Smooth curve through points with pgfplots

Question

I know that one can get smooth point connections with option smooth to \addplot that takes the previous and the next point into account, but this still connects all the points.

How can I draw a smooth curve through the points using pgfplots that are not necessarily connected? I'm not fully sure if this is correct, but I think I'm looking for "bezier curves" (correct me if wrong). To be clear: I do not want curve-fitting like one can do with gnuplot, just some "sloppy-smooth" connecting of points.

Example picture (not from my data!):

Here is my real data, they don't follow a known, analytical, mathematical function:

43  3.22
44  3.26
45  3.28
46  3.40
47  3.60
48  3.53
49  3.50
50  3.60
51  3.59
52  3.54
53  3.55
54  3.51
55  3.35
56  3.45
57  3.42
58  3.43
59  3.42
60  3.42
61  3.43
62  3.47
63  3.45
64  3.40
65  3.20
66  3.21
67  3.17
68  3.20
69  3.22
70  3.36
71  3.37
72  3.37
73  3.30
74  3.33
75  3.39
76  3.41
77  3.34
78  3.45
79  3.42
80  3.38
81  3.33
82  3.15
83  3.35
84  3.33
85  3.20
86  3.24
87  3.20

Answer 1

Using the gnuplot backend, put your points in a file.dat, and compile twice with -shell-escape

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
  \begin{axis}
    \addplot +[no markers, raw gnuplot] gnuplot {
        plot 'file.dat' smooth sbezier;
    };
    \addplot +[only marks, raw gnuplot] gnuplot {
        plot 'file.dat' with points;
    };
  \end{axis}
\end{tikzpicture}
\end{document}

Answer 2

One thing you could do is to calculate a LOESS smooth of the data. I don't know of a way to do this in LaTeX directly, but you could preprocess your data in R (which is free and useful to know, at any rate).

The following code reads the data from a file called data.dat and smoothes it using a span of 0.3 (i.e. it takes 30% of the data around each point into account for calculating a polynomial), and then writes it to a file called smooth.dat:

datapoints = read.delim('data.dat', header=F)
smooth=loess(datapoints$V2 ~ datapoints$V1, span=0.3)
write.table(data.frame(smooth$x,smooth$fitted), 'smooth.dat',sep='\t', quote=F, col.names=F, row.names=F)

Which you can then plot using:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}
\addplot [only marks] table {../data.dat};
\addplot [red, smooth] table {../smooth.dat};
\end{axis}

\end{tikzpicture}
\end{document}

Answer 3

here is your data with a Bezier curve:

\documentclass{article}% run with xelatex
%\usepackage[pdf]{pstricks}% for pdflatex --shell-escape
\usepackage{pst-plot}
\begin{document}
\psset{xunit=0.2,yunit=5}
\begin{pspicture}(0,0)(50,1)
\pstScalePoints(1,1){40 sub}{3 sub}
\psaxes[ticksize=0 5pt,Dy=0.2,Dx=10,Ox=40,Oy=3]{->}(0,0)(50,1)
\readdata\data{data0.dat}
\listplot[linecolor=red,linewidth=1.5pt,plotstyle=bezier]{43 3.22 \data}
\listplot[plotstyle=dots]{43 3.22 \data}
\end{pspicture}

\end{document}