Riemann surface
matlab

1.1.1 Example: Planets data
Six astronomical variables are given on each of the historical nine planets (or eight planets, plus Pluto). The variables are (average) distance in millions of miles from the Sun, length of day in Earth days, length of year in Earth days, diameter in miles, temperature in degrees Fahrenheit, and number of moons. The data matrix:
\begin{tabular}{lrrrrrr}
& Dist & Day & Year & Diam & Temp & Moons \
\hline Mercury & 35.96 & 59.00 & 88.00 & 3030 & 332 & 0 \
Venus & 67.20 & 243.00 & 224.70 & 7517 & 854 & 0 \
Earth & 92.90 & 1.00 & 365.26 & 7921 & 59 & 1 \
Mars & 141.50 & 1.00 & 687.00 & 4215 & -67 & 2 \
Jupiter & 483.30 & 0.41 & 4332.60 & 88803 & -162 & 16 \
Saturn & 886.70 & 0.44 & 10759.20 & 74520 & -208 & 18 \
Uranus & 1782.00 & 0.70 & 30685.40 & 31600 & -344 & 15 \
Neptune & 2793.00 & 0.67 & 60189.00 & 30200 & -261 & 8 \
Pluto & 3664.00 & 6.39 & 90465.00 & 1423 & -355 & 1
\end{tabular}
The data can be found in Wright [1997], for example.

The first statement centers and scales the variables. The plot of the first two columns of pc is the first plot in Figure 1.7. The procedure we used for entropy is negent3D in Listing A.3, explained in Appendix A.1. The code is
\begin{aligned} & \text { gstar }<- \text { negent } 3 D(y \text {, nstart }=10) \text { Svectors } \ & \text { ent }<-y \% * \% \text { gstar } \end{aligned}
To create plots like the ones in Figure 1.7, use
\begin{aligned} & \operatorname{par}(m f r o w=c(1,2)) \ & \text { sp }<-\operatorname{rep}\left(c\left(‘ s^{\prime}, ‘ v^{\prime}, ‘ g^{\prime}\right), c(50,50,50)\right) \ & \text { plot(pc[,1:2],pch=sp) # pch specifies the characters to plot. } \ & \text { plot(ent[,1:2],pch=sp) } \end{aligned}

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