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LMMsolver (version 1.0.9)

ADchol: construct object for Automated Differentiation Cholesky decomposition

Description

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.

Usage

ADchol(lP)

Value

An object of class ADchol. This object is used to calculate the partial partial derivatives of \(log|C|\) in an efficient way.

Arguments

lP

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.

References

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.