dimensions

calcGeomPar

calcIntDim

calcAmbDim

calcTanDim

`calcGeomPar` calculates geometric parameter.
`calcIntDim` calculates the intrinsic dimensions.
`calcAmbDim` calculates the ambient dimensions.
`calcTanDim` calculates the number of tuples used to represent a tangent vector.

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

dimensions function

<dl><dt>mfd</dt>
<dd>A manifold object created by <code>createM</code></dd>
<dt>dimAmbient</dt>
<dd>Dimension of the ambient space.</dd>
<dt>dimIntrinsic</dt>
<dd>Intrinsic dimension of the manifold.</dd>
<dt>dimTangent</dt>
<dd>The length of a tangent vector</dd>
<dt>geomPar</dt>
<dd>The geometric parameter (e.g., SO(*))</dd></dl>

Arguments

Dimensions in this package — dimensions

<dl>

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


<dt>dimAmbient</dt>
<dd>Dimension of the ambient space.</dd>


<dt>dimIntrinsic</dt>
<dd>Intrinsic dimension of the manifold.</dd>


<dt>dimTangent</dt>
<dd>The length of a tangent vector</dd>


<dt>geomPar</dt>
<dd>The geometric parameter (e.g., SO(*))</dd>

</dl>

dimensions: Dimensions in this package

Description

Usage

Value

Arguments