Hi Gabriel,
I can confirm some problems with eigs on OSX. Seems with each call one gets
one of the eigenvalues/eigenvectors of T, but not necessarily the largest
one:
julia> T
3x3 Array{Float64,2}:
0.9 0.05 0.05
0.8 0.1 0.1
0.7 0.1 0.2
julia> eig(T)
([1.0,0.170711,0.0292893],
3x3 Array{Float64,2}:
-0.57735 -0.0873799 0.0282726
-0.57735 0.3371 -0.908743
-0.57735 0.937405 0.416397 )
julia> d,v,nconv = eigs(T,nev=1,which=:LM); v
3x1 Array{Complex{Float64},2}:
0.57735+0.0im
0.57735+0.0im
0.57735+0.0im
julia> d,v,nconv = eigs(T,nev=1,which=:LM); v
3x1 Array{Complex{Float64},2}:
0.0873799+0.0im
-0.3371+0.0im
-0.937405+0.0im
julia> d,v,nconv = eigs(T,nev=1,which=:LM); v
3x1 Array{Complex{Float64},2}:
0.57735+0.0im
0.57735+0.0im
0.57735+0.0im
julia> d,v,nconv = eigs(T,nev=1,which=:LM); v
3x1 Array{Complex{Float64},2}:
-0.57735+0.0im
-0.57735+0.0im
-0.57735+0.0im
julia> d,v,nconv = eigs(T,nev=1,which=:LM); v
3x1 Array{Complex{Float64},2}:
0.57735+0.0im
0.57735+0.0im
0.57735+0.0im
julia> d,v,nconv = eigs(T,nev=1,which=:LM); v
3x1 Array{Complex{Float64},2}:
-0.57735+0.0im
-0.57735+0.0im
-0.57735+0.0im
julia> d,v,nconv = eigs(T,nev=1,which=:LM); v
3x1 Array{Complex{Float64},2}:
0.0873799+0.0im
-0.3371+0.0im
-0.937405+0.0im
julia> d,v,nconv = eigs(T,nev=1,which=:LM); v
3x1 Array{Complex{Float64},2}:
0.0282726+0.0im
-0.908743+0.0im
0.416397+0.0im
Unfortunately I don't have an older version of Julia at hand to test if
this is a regression. I don't think that this behavior is correct and it
would be great if you could file an issue.
Regarding your second question I would say it depends on the details of
your problem (size, sparsity, symmetries, ...), but eigs appears to be a
reasonable starting point.
Best,
Alex.
