norm.Euclidean

norm

norm.default

norm.L2

norm.HS

norm.Dens

norm.SO

norm.LogEu

norm.AffInv

norm.Sphere

Norm on the tangent space induced by the Riemannian metric

Implements operations for Riemannian manifolds, e.g., geodesic distance, Riemannian metric, exponential and logarithm maps, etc. Also incorporates random object generator on the manifolds. See Dai, Lin, and Müller (2021) <doi:10.1111/biom.13385>.

Xiongtao Dai

manifold

Operations for Riemannian Manifolds

Zhenhua Lin

norm.Euclidean function

<dl><dt>mfd</dt>
<dd>A manifold object created by <code>createM</code></dd>
<dt>p, U</dt>
<dd>Matrices with n columns. p stands for the base point(s) and U the tangent vector(s). The norm of each column in U is calculated w.r.t. the corresponding column in p.</dd></dl>

Arguments

<ul>
<li><code>norm(Euclidean)</code>: Method</li>
<li><code>norm(default)</code>: Method</li>
<li><code>norm(L2)</code>: Method</li>
<li><code>norm(HS)</code>: Method</li>
<li><code>norm(Dens)</code>: Method</li>
<li><code>norm(SO)</code>: Method</li>
<li><code>norm(LogEu)</code>: Method</li>
<li><code>norm(AffInv)</code>: Method</li>
<li><code>norm(Sphere)</code>: Method</li>
</ul>

Methods (by class)

Norm on the tangent space induced by the Riemannian metric — norm.Euclidean

<dl>

<dt>mfd</dt>
<dd>A manifold object created by <code>createM</code></dd>


<dt>p, U</dt>
<dd>Matrices with n columns. p stands for the base point(s) and U the tangent vector(s). The norm of each column in U is calculated w.r.t. the corresponding column in p.</dd>

</dl>

norm.Euclidean: Norm on the tangent space induced by the Riemannian metric

Description

Usage

Value

Arguments

Methods (by class)