spdep (version 0.5-88)

lextrB: Find extreme eigenvalues of binary symmetric spatial weights

Description

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).

Usage

lextrB(lw, zero.policy = TRUE, control = list())
lextrW(lw, zero.policy=TRUE, control=list())
lextrS(lw, zero.policy=TRUE, control=list())
l_max(lw, zero.policy=TRUE, control=list())

Arguments

lw

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

zero.policy

default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA

control

a list of control arguments

Value

• The functions return approximations to the extreme eigenvalues with the eigenvectors returned as attributes of this object.

References

Griffith, D. A. (2004). Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses. Linear Algebra and its Applications, 388:201–219.

Examples

data(boston)
ab.listb <- nb2listw(boston.soi, style="B")
er <- range(eigenw(ab.listb))
er
res_1 <- lextrB(ab.listb)
c(res_1)
if (require(igraph)) {
  B <- as(ab.listb, "symmetricMatrix")
  n <- length(boston.soi)
  f2 <- function(x, extra=NULL) {as.vector(B %*% x)}
  ar1 <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
    which="LA", maxiter=200))
  print(ar1$values)
  arn <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
    which="SA", maxiter=200))
  print(arn$values)
#  ar1 <- arpack(f2, sym=TRUE, options=list(n=n, nev=2, ncv=8,
#    which="BE", maxiter=300))
# "BE" gives: At line 558 of file dsaup2.f: Fortran runtime error: 
# Index '9' of dimension 1 of array 'bounds' above upper bound of 8
# "BE" 
#  print(ar1$values)
}
k5 <- knn2nb(knearneigh(boston.utm, k=5))
c(l_max(nb2listw(k5, style="B")))
max(Re(eigenw(nb2listw(k5, style="B"))))
c(l_max(nb2listw(k5, style="C")))
max(Re(eigenw(nb2listw(k5, style="C"))))
ab.listw <- nb2listw(boston.soi, style="W")
er <- range(eigenw(similar.listw(ab.listw)))
er
res_1 <- lextrW(ab.listw)
c(res_1)
if (require(igraph)) {
  B <- as(similar.listw(ab.listw), "symmetricMatrix")
  ar1 <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
    which="LA", maxiter=400))
  print(ar1$values)
  arn <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
    which="SA", maxiter=400))
  print(arn$values)
#  ar1 <- arpack(f2, sym=TRUE, options=list(n=n, nev=2, ncv=8,
#    which="BE", maxiter=300))
# "BE" gives: At line 558 of file dsaup2.f: Fortran runtime error: 
# Index '9' of dimension 1 of array 'bounds' above upper bound of 8
#  print(ar1$values)
}
ab.listw <- nb2listw(boston.soi, style="S")
er <- range(eigenw(similar.listw(ab.listw)))
er
res_1 <- lextrS(ab.listw)
c(res_1)
if (require(igraph)) {
  B <- as(similar.listw(ab.listw), "symmetricMatrix")
  ar1 <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
    which="LA", maxiter=300))
  print(ar1$values)
  arn <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
    which="SA", maxiter=300))
  print(arn$values)
#  ar1 <- arpack(f2, sym=TRUE, options=list(n=n, nev=2, ncv=8,
#    which="BE", maxiter=300))
# "BE" gives: At line 558 of file dsaup2.f: Fortran runtime error: 
# Index '9' of dimension 1 of array 'bounds' above upper bound of 8
#  print(ar1$values)
}