Rescaling ticks

Question

I have created a simple 2D plot from a table (xy-data) and now I would like to both translate and scale the x-axis. (I would prefer not to scale the actual data only the axis).

As an example, let's say the x-values runs between (a,b) and I now want them to be between (0,1) instead. How would I go about doing this? I have found an example on how to subtract a constant but I cannot get it to work with multiplication. Any help would be much appreciated.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}

\begin{tikzpicture}
\begin{axis}[scaled x ticks=manual:{}{% 
\pgfmathfloatcreate{1}{6.0}{0}%
\pgfmathfloatsubtract{#1}{\pgfmathresult}%
}] 
\addplot coordinates {
(6, 2)
(8, 3)
};
\end{axis} 
\end{tikzpicture}

\end{document}

Answer 1

You can do the subtraction and division in one command, using scaled x ticks=manual:{}{\pgfmathparse{ (#1 - 6) / 2 } }.

If you want to make this a bit more comfortable, you can define a new style using

\pgfplotsset{
    normalise/.style 2 args={
        scaled x ticks=manual:{}{% 
            \pgfmathparse{ ( ##1 - (#1) ) / (#2 - #1) }%
        }
    }
}

You can then call normalise={<lower>}{<upper>} in the axis options to normalise the ticks.

Note that this only scales each tick label, which means you might end up with unelegant tick positions (try normalising between 6 and 9).

I would recommend to normalise the coordinates themselves instead. You can do this using x filter/.code instead of scaled x ticks. This will alter the coordinates themselves, instead of just the tick labels. This means that the algorithm that determines which tick positions to display can work with the scaled coordinates, which will usually yield better results:

\documentclass{article}

\usepackage{pgfplots}
\begin{document}

\begin{tikzpicture}

\pgfplotsset{
    normalise/.style 2 args={
        x filter/.code={% 
            \pgfmathparse{ ( ##1 - (#1) ) / (#2 - #1) }%
        }
    }
}

\begin{axis}[
    normalise={6}{9}
] 
\addplot coordinates {
    (6, 2)
    (8, 3)
    (9,1)
};
\end{axis} 
\end{tikzpicture}

\end{document}

---

For comparison, here's the output you'd get if you used scaled x ticks instead. Note that there are seven tick labels instead of 6:

Answer 2

I think normalization is quite easier, but you can set and name the ticks manually for example for a range from a to e, [a:e]:

\begin{axis}[xtick={a,b,c,d,e},
             xticklabels={0, 0.25, 0.5, 0.75, 1},
            ]