[R] ploting an ellipse keeps giving errors

Martin Maechler maechler at stat.math.ethz.ch
Thu Oct 28 11:18:34 CEST 2004

>>>>> "Sun" == Sun  <sun at cae.wisc.edu>
>>>>>     on Wed, 27 Oct 2004 04:25:00 -0500 writes:

    Sun> Thank you. I found there are two ellipses
    Sun> 1.
    Sun> R2.0
    Sun> library (car)

    Sun> 2.
    Sun> R1.9 and R2.0
    Sun> library (ellipse)

    Sun> And they are different! I can't run 1.

    Sun> But the 2. is kind of specialized for t-distribution confidence and so on.

    Sun> I need to find a general ellipse for an ellipse equation like
    Sun> (x-x0)^2/a + (y-y0)^2/b =1

    Sun> . Since I used chi-square percentile not t. I am trying to obtain the large
    Sun> sample 95% simultaneous confidence ellipse for two population means (say,
    Sun> weight and height). The input are the two sample means and their
    Sun> covariances.

    Sun> Maybe I have to make my own ellipse function.

maybe not.
There is more (than you mentioned above) available:

1) The recommended (i.e. you don't have to install it) package
  "cluster" has

  a. ellipsoidhull()   {which is not what you need directly}
    which returns an (S3) object of class 'ellipsoid'
    and there's methods for such objects:
    predict(<ellipsoid>) computes points you can draw.

    Note that
    tells you how an "ellipsoid" object must look like.
    (they *are* defined in terms of  cov()-matrix , center and "radius^2")
    and also has examples.

  b. ellipsoidPoints() is the function you can really directly use:

    A version of the following example will be in the next
    version of cluster:

    ## Robust vs. L.S. covariance matrix
    x <- rt(200, df=3)
    y <- 3*x + rt(200, df=2)
    plot(x,y, main="non-normal data (N=200)")
    X <- cbind(x,y)
    C.ls <- cov(X) ; m.ls <- colMeans(X)
    Cxy <- cov.rob(cbind(x,y))
    lines(ellipsoidPoints(C.ls,    d2 = 2, loc=m.ls),       col="green")
    lines(ellipsoidPoints(Cxy$cov, d2 = 2, loc=Cxy$center), col="red")

2) The 'sfsmisc' package has a complementary useful
   ellipsePoints() function for ellipses ``given by geometry''
   the help of which starts with

 >> Compute Radially Equispaced Points on Ellipse
 >> Description:
 >>      Compute points on (the boundary of) an ellipse which is given by
 >>      elementary geometric parameters.
 >> Usage:
 >>      ellipsePoints(a, b, alpha = 0, loc = c(0, 0), n = 201)
 >> Arguments:
 >>      a,b: length of half axes in (x,y) direction.
 >>    alpha: angle (in degrees) giving the orientation of the ellipse,
 >>           i.e., the original (x,y)-axis ellipse is rotated by 'angle'.
 >>      loc: center (LOCation) of the ellipse.
 >>        n: number of points to generate.

  has a "nice" example of ellipse drawing,
  even a movie of a rotating ellipse...

Martin Maechler, ETH Zurich

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