posting all of it.

As I've also mentioned before, you are fighting pgfplots tooth and nail to get the axes to look the way you want, while at the same time, the functions/other things you are plotting don't really need the advanced capabilities of pgfplots. If you really want this level of control over things pgfplots tries so hard to hide from you (axis scaling, in this instance), you may find it easier to work in tikz directly, without involving pgfplots. Here's some code that gives the output you're after without having to fight pgfplots' default styling/scaling:

\documentclass[tikz]{standalone}
\tikzset{
  axisline/.style={latex-latex},
  tickmark/.style={gray},
  ticklabel/.style={font=\tiny,fill=white,text=black},
}

\begin{document}
\begin{tikzpicture}[x=0.25in,y=0.001in]
  \foreach \y in {500,1000,...,3000} {% y-ticks
    \draw[tickmark] (2pt,\y) -- ++(-4pt,0) % draw the tick mark
      node[left,ticklabel] {$\pgfmathprintnumber{\y}$}; % label it
  }
  \foreach \x in {-2,2,4,...,20} {% x-ticks
    \draw[tickmark] (\x,2pt) -- ++(0,-4pt) % draw the tick mark
      node[below,ticklabel] {$\pgfmathprintnumber{\x}$}; % label it
  }
  \draw[tickmark] (11.547,2pt) -- ++(0,-4pt) % an extra x tick
    node[below,ticklabel] {$20/\sqrt{3}$}; % its label
  \draw[axisline] (0,3000) +(0,0.5cm) node[above right] {$y$} -- (0,-100) -- +(0,-0.5cm); % the y-axis
  \draw[axisline] (-2,0) +(-0.5cm,0) -- (20,0) -- +(0.5cm,0) node[below right] {$x$}; % the x-axis
  \begin{scope}
    \clip (-2.1,-100) rectangle (20.1,3000); % "restrict y to domain"
    \draw[blue,domain=-2:20,samples=100] plot (\x,400*\x - \x^3);
  \end{scope}
\end{tikzpicture}
\end{document}