remoteCalcChol: Calculate Distributed Cholesky Decomposition

Description

remoteCalcChol calculates a distributed Cholesky decomposition from a distributed positive definite matrix. The Cholesky factor and the original matrix can both be contained within environments and ReferenceClass objects as well as the global environment on the slave processes.

Usage

remoteCalcChol(matName, cholName, matPos = '.GlobalEnv', cholPos = '.GlobalEnv', n, h = 1)

Arguments

matName: name of the input (positive definite) matrix, given as a character string, giving the name of the object on the slave processes.
cholName: an name, given as a character string, giving the name to be used for the Cholesky factor matrix on the slave processes.
matPos: where to look for the input matrix, given as a character string (unlike get). This can indicate an environment, a list, or a ReferenceClass object.
cholPos: where to do the assignment of the Cholesky factor matrix, given as a character string (unlike assign). This can indicate an environment or a ReferenceClass object.
n: a positive integer, the number of rows and columns of the input matrix.
h: a positive integer, the block replication factor, \(h\), relevant for the input matrix and used for the Cholesky factor as well.

Details

Computes the distributed Cholesky decomposition using a blocked algorithm similar to that in ScaLapack. When \(h\) is 1, the number of blocks, representing the lower triangle of the original matrix and of the Cholesky factor, is equal to the number of processes. For larger values of \(h\), there are multiple blocks assigned to each process.

References

Paciorek, C.J., B. Lipshitz, W. Zhuo, Prabhat, C.G. Kaufman, and R.C. Thomas. 2015. Parallelizing Gaussian Process Calculations in R. Journal of Statistical Software, 63(10), 1-23. tools:::Rd_expr_doi("10.18637/jss.v063.i10").

Paciorek, C.J., B. Lipshitz, W. Zhuo, Prabhat, C.G. Kaufman, and R.C. Thomas. 2013. Parallelizing Gaussian Process Calculations in R. arXiv:1305.4886. https://arxiv.org/abs/1305.4886.

Examples

Run this code

if (FALSE) {
if(require(fields)) {
  SN2011fe <- SN2011fe_subset
  SN2011fe_newdata <- SN2011fe_newdata_subset
  SN2011fe_mle <- SN2011fe_mle_subset
  nProc <- 3
n <- nrow(SN2011fe)
m <- nrow(SN2011fe_newdata)
nu <- 2
inputs <- c(as.list(SN2011fe), as.list(SN2011fe_newdata), nu = nu)
prob <- krigeProblem$new("prob", numProcesses = nProc, n = n, m = m,
predMeanFunction = SN2011fe_predmeanfunc, crossCovFunction = SN2011fe_crosscovfunc,
predCovFunction = SN2011fe_predcovfunc, meanFunction = SN2011fe_meanfunc,
 covFunction = SN2011fe_covfunc,  inputs = inputs, params = SN2011fe_mle$par,
data = SN2011fe$flux, packages = c("fields"))
remoteCalcChol(matName = 'C', cholName = 'L', matPos = 'prob',
  cholPos = 'prob', n = n, h = prob$h_n)
L <- collectTriangularMatrix('L', objPos = 'prob', n = n, h = prob$h_n)
}
}