Implement KrylovKit.eigsolve for Tensors

[jofrevalles]

Summary

This PR extends the KrylovKit.eigsolve function for Tensors. We added some tests to cover this function too.

Example

julia> using KrylovKit

julia> using Muscle; using LinearAlgebra; using Test

julia> A = rand(ComplexF64, 4, 4)
4×4 Matrix{ComplexF64}: ...

julia> data = (A + A') / 2 # Make it Hermitian

julia> tensor = Tensor(data, [Index(:i), Index(:j)])
4×4 Tensor{ComplexF64, 2, Matrix{ComplexF64}}: ..

julia> vals, vecs, info = eigsolve(tensor, Tensor(rand(ComplexF64, 4), [Index(:i)]), 4, :SR, Lanczos(; krylovdim=4, tol=1e-16); left_inds=[Index(:i)], right_inds=[Index(:j)]) # Perform eigensolve
...

julia> V_matrix = hcat([reshape(parent(vec), :) for vec in vecs]...) # Convert vecs to matrix form for reconstruction
4×4 Matrix{ComplexF64}: ...

julia> D_matrix = Diagonal(vals)
4×4 Diagonal{Float64, Vector{Float64}}:
 -0.573245   ⋅          ⋅         ⋅ 
   ⋅        0.0709279   ⋅         ⋅ 
   ⋅         ⋅         0.430396   ⋅ 
   ⋅         ⋅          ⋅        2.32354

julia> reconstructed_matrix = V_matrix * D_matrix * inv(V_matrix)
4×4 Matrix{ComplexF64}: ...

julia> @test isapprox(reconstructed_matrix, parent(tensor))
Test Passed

[Copilot]

Pull Request Overview

This PR extends the KrylovKit.eigsolve functionality to support Tensor types and adds integration tests for this new feature.

• Implement Tensor reshaping and permutation logic before eigendecomposition.
• Add integration tests covering both default and Lanczos algorithm usage.
• Include the new Tensor functionality in the test suite.

Reviewed Changes

Copilot reviewed 3 out of 4 changed files in this pull request and generated 1 comment.

File	Description
test/runtests.jl	Added integration test inclusion for KrylovKit.
test/integration/KrylovKit_test.jl	Added integration tests for eigsolve with various Tensor scenarios.
ext/MuscleKrylovKitExt.jl	Introduced Tensor reshaping utility and eigsolve overloads for Tensors.

[Copilot]

The error message references '$prod_x₀_sizes' which is not defined. Consider computing prod_x₀_sizes (e.g., prod_x₀_sizes = prod(size.((x₀,), left_inds))) before using it in the error message.

Suggested change

	prod(size.((x₀,), left_inds)) != prod_left_sizes && throw(
	prod_x₀_sizes = prod(size.((x₀,), left_inds))
	prod_x₀_sizes != prod_left_sizes && throw(

[jofrevalles]

Hola copilot, sí que està definit... Les IA encara no esteu preparades per ser reviewers...

[starsfordummies]

nice! next step would be to get it to work with sergio's dmrg example (using a function to compute H\psi instead of storing H, that should be al least a cost cut chi^4 -> chi^3

[mofeing]

After reading the documentation of KrylovKit.jl, this package extension is not needed and actually goes against the recommended usage. Instead, I made Tensor implement the "Vector interface" from VectorInterface.jl in f3f78d6 and works flawlessly, also for cases where the effective Hamiltonian is factorized.

I'm not yet closing this PR because the tests are still useful.