lextrB.Rd
The functions find extreme eigenvalues of binary symmetric spatial weights, when these form planar graphs; general weights are not permiited. l_max
finds the largest eigenvalue using Rayleigh quotient methods of any “listw” object. lextrB
first calls l_max
, and uses its output to find the smallest eigenvalue in addition for binary symmetric spatial weights. lextrW
extends these to find the smallest eigenvalue for intrinsically symmetric row-standardized binary weights matrices (transformed to symmetric through similarity internally). lextrS
does the same for variance-stabilized (“S” style) intrinsically symmetric binary weights matrices (transformed to symmetric through similarity internally).
a binary symmetric listw
object from, for example, nb2listw
with style “B” for lextrB
, style “W” for lextrW
and style “S” for lextrS
; for l_max
, the object may be asymmetric and does not have to be binary
default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
a list of control arguments
report values in while loops, default NULL assuming FALSE; logical
tolerance for breaking while loops, default .Machine$double.eps^(1/2)
; numeric
maximum number of iterations in while loops, default 6 * (length(lw$neighbours) - 2
; integer
use C code, default TRUE, logical (not in l_max
)
The functions return approximations to the extreme eigenvalues with the eigenvectors returned as attributes of this object.
Griffith, D. A. (2004). Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses. Linear Algebra and its Applications, 388:201--219.
It may be necessary to modify control arguments if warnings about lack of convergence are seen.
data(boston, package="spData")
#require(spdep, quietly=TRUE)
ab.listb <- spdep::nb2listw(boston.soi, style="B")
er <- range(eigenw(ab.listb))
er
#> [1] -3.039465 5.306204
res_1 <- lextrB(ab.listb)
c(res_1)
#> lambda_n lambda_1
#> -3.039374 5.306203
run <- FALSE
if (require("RSpectra", quietly=TRUE)) run <- TRUE
if (run) {
B <- as(ab.listb, "CsparseMatrix")
eigs(B, k=1, which="SR")$values
}
#> [1] -3.039465
if (run) {
eigs(B, k=1, which="LR")$values
}
#> [1] 5.306204
k5 <- spdep::knn2nb(spdep::knearneigh(boston.utm, k=5))
c(l_max(spdep::nb2listw(k5, style="B")))
#> [1] 5
max(Re(eigenw(spdep::nb2listw(k5, style="B"))))
#> [1] 5
c(l_max(spdep::nb2listw(k5, style="C")))
#> [1] 1
max(Re(eigenw(spdep::nb2listw(k5, style="C"))))
#> [1] 1
ab.listw <- spdep::nb2listw(boston.soi, style="W")
er <- range(eigenw(similar.listw(ab.listw)))
er
#> [1] -0.9708644 1.0000000
res_1 <- lextrW(ab.listw)
c(res_1)
#> lambda_n lambda_1
#> -0.9708644 0.9999991
if (run) {
B <- as(similar.listw(ab.listw), "CsparseMatrix")
eigs(B, k=1, which="SR")$values
}
#> [1] -0.9708644
if (run) {
eigs(B, k=1, which="LR")$values
}
#> [1] 1
if (FALSE) {
ab.listw <- spdep::nb2listw(boston.soi, style="S")
er <- range(eigenw(similar.listw(ab.listw)))
er
res_1 <- lextrS(ab.listw)
c(res_1)
}
if (run) {
B <- as(similar.listw(ab.listw), "CsparseMatrix")
eigs(B, k=1, which="SR")$values
}
#> [1] -0.9708644
if (run) {
eigs(B, k=1, which="LR")$values
}
#> [1] 1