How to set up the tick labels of the a logarithmic axis?

Question

See my MWE:

\documentclass{scrartcl}
\usepackage{tikz}
\usepackage[per-mode = fraction]{siunitx}
\usetikzlibrary{datavisualization.formats.functions}
\begin{document}
\begin{tikzpicture}
    \datavisualization[
                       scientific axes = clean,
                       all axes = grid,
                       x axis = {
                                 logarithmic,
                                 ticks = {
                                          step = 1,
                                          minor steps between steps = 9
                                         },
                                 label = $\omega,\si{\radian\per\s}$
                                },
                       y axis = {
                                 ticks = {step = 45},
                                 label = $\frac{\varphi(\omega)}{\si{\degree}}$
                                },
                       visualize as line/.list = {
                                                  P,
                                                  PD 1,
                                                  PD 2,
                                                  I,
                                                  PT_1 1,
                                                  PT_1 2,
                                                  phase
                                                 },
                       style sheet = vary thickness and dashing,
                       P = {label in legend = {text = P}},
                       PD 1 = {label in legend = {text = PD (1)}},
                       PD 2 = {label in legend = {text = PD (2)}},
                       I = {label in legend = {text = I}},
                       PT_1 1 = {label in legend = {text = PT${1,1}$}},
                       PT_1 2 = {label in legend = {text = PT${1,2}$}},
                       phase = {label in legend = {text = $\arg{G_S(j\omega)}$}}
                      ]
    data[set = P] {
                   x,          y
                        .0001, 0
                   10000,      0
                  }
    data[set = PD 1] {
                      x,          y
                           .0001,  0
                           .001,   0
                           .1,    90
                      10000,      90
                     }
    data[set = PD 2] {
                      x,          y
                           .0001,  0
                         10,       0
                       1000,      90
                      10000,      90
                     }
    data[set = I] {
                   x,          y
                        .0001, -90
                   10000,      -90
                  }
    data[set = PT_1 1] {
                        x,          y
                             .0001,   0
                             .01,     0
                            1,      -90
                        10000,      -90
                       }
    data[set = PT_1 2] {
                        x,          y
                             .0001,   0
                            1,        0
                          100,      -90
                        10000,      -90
                       }
    data[set = phase] {
                       x,          y
                            .0001,  -90
                            .001,   -90
                            .01,    -45
                            .1,     -45
                          10,      -135
                         100,      -135
                        1000,       -90
                       10000,       -90
                      };
  \end{tikzpicture}
\end{document}

With the result

As you can see the ticks labels of the frequency axis are overlapping. How can one achieve following behavior?

Thank you for your help and effort in advance!

This post might help: https://tex.stackexchange.com/questions/207212/how-do-i-change-the-font-size-of-the-axis-tick-labels-in-pgfplots — Arne, Jan 29 '21 at 14:41
Thank you for your comment @Arne! Sorry for the long absence! In fact I don't want to change the font size (if even possible, if not, than the font size can be slightly decreased). I wish that the ticks are displayed uniform as the power of ten (without the leading 1\cdot). — Su-47, Jan 31 '21 at 23:36

schtandard · Accepted Answer · 2021-02-03T22:40:05.533

You can change the function that typesets the tick labels using the tick typesetter key and make them smaller using the node style key.

\documentclass{scrartcl}
\usepackage{tikz}
\usepackage[per-mode = fraction]{siunitx}
\usetikzlibrary{datavisualization.formats.functions}
\def\printonlypower#1{%
  \pgfmathparse{int(round(log10{#1}))}%
  (10^{\pgfmathresult})%
}
\def\printonlyexponent#1{%
  \pgfmathparse{int(round(log10{#1}))}%
  (\pgfmathresult)%
}
\begin{document}
\begin{tikzpicture}
  \datavisualization [
    scientific axes = clean,
    all axes = grid,
    x axis = {
      logarithmic,
      ticks = {
        step = 1,
        minor steps between steps = 9,
        node style={font=\tiny},
        tick typesetter/.code={\printonlypower{##1}},
      },
      label = $\omega,\si{\radian\per\s}$,
    },
    y axis = {
      ticks = {step = 45},
      label = $\frac{\varphi(\omega)}{\si{\degree}}$
    },
    visualize as line/.list = {
      P,
      PD 1,
      PD 2,
      I,
      PT_1 1,
      PT_1 2,
      phase
    },
    style sheet = vary thickness and dashing,
    P = {label in legend = {text = P}},
    PD 1 = {label in legend = {text = PD (1)}},
    PD 2 = {label in legend = {text = PD (2)}},
    I = {label in legend = {text = I}},
    PT_1 1 = {label in legend = {text = PT${1,1}$}},
    PT_1 2 = {label in legend = {text = PT${1,2}$}},
    phase = {label in legend = {text = $\arg{G_S(j\omega)}$}},
    ]
  data[set = P] {
                 x,          y
                      .0001, 0
                 10000,      0
                }
  data[set = PD 1] {
                    x,          y
                         .0001,  0
                         .001,   0
                         .1,    90
                    10000,      90
                   }
  data[set = PD 2] {
                    x,          y
                         .0001,  0
                       10,       0
                     1000,      90
                    10000,      90
                   }
  data[set = I] {
                 x,          y
                      .0001, -90
                 10000,      -90
                }
  data[set = PT_1 1] {
                      x,          y
                           .0001,   0
                           .01,     0
                          1,      -90
                      10000,      -90
                     }
  data[set = PT_1 2] {
                      x,          y
                           .0001,   0
                          1,        0
                        100,      -90
                      10000,      -90
                     }
  data[set = phase] {
                     x,          y
                          .0001,  -90
                          .001,   -90
                          .01,    -45
                          .1,     -45
                        10,      -135
                       100,      -135
                      1000,       -90
                     10000,       -90
                    };
\end{tikzpicture}
\end{document}

However, I would strongly advise you against making the tick labels that small; it's just too hard to read. Instead, make the plot larger, so the tick labels fit. With scale=1.5 you get this:

Much better. If you are really constrained and cannot make the plot larger for some insurmountable reason, the next best option is to only print the exponents and adjust the axis label accordingly. You can use \printonlyexponent as defined in the MWE above.

Some asides:

I would recommend not rotating the y axis label. It's much harder to read this way.
Your x axis label looks wrong. You probably mean \omega\,\si{\s\per\radian}.

Hello @schtandard! Thank you for your great answer! I don't understand why should the angular frequency measured in seconds per radian? A phase response shows typically the angle measured in degree over the angular frequency which is measured in radian per seconds, see for example the Bodeplot. — Su-47, Feb 06 '21 at 16:52
Yes, the unit of \omega is \radians\per\second. In order to get the unit-less numbers on the tick labels, you need to divide \omega by its unit (or multiply with the reciprocal unit). Just like you did for \varphi. — schtandard, Feb 06 '21 at 19:19

How to set up the tick labels of the a logarithmic axis?

1 Answers1