ArnoldiMethod.jl
The Implicitly Restarted Arnoldi Method, natively in Julia.
Docs
Goal
Make eigs a native Julia function.
Installation
Open the package manager in the REPL via ] and run
(v1.0) pkg> add ArnoldiMethod
Example
julia> using ArnoldiMethod, LinearAlgebra, SparseArrays
julia> A = spdiagm(
-1 => fill(-1.0, 99),
0 => fill(2.0, 100),
1 => fill(-1.0, 99)
);
julia> decomp, history = partialschur(A, nev=10, tol=1e-6, which=SR());
julia> decomp
PartialSchur decomposition (Float64) of dimension 10
eigenvalues:
10-element Array{Complex{Float64},1}:
0.0009674354160236865 + 0.0im
0.003868805732811139 + 0.0im
0.008701304061962657 + 0.0im
0.01546025527344699 + 0.0im
0.024139120518486677 + 0.0im
0.0347295035554728 + 0.0im
0.04722115887278571 + 0.0im
0.06160200160067088 + 0.0im
0.0778581192025522 + 0.0im
0.09597378493453936 + 0.0im
julia> history
Converged: 10 of 10 eigenvalues in 174 matrix-vector products
julia> norm(A * decomp.Q - decomp.Q * decomp.R)
6.39386920955869e-8
julia> λs, X = partialeigen(decomp);
julia> norm(A * X - X * Diagonal(λs))
6.393869211477937e-8