Matrix (version 1.7-1)

USCounties: Contiguity Matrix of U.S. Counties

Description

This matrix gives the contiguities of 3111 U.S. counties, using the queen criterion of at least one shared vertex or edge.

Usage

data(USCounties)

Format

A \(3111 \times 3111\) sparse, symmetric matrix of class dsCMatrix, with 9101 nonzero entries.

References

Ord, J. K. (1975). Estimation methods for models of spatial interaction. Journal of the American Statistical Association, 70(349), 120-126. tools:::Rd_expr_doi("10.2307/2285387")

Examples

 
library(stats, pos = "package:base", verbose = FALSE)
library(utils, pos = "package:base", verbose = FALSE)

data(USCounties, package = "Matrix")
(n <- ncol(USCounties))
I <- .symDiagonal(n)

set.seed(1)
r <- 50L
rho <- 1 / runif(r, 0, 0.5)

system.time(MJ0 <- sapply(rho, function(mult)
    determinant(USCounties + mult * I, logarithm = TRUE)$modulus))

## Can be done faster by updating the Cholesky factor:

C1 <- Cholesky(USCounties, Imult = 2)
system.time(MJ1 <- sapply(rho, function(mult)
    determinant(update(C1, USCounties, mult), sqrt = FALSE)$modulus))
stopifnot(all.equal(MJ0, MJ1))

C2 <- Cholesky(USCounties, super = TRUE, Imult = 2)
system.time(MJ2 <- sapply(rho, function(mult)
    determinant(update(C2, USCounties, mult), sqrt = FALSE)$modulus))
stopifnot(all.equal(MJ0, MJ2))