remoteForwardsolve: Solve a Distributed Triangular System

Description

Solves a distributed system of linear equations where the coefficient matrix is lower triangular. remoteBacksolve solves $L^{\top} X = C$ for vector or matrix $X$, while remoteForwardsolve solves $L X = C$. Any of the matrices or vectors can be contained within environments and ReferenceClass objects as well as the global environment on the slave processes.

Usage

remoteBacksolve(cholName, inputName, outputName, cholPos = '.GlobalEnv',
 inputPos = '.GlobalEnv', outputPos = '.GlobalEnv', n1, n2 = NULL, h1 = 1,
h2 = NULL)
remoteForwardsolve(cholName, inputName, outputName, cholPos =
'.GlobalEnv', inputPos = '.GlobalEnv', outputPos = '.GlobalEnv', n1, n2
= NULL, h1 = 1, h2 = NULL)

Arguments

Details

Computes the solution to a distributed set of linear equations, with either a single or multiple right-hand side(s) (i.e., solving into a vector or a matrix). Note that these functions work for any distributed lower triangular matrix, but bigGP currently only provides functionality for computing distributed Cholesky factors, hence the argument names cholName and cholPos.

When the right-hand side is vector that is stored as a vector, such as created by distributeVector or remoteConstructRnormVector, use n2 = NULL. When multiplying by a one-column matrix, use n2 = 1.

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, in press. http://jstatsoft.org.

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. http://arxiv.org/abs/1305.4886.

Examples

Run this code

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)
remoteForwardsolve(cholName = "L", inputName = "data", outputName =
"tmp", cholPos = "prob", inputPos = "prob", n1 = n, h1 = prob$h_n)
LinvY <- collectVector("tmp", n = n, h = prob$h_n)
remoteBacksolve(cholName = "L", inputName = "tmp", outputName =
"tmp2", cholPos = "prob", inputPos = "prob", n1 = n, h1 = prob$h_n)
CinvY <- collectVector("tmp2", n = n, h = prob$h_n)
}