isBounded

isBounded.gell

isFat

isFat.gell

isFlat

isFlat.gell

isUnbounded

isUnbounded.gell

These functions provide tests for classes of generalized ellipsoids in the
(U, D) representation, based on the numbers of positive, zero and infinite
singular values in D.
They are included here mainly as computational definitions of the terms
&#8216;bounded&#8217; for an ellipsoid with finite extent, 
&#8216;fat&#8217;, for a bounded ellipsoid with non-empty interior, 
&#8216;flat&#8217;, for degenerate (singular) ellipsoids 
in \(R^p\) with empty interior.

logic

Represents generalized geometric ellipsoids with the "(U,D)" representation. It allows degenerate
and/or unbounded ellipsoids, together with methods for linear and duality transformations, and for plotting.
Thus ellipsoids are naturally extended to include lines, hyperplanes, points, cylinders, etc.
This permits exploration of a variety to statistical issues that can be visualized using ellipsoids
as discussed by Friendly, Fox & Monette (2013), Elliptical Insights: Understanding Statistical Methods
Through Elliptical Geometry <doi:10.1214/12-STS402>.

Michael Friendly

gellipsoid

Generalized Ellipsoids

isBounded function

<dl><dt>x</dt>
<dd>A class <code>"gell"</code> object</dd>
<dt>...</dt>
<dd>Other arguments, not used.</dd></dl>

Arguments

Author

Tests for Classes of Generalized Ellipsoids — isBounded

<dl>

<dt>x</dt>
<dd>A class <code>"gell"</code> object</dd>


<dt>...</dt>
<dd>Other arguments, not used.</dd>

</dl>

Tests for Classes of Generalized Ellipsoids

isBounded: Tests for Classes of Generalized Ellipsoids

Description

Usage

Value

Arguments

Author

References

See Also

Examples