Transform covariances matrices to a “packed” representation or compute the inverse transformation.
cov2theta(Sigma)
theta2cov(theta)A vector like theta (cov2theta) or a matrix like
Sigma (theta2cov); see ‘Details’.
an \(n\)-by-\(n\) real, symmetric positive definite matrix. Only the upper triangle is “seen”.
a numeric vector of length \(n(n+1)/2\) whose first \(n\) elements are positive.
An \(n\)-by-\(n\) real, symmetric, positive definite matrix \(\Sigma\) can be factorized as $$\Sigma = R' R\,.$$ The upper triangular Cholesky factor \(R\) can be written as $$R = R_{1} D^{-1/2} D_{\sigma}^{1/2}\,,$$ where \(R_{1}\) is a unit upper triangular matrix and \(D = \mathrm{diag}(\mathrm{diag}(R_{1}' R_{1}))\) and \(D_{\sigma} = \mathrm{diag}(\mathrm{diag}(\Sigma))\) are diagonal matrices.
cov2theta takes \(\Sigma\) and returns the vector \(\theta\)
of length \(n(n+1)/2\) containing the log diagonal entries
of \(D_{\sigma}\) followed by (in column-major order) the strictly
upper triangular entries of \(R_{1}\). theta2cov computes the
inverse transformation.