# lextrB: Find extreme eigenvalues of binary symmetric spatial weights In r-spatial/spatialreg: Spatial Regression Analysis

## 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

 ```1 2 3 4``` ```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.

## 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`)

## Note

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

## Author(s)

Roger Bivand, Yongwan Chun, Daniel Griffith

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48``` ```data(boston, package="spData") #require(spdep, quietly=TRUE) ab.listb <- spdep::nb2listw(boston.soi, style="B") er <- range(eigenw(ab.listb)) er res_1 <- lextrB(ab.listb) c(res_1) run <- FALSE if (require("RSpectra", quietly=TRUE)) run <- TRUE if (run) { B <- as(ab.listb, "CsparseMatrix") eigs(B, k=1, which="SR")\$values } if (run) { eigs(B, k=1, which="LR")\$values } k5 <- spdep::knn2nb(spdep::knearneigh(boston.utm, k=5)) c(l_max(spdep::nb2listw(k5, style="B"))) max(Re(eigenw(spdep::nb2listw(k5, style="B")))) c(l_max(spdep::nb2listw(k5, style="C"))) max(Re(eigenw(spdep::nb2listw(k5, style="C")))) ab.listw <- spdep::nb2listw(boston.soi, style="W") er <- range(eigenw(similar.listw(ab.listw))) er res_1 <- lextrW(ab.listw) c(res_1) if (run) { B <- as(similar.listw(ab.listw), "CsparseMatrix") eigs(B, k=1, which="SR")\$values } if (run) { eigs(B, k=1, which="LR")\$values } ## Not run: ab.listw <- spdep::nb2listw(boston.soi, style="S") er <- range(eigenw(similar.listw(ab.listw))) er res_1 <- lextrS(ab.listw) c(res_1) ## End(Not run) if (run) { B <- as(similar.listw(ab.listw), "CsparseMatrix") eigs(B, k=1, which="SR")\$values } if (run) { eigs(B, k=1, which="LR")\$values } ```

r-spatial/spatialreg documentation built on Dec. 1, 2019, 4:20 a.m.