Calculate Generalized Eigenvalues from a Generalized Schur decomposition

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Description

Computes the generalized eigenvalues from an object constructed with gqz.

Usage

1

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

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# 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