Is there an easy way of using line thickness as error indicator in a plot?

Question

I have several curves/datasets (obtained from Monte Carlo simulations) with x-dependent y errors I would like to plot with the errors somehow indicated. Since each curve consists of quite a large number of data points with rather small errors, using ordinary errorbars doesn't seem to be the most informative/aestethic solution. Instead, I think it would be nicer to indicate the error by (local) line thickness (or thickness in the y-direction). It could e.g. be done by plotting y(x)+dy(x) and y(x)-dy(x) and fill between the two curves. But how does one do that (in a reasonably easy way - remember: I have several curves!) in Pgfplots?

My question is maybe somewhat similar to this one, but I don't know how to do the table manipulations (within Pgfplots) needed in my case.

Here's a simplified example of how my datafiles look:

x y dy
0 2 0.1
1 4 0.5
2 3 0.2
3 3 0.3

Answer 1

You can use stacked plots to draw the uncertainty bands before plotting the actual data line. First you'd say \addplot table [y expr=\thisrow{<data col>}-\thisrow{<error col}] {<datatable>}; to determine the lower bound, and then \addplot [fill=<colour>] table [y expr=2*\thisrow{<error col}] {<datatable>} \closedcycle; to fill the area between the lower and upper bound.

You can wrap these two \addplot commands in a macro to make generating the plots easier. If you define

\newcommand{\errorband}[5][]{ % x column, y column, error column, optional argument for setting style of the area plot
\pgfplotstableread[col sep=comma, skip first n=2]{#2}\datatable
    % Lower bound (invisible plot)
    \addplot [draw=none, stack plots=y, forget plot] table [
        x={#3},
        y expr=\thisrow{#4}-\thisrow{#5}
    ] {\datatable};

    % Stack twice the error, draw as area plot
    \addplot [draw=none, fill=gray!40, stack plots=y, area legend, #1] table [
        x={#3},
        y expr=2*\thisrow{#5}
    ] {\datatable} \closedcycle;

    % Reset stack using invisible plot
    \addplot [forget plot, stack plots=y,draw=none] table [x={#3}, y expr=-(\thisrow{#4}+\thisrow{#5})] {\datatable};
}

you can generate a plot with an error band using

\errorband[<plot options>]{<data file>}{<x column>}{<y column>}{<error column>}

Here's an example plotting the average northern hemisphere sea ice extent according to the NSIDC:

\documentclass{article}
\usepackage{pgfplots, pgfplotstable}


\begin{document}

\newcommand{\errorband}[5][]{ % x column, y column, error column, optional argument for setting style of the area plot
\pgfplotstableread[col sep=comma, skip first n=2]{#2}\datatable
    % Lower bound (invisible plot)
    \addplot [draw=none, stack plots=y, forget plot] table [
        x={#3},
        y expr=\thisrow{#4}-2*\thisrow{#5}
    ] {\datatable};

    % Stack twice the error, draw as area plot
    \addplot [draw=none, fill=gray!40, stack plots=y, area legend, #1] table [
        x={#3},
        y expr=4*\thisrow{#5}
    ] {\datatable} \closedcycle;

    % Reset stack using invisible plot
    \addplot [forget plot, stack plots=y,draw=none] table [x={#3}, y expr=-(\thisrow{#4}+2*\thisrow{#5})] {\datatable};
}




\begin{tikzpicture}
\begin{axis}[
    compat=1.5.1,
    no markers,
    enlarge x limits=false,
    ymin=0,
    xlabel=Day of the Year,
    ylabel=Sea Ice Extent\quad/\quad $10^6\,\mathrm{km}^2$,
    legend entries={
        $\pm$ 2 Standard Deviation,
        NH 1997 to 2000 Average,
        $\pm$ 2 Standard Deviation,
        SH 1997 to 2000 Average,
        NH 2012,
        SH 2012
    },
    legend reversed,
    legend pos=outer north east,
    legend cell align=left,
    x post scale=1.2
]

% Northern Hemisphere Average
\errorband[orange, opacity=0.5]{NH_seaice_extent_climatology_1979-2000.csv}{0}{3}{4}

% Northern Hemisphere 2012
\addplot [thick, orange!50!black] table [
    x index=0,
    y index=3,
    skip first n=2,
    col sep=comma,
] {NH_seaice_extent_climatology_1979-2000.csv};

% Southern Hemisphere Average
\errorband[cyan, opacity=0.5]{SH_seaice_extent_climatology_1979-2000.csv}{0}{3}{4}


% Southern Hemisphere 2012
\addplot [thick, cyan!50!black] table [
    x index=0,
    y index=3,
    skip first n=2,
    col sep=comma,
] {SH_seaice_extent_climatology_1979-2000.csv};




\addplot [ultra thick,red] table [
    col sep=comma,
    skip first n=367,
    x expr=\coordindex,
    y index=3
] {NH_seaice_extent_nrt.csv};

\addplot [ultra thick,blue] table [
    col sep=comma,
    skip first n=367,
    x expr=\coordindex,
    y index=3
] {SH_seaice_extent_nrt.csv};
%

\end{axis}
\end{tikzpicture}


\end{document}

Answer 2

You can use a mesh plot with varying line width. However, this causes unsmooth transitions from one line segment to the next. But perhaps it is feasible:

in case you have smaller data sets, markers can hide the transitions:

Here is the code:

\documentclass{standalone}

\usepackage{pgfplots}

\pgfplotsset{compat=1.5}

\begin{document}

\begin{tikzpicture}
% avoid false-positive compilation errors:
\def\pgfplotspointmetatransformed{1000}

    \begin{axis}[ymin=0,ymax=10]
    \addplot+[
        mesh,
        blue,
        %no marks,
        every mark/.append style={line width=1pt,mark size=4pt,fill=blue!80!black},
        shader=flat corner,
        line width=1pt+5pt*\pgfplotspointmetatransformed/1000
    ] 
    table[point meta=\thisrow{dy}] {
    x y dy
    0 2 0.1
    1 4 0.5
    2 3 0.2
    3 3 0.3
    };
    \end{axis}
\end{tikzpicture}
\end{document}

The key idea is that (a) a mesh plot draws individual line segments and (b) \pgfplotspointmetatransformed contains the point meta data in a fully normalized way: the smallest meta data entry (0.1 here) gets \pgfplotspointmetatransformed=0 and the largest one (0.5 here) gets \pgfplotspointmetatransformed=1000. The values in-between are interpolated linearly. Consequently, we can safely use them for line width as above.

Note that the options are evaluated in contexts where this point meta macro is unavailable. To this end, I defined it as 1000 globally (which should be fine for these contexts).