ADchol function

construct object for Automated Differentiation Cholesky decomposition

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)

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.

Returns

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

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.