log_cholesky_exp

This function computes the Riemannian exponential map using the Log-Cholesky metric for symmetric positive-definite matrices. The map operates by transforming the tangent vector via Cholesky decomposition of the reference point.

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

log_cholesky_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 Log-Cholesky Exponential — log_cholesky_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>

log_cholesky_exp: Compute the Log-Cholesky Exponential

Description

Usage

Value

Arguments