bures_wasserstein_exp

This function computes the Riemannian exponential map using the Bures-Wasserstein metric for symmetric positive-definite matrices. The map operates by solving a Lyapunov equation and then constructing the exponential.

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

bures_wasserstein_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 symmetric matrix of class <code>dspMatrix</code>, representing the tangent vector to be mapped.</dd>
<dt>validate</dt>
<dd>A logical value indicating whether to validate input arguments. Default is FALSE.</dd></dl>

Arguments

Compute the Bures-Wasserstein Exponential — bures_wasserstein_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 symmetric matrix of class <code>dspMatrix</code>, representing the tangent vector to be mapped.</dd>


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

</dl>

bures_wasserstein_exp: Compute the Bures-Wasserstein Exponential

Description

Usage

Value

Arguments