wrangle_ellipse: Ellipse Wrangeler
In fellov: Feasible Ellipse Overlap

Description Usage Arguments Details Value Examples

View source: R/wrangle_ellipse.R

wrangle_ellipse is used to wrangle one or more ellipses from one parametrization to another.

1	wrangle_ellipse(ell, out_params = c("c", "P", "r"))

`ell`	a list of (non degenerate) ellipses to be wrangled. An ellipse is a named list and each entry corresponds to a parameter. To ensure all `out_params` can be calculated one of the parametrizations listed below in the description must be specified. Some `out_params` do not require a fully parametrized ellipse and so partially specified ellipses can be used.
`out_params`	a vector of names of the output parameters. A list of possible parameters is given below in the details.

Takes ellipse parameters and and calculates the wanted out_params. A parameterization is a named list, where each named entry is a parameter. The following parameters are accepted both input and output:

n : dimension of ellipse; an integer.
c : center of the ellipse; a vector.
P : precision matrix - inverse of S; a positive definit, symmetric matrix.
S : deviation matrix - inverse of P; a positive definit, symmetric matrix.
r : radius; a positive number.
q : cross term -Pc; a vector.
L : Cholesky decomposition of P
e : eigen values of P; a vector of eigenvalues.
U : eigen vectors of P; a matrix, where each column is an eigen vector.
D : diagnonal matrix with sqrt(e) as diagonal entries.

An ellipse E may be fully parameterized using the above parameters in the following ways:

E = { x ∈ R^p : (x - c)^T P (x - c) ≤ r } E = { x ∈ R^p : (x - c)^T S^-1 (x - c) ≤ r } E = { x ∈ R^p : (x - c)^T LL^T (x - c) ≤ r } E = { x ∈ R^p : (x - c)^T UD²U^T (x - c) ≤ r } E = { x ∈ R^p : || L^T(x - c) ||₂ ≤ r } E = { x ∈ R^p : || DU^T(x - c) ||₂ ≤ r } E = { x ∈ R^p : c + L^-Tw, ||w|| ≤ r } E = { x ∈ R^p : c + UD^-1w, ||w|| ≤ r }

To ensure that all of the above parameters can be calculated it is advised (but in some cases not needed) that the input ellipses are fully parameterized.

A list of wrangled ellipses. The wrangled ellipses are now given by the out_params.

# two dimensional unite ball
e2d <- list(c = c(0,0), S = matrix(c(1,0,0,1), ncol = 2), r = 1)

# three dimensional ellipse
e3d <- list(c = c(3,2,1), P = matrix(c(3,1,2,1,5,0,2,0,2), ncol = 3))

f1 <- wrangle_ellipse(e2d) # (c,P,r) parameterization
f2 <- wrangle_ellipse(e2d, out_params = c("c", "e", "U", "r"))
f3 <- wrangle_ellipse(list("ellipse1" = e2d, "ellipse2" = e3d),
                      c("n", "c", "U", "D"))