Matrix (version 1.5-1)

wrld_1deg: World 1-degree grid contiguity matrix

Description

This matrix represents the distance-based contiguities of 15260 one-degree grid cells of land areas. The representation is as a row standardised spatial weights matrix transformed to a symmetric matrix (see Ord (1975), p. 125).

Usage

data(wrld_1deg)

Format

A \(15260 ^2\) symmetric sparse matrix of class dsCMatrix with 55973 non-zero entries.

Details

The data were created into R using the coordinates of a ‘SpatialPixels’ object containing approximately one-degree grid cells for land areas only (world excluding Antarctica), using package spdep's dnearneigh with a cutoff distance of sqrt(2), and row-standardised and transformed to symmetry using nb2listw and similar.listw. This spatial weights object was converted to a dsTMatrix using as_dsTMatrix_listw and then coerced (column-compressed).

References

Ord, J. K. (1975) Estimation methods for models of spatial interaction; Journal of the American Statistical Association 70, 120--126.

Examples

data(wrld_1deg)
(n <- ncol(wrld_1deg))
IM <- .symDiagonal(n)
doExtras <- interactive() || nzchar(Sys.getenv("R_MATRIX_CHECK_EXTRA"))
nn <- if(doExtras) 20 else 3
set.seed(1)
rho <- runif(nn, 0, 1)
system.time(MJ <- sapply(rho,
                   function(x) determinant(IM - x * wrld_1deg,
                                           logarithm = TRUE)$modulus))
nWC <- -wrld_1deg
C1 <- Cholesky(nWC, Imult = 2)
## Note that det() = det(L) = sqrt(det(A))
## ====> log det(A) = log( det(L)^2 ) = 2 * log det(L) :
system.time(MJ1 <- n * log(rho) +
   sapply(rho, function(x) c(2* determinant(update(C1, nWC, 1/x))$modulus))
)
stopifnot(all.equal(MJ, MJ1))
C2 <- Cholesky(nWC, super = TRUE, Imult = 2)
system.time(MJ2 <- n * log(rho) +
   sapply(rho, function(x) c(2* determinant(update(C2, nWC, 1/x))$modulus))
)
system.time(MJ3 <- n * log(rho) + Matrix:::ldetL2up(C1, nWC, 1/rho))
system.time(MJ4 <- n * log(rho) + Matrix:::ldetL2up(C2, nWC, 1/rho))
stopifnot(all.equal(MJ, MJ2),
          all.equal(MJ, MJ3),
          all.equal(MJ, MJ4))