lextrB

0th

Percentile

Find extreme eigenvalues of binary symmetric spatial weights

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).

Keywords
spatial
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_max, the object may be asymmetric and does not have to be binary
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.

Note

It may be necessary to modify control arguments if warnings about lack of convergence are seen.

Control arguments

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.

Aliases
  • lextrB
  • lextrW
  • lextrS
  • l_max
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)
}
Documentation reproduced from package spdep, version 0.6-9, License: GPL (>= 2)

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