ell: Ellipses in 2D

In gmonette/spida2: Collection of tools developed for the Summer Programme in Data Analysis 2000-2012

Ellipses in 2D

Description

Tools to generate 2D data, concentration and confidence ellipses given a center and a 'variance' matrix. Also tools to generate points on a ellipse in a given direction or conjugate to that direction, axes along a vector or conjugate to it, tangent lines at a point or parallel to a vector.

Generates an ellipse augmented with conjugate axes and tangents

ell is a utility function used to calculate the (X, Y) coordinates of a 2D ellipse for the purpose of drawing statistical diagrams and plots.

Usage

ell(center = rep(0, 2), shape = diag(2), radius = 1, n = 100)

ellplus(
  center = rep(0, 2),
  shape = diag(2),
  radius = 1,
  n = 100,
  angles = (0:n) * 2 * pi/n,
  fac = chol,
  ellipse = all,
  diameters = all,
  box = all,
  all = FALSE
)

dellplus(x, y, ...)

ell(center = rep(0, 2), shape = diag(2), radius = 1, n = 100)

Arguments

center	X,Y location of the center of the ellipse
shape	A 2x2 matrix, typically a covariance matrix of data (for a data ellipse), or a covariance matrix of estimated parameters in a model (for a confidence ellipse).
radius	Radius of the ellipse-generating unit circle. The default, radius=1 corresponds to a "standard" ellipse.
n	Number of points on the unit circle used to calculate the ellipse
angles	Angles around the unit circle used to calculate the ellipse
fac	A function defining the conjugate axes used to transform the unit circle into an ellipse. The default, chol, uses the right Cholesky factor of shape.
ellipse	Logical to indicate if the points on the ellipse should be returned
diameters	Logical to indicate if the points defining the ends of the conjugate axes of the ellipse should be returned
box	Logical to indicate if the points on the conjugate-axes bounding box should be returned
all	Logical to request all of ellipse, diameters and box. If FALSE, only the components specified separately by ellipse, diameters and box are returned.
x, y	data values
...	arguments passed to ellplus
na.rm	remove missing data in forming data ellipse, default TRUE

Details

The ellipse is contour of the bivariate normal distribution with variance 'shape'.

ellplus can produce, in addition to the points of an ellipse, the conjugate axes corresponding to a chol or other decomposition and the surrounding parallelogram.

ellplus can produce, in addition, the conjugate axes corresponding to a chol or other decomposition and the surrounding parallelogram defined by these axes.

Add function that works with direction to compute slices and conjugate directions.

Value

Returns a 2-column matrix of (X,Y) coordinates suitable for drawing with lines().

For ellplus, when more than one of the options ellipse, diameters, and box is TRUE, the different parts are separated by a row of NA.

Functions

• ellplus(): tangents and axes

• dellplus(): data ellipse with tangents and axes

Author(s)

Georges Monette

See Also

cell, dell, dellplus,

Examples

plot( x=0,y=0, xlim = c(-3,3), ylim = c(-3,3),
      xlab = '', ylab = '', type = 'n', asp=1)
abline( v=0, col="gray")
abline( h=0, col="gray")
A <- cbind( c(1,2), c(1.5,1))
W <- A %*% t(A)

lines( ell(center=c(0,0), shape = W ), col = 'blue', lwd=3)
lines( ellplus(center=c(0,0), shape = W, box=TRUE, diameters=TRUE ), col = 'red')

# show conjugate axes for PCA factorization
pca.fac <- function(x) {
    xx <- svd(x)
    ret <- t(xx$v) * sqrt(pmax( xx$d,0))
    ret
}

plot( x=0,y=0, xlim = c(-3,3), ylim = c(-3,3),
      xlab = '', ylab = '', type = 'n', asp=1)
abline( v=0, col="gray")
abline( h=0, col="gray")
lines( ell(center=c(0,0), shape = W ), col = 'blue', lwd=3)
lines( ellplus(center=c(0,0), shape = W, box=TRUE, diameters=TRUE, fac=pca.fac ), col = 'red')

gmonette/spida2 documentation built on Aug. 20, 2023, 7:21 p.m.