R: Generalized Eigen Problem of the Form ' A P = B P Lambda'...

Geigen {lazy.mat}

R Documentation

Generalized Eigen Problem of the Form
`A P = B P Lambda`
where `t(P) B P = I`.

Description

Generalized Eigen Problem of the Form
A P = B P Lambda
where t(P) B P = I.

Usage

Geigen(A, B = diag(nrow(A)), ndim = nrow(A), check = 0)

Arguments

`A`	the input symmetric matrix of size `n`
`B`	the input symmetric matrix of size `n`
`ndim`	# of eigen values/vectors to return.
`check`	= 1 to check if `A P - B P Lambda = 0`.

Details

The eigen decomposition of B^{-1/2} A B^{-1/2} is used.

Value

A list of
values The ndim largest eigen values.
vectors The n x ndim matrix of the eigen vectors.
tPBP The value of t(P) B P
tPAP The value of t(P) A P
maxad max(abs(A P - B P Lambda))

Examples

n=5
set.seed(1701)
A <- matrix(rnorm(n^2), n,n)
A <- t(A)%*%A
B <-  matrix(rnorm(n^2), n,n)
B <- t(B)%*%B
Geigen(A,B, check=1)

[Package lazy.mat version 0.1.6 ]