Abstract

'Fields' is a widely used, open source, and freely available spatial statistics package in R that can be used to analyze spatial variation in anything from global temperatures to restaurant ratings. Increasingly, however, it has become necessary to analyze larger and larger datasets. In order to ... Show more'Fields' is a widely used, open source, and freely available spatial statistics package in R that can be used to analyze spatial variation in anything from global temperatures to restaurant ratings. Increasingly, however, it has become necessary to analyze larger and larger datasets. In order to accomplish this task, primary linear algebra algorithms used in Fields must be enhanced to take advantage of parallel computing techniques. The performance of Fields and another standard spatial statistics package in R, GeoR, are evaluated on spatial datasets of increasing size. The most computationally intensive areas in Fields' main spatial analysis functions are identified to be the eigen and Cholesky decompositions in the Krig and mKrig functions respectively. In particular, for spatial datasets with more than 10,000 observations, a single Cholesky decomposition takes 80 percent or more of the computation time of mKrig. Moreover, one surprising result is that in some circumstances a single eigendecompostion is competitive with a sequence of Cholesky decompositions for estimating statistical parameters. The results confirm the well-known polynomial dependence of analysis time on data set size. Given these findings, a method is presented for parallel optimization that efficiently distributes the matrix decompositions. Show less