GeneralizedEigenvalues

A package for the computation of generalized eigenvalues. These are the values $\lambda$ satisfying $Ax = \lambda B x$ for two given matrices $A$ and $B$.

The package is implemented in Julia, hence the computation is generic. In particular the package implements the routine generalized_eigvals! and defines

LinearAlgebra.eigvals!(A::AbstractMatrix{T}, B::AbstractMatrix{T}; kwargs...) where {T <: Number} =
    generalized_eigvals!(A, B; kwargs...)

Note: the intention is for this package to be temporary and to remain unregistered. Once the functionality is validated with sufficient testing, the goal is to merge into the GenericLinearAlgebra package. Meanwhile, anybody using this functionality, feel free to submit issues, tests or code.

How to use

julia> using LinearAlgebra, GeneralizedEigenvalues

julia> A = rand(BigFloat, 4, 4); B = rand(BigFloat, 4, 4);

julia> eigvals(A, B)
4-element Vector{Complex{BigFloat}}:
 -1.177518817295070669604971559985944058233157194009907413729886903454997250952444 - 1.976184214307596326495074265168079377563480081756809493383013442251886672508137im
 -1.177518817295070669604971559985944058233157194009907413729886903454997250952444 + 1.976184214307596326495074265168079377563480081756809493383013442251886672508137im
 0.1023675480850108409048085676574292182205270437393180274439073767290659164355778 + 0.0im
 0.8914521716628669627775377453285786522762398515948895489745740716735863657953472 + 0.0im

History and development

The code in this package has been written bij @thijssteel. It was originally submitted as a pull request to GenericLinearAlgebra.jl. By making it available as a package it can be used "as is", and hopefully tests can be added to improve robustness and help integration in other packages.