I have the following matlab code:

```
function [ DomRVec, DomEig, Error ] = MyEigs( Tup, Tdn, NumofValue, SpeString, Dbond, Dspin, InitVec )
VecDim = Dbond^2;
Tup = reshape( permute( Tup, [ 1, 3, 2 ] ), [ Dbond * Dspin, Dbond ] ); % A(lrm) => A(lm,r), placed at upper
Tdn = reshape( permute( Tdn, [ 3, 2, 1 ] ), [ Dspin * Dbond, Dbond ] ); % B(lrm) => B(mr,l), placed at lower
ActionFun = @( x ) Action( Tup, Tdn, x, Dbond, Dspin );
[ DomRVec, DomEig ] = eigs( ActionFun, VecDim, NumofValue, SpeString, 'IsFunctionSymmetric', 0, 'Tolerance', 1E-14, 'MaxIterations', 300, 'StartVector', InitVec, ...
'Display', 0 );
Error = Maxdiff( Action( Tup, Tdn, DomRVec, Dbond, Dspin ), DomRVec * DomEig );
end
function [ y ] = Action( Tup, Tdn, x, Dbond, Dspin )
d = size( x, 2 );
x = reshape( x, [ Dbond, Dbond * d ] );
if( d == 1 )
y = reshape( Tup * x, [ Dbond, Dspin * Dbond ] );
y = reshape( y * Tdn, [ Dbond^2, 1 ] );
elseif( d > 1)
y = reshape( Tup * x, [ Dbond, Dspin * Dbond, d ] );
y = reshape( permute( y, [ 1, 3, 2 ] ), [ Dbond * d, Dspin * Dbond ] );
y = reshape( y * Tdn, [ Dbond, d, Dbond ] );
y = reshape( permute( y, [ 1, 3, 2 ] ), [ Dbond * Dbond, d ] );
end
end
```

After referring to the documentation and source code of *Arpack.jl*, I wrote the following code. It runs without errors, but the results are significantly different from those obtained with MATLAB. Moreover, the results vary each time I run the code. I can’t figure out what’s causing this inconsistency. Could anyone point out where the mistake might be, or suggest alternative methods to achieve the same functionality?

```
using LinearAlgebra
using Arpack
struct MyMatrix{T,S} <: AbstractArray{T, 2}
Tup::S
Tdn::S
Dbond::Int
Dspin::Int
end
function MyMatrix(Tup, Tdn, Dbond, Dspin)
Tnew = typeof(zero(eltype(Tup))/sqrt(one(eltype(Tup))))
Tup_new = convert(AbstractMatrix{Tnew}, Tup)
Tdn_new = convert(AbstractMatrix{Tnew}, Tdn)
MyMatrix{Tnew,typeof(Tup_new)}(Tup_new, Tdn_new, Dbond, Dspin)
end
function LinearAlgebra.mul!(y::StridedVector{T}, A::MyMatrix{T}, x::StridedVector{T}) where T
d = 1
x = reshape(x, (A.Dbond, A.Dbond * d))
if d == 1
y = reshape(A.Tup * x, (A.Dbond, A.Dspin * A.Dbond))
y = reshape(y * A.Tdn, (A.Dbond^2, 1))
return y
end
Base.size(A::MyMatrix) = (A.Dbond^2, A.Dbond^2)
LinearAlgebra.ishermitian(A::MyMatrix) = true
Tup, Tdn, Dbond, Dspin = reshape(1:18,3,3,2),reshape(2:19,3,3,2),3,2
Tup = reshape( permutedims( Tup, [ 1, 3, 2 ] ), Dbond * Dspin, Dbond )
Tdn = reshape( permutedims( Tdn, [ 3, 2, 1 ] ), Dspin * Dbond, Dbond )
A = MyMatrix(Tup, Tdn, Dbond, Dspin)
λ, ϕ = eigs(A; nev=1,which=:LR)
```