an> to the <span class="math inline">\(K \times K\)</span> lower-triangular Cholesky factor <span class="math inline">\(x\)</span>. The inverse transform is based on the hyperbolic tangent function, <span class="math inline">\(\tanh\)</span>, which satisfies <span class="math inline">\(\tanh(x) \in (-1,1)\)</span>. Here it will function like an inverse logit with a sign to pick out the direction of an underlying canonical partial correlation; see the <a href="correlation-matrix-transform-section.html#correl