How to sample a function non-uniformly?

Question

See this example code:

\documentclass{article} 
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}
\begin{document}
  \begin{tikzpicture}
    \begin{axis}[
                 xmin=-0.1,
                 xmax=1.1,
                 ymin=-1.1,
                 ymax=1.1,
                 domain=0:1,
                 samples=30
                ]
      \addplot[blue] {sqrt(x)};
      \addplot[purple] {-sqrt(x)};
    \end{axis}
  \end{tikzpicture}
\end{document}

The result appears acceptable far from zero, but near zero it's too much undersampled:

Increasing samples value makes the plot nice, but it considerably slows down processing. As a workaround I could just plot the inverse in a parametric plot (i.e. (y^2,y)), but in my actual code it'd require quite a bit of additional work.

Is there a way to provide a custom sampling function or specify different density of samples in different parts of the domain?

score 10 · Accepted Answer · edited Apr 13 '17 at 12:35

10

samples and domain can be used as plot options and you can repeat same function for several domains. This is not a solution but more a workaround. An example is shown as upper part (orange+blue) in following graph.

Another option (suggested by percusse) consists in specifying samples with samples at option. This options follows a foreach (TikZ - pgffor) syntax. An example is shown as lower part (purple) below.

\documentclass{article} 
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}
\begin{document}
  \begin{tikzpicture}
    \begin{axis}[
                 xmin=-0.1,
                 xmax=1.1,
                 ymin=-1.1,
                 ymax=1.1,
                 domain=0:1,
                % samples=30
                ]
      \addplot[blue, domain=0:.2,samples=30] {sqrt(x)};
      \addplot[orange, domain=0.2:1,samples=10] {sqrt(x)};
      \addplot[purple, samples at={0,0.005,...,0.1,0.15,...,1}] {-sqrt(x)};
    \end{axis}
  \end{tikzpicture}
\end{document}

edited Apr 13 '17 at 12:35

Community

1

answered Mar 08 '16 at 08:46

Ignasi

136,588

Looks like a viable workaround, but still only a workaround. What if the function is more complicated? Do I necessarily have to copy&paste it? – Ruslan Mar 08 '16 at 08:49
1

Or you can go about it with samples at={0,0.005,...,0.1,0.15,...,1} – percusse Mar 08 '16 at 08:51
@percusse this looks like a completely another answer. If you posted it, I think I'd accept it. – Ruslan Mar 08 '16 at 11:24
@Ruslan. I've included percusse's solution. – Ignasi Mar 08 '16 at 14:51
It is my pleasure – percusse Mar 08 '16 at 15:05

How to sample a function non-uniformly?

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