TikZ: Bins in the histogram are not displayed correctly

Question

I am trying to create a tikzpicture similar to what I have made in MATLAB. MATLAB gives me the following result after running histogram:

myhistnorm = [ 0.1231   0   0   0   0   0   0   0.0001  0.0001  0.0004  0.001   0.0048  0.0313  0.1562  0.3464  0.2684  0.0645  0.0036  0 ]

I have used the following bin:

mybin = [ 1e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 1e+1 1e+2 1e+3 ]

The image of the figure, which is created in MATLAB, can be found in the following figure:

Although I created a normalized histogram using TikZ, it differs from the non-normalized figure that MATLAB has created in some other aspects.

\begin{tikzpicture}
\begin{axis}[
    width=\figurewidth,
    height=\figureheight,
    axis on top,
    scale only axis,
    xmode=log,
    ymode=log,
    ybar interval,
    x tick label as interval=false,
    xlabel = {$\boldsymbol{\nabla}\cdot{\bf u}_{int}$},
    xtick={},
    xtickten={-16,-14,-12,...,4},
    yticklabel={},
    xmin=1e-16, xmax=1e+4,
    ymax=1,
    grid=none,
    ymajorgrids,
]
\addplot [fill=gray!50] table [x=Lower, y=Count] {
Lower Upper Count
9.9e-15 1e-14    0.1231
1e-14 1e-13      0.0000
1e-13 1e-12      0.0000
1e-12 1e-11      0.0000
1e-11 1e-10      0.0000
1e-10 1e-9       0.0000
1e-9  1e-8       0.0000
1e-8  1e-7       0.0001
1e-7  1e-6       0.0001
1e-6  1e-5       0.0004
1e-5  1e-4       0.0010
1e-4  1e-3       0.0048
1e-3  1e-2       0.0313
1e-2  1e-1       0.1562
1e-1  1e+0       0.3464
1e+0  1e+1       0.2684
1e+1  1e+2       0.0645
1e+2  1e+3       0.0036
1e+3  1e+10      0.0000
};
\end{axis}
\end{tikzpicture}    

The result of compiling the above code is shown in the following figure

My question is that why the bin between 1e-14 to 1e-8 are displayed differently than what I have entered in the table in the code? They should be all zero and only the first bin should have 0.1231 counts. Also, the bin (1e+2)-(1e+3) is also missing in the figure.

Thanks.

Answer 1

The problem comes from the fact that zero values can't be handled properly in a logarithmic context. PGFPlots filters the entries with counts of zero out of the list, and then proceeds as if they had never been there, resulting in the wide first bar.

To work around this, you can manually specify a minimum y value, and assign the bars with a count of zero a value that's below the minimum value instead. That way, the width of the first bar will be calculated correctly, but the zero-bars won't show up in the plot. The behaviour isn't entirely intuitive, so you might want to consider posting a feature request to handle data points with values of zero even in logarithmic contexts for determining the bar width of interval plots.

\documentclass[border=5mm]{standalone}

\usepackage{pgfplots}
\pgfplotsset{compat=1.7}


\begin{document}
\begin{tikzpicture}
\begin{axis}[
    axis on top,
    scale only axis,
    xmode=log,
    ymode=log,
    ybar interval,
    x tick label as interval=false,
    xtick={},
    xtickten={-16,-14,-12,...,4},
    yticklabel={},
    xmin=1e-16, xmax=1e+4,
    ymin=1e-5,ymax=1,
    grid=none,
    ymajorgrids,
    log origin=infty
]
\addplot [fill=gray!50] table [x=Lower, y=Count] {
Lower Upper Count
9.9e-15 1e-14    0.1231
1e-14 1e-13      1e-6
1e-13 1e-12      0.0000
1e-9  1e-8       0.0000
1e-8  1e-7       0.0001
1e-7  1e-6       0.0001
1e-6  1e-5       0.0004
1e-5  1e-4       0.0010
1e-4  1e-3       0.0048
1e-3  1e-2       0.0313
1e-2  1e-1       0.1562
1e-1  1e+0       0.3464
1e+0  1e+1       0.2684
1e+1  1e+2       0.0645
1e+2  1e+3       0.0036
1e+3  1e+10      0.0000
};
\end{axis}
\end{tikzpicture}   
\end{document}