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 Tenet; using LinearAlgebra; using Test

julia> using KrylovKit
┌ Warning: The project dependencies or compat requirements have changed since the manifest was last resolved.
│ It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary.
└ @ Pkg.API ~/.julia/juliaup/julia-1.10.2+0.x64.linux.gnu/share/julia/stdlib/v1.10/Pkg/src/API.jl:1807
[ Info: Precompiling TenetKrylovKitExt [29b5df5b-24ac-5557-97d4-3d2f1208de95]

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

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

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

julia> vals, vecs = eigsolve(tensor; left_inds=[:i], right_inds=[:j]) # Perform eigensolve
([2.3507038036026553, -0.7165812403097447, 0.3433988271360078, 0.18227647730800145], Tensor{ComplexF64, 1, Vector{ComplexF64}}[[0.4141738753940685 + 0.3073367327846263im, 0.41661203124364915 + 0.1853467004548118im, 0.29906239280853125 + 0.35035248351300025im, 0.38944025132705234 + 0.40278562887237646im], [0.26352280677272105 + 0.5511773506958907im, -0.14761808542348484 - 0.708632804563461im, -0.24984012828454633 - 0.13660399464451234im, -0.04906317004703921 + 0.13899558206566603im], [-0.011943074391772727 + 0.2694131820645913im, -0.3347917377550906 + 0.3074609885080383im, 0.3989980157520261 - 0.7061959066874091im, 0.10617448539651439 + 0.22687229146630172im], [-0.0816029957725681 + 0.5304509811449717im, -0.16119745313827308 + 0.1884862838094723im, 0.07319838199527906 + 0.20848022238811795im, 0.26215618954309244 - 0.7300021476894631im]])

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}}:
 2.3507    ⋅         ⋅         ⋅ 
  ⋅      -0.716581   ⋅         ⋅ 
  ⋅        ⋅        0.343399   ⋅ 
  ⋅        ⋅         ⋅        0.182276

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

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

[jofrevalles]

@mofeing can we merge this?

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 17 lines in your changes missing coverage. Please review.

Project coverage is 55.16%. Comparing base (5ee9b93) to head (34281ef).
Report is 30 commits behind head on master.

Files	Patch %	Lines
ext/TenetKrylovKitExt.jl	0.00%	17 Missing ⚠️

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Additional details and impacted files

@@             Coverage Diff             @@
##           master     #157       +/-   ##
===========================================
- Coverage   68.76%   55.16%   -13.60%     
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  Files          19       20        +1     
  Lines        1050     1084       +34     
===========================================
- Hits          722      598      -124     
- Misses        328      486      +158     

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