source('../Chapter3/utils.R')
source('utils.R')

A = matrix(data=c(-2, 0, 1, 0, 0, -2, 0, 1, 1, 0, -2, 0, 0, 1, 0, -2), nrow=4, ncol=4, byrow=FALSE)
##print(A)

M = matrix(data=c(2, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2), nrow=4, ncol=4, byrow=FALSE)
##print(M)

n = dim(A)[1]

## The eigenvalues are the roots of the following function:
##
natural_frequency_fn = function(x){
    determinant_from_GE(A - x * M)
}

## Lets get a feel for where the zeros of det(A - lambda M) lie:
##
xs = seq(-3.5, +0.5, length.out=1000)
ys = sapply(xs, natural_frequency_fn)
plot(xs, ys, 'l', ylab='det(A-xM)')
grid()

res = mullers_iteration(c(-4.0, -2.0, 0.0), natural_frequency_fn, n, verbose=FALSE)
print(res)