This matrix represents the contiguities of 3111 US counties using the Queen criterion of at least a single shared boundary point. The representation is as a row standardised spatial weights matrix transformed to a symmetric matrix (see Ord (1975), p. 125).
A 3111 ^2 symmetric sparse matrix of class
dsCMatrix with 9101 non-zero entries.
The data were read into R using
row-standardised and transformed to symmetry using
This spatial weights object was converted to class
as_dsTMatrix_listw and coercion.
The data were retrieved from
files “usc.txt” and “usc_q.GAL”, with permission for use
and distribution from Luc Anselin (in early 2008).
Ord, J. K. (1975) Estimation methods for models of spatial interaction; Journal of the American Statistical Association 70, 120–126.
data(USCounties) (n <- ncol(USCounties)) IM <- .symDiagonal(n) nn <- 50 set.seed(1) rho <- runif(nn, 0, 1) system.time(MJ <- sapply(rho, function(x) determinant(IM - x * USCounties, logarithm = TRUE)$modulus)) ## can be done faster, by update()ing the Cholesky factor: nWC <- -USCounties C1 <- Cholesky(nWC, Imult = 2) system.time(MJ1 <- n * log(rho) + sapply(rho, function(x) 2 * c(determinant(update(C1, nWC, 1/x))$modulus))) all.equal(MJ, MJ1) C2 <- Cholesky(nWC, super = TRUE, Imult = 2) system.time(MJ2 <- n * log(rho) + sapply(rho, function(x) 2 * c(determinant(update(C2, nWC, 1/x))$modulus))) all.equal(MJ, MJ2) system.time(MJ3 <- n * log(rho) + Matrix:::ldetL2up(C1, nWC, 1/rho)) stopifnot(all.equal(MJ, MJ3)) system.time(MJ4 <- n * log(rho) + Matrix:::ldetL2up(C2, nWC, 1/rho)) stopifnot(all.equal(MJ, MJ4))
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