[Tex/LaTex] Plotting error Bars in PGF plots

pgfplots

I want to plot error bars in PGFplots using the following Latex code but its not showing any error neither the error bars.

I know I should mention the error values explicitly but what if i do not want to calculate errors (standard deviation) of every point manually.

Any help regarding this would be highly appreciated. Thanks.

\documentclass[conference]{IEEEtran}
\ifCLASSINFOpdf
\else
\fi
\hyphenation{op-tical net-works semi-conduc-tor}
\usepackage[pdftex]{graphics}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepgfplotslibrary{dateplot}
\usepgfplotslibrary{patchplots}
\pgfplotsset{compat=1.7}



\pgfplotsset{footnotesize,samples=10}
\begin{figure}[t]
\centering
\begin{tikzpicture}
\begin{axis}[ % The height and width argument only apply to the actual axis
title style={at={(0.3,0.2)},anchor=north,yshift=-0.1},
title =\textbf{Correlation= 0.672658953},
height=5cm,
width=8cm,
legend style={at={(0.5,1.3)},anchor=north},
ylabel={PDR},
xlabel={LQI},
xmin=85, xmax=120,
ymin=80, ymax=100,
xtick= {85,90,95,100,105,110,115,120},
ytick= {80,85,90,95,100},
legend columns=4,
ymajorgrids=true,
grid style=dashed,
]
\addplot[
mark=o,
mark size=1.4pt,
only marks,
]
plot [error bars/.cd, y dir = both, y explicit]
coordinates {
(104,   97)(98  ,97)(105,   98)(103,    97)(104,    98)(85  ,80)(91 ,86)(103,   97)(105,    98)
};
%\label{plot_two}
%\addlegendentry{id-05m-hor}

\addplot[
mark size=1.4pt,
only marks,
mark=o,
]
plot [error bars/.cd, y dir = both, y explicit]
coordinates {
(107,   100)(106,   100)(106,   99)(106,    99)(106,    99)(120,    97)(102,    95)(104,    97)(105,    98)
};
%\addlegendentry{id-05m-ver}

\addplot[
mark=o,
mark size=1.4pt,
only marks,
]
plot [error bars/.cd, y dir = both, y explicit]
coordinates {
(106,   98)(106,    98)(107,    99)(106,    98)(104,    86)(103,    97)(104,    98)(105,    99)(105,    97)
};
%\addlegendentry{id-15m-hor}
\addplot[
mark=o,
mark size=1.4pt,
only marks,
]
plot [error bars/.cd, y dir = both, y explicit]
coordinates {
(104,   97)(106,    99)(105,    98)(106,    98)(104,    98)(105,    98)(105,    98)(104,    98)(105,    88)
};
%\addlegendentry{id-15m-ver}
\addplot[
mark=o,
mark size=1.4pt,
only marks,
]
plot [error bars/.cd, y dir = both, y explicit]
coordinates {
(107,   97)(107,    95)(107,    90)(106,    96)(107,    97)(106,    96)(106,    97)(106,    96)(106,    96)(107,    55)(106,    97)(107,    96)
};
%\label{plot_two}
%\addlegendentry{od-05m-hor}
\addplot[
mark=o,
mark size=1.4pt,
only marks,
]
plot [error bars/.cd, y dir = both, y explicit]
coordinates {
(106,97)(106,97)(107,97)(107,95)(107,97)(107,97)(106,97)(107,95)(105,96)(107,97)(106,97)(107,97)
};
%\addlegendentry{od-05m-ver}

\addplot[
mark=o,
mark size=1.4pt,
only marks,
]
plot [error bars/.cd, y dir = both, y explicit]
coordinates {
(107,98)(107,97)(107,97)(106,97)(106,97)(106,97)(106,99)(107,99)(106,97)(104,99)(106,98)(106,49)
};
%\addlegendentry{od-15m-hor}
\addplot[
mark=*,
mark size=1.4pt,
only marks,
]
plot [error bars/.cd, y dir = both, y explicit]
coordinates {
(106,94)(107,97)(106,96)(107,97)(106,97)(106,97)(107,98)(107,96)(106,100)(102,96)(106,97)(106,99)
};
%\addlegendentry{od-15m-ver}

\end{axis}
\end{tikzpicture}
\end{figure}

Best Answer

Have a look at section 4.12 Error bars in the pgfplots manual.

When you say y explicit, you need to specify the error value for each point separately in the coordinate stream. For example

(107,100) +- (0,2)

indicates a y-error of 2 and x-error of 0. You must specify both I think, even if you only use the y-error.

But if you want to use the same error value for all the points in a plot, you can use y fixed=<value> instead of y explicit. For example,

\addplot+ [
   error bars/.cd,
   y dir=both,
   y fixed=1
] ...

gives you a y-error of 1 for all the points in the plot. But I don't think there is a built-in way of getting e.g. standard deviation of the plotted data, so if that is what you're after you need to calculate it first, and then use y fixed with the calculated value.

Unrelated comment:

Why do you use this?

\addplot [<some options>] plot[<other options>] ...

You're mixing pgfplots syntax with plain TikZ syntax, the correct would by to have all the options in the same set of brackets, and not use the plot keyword, i.e.

\addplot [<all options>] ...

ROOT data export

Before, I generated the scatter plot values via ROOT's Python bindings as:

import csv

def th2f_to_csv(hist, csv_file):
    """Print TH2F bin data to CSV file."""
    xbins, ybins = hist.GetNbinsX(), hist.GetNbinsY()
    xaxis, yaxis = hist.GetXaxis(), hist.GetYaxis()
    with open(csv_file, 'w') as f:
        c = csv.writer(f, delimiter=' ', lineterminator='\n')
        for xbin in xrange(xbins+2):
            xcenter = xaxis.GetBinCenter(xbin)
            for ybin in xrange(ybins+2):
                ycenter = yaxis.GetBinCenter(ybin)
                weight = hist.GetBinContent(xbin, ybin)
                if weight > 0:
                    c.writerow((xcenter, ycenter, weight))

The input argument hist is a TH2F object. See the ROOT and PyROOT documentation for more information.

The "+2" in xrange handles that ROOT saves an underflow and an overflow bin on top of the bins that are actually drawn. I at this stage explicitly threw out the points with no content to keep the "scatter plot" in PGFPlots clean.

But now I instead want to output a complete matrix, which I did as follows:

import csv

def th2f_to_csv(hist, csv_file):
    """Print TH2F bin data to CSV file."""
    xbins, ybins = hist.GetNbinsX(), hist.GetNbinsY()
    xaxis, yaxis = hist.GetXaxis(), hist.GetYaxis()
    with open(csv_file, 'w') as f:
        c = csv.writer(f, delimiter=' ', lineterminator='\n')
        for ybin in xrange(1, ybins+2):
            y_lowedge = yaxis.GetBinLowEdge(ybin)
            for xbin in xrange(1, xbins+2):
                x_lowedge = xaxis.GetBinLowEdge(xbin)
                weight = hist.GetBinContent(xbin, ybin)
                c.writerow((x_lowedge, y_lowedge, weight))

I now discard the underflow bin by starting the range from 1, and I also discard the overflow bin, since the last bin will not be shown when choosing shader=flat corner in PFDPlots later. I could have just given a dummy value instead of the actual overflow value, but it does not matter (EDIT: actually, it might matter if the overflow value is larger/smaller than the maximum/minimum "real" value — it would then affect the color map scale, so beware).

Instead of extracting the center of the bins, I now am interested in the lower bin edges.

I also change the order of the x and y loops to get the matrix data in a form that PGFPlots processes more efficiently, as described in section 7.2.1 in the manual: "Importing Mesh Data From Matlab To PGFPlots". This made a noticeable difference in compilation time.

Working examples

Now that I have the matrix, a minimal working example of plotting this data (matrix.csv) as a 2D histogram was:

\documentclass{article}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}

\begin{tikzpicture}
  \begin{axis}[
    view={0}{90},
    colorbar,
  ]
    \addplot3[
      surf,
      shader=flat corner,
      mesh/cols=51,
      mesh/ordering=rowwise,
    ] file {matrix.csv};
  \end{axis}
\end{tikzpicture}

\end{document}

Minimum working example.

Section 7.2.1 in the manual and the earlier linked question explains the parameters. mesh/cols=51 comes from the known fact that the histogram contains 50 horizontal bins, and the extra one accounts for the "dummy bin" mentioned in the above linked TeX.SE question. The bin count could be output to a CSV specific configuration file along with the data if more automation is needed.

One issue was that the compiler (xelatex in this case) threw exactly 5000 rows to the terminal with content:

pgfplotsplothandlermesh@get@flat@color

There should be 50⨯100 = 5000 "cells" to be rendered in total in the image. This excess of messages might be a bug in itself, or something that I could have suppressed in some way.

Another issue is that the "background", i.e. the parts of the graph that represents value zero, is colored in, which is not optimal. The most obvious solution to this I found was to create a color map that "began" at white, which makes sense for these types of graphs anyway.

Along with some minor other formatting fixes, this gave the following result:

\documentclass{article}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepackage{siunitx}

\begin{document}

\pgfplotsset{
  /pgfplots/colormap={coldredux}{
    [1cm]
    rgb255(0cm)=(255,255,255)
    rgb255(2cm)=(0,192,255)
    rgb255(4cm)=(0,0,255)
    rgb255(6cm)=(0,0,0)
  }
}

\begin{tikzpicture}
  \begin{axis}[
    view={0}{90},
    xlabel={$\theta$ /degrees},
    ylabel={Energy /\si{\MeV}},
    minor tick num=4,
    colorbar,
    colorbar style={ylabel={Counts}},
  ]
    \addplot3[
      surf,
      shader=flat corner,
      mesh/cols=51,
      mesh/ordering=rowwise,
      x filter/.code={\pgfmathparse{#1*180}\pgfmathresult},
      y filter/.code={\pgfmathparse{#1/1000}\pgfmathresult},
    ] file {matrix.csv};
  \end{axis}
\end{tikzpicture}

\end{document}

Graphically updated version of histogram.

I will implement the x filter and y filter transformations in the analysis stage instead of the plotting stage.

Probably not a finished "product" yet, but now I can apply styling freely, and it is produced with a definitely manageable amount of code.

Best Answer

Related Solutions

[Tex/LaTex] pgfplots: Points with no marks but errorbars

[Tex/LaTex] Building a 2D histogram with PGFPlots

ROOT data export

Working examples

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