Precision for semilogyaxis

Question

I have a semilogyaxis with log ticks with fixed point option. What I don't like is that the label for 1.013 is truncated to 1.01. I tried to sort that out with /pgf/number format/precision key, but it did not help. Do you have any idea what went wrong?

\documentclass[tikz]{standalone}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{semilogyaxis}[log ticks with fixed point,xmin=0,xmax=400,ymin=1E-5,ymax=1E4,ytick={1E-5,6.1E-3,1.013,221,1E4},yticklabel style={/pgf/number format/precision=4}]

\end{semilogyaxis} 
\end{tikzpicture}

\end{document}

Answer 1

By default, /pgfplots/log ticks with fixed point prints numbers using this:

\pgfqkeys{/pgf/number format}{fixed relative, precision=3}

However, it accepts an argument which is fed as options to \pgfmathprintnumber and can override these defaults. Thus, your problem should normally be solved using log ticks with fixed point={precision=4}. Unfortunately, due to—as far as I understand it—numerical errors caused by the relatively small number of significant digits in computations done with the PGF fpu library, the lowest y tick would then show as 0.000009999 instead of 0.00001, which isn't very pleasant.

In order to solve this problem, I propose two solutions based on /pgfplots/log number format code (I'd favor the former).

Using the fixedpointarithmetic TikZ library

\documentclass[tikz, border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepackage{fp}
\usetikzlibrary{fixedpointarithmetic}

\begin{document}

\begin{tikzpicture}
\begin{semilogyaxis}[
  log number format code/.code={%
    \begingroup
      \pgfset{fixed point arithmetic,
              number format/.cd, fixed relative, precision=4}%
      \pgfmathparse{exp(#1)}%
      \pgfmathprintnumber{\pgfmathresult}%
    \endgroup
  },
  xmin=0, xmax=400,
  ymin=1E-5, ymax=1E4,
  ytick={1E-5,6.1E-3,1.013,221,1E4},
  ]
\end{semilogyaxis}
\end{tikzpicture}

\end{document}

Direct computation with the fpu TikZ library

/pgfplots/log ticks with fixed point already uses the fpu TikZ library, but it computes y ticks as exp(nln(10)) for the relevant values of n. The chain of computations—one multiplication then exponentiation—leads to errors due to the small number of significant digits in fpu computations (TeX \dimen registers are used to represent the mantissa). The code below has slightly better numeric precision: it computes exp(x), where x is the natural logarithm of the tick value, provided as the argument of /pgfplots/log number format code. Less computations leads to less accumulation of numerical errors. This way, the result is satisfactory too—it is identical to the above screenshot.

\documentclass[tikz, border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\begin{document}

\begin{tikzpicture}
\begin{semilogyaxis}[
  log number format code/.code={%
    \begingroup
      \pgfset{fpu, number format/.cd, fixed relative, precision=4}%
      \pgfmathparse{exp(#1)}%
      \pgfmathprintnumber{\pgfmathresult}%
    \endgroup
  },
  xmin=0, xmax=400,
  ymin=1E-5, ymax=1E4,
  ytick={1E-5,6.1E-3,1.013,221,1E4},
  ]
\end{semilogyaxis}
\end{tikzpicture}

\end{document}

P.S.: dont forget to set the pgfplots compatibility level (as I did here with \pgfplotsset{compat=1.16}).