R: Calculate Generalized Eigenvalues from a Generalized Schur...

gevalues {geigen} | R Documentation

## Calculate Generalized Eigenvalues from a Generalized Schur decomposition

### Description

Computes the generalized eigenvalues from an object constructed with `gqz`.

### Usage

    gevalues(x)

### Arguments

`x` | an object created with `gqz`.

### Details

The function calculates the generalized eigenvalues from elements of the object returned by the function `gqz`. The generalized eigenvalues are computed from a ratio where the denominator (the beta component of the argument) may be zero. The function attempts to guard against nonsensical complex `NaN` values when dividing by zero which may happen on some systems.

### Value

A vector containing the generalized eigenvalues. The vector is numeric if the imaginary parts of the eigenvalues are all zero and complex otherwise.

### See Also

`geigen`, `gqz`

### Examples

    # Real matrices
    # example from NAG: http://www.nag.com/lapack-ex/node116.html
    # Find the generalized Schur decomposition with the real eigenvalues ordered to come first

    A <- matrix(c(  3.9, 12.5,-34.5,-0.5,
                    4.3, 21.5,-47.5, 7.5,
                    4.3, 21.5,-43.5, 3.5,
                    4.4, 26.0,-46.0, 6.0), nrow=4, byrow=TRUE)

    B <- matrix(c( 1.0, 2.0, -3.0, 1.0,
                   1.0, 3.0, -5.0, 4.0,
                   1.0, 3.0, -4.0, 3.0,
                   1.0, 3.0, -4.0, 4.0), nrow=4, byrow=TRUE)

    z <- gqz(A, B,"R")
    z
    # compute the generalized eigenvalues
    ger <- gevalues(z)
    ger

[Package geigen version 2.1 Index]