CAex: Albers' example Matrix with "Difficult" Eigen Factorization

CAexR Documentation

Albers' example Matrix with "Difficult" Eigen Factorization


An example of a sparse matrix for which eigen() seemed to be difficult, an unscaled version of this has been posted to the web, accompanying an E-mail to R-help (, by Casper J Albers, Open University, UK.




This is a 72 \times 72 symmetric matrix with 216 non-zero entries in five bands, stored as sparse matrix of class dgCMatrix.


Historical note (2006-03-30): In earlier versions of R, eigen(CAex) fell into an infinite loop whereas eigen(CAex, EISPACK=TRUE) had been okay.


data(CAex, package = "Matrix")
str(CAex) # of class "dgCMatrix"

image(CAex)# -> it's a simple band matrix with 5 bands
## and the eigen values are basically 1 (42 times) and 0 (30 x):
zapsmall(ev <- eigen(CAex, only.values=TRUE)$values)
## i.e., the matrix is symmetric, hence
sCA <- as(CAex, "symmetricMatrix")
## and
stopifnot(class(sCA) == "dsCMatrix",
          as(sCA, "matrix") == as(CAex, "matrix"))

Matrix documentation built on Nov. 14, 2023, 5:06 p.m.