Contiguity Matrix of World One-Degree Grid Cells

This matrix gives the contiguities of 15260 one-degree grid cells of world land areas, using a criterion based on the great-circle distance between centers.

data(wrld_1deg)

Format

A \(15260 \times 15260\) sparse, symmetric matrix of class dsCMatrix, with 55973 nonzero entries.

Source

Shoreline data were read into R from the GSHHS database using function Rgshhs from package maptools. Antarctica was excluded. An approximately one-degree grid was generated using function Sobj_SpatialGrid, also from maptools. Grid cells with centers on land were identified using the over method for classes SpatialPolygons and SpatialGrid, defined in package sp. Neighbours of these were identified by passing the resulting SpatialPixels object to function dnearneigh from package spdep, using as a cut-off a great-circle distance of sqrt(2) kilometers between centers.

Neighbour lists were augmented with row-standardized (and then symmetrized) spatial weights, using functions nb2listw and similar.listw from packages spdep and spatialreg. The resulting listw object was coerced to class dsTMatrix using as_dsTMatrix_listw from spatialreg, and subsequently to class dsCMatrix.

References

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

Examples

data(wrld_1deg, package = "Matrix")
(n <- ncol(wrld_1deg))
#> [1] 15260
I <- .symDiagonal(n)

doExtras <- interactive() || nzchar(Sys.getenv("R_MATRIX_CHECK_EXTRA"))
set.seed(1)
r <- if(doExtras) 20L else 3L
rho <- 1 / runif(r, 0, 0.5)

system.time(MJ0 <- sapply(rho, function(mult)
    determinant(wrld_1deg + mult * I, logarithm = TRUE)$modulus))
#>    user  system elapsed 
#>   0.092   0.000   0.092 

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

C1 <- Cholesky(wrld_1deg, Imult = 2)
system.time(MJ1 <- sapply(rho, function(mult)
    determinant(update(C1, wrld_1deg, mult), sqrt = FALSE)$modulus))
#>    user  system elapsed 
#>   0.041   0.000   0.042 
stopifnot(all.equal(MJ0, MJ1))

C2 <- Cholesky(wrld_1deg, super = TRUE, Imult = 2)
#> Warning: CHOLMOD warning 'matrix not positive definite' at file 'Supernodal/t_cholmod_super_numeric_worker.c', line 1114
#> Error in .local(A, ...): leading principal minor of order 813 is not positive
system.time(MJ2 <- sapply(rho, function(mult)
    determinant(update(C2, wrld_1deg, mult), sqrt = FALSE)$modulus))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'determinant': error in evaluating the argument 'object' in selecting a method for function 'update': object 'C2' not found
#> Timing stopped at: 0.001 0 0.001
stopifnot(all.equal(MJ0, MJ2))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'current' in selecting a method for function 'all.equal': object 'MJ2' not found