Hello, I have obtained strange results using eigen on a symmetric matrix:
# this function perform a double centering of a matrix (xij-rowmean(i)-colmean(j)+meantot)
dbcenter=function(mat){
rmean=apply(mat,1,mean)
cmean=apply(mat,2,mean)
newmat=sweep(mat,1,rmean,"-")
newmat=sweep(newmat,2,cmean,"-")
newmat=newmat+mean(mat)
newmat}
# i use spdep package to create a spatial contiguity matrix library(spdep) x=dbcenter(nb2mat(cell2nb(3,3),style="B"))
#compute eigenvalues of a 9 by 9 matrix res=eigen(x)
# some eigenvalues are equal to 0
eq0 <- apply(as.matrix(res$values),1,function(x) identical(all.equal(x, 0), TRUE))
# I remove the corresponding eigenvectors res0=res$vec[,-which(eq0)]
# then I compute the Froebenius norm with the identity matrix sum((diag(1,ncol(res0))-crossprod(res0))^2)
[1] 1.515139e-30
# The results are correct, # then I do it again with a biggest matrix(100 by 100)
x=dbcenter(nb2mat(cell2nb(10,10),style="B"))
res=eigen(x)
eq0 <- apply(as.matrix(res$values),1,function(x) identical(all.equal(x, 0), TRUE))
res0=res$vec[,-which(eq0)]
sum((diag(1,ncol(res0))-crossprod(res0))^2)
[1] 3.986387
I have try the same with res=eigen(x,EISPACK=T):
x=dbcenter(nb2mat(cell2nb(10,10),style="B"))
res=eigen(x,EISPACK=T)
eq0 <- apply(as.matrix(res$values),1,function(x) identical(all.equal(x, 0), TRUE))
res0=res$vec[,-which(eq0)]
sum((diag(1,ncol(res0))-crossprod(res0))^2)
[1] 1.315542e-27
So I wonder I there is a bug in the LAPACK algorithm or if there are some things that I have not understood. Note that my matrix has some pairs of equal eigenvalues.
Thanks in advance.
St�phane DRAY
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