PGFPlots: Mathematical expressions

Question

Question

Is there a way to include mathematical expressions in PGFPlots, for example, [domain=1/3:e^5/3]?

PGFPlots is fairly useful, however the ability to put mathematical expressions directly into Tikz makes life much easier.

The only way around this problem that I know of is to define a bunch of constants above the before entering the axis environment. I find this a little obnoxious.

MWE

\documentclass{memoir}

\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{amsmath}

\usetikzlibrary{calc, positioning}

\begin{document}

\begin{tikzpicture}[domain=1/3:e^5/3,x=0.1cm, scale=1]

    % Axes
    \draw[help lines]   (-0.2 cm,0) -- (e^5/3+0.2,0) node[right] {$x$};
    \draw[help lines]   (0,-0.2) -- (0,6) node[above] {$y$};
    \draw[gray, thick]  (e^5/3,5) -- (-0.075/0.1,5) node[left] {$y=5$};
    \draw[gray, thick]  (e^5/3,4) -- (-0.075/0.1,4) node[left] {$y=4$};

    % Curves
    \draw[blue, thick] plot[id=lnx] (\x,{ln(3*\x)}) node[right] {$\ln 3x$};
\end{tikzpicture}

\end{document}

Answer 1

You can define a slightly modified version of the domain key to save yourself the trouble of manually parsing the expressions first. If you include the following snippet in your document, you'll be able to type domain*=1/3:e^5/3 even when you're using logarithmic axes (and similarly for xmin, ymax, etc.):

\makeatletter
\pgfplotsset{
    domain*/.code args={#1:#2}{
        \pgfmathsetmacro\pgfplots@lower{#1}
        \pgfmathsetmacro\pgfplots@upper{#2}
        \pgfplotsset{domain=\pgfplots@lower:\pgfplots@upper}
    },
    xmin*/.code={
        \pgfmathparse{#1}
        \pgfplotsset{xmin=\pgfmathresult}
    },
    xmax*/.code={
        \pgfmathparse{#1}
        \pgfplotsset{xmax=\pgfmathresult}
    },  
    ymin*/.code={
        \pgfmathparse{#1}
        \pgfplotsset{ymin=\pgfmathresult}
    },
    ymax*/.code={
        \pgfmathparse{#1}
        \pgfplotsset{ymax=\pgfmathresult}
    }
}
\makeatother

Your plot could be implemented in PGFPlots using something like this:

\documentclass{memoir}

\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{amsmath}

\usetikzlibrary{calc, positioning}

\begin{document}

\makeatletter
\pgfplotsset{
    domain*/.code args={#1:#2}{
        \pgfmathsetmacro\pgfplots@lower{#1}
        \pgfmathsetmacro\pgfplots@upper{#2}
        \pgfplotsset{domain=\pgfplots@lower:\pgfplots@upper}
    }
}
\makeatother

\begin{tikzpicture}
\begin{axis}[
    xmode=log,
    log ticks with fixed point,
    axis lines*=left,
    xlabel=$x$,
    every axis x label/.style={
        at={(rel axis cs:1,0)},
        anchor=west
    },
    ylabel=$y$,
    every axis y label/.style={
        at={(rel axis cs:0,1)},
        anchor=south
    },
    ymin=0,
    xmin=0.1,
    enlarge x limits=false,
    domain*=1/3:e^5/3,
    ytick={0,4,5},
    ymajorgrids,
    yticklabel={$y = \pgfmathprintnumber{\tick}$},
    clip=false
]
\addplot [thick, red] {ln(3*x)} node [anchor=west] {$\ln 3x$};
\end{axis}
\end{tikzpicture}

\end{document}

Answer 2

Pgfplot Workaround

As an answer, here's the Pgfplot workaround I mentioned, which defines variables using \pgfmathsetmacro before the axis environment. The advantage of this workaround is that it is extremely easy to understand and can be reused easily for similar graphs, which is useful for Calculus 1–3-level homework problems.

MWE

\documentclass{memoir}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\usepackage{amsmath}

\usetikzlibrary{calc, positioning}

\begin{document}

\begin{tikzpicture}[scale=1.5]

\pgfmathsetmacro\xDomainMin{0}
\pgfmathsetmacro\xDomainMax{e^5/3*3}
\pgfmathsetmacro\xMin{-10}
\pgfmathsetmacro\xMax{\xDomainMax+\xDomainMax/50}
\pgfmathsetmacro\yMin{-1}
\pgfmathsetmacro\yMax{6}
\pgfmathsetmacro\xRotation{(e^5/3+5)/2}
\pgfmathsetmacro\yRotation{0}

\begin{semilogyaxis}[    
    axis x line=center,
    axis y line=center,
    axis z line=center,
    xlabel={$x$},
    ylabel={$y$},
    zlabel={$z$},
    axis line style=help lines,
    gray,
    every axis/.append style={font=\tiny},
    width=10cm,
    height=8cm,
    domain=\xDomainMin:\xDomainMax,
    xmin=\xMin, xmax=\xMax,
    ymin=\yMin, ymax=\yMax,
    xtick=\empty,
    ytick={4,5},
    yticklabels={$y=4$,$y=5$},
    area style,
]
    \addplot[id=five, gray, very thin, fill=blue, opacity=0.1] {5} \closedcycle;
    \addplot[id=lnx, white, very thin, mark=none, samples=200, fill=white,]
        {ln(3*x)}\closedcycle;
    \addplot[id=four, gray, very thin, fill=white] {4} \closedcycle;
    \addplot[id=five, gray, very thin,] {5};
    \addplot[id=five, white, very thin, fill=white,
            domain=\xDomainMax-0.1:\xDomainMax+1] {5} \closedcycle;
\addplot[id=lnx, blue, very thin, mark=none, samples=200,]
        {ln(3*x)} node [right]{\color{blue}$\ln x$};

\draw[->,gray, thick]
    (axis cs:6,4.5) arc (-30:-150:8 pt);


\end{semilogyaxis}

\end{tikzpicture}

\end{document}