API

eigs(A; nev=6, ncv=max(20,2*nev+1), which=:LM, tol=0.0, maxiter=300, sigma=nothing, ritzvec=true, explicittransform=:auto, v0=zeros((0,)), check=0) -> (d,[v,],nconv,niter,nmult,resid)

Computes eigenvalues d of A using implicitly restarted Lanczos or Arnoldi iterations for real symmetric or general nonsymmetric matrices respectively. See the manual for more information.

eigs returns the nev requested eigenvalues in d, the corresponding Ritz vectors v (only if ritzvec=true), the number of converged eigenvalues nconv, the number of iterations niter and the number of matrix vector multiplications nmult, as well as the final residual vector resid. The parameter explicittransform takes the values :auto, :none or :shiftinvert, specifying if shift and invert should be explicitly invoked in julia code.

When check = 0, an error is thrown if maximum number of iterations taken (info = 1). This usually means all possible eigenvalues has been found according to ARPACK manual. When check = 1, return currently converged eigenvalues when info = 1. And a @warn will given. When check = 2, return currently converged eigenvalues when info = 1.

Examples

julia> using LinearAlgebra, Arpack

julia> A = Diagonal(1:4);

julia> λ, ϕ = eigs(A, nev = 2);

julia> λ
2-element Array{Float64,1}:
 3.9999999999999996
 3.000000000000001

eigs(A, B; nev=6, ncv=max(20,2*nev+1), which=:LM, tol=0.0, maxiter=300, sigma=nothing, ritzvec=true, v0=zeros((0,)), check=0) -> (d,[v,],nconv,niter,nmult,resid)

Computes generalized eigenvalues d of A and B using implicitly restarted Lanczos or Arnoldi iterations for real symmetric or general nonsymmetric matrices respectively. See the manual for more information.

When check = 0, an error is thrown if maximum number of iterations taken (info = 1). This usually means all possible eigenvalues has been found according to ARPACK manual. When check = 1, return currently converged eigenvalues when info = 1. And a @warn will given. When check = 2, return currently converged eigenvalues when info = 1.

svds(A; nsv=6, ritzvec=true, tol=0.0, maxiter=1000, ncv=2*nsv, v0=zeros((0,))) -> (SVD([left_sv,] s, [right_sv,]), nconv, niter, nmult, resid, check=0)

Computes the largest singular values s of A using implicitly restarted Lanczos iterations derived from eigs. See the manual for more information.

When check = 0, an error is thrown if maximum number of iterations taken (info = 1). This usually means all possible eigenvalues has been found according to ARPACK manual. When check = 1, return currently converged eigenvalues when info = 1. And a @warn will given. When check = 2, return currently converged eigenvalues when info = 1.