Construct object for reverse Automated Differentiation of Cholesky decomposition,
with as input a list of semi-positive symmetric sparse matrices \(P_i\), each of
dimension \(q \times q\). The function ADchol
calculates the matrix \(C\), the sum
the precision matrices \(P_i\): \(C = \sum_{i} P_i\). Next, it calculates the Cholesky
Decomposition using the multiple minimum degree (MMD) algorithm
of the spam
package.
ADchol(lP)
An object of class ADchol
. This object is used to calculate the partial
partial derivatives of \(log|C|\) in an efficient way.
a list of symmetric matrices of class spam, each of dimension \(q \times q\), and with sum of the matrices assumed to be positive definite.
Furrer, R., & Sain, S. R. (2010). spam: A sparse matrix R package with emphasis on MCMC methods for Gaussian Markov random fields. Journal of Statistical Software, 36, 1-25.