ellipse {cwhmisc} | R Documentation |
Given a positive definite symmetric matrix A
of dimension 2 by
2 and a constant cn
, or the axes a, b
and an angle
phi
(in radian, counter clockwise), and the midpoint
coordinates m
, points on the ellipse (y-m)'*A^{(-1)}*(y-m) = cn^2 or
rotm(2,1,2,phi) %*% matrix(c(a,0,0,b), 2, 2) will be generated.
ellipse(k, m, A = NULL, cn = NULL, a = NULL, b = NULL, phi = NULL)
ellipse(k, m, A, cn) ellipse(k, m, a=, b=, phi=) conf.ellipse(k, m, A, df, level = 0.95)
k |
the number of generated points on the ellipse. |
m |
vector of length 2 containing the midpoint coordinates of the ellipse. |
A |
positive definite symmetric matrix of dimension 2 by 2 |
cn |
positive constant. |
a |
major axis |
b |
minor axis |
phi |
angle in radian describing the counter clockwise rotation from the x-axis to the major axis. |
df |
degree of freedom of F-distribution. |
level |
probability level of F-distribution F(2,df). |
The matrix with columns consisting of the x and y coordinates of the ellipse.
Of ellipse: originally Bernhard Flury and Marco Bee for Flury's
book "A First Course in Multivariate Statistics" (Springer 1997).
Of conf.ellipse: Roger Koenker
roger@ysidro.econ.uiuc.edu, http://www.econ.uiuc.edu May 19, 1999.
Refined by: Christian W. Hoffmann <christian.hoffmann@wsl.ch>
http://www.wsl.ch/personal_homepages/hoffmann/index_EN
A <- matrix(c(1,1,1,2), ncol = 2) # define matrix A m <- c(3, 4) # define vector m plot(ellipse(1000,m,A,1)) plot(pe <- ellipse(800,m,A,1),pch=".",type="n") lines(rbind(pe,pe[1,])) lines({pe <- ellipse(600,m,A,0.5); rbind(pe,pe[1,])}) lines({pe <- ellipse(400,m,A,0.25); rbind(pe,pe[1,])}) lines(conf.ellipse(51,m,A,20,0.9),lty=4,col="red") lines(conf.ellipse(51,m,A,20,0.8),lty=4,col="green")