Dimension mismatch in SVD pullback due to `rank_atol` for `FixedSVD`

[pbrehmer]

I was running into a dimension mismatch error in the pullback of FixedSVD due to the default finite rank_atol for MatrixAlgebraKit's svd_pullback function. Note that we here compute the forward using a full SVD such that we can utilize the full SVD pullback. Here's the full error message:

Details

...the stacktrace before and after this part make the message to long for GitHub...

nested task error: DimensionMismatch: second dimension of ΔU (40) does not match rank of S (25)
    Stacktrace:
      [1] svd_pullback!(ΔA::Base.ReshapedArray{ComplexF64, 2, SubArray{ComplexF64, 1, Vector{ComplexF64}, Tuple{UnitRange{Int64}}, true}, Tuple{}}, A::Base.ReshapedArray{ComplexF64, 2, SubArray{ComplexF64, 1, Vector{ComplexF64}, Tuple{UnitRange{Int64}}, true}, Tuple{}}, USVᴴ::Tuple{Base.ReshapedArray{ComplexF64, 2, SubArray{ComplexF64, 1, Vector{ComplexF64}, Tuple{UnitRange{Int64}}, true}, Tuple{}}, LinearAlgebra.Diagonal{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}}, Base.ReshapedArray{ComplexF64, 2, SubArray{ComplexF64, 1, Vector{ComplexF64}, Tuple{UnitRange{Int64}}, true}, Tuple{}}}, ΔUSVᴴ::Vector{Any}, ind::UnitRange{Int64}; rank_atol::Float64, degeneracy_atol::Float64, gauge_atol::Float64)
        @ MatrixAlgebraKit ~/.julia/packages/MatrixAlgebraKit/x7OBV/src/pullbacks/svd.jl:58
      [2] (::TensorKit.Factorizations.var"#163#164"{@Kwargs{gauge_atol::Float64, degeneracy_atol::Float64}, Tuple{TensorMap{ComplexF64, ComplexSpace, 3, 1, Vector{ComplexF64}}, DiagonalTensorMap{Float64, ComplexSpace, Vector{Float64}}, TensorMap{ComplexF64, ComplexSpace, 1, 3, Vector{ComplexF64}}}, Vector{Any}, TensorKit.SortedVectorDict{Trivial, UnitRange{Int64}}})(c::Trivial, ::Tuple{Base.ReshapedArray{ComplexF64, 2, SubArray{ComplexF64, 1, Vector{ComplexF64}, Tuple{UnitRange{Int64}}, true}, Tuple{}}, Base.ReshapedArray{ComplexF64, 2, SubArray{ComplexF64, 1, Vector{ComplexF64}, Tuple{UnitRange{Int64}}, true}, Tuple{}}})
        @ TensorKit.Factorizations ~/.julia/packages/TensorKit/JBtTy/src/factorizations/pullbacks.jl:40
      [3] #150
        @ ~/.julia/packages/TensorKit/JBtTy/src/tensors/blockiterator.jl:37 [inlined]
      [4] foreach(f::TensorKit.var"#150#151"{TensorKit.Factorizations.var"#163#164"{@Kwargs{gauge_atol::Float64, degeneracy_atol::Float64}, Tuple{TensorMap{ComplexF64, ComplexSpace, 3, 1, Vector{ComplexF64}}, DiagonalTensorMap{Float64, ComplexSpace, Vector{Float64}}, TensorMap{ComplexF64, ComplexSpace, 1, 3, Vector{ComplexF64}}}, Vector{Any}, TensorKit.SortedVectorDict{Trivial, UnitRange{Int64}}}, Tuple{TensorMap{ComplexF64, ComplexSpace, 3, 3, Vector{ComplexF64}}, TensorMap{ComplexF64, ComplexSpace, 3, 3, Vector{ComplexF64}}}}, d::Dictionaries.Indices{Trivial})
        @ Dictionaries ~/.julia/packages/Dictionaries/P05gc/src/foreach.jl:36
      [5] #foreachblock#148
        @ ~/.julia/packages/TensorKit/JBtTy/src/tensors/blockiterator.jl:36 [inlined]
      [6] foreachblock
        @ ~/.julia/packages/TensorKit/JBtTy/src/tensors/blockiterator.jl:33 [inlined]
      [7] #svd_pullback!#161
        @ ~/.julia/packages/TensorKit/JBtTy/src/factorizations/pullbacks.jl:35 [inlined]
      [8] (::PEPSKit.var"#svd_trunc!_full_pullback#72"{TensorMap{ComplexF64, ComplexSpace, 3, 3, Vector{ComplexF64}}, SVDAdjoint{PEPSKit.FixedSVD{TensorMap{ComplexF64, ComplexSpace, 3, 1, Vector{ComplexF64}}, DiagonalTensorMap{Float64, ComplexSpace, Vector{Float64}}, TensorMap{ComplexF64, ComplexSpace, 1, 3, Vector{ComplexF64}}, TensorMap{ComplexF64, ComplexSpace, 3, 1, Vector{ComplexF64}}, DiagonalTensorMap{Float64, ComplexSpace, Vector{Float64}}, TensorMap{ComplexF64, ComplexSpace, 1, 3, Vector{ComplexF64}}, TensorKit.SortedVectorDict{Trivial, UnitRange{Int64}}}, PEPSKit.FullSVDPullback}, PEPSKit.var"#_get_pullback_gauge_tol##0#_get_pullback_gauge_tol##1", TensorKit.SortedVectorDict{Trivial, UnitRange{Int64}}, TensorMap{ComplexF64, ComplexSpace, 1, 3, Vector{ComplexF64}}, DiagonalTensorMap{Float64, ComplexSpace, Vector{Float64}}, TensorMap{ComplexF64, ComplexSpace, 3, 1, Vector{ComplexF64}}})(ΔUSV′::ChainRulesCore.Tangent{Any, Tuple{TensorKit.AdjointTensorMap{ComplexF64, ComplexSpace, 3, 1, TensorMap{ComplexF64, ComplexSpace, 1, 3, Vector{ComplexF64}}}, TensorMap{ComplexF64, ComplexSpace, 1, 1, Vector{ComplexF64}}, TensorKit.AdjointTensorMap{ComplexF64, ComplexSpace, 1, 3, TensorMap{ComplexF64, ComplexSpace, 3, 1, Vector{ComplexF64}}}, ChainRulesCore.ZeroTangent}})
        @ PEPSKit ~/.julia/packages/PEPSKit/coqnJ/src/utility/svd.jl:373

...

I think this could easily be fixed by just setting rank_atol = 0 for FixedSVD. I will open up a PR.