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

CAex {Matrix} | R Documentation

## Albers' example Matrix with "Difficult" Eigen Factorization

### Description

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 (https://stat.ethz.ch/mailman/listinfo/r-help), by Casper J Albers, Open University, UK.

### Usage

    data(CAex)

### Format

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

### Details

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.

### Examples

    data(CAex)
    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"))

[Package Matrix version 1.2-12 Index]