pgfplots: How can I customize number formatting styles for log plots based on the numbers?

Question

We have seen in another question how to set the tick numbers on logarithmic axes in a sans serif font when the style is for 10^x numbering. Pgfplots offers additional options for numbering log ticks, specifically log ticks with fixed point and the option to shift from exponents to fixed point selectively depending on the magnitude of the number \pgfmathprintnumber[std={-2:2}, precision=1]{...}.

In the first instance, fixed point, the code below produces the following chart:

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}

\begin{tikzpicture}
\begin{loglogaxis}[log ticks with fixed point,]
 \addplot [domain=1:1000, ultra thick, color=blue] {x^1.5};
\end{loglogaxis}
\end{tikzpicture}

\end{document}

Question 1: how can we set these tick numbers in a sans serif font (\mathsf{..})?

In the second instance, we desire to use the functionality of \pgfmathprintnumber[std={-2:2}, precision=1]{...} to set the numbers beyond 100 in exponential format with the smaller numbers in fixed point, again in a sans font.

Question 2: How can we exploit std={x:y} behavior on log axes using san serif fonts? The desired result might look like the image below (obtained in this case by editing the pdf file directly)

Answer 1

The comment from filippo prompted me to look at this again, and I have an answer to Question 1.

Fixed point, sans serif, log axis ticks can be achieved using by modification of the approach for 10ⁿ axes as follows:

 \begin{tikzpicture}
 \begin{loglogaxis}[
   log number format basis/.code 2 args={$\pgfmathparse{#1^(#2)}\mathsf{\pgfmathprintnumber{\pgfmathresult}}$},
 ]
 \addplot [domain=1:1000, ultra thick, color=blue] {x^1.5};
 \end{loglogaxis}
 \end{tikzpicture}

So with this, we have solutions for linear axes, 10ⁿ in either semi-log or log-log axes, and fixed point on either semi-log or log axes. To summarize these (combine as necessary for semi-log):

Linear axis:

xticklabel={$\mathsf{\pgfmathprintnumber{\tick}}$},

Log axis, 10ⁿ ticks:

log number format basis/.code 2 args={$\mathsf{#1^{\pgfmathprintnumber{#2}}}$},

Log axis, fixed-point ticks:

log number format basis/.code 2 args={$\pgfmathparse{#1^(#2)}\mathsf{\pgfmathprintnumber{\pgfmathresult}}$},

We still lack a direct solution for Question 2 above. However, a brute force approach is possible by simply manually coding the ticks:

\begin{tikzpicture}
\begin{loglogaxis}[
   xtick = {1, 10, 100, 1000},
   xticklabels={$\mathsf{1}$, $\mathsf{10}$, $\mathsf{100}$, $\mathsf{10^3}$}, 
   ytick = {1, 10, 100, 1000, 10000},
   yticklabels={$\mathsf{1}$, $\mathsf{10}$, $\mathsf{100}$, $\mathsf{10^3}$, $\mathsf{10^4}$},        
]
\addplot [domain=1:1000, ultra thick, color=red] {x^1.5};
\end{loglogaxis}
\end{tikzpicture}

(Note: My figures have a few style options set on the tick marks themselves, which are not displayed here; these are irrelevant to the numbering issue.)

Answer 2

Building on Stefan's suggestion to use \ifdim, I've added keys for an upper and lower limit (eupper, elower) beyond which an exponent will be used rather than fixed point tick labeling. This code will create exponents for log bases other than 10 and incorporates \sffamily for the text font. This comes close to answering Question 2 above, although it has not truly adjusted the std={x:y} functionality of pgfplots.

\pgfkeys{/tikz/.cd,
  elower/.store in=\elower,
  elower=-1,   %% default, so (base)^0 will print as 1
  eupper/.store in=\eupper,
  eupper=1   %% default 
   }

\pgfplotsset{    
log number format basis/.code 2 args={
            \ifdim#2pt>\elower pt
                \ifdim#2pt<\eupper pt
                   \pgfmathparse{#1^(#2)}%
                   $\mathsf{\pgfmathprintnumber{\pgfmathresult}}$
                \else
                   $\mathsf{#1^{\pgfmathprintnumber{#2}}}$
                \fi
             \else
                $\mathsf{#1^{\pgfmathprintnumber{#2}}}$
             \fi
},
/tikz/font={\sffamily},
typeset ticklabels with strut,
}

\begin{tikzpicture}
\begin{loglogaxis}[
    elower=-2, 
    eupper=1,
    log basis  x = 5, %% just to illustrate for a base other than 10
    log basis  y = 10,
    xlabel= {Abscissa label [units]}, 
    ylabel= {Ordinate label [units]},
]
 \addplot [domain=0.01:10, ultra thick, color=red] {x^1.5};
  \node[right, fill=white, rectangle, thin, draw] at (0.5,0.01) {log-log};
\end{loglogaxis}
\end{tikzpicture}

\vspace*{3em}

\begin{tikzpicture}
\begin{semilogyaxis}[
     eupper = 3,
     minor x tick num=1, 
     xticklabel={$\mathsf{\pgfmathprintnumber[zerofill, precision=1]{\tick}}$},
     xlabel= {Abscissa label [units]}, 
     ylabel={Ordinate label [units]},
]
 \addplot [domain=0:10, ultra thick,color=blue] {exp(x)};
 \node[right, fill=white, rectangle, thin, draw] at (5,8) {semi-log};
\end{semilogyaxis}
\end{tikzpicture}

The examples from this code follow. The font used is Lucida Sans OT (under LuaLatex) and as before there are some unrelated stylistic adjustments to the tick marks and plot sizes.

Answer 3

I assume that you want to change the font in general to sans serif when you are inside a tikzpicture environment, right? (Otherwise it would look quite strange.) Then please find a solution where only inside the environment the font is changed, but not for the "normal" text and math stuff.

And please find also an automated way to create the ticklabels as you requested, although this is quite inconsistent and I don't like it.

For details please have a look at the comments in the code.

% used PGFPlots v1.15
\documentclass[border=5pt,varwidth]{standalone}
% needed to execute stuff "automatically"
\usepackage{etoolbox}
    % change fonts to sans serif then `tikzpicture' environment is started
    \BeforeBeginEnvironment{tikzpicture}{
        \begingroup
            \changeFonts
    }
    % end scope (for font change)
    \AfterEndEnvironment{tikzpicture}{
        \endgroup
    }
\usepackage{sansmath}
    % create a command to switch fonts in `tikzpicture' environments to a
    % sans serif font
    \newcommand*\changeFonts{
        \sffamily\sansmath
    }
\usepackage{pgfplots}
    \pgfplotsset{
        compat=1.3,
        % change `log number format basis' so that all numbers below 10^3
        % are written in "fixed" number format and all others in "sci" number
        % format
        log number format basis/.code 2 args={
            \ifdim#2pt<3pt
                \pgfmathparse{10^(#2)}%
                $\pgfmathprintnumber{\pgfmathresult}$
            \else
                $10^{\pgfmathprintnumber{\pgfmathresult}}$
            \fi
        },
    }
\begin{document}
The following plot shows $f(x) = x^{1.5}$.\par

\begin{tikzpicture}
    \begin{loglogaxis}[
        xlabel=$x$-axis,
        ylabel=$y$-axis,
    ]
        \addplot [domain=1:1000, ultra thick, color=blue] {x^1.5};
    \end{loglogaxis}
\end{tikzpicture}
\end{document}

Answer 4

As a further follow-up, when sans-serif unicode math fonts are available, we may use fontspec and unicode-math to change the plot fonts, as in the following example. This approach is easier when the axis labels include sans-serif math expressions, especially those with Greek letters. I've taken the two such fonts and paired them with STIX Two as the main font (not an ideal match, but makes the point).

    \documentclass{article}
    \usepackage[svgnames,x11names]{xcolor}

    \usepackage{pgfplots} 
    \pgfplotsset{compat=1.15}

    \pgfplotsset{%
         width=0.9\textwidth,%
         height=0.6\textwidth,%
        every axis/.append style={thick},
        every minor tick/.append style={very thin,black},
        every minor grid/.append style={very thin, color=Snow4},
        every major tick/.append style={thin, black},
        every major grid/.append style={thin, color=Snow4},
        major tick length={1.2em},
        minor tick length={0.5em},
    }

    \usepackage{unicode-math}

    \setmainfont{STIX Two Text}
    \setmathfont[Scale=MatchUppercase, RawFeature = {-ss01, +ss02, +ss08}]{STIX Two Math}  

    \newfontfamily\GFS[Scale=MatchUppercase]{GFS Neohellenic}
    \newfontfamily\FiraGO[Scale=MatchUppercase, RawFeature = {+ss05,+ss06}]{FiraGo}

    \setmathfont[version = Fira, Scale=MatchUppercase]{Fira Math}
    \setmathfont[version = GFSMath, Scale=MatchUppercase]{GFS Neohellenic Math}

    \newcommand*{\Sphinx}{Sphinx of black quartz, judge my vow.}

    \begin{document}

    \Sphinx

    \vspace*{1em}

    {
    \mathversion{Fira}\FiraGO

    \begin{tikzpicture}
    \begin{loglogaxis}[
         xlabel= {Abscissa label, $\lambda(\beta)^2$ [units]}, 
         ylabel={Ordinate label, $gf_{\kern-0.05em u}(\pi)$ [units]},
    ]
     \addplot [domain=1:1000, ultra thick, color=blue] {x^1.5};
     \node[right, fill=white, rectangle, thin, draw] at (30,7) {FiraGO, Fira Math};
    \end{loglogaxis}
    \end{tikzpicture}

    \mathversion{normal}
    }

    \vspace*{1em}

    \Sphinx

    \[
    \frac{d\Gamma}{dt}  = \iint_{\symcal{S}}  \nabla p \times \nabla \left( \frac{1}{\rho}\right) \cdot d\symbf{A}
    \]

    \vspace*{1em}


    {
    \mathversion{GFSMath}\GFS
    \begin{tikzpicture}
    \begin{loglogaxis}[
         xlabel= {Abscissa label, $\lambda(\beta)^2$  [units]}, 
         ylabel={Ordinate label, $gf_{u}(\pi)$ [units]},
    ]
     \addplot [domain=1:1000, ultra thick, color=blue] {x^1.5};
     \node[right, fill=white, rectangle, thin, draw] at (30,7) {GFS Neohellenic};
    \end{loglogaxis}
    \end{tikzpicture}
    \mathversion{normal}
    }

    \Sphinx

    \end{document}