[Tex/LaTex] Histogram with overlaying Gauss curve (pgfplots)

pgfplots

I am struggling to create a histogram with an overlaying normal (Gauss) curve using PGFplots. To be more specific, I want to recreate this SPSS plot:

Histogram with Gauss curve overlay (SPSS)

Creating the histogram using PGFplots is no problem for me. The plot looks like this:

enter image description here

The code for the plot above is:

% Gauss function, parameters mu and sigma
\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}

% Histogram
\begin{tikzpicture}
    \begin{axis}[
        height=7cm,
        width=6cm,
        xmin=0.67,
        xmax=0.75,
    ]

    \addplot[
        black,
        fill=lightgray,
        hist,
        hist/bins=20,
    ] table[
        y=true-error,
    ] {Data/compare-cv-normality-1002-error.dat};

    %\addplot {\gauss{0.71}{0.00944}};

    \end{axis}
\end{tikzpicture}

As you can see, I already have the code for the Gauss plot inserted, but is commented because it produces the following errors:

Dimension too large. ^^I^^I\addplot {\gauss{0.71}{0.00944}};
Arithmetic overflow. ^^I^^I\addplot {\gauss{0.71}{0.00944}};

Also, the second problem is that adding the Gauss sets the X axis to (-5, 5) range and I have to manually readjust it according to the histogram data. So far, this is my least priority as the solution is quite trivial. But if you could solve it without setting the xmin and xmax, I would appreciate it.

Contents of the data file:

true-error
0.6949672084402624
0.7182777302537782
0.7026660963786713
0.7184915882520673
0.7052323923581408
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Best Answer

Without explicit instructions to the contrary, pgfplots is trying to evaluate the Gaussian way outside the domain you’re interested in, causing arithmetic errors as the argument of the exponential gets large.

\addplot[domain={0.67:0.75}]{\gauss{0.71}{0.00944}};

will do the trick (though of course to match the SPSS plot you probably want to include a scale parameter in the Gaussian as well).

Edit by HK

In addition to domain, to match the peak of gauss with bar, you may use ysacle=4.25. Adding samples=150 makes the gauss smoother.

 \addplot[domain={0.67:0.75},yscale=4.25,samples=150] {\gauss{0.71}{0.00944}};

gives

enter image description here

Edit by alesc

The scaling factor is calculated via the following equation:

0.997 * num_samples * (xmax - xmin) / num_bins

Provided that xmax and xmin is calculated via the +-3 sigma rule. This is also the reason for multiplying the equation with 0.997.

MWE: With x,y-labels

\documentclass[border=3mm,tikz,preview]{standalone}
\usepackage{pgfplots}

\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}
\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        height=7cm,
        width=6cm,
        xmin=0.67,
        xmax=0.75,
        xlabel = truerror,
        ylabel = Frequency
]

    \addplot[
        black,
        fill=lightgray,
        hist,
        hist/bins=20,
    ] table[
        y=true-error,
    ] {error.dat};

    \addplot[domain={0.67:0.75},yscale=4.25,samples=150] {\gauss{0.71}{0.00944}};

    \end{axis}
\end{tikzpicture}
\end{document}

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.

[Tex/LaTex] PGFPLOTS: How to merge 2 tables for histogram

pgfplotstable comes with a method named \pgfplotstablevertcat which concatenates tables vertically. "Concatenate vertically" means: append rows.

Here is a minimal example which concatenates the tables along with a very minimal visualization:

\documentclass{standalone}

\usepackage{pgfplots}
\pgfplotsset{compat=1.9}

\usepackage{pgfplotstable}

\begin{filecontents}{dataA.csv}
Miles,   Bike,    rdate,   desc
12.5,    Yel-11,  {$\stackrel{\hbox{Yel-11}}{\hbox{\tiny 03-30-14}}$},   {12.5 miles:\ Mohawk}
16.5,    Fuji,    {$\stackrel{\hbox{Fuji}}{\hbox{\tiny 04-23-14}}$},     {16.5 miles:\ Snow}
21.0,    8000SHX, {$\stackrel{\hbox{8000SHX}}{\hbox{\tiny 05-18-14}}$},  {21.0 miles:\ Ojibway Road}
24.2,    Yel-11,  {$\stackrel{\hbox{Yel-11}}{\hbox{\tiny 05-24-14}}$},   {24.2 miles:\ Ojibway Road}
23.4,    YFoil,   {$\stackrel{\hbox{YFoil 77}}{\hbox{\tiny 05-29-14}}$}, {23.4 miles:\ Snow}
21.1,    Y-22,    {$\stackrel{\hbox{Y-22}}{\hbox{\tiny 05-30-14}}$},     {21.1 miles:\ Ojibway Road}
\end{filecontents}
\begin{filecontents}{dataB.csv}
Miles,   Bike,    rdate,   desc
23.9,    YFoil,   {$\stackrel{\hbox{YFoil 77}}{\hbox{\tiny 06-01-14}}$}, {23.9 miles:\ Snow}
32.5,    Fuji,    {$\stackrel{\hbox{Fuji}}{\hbox{\tiny 06-05-14}}$},     {32.5 miles:\ Phoenix Church}
23.8,    YFoil,   {$\stackrel{\hbox{YFoil 77}}{\hbox{\tiny 06-17-14}}$}, {23.8 miles:\ Snow}
27.0,    YFoil,   {$\stackrel{\hbox{YFoil 77}}{\hbox{\tiny 06-22-14}}$}, {27.0 miles:\ Snow}
34.0,    Y-22,    {$\stackrel{\hbox{Y-22}}{\hbox{\tiny 06-27-14}}$},     {34.0 miles:\ Central Mine}
20.0,    Fuji,    {$\stackrel{\hbox{Fuji}}{\hbox{\tiny 06-29-14}}$},     {20.0 miles:\ Snow}
\end{filecontents}

\begin{document}
\pgfplotstableset{col sep=comma}
\pgfplotstablevertcat{\output}{dataA.csv} % loads `dataA.csv' -> `\output'
\pgfplotstablevertcat{\output}{dataB.csv} % appends rows of dataB.csv

\pgfplotstabletypeset[columns=Miles,fixed zerofill]{\output}

\begin{tikzpicture}[baseline]
    \begin{axis}[anchor=center]
    \addplot table[x expr=\coordindex,y index=0] {\output}; 
    \end{axis}
\end{tikzpicture}
\end{document}

enter image description here

Note that [baseline] and anchor=center are merely here for alignment with the table.

Best Answer

Related Solutions

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

ROOT data export

Working examples

[Tex/LaTex] PGFPLOTS: How to merge 2 tables for histogram

Related Question