# gevalues: Calculate Generalized Eigenvalues from a Generalized Schur... In geigen: Calculate Generalized Eigenvalues, the Generalized Schur Decomposition and the Generalized Singular Value Decomposition of a Matrix Pair with Lapack

## Description

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

## Usage

 `1` ```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.

`geigen`, `gqz`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# 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 ```