Methods to diagonalize a Matrix{BigFloat}?

Specific Domains Numerics
21

Great. Thank you.

22

There is a problem when the determinant of the matrix is zero, per example :

julia> using LinearAlgebra

julia> using GenericSchur

julia> eigvecs(BigFloat.([0 0 1 0; 0 0 0 0; -1 0 0 0; 0 0 0 0]))
ERROR: ArgumentError: iteration limit 400 reached
Stacktrace:
 [1] _gschur!(::Hessenberg{BigFloat,UpperHessenberg{BigFloat,Array{BigFloat,2}},Array{BigFloat,2},Array{GenericSchur.Householder{BigFloat,S} where S<:(StridedArray{T, 1} where T),1},Bool}, ::Array{BigFloat,2}; tol::BigFloat, debug::Bool, shiftmethod::Symbol, maxiter::Int64, standardize::Bool, kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /Users/ymocquar/.julia/packages/GenericSchur/YzsRq/src/GenericSchur.jl:377
 [2] _gschur! at /Users/ymocquar/.julia/packages/GenericSchur/YzsRq/src/GenericSchur.jl:359 [inlined]
 [3] gschur!(::Array{BigFloat,2}; wantZ::Bool, scale::Bool, kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /Users/ymocquar/.julia/packages/GenericSchur/YzsRq/src/GenericSchur.jl:630
 [4] gschur! at /Users/ymocquar/.julia/packages/GenericSchur/YzsRq/src/GenericSchur.jl:617 [inlined]
 [5] #schur!#1 at /Users/ymocquar/.julia/packages/GenericSchur/YzsRq/src/GenericSchur.jl:12 [inlined]
 [6] schur! at /Users/ymocquar/.julia/packages/GenericSchur/YzsRq/src/GenericSchur.jl:12 [inlined]
 [7] schur at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.5/LinearAlgebra/src/schur.jl:143 [inlined]
 [8] eigen!(::Array{BigFloat,2}; permute::Bool, scale::Bool, sortby::typeof(LinearAlgebra.eigsortby)) at /Users/ymocquar/.julia/packages/GenericSchur/YzsRq/src/GenericSchur.jl:69
 [9] eigen(::Array{BigFloat,2}; permute::Bool, scale::Bool, sortby::typeof(LinearAlgebra.eigsortby)) at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.5/LinearAlgebra/src/eigen.jl:237
 [10] eigen at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.5/LinearAlgebra/src/eigen.jl:235 [inlined]
 [11] #eigvecs#70 at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.5/LinearAlgebra/src/eigen.jl:257 [inlined]
 [12] eigvecs(::Array{BigFloat,2}) at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.5/LinearAlgebra/src/eigen.jl:257
 [13] top-level scope at REPL[35]:1
23

Thanks for the report. Iā€™m currently revising the methods for real element types, to deal with edge cases like this. In the interim please try adding 0im to make the matrix complex.