geigen (version 2.3)

gevalues: 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.

Value

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

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.

See Also

geigen, gqz

Examples

# NOT RUN {
# 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
# }