| cov2theta {epigrowthfit} | R Documentation |
Compute a Packed Representation of a Covariance Matrix
Description
Transform covariances matrices to a “packed” representation or compute the inverse transformation.
Usage
cov2theta(Sigma)
theta2cov(theta)
Arguments
Sigma |
an |
theta |
a numeric vector of length |
Details
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.
Value
A vector like theta (cov2theta) or a matrix like
Sigma (theta2cov); see ‘Details’.