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

cholName: name of the input lower triangular matrix matrix (the matrix of coefficients), given as a character string, of the object on the slave processes.
inputName: name of the vector or matrix being solved into (the right-hand side(s) of the equations), given as a character string, of the object on the slave processes.
outputName: the name to use for the output object, the solution vector or matrix, on the slave processes.
cholPos: where to look for the lower triangular matrix, given as a character string (unlike get). This can indicate an environment, a list, or a ReferenceClass object.
inputPos: where to look for the input right-hand side matrix or vector, given as a character string (unlike get). This can indicate an environment, a list, or a ReferenceClass object.
outputPos: where to do the assignment of the output matrix or vector, given as a character string (unlike assign). This can indicate an environment or a ReferenceClass object.
n1: a positive integer, the number of rows and columns of the input matrix.
n2: a positive integer, the number of columns of the right-hand side values. When equal to one, indicates a single right-hand side vector.
h1: a positive integer, the block replication factor, \(h\), relevant for the input matrix and used for the solution (either for a vector, or the rows of the solution for a matrix).
h2: a positive integer, the block replication factor, \(h\), relevant for the columns of the solution when the right-hand side is a matrix.

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, 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)
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)
}
}