remoteMultChol: Distributed Multiplication of Lower Triangular Matrix and a Vector or Matrix

Description

remoteMultChol multiplies a distributed lower triangular matrix by a distributed vector or matrix. The objects can both be contained within environments or ReferenceClass objects as well as the global environment on the slave processes.

Usage

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

Arguments

cholName: name of the lower triangular matrix, given as a character string, giving the name of the object on the slave processes.
inputName: name of the vector or matrix being multiplied by, given as a character string, giving the name of the object on the slave processes.
outputName: the name to use for resulting vector or matrix product, 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 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 lower triangular matrix.
n2: a positive integer, the number of columns of the vector or matrix being multiplied by. When equal to one, indicates multiplication by a 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 input and output matrices when the lower triangular matrix is multiplied by a matrix.

Details

Computes the distributed product using a blocked algorithm. Note that the function works 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 multiplying by a 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)
remoteConstructRnormVector('z', n = n, h = prob$h_n)
remoteMultChol(cholName = 'L', inputName = 'z', outputName = 'result',
cholPos = 'prob', n1 = n, h1 = prob$h_n)
realiz <- collectVector('result', n = n, h = prob$h_n)
}
}