Draw ellipses

Description

Draws ellipses from a mean and a variance into a plot.

Usage

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   ellipses(mean,...)
  ## S3 method for class 'acomp'
ellipses(mean,var,r=1,...,steps=72,
                                         thinRatio=NULL,aspanel=FALSE)
  ## S3 method for class 'rcomp'
ellipses(mean,var,r=1,...,steps=72,
                                         thinRatio=NULL,aspanel=FALSE)
  ## S3 method for class 'aplus'
ellipses(mean,var,r=1,...,steps=72,thinRatio=NULL)
  ## S3 method for class 'rplus'
ellipses(mean,var,r=1,...,steps=72,thinRatio=NULL)
  ## S3 method for class 'rmult'
ellipses(mean,var,r=1,...,steps=72,thinRatio=NULL)
          

Arguments

mean

a compositional dataset or value of means or midpoints of the ellipses

var

a variance matrix or a set of variance matrices given by var[i,,] (multiple covariance matrices are not consitently implemented as of today). The principal axis of the variance give the axis of the ellipses, whereas the square-root of the eigenvalues times r give the half-diameters of the ellipse.

r

a scaling of the half-diameters

...

further graphical parameters

steps

the number of discretisation points to draw the ellipses.

thinRatio

The ellipse function now be default plots the whole ellipsiod by giving its principle circumferences. However this is not reasonable for the thinner directions. If a direction other than the first two eigendirections has an eigenvalue not bigger than thinRatio*rmax it is not plotted. Thus thinRatio=1 reinstantiates the old behavior of the function. Later thinratio=NULL will become the default, in which case the projection of the ellipse is plotted. However this is not implemented yet.

aspanel

Is the function called as slave to draw in a panel of a gsi.pairs plot, or as a user function setting up the plots.

Details

The ellipsoid/ellipse drawn is given by the solutions of

(x-mean)^tvar^{-1}(x-mean)=r^2

in the respective geometry of the parameter space. Note that these ellipses can be added to panel plots (by means of orthogonal projections in the corresponding geometry).

There are actually three possibilities of drawing a a hyperdimensional ellipsoid or ellipse and non of them is perfect.

  • thinRatio=1.1 This works like, what was implemented in the older versions of compositons, but never correctly documented. It draws an ellipse with main axes given by the two largest Eigendirections of the var-Matrix given.

  • thinRatio=0 Draws all the ellipses given by every pair of eigendirections. In this way we get a visual impression of the high dimensional ellipsoid represend by the variance matrix. However the plots gets fastly cluttered in dimensions, when D>4. A 0<thinRatio<1 can avoid using eigendirection with small extend (i.e. smaller than thinRatio*largest Eigenvalue.

  • thinRatio=NULL Draws in each Panel a two dimensional ellipse representing the marginal variance in the projection of the plot, if var was to be interpreted as a variance matrix. This can be seen as some sort of projection of the high dimensional ellipsoid, but is not necessarily its visual outline.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

plot.acomp,

Examples

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data(SimulatedAmounts)

plot(acomp(sa.lognormals))
tt<-acomp(sa.lognormals); ellipses(mean(tt),var(tt),r=2,col="red")
tt<-rcomp(sa.lognormals); ellipses(mean(tt),var(tt),r=2,col="blue")

plot(aplus(sa.lognormals[,1:2]))
tt<-aplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="red")
tt<-rplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="blue")

plot(rplus(sa.lognormals[,1:2]))
tt<-aplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="red")
tt<-rplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="blue")
tt<-rmult(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="green")

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