airm_exp

This function computes the Riemannian exponential map for the Affine-Invariant Riemannian Metric (AIRM).

Implements various Riemannian metrics for symmetric positive definite matrices, including AIRM (Affine Invariant Riemannian Metric, <doi:10.1007/s11263-005-3222-z>), Log-Euclidean (<doi:10.1002/mrm.20965>), Euclidean, Log-Cholesky (<doi:10.1137/18M1221084>), and Bures-Wasserstein metrics (<doi:10.1016/j.exmath.2018.01.002>). Provides functions for computing logarithmic and exponential maps, vectorization, and statistical operations on the manifold of positive definite matrices.

Nicolas Escobar

riemtan

Riemannian Metrics for Symmetric Positive Definite Matrices

Jaroslaw Harezlak

airm_exp function

<dl><dt>sigma</dt>
<dd>A symmetric positive-definite matrix of class <code>dppMatrix</code>, representing the reference point.</dd>
<dt>v</dt>
<dd>A tangent vector of class <code>dspMatrix</code>, to be mapped back to the manifold at <code>sigma</code>.</dd>
<dt>validate</dt>
<dd>A logical value indicating whether to validate input arguments. Default is FALSE.</dd></dl>

Arguments

Compute the AIRM Exponential — airm_exp

<dl>

<dt>sigma</dt>
<dd>A symmetric positive-definite matrix of class <code>dppMatrix</code>, representing the reference point.</dd>


<dt>v</dt>
<dd>A tangent vector of class <code>dspMatrix</code>, to be mapped back to the manifold at <code>sigma</code>.</dd>


<dt>validate</dt>
<dd>A logical value indicating whether to validate input arguments. Default is FALSE.</dd>

</dl>

airm_exp: Compute the AIRM Exponential

Description

Usage

Value

Arguments