log_cholesky_log

This function computes the Riemannian logarithmic map using the Log-Cholesky metric for symmetric positive-definite matrices. The Log-Cholesky metric operates by transforming matrices via their Cholesky decomposition.

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_log function

<dl><dt>sigma</dt>
<dd>A symmetric positive-definite matrix of class <code>dppMatrix</code>, representing the reference point.</dd>
<dt>lambda</dt>
<dd>A symmetric positive-definite matrix of class <code>dppMatrix</code>, representing the target point.</dd>
<dt>validate</dt>
<dd>A logical value indicating whether to validate input arguments. Default is FALSE.</dd></dl>

Arguments

Compute the Log-Cholesky Logarithm — log_cholesky_log

<dl>

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


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


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

</dl>

log_cholesky_log: Compute the Log-Cholesky Logarithm

Description

Usage

Value

Arguments