spdep (version 0.8-1)

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())

Value

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

Control arguments

trace

report values in while loops, default NULL assuming FALSE; logical

tol

tolerance for breaking while loops, default .Machine$double.eps^(1/2); numeric

maxiter

maximum number of iterations in while loops, default 6 * (length(lw$neighbours) - 2; integer

useC

use C code, default TRUE, logical (not in l_max)

References

Griffith, D. A. (2004). Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses. Linear Algebra and its Applications, 388:201<U+2013>219.

Examples

# NOT RUN {
data(boston, package="spData")
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$values)
# At line 409 of file dsaupd.f: Fortran runtime error: Actual string
# length is shorter than the declared one for dummy argument 'which' (0/2)
#  arn <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
#    which="SA", maxiter=200))
#  print(arn$values)
# At line 409 of file dsaupd.f: Fortran runtime error: Actual string
# length is shorter than the declared one for dummy argument 'which' (0/2)
#  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)
# At line 409 of file dsaupd.f: Fortran runtime error: Actual string
# length is shorter than the declared one for dummy argument 'which' (0/2)
#  arn <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
#    which="SA", maxiter=400))
#  print(arn$values)
# At line 409 of file dsaupd.f: Fortran runtime error: Actual string
# length is shorter than the declared one for dummy argument 'which' (0/2)
#  ar1 <- arpack(f2, sym=TRUE, options=list(n=n, nev=2, ncv=8,
#    which="BE", maxiter=300))
# "BE" gives: At line 558 of file dsaup2.f: Fortran runtime error: 
# Index '9' of dimension 1 of array 'bounds' above upper bound of 8
#  print(ar1$values)
#}
# }
# NOT RUN {
ab.listw <- nb2listw(boston.soi, style="S")
er <- range(eigenw(similar.listw(ab.listw)))
er
res_1 <- lextrS(ab.listw)
c(res_1)
# }
# NOT RUN {
#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$values)
# At line 409 of file dsaupd.f: Fortran runtime error: Actual string
# length is shorter than the declared one for dummy argument 'which' (0/2)
#  arn <- arpack(f2, sym=TRUE, options=list(n=n, nev=1, ncv=8,
#    which="SA", maxiter=300))
#  print(arn$values)
# At line 409 of file dsaupd.f: Fortran runtime error: Actual string
# length is shorter than the declared one for dummy argument 'which' (0/2)
#  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)
#}
# }