SyScSelection (version 1.0.1)

vertices: Finds the d d-dimensional positive vertices for the given ellipsoid. A "positive" vertex is one where a principal axis for the ellipsoid intersects the surface of the ellipsoid in the direction of the corresponding eigenvector. (Recall that each of the eigenvectors of the ellipsoid's shape matrix is collinear with one of the principal axes.) This function does not assume that the ellipsoid is centered at the origin. Because the direction of each unit eigenvector is arbitrary (i.e., multiplication by -1 still yields a unit eigenvector), a simple algorithm is used to pick a consistent orientation for the vertex points.

Description

Finds the d d-dimensional positive vertices for the given ellipsoid. A "positive" vertex is one where a principal axis for the ellipsoid intersects the surface of the ellipsoid in the direction of the corresponding eigenvector. (Recall that each of the eigenvectors of the ellipsoid's shape matrix is collinear with one of the principal axes.) This function does not assume that the ellipsoid is centered at the origin. Because the direction of each unit eigenvector is arbitrary (i.e., multiplication by -1 still yields a unit eigenvector), a simple algorithm is used to pick a consistent orientation for the vertex points.

Usage

vertices(hellip)

Arguments

hellip

defines the polar vertices

Value

A d x d array with each column a positive vertex

Examples

# NOT RUN {
hellip <- hyperellipsoid()
vertices(hellip)
# }