Singular Value Decomposition

julia> t = Tensor(rand(2,2,2,2), [:i,:j,:k,:l]);
julia> u, s, v = tensor_svd_thin(
           t;
           inds_u = Index.([:i, :k]),
           inds_v = Index.([:j, :l]),
           ind_s = Index(:x)
       );
julia> u2×2×4 Tensor{Float64, 3, Array{Float64, 3}}:
[:, :, 1] =
 -0.514988  -0.499198
 -0.487813  -0.497621

[:, :, 2] =
  0.808864  -0.0145201
 -0.427464  -0.403488

[:, :, 3] =
 0.211417  -0.606767
 0.704692  -0.300908

[:, :, 4] =
  0.189286  -0.618404
 -0.287614   0.706417
julia> s4-element Tensor{Float64, 1, Vector{Float64}}:
 2.3102958050973035
 0.7080279415076962
 0.35749105970411915
 0.2031081332601505
julia> v2×2×4 Tensor{Float64, 3, Base.ReshapedArray{Float64, 3, LinearAlgebra.Transpose{Float64, Matrix{Float64}}, Tuple{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64}}}}:
[:, :, 1] =
 -0.357676  -0.467749
 -0.393981  -0.705732

[:, :, 2] =
 -0.719962   0.52093
  0.408474  -0.208411

[:, :, 3] =
  0.351106   0.708871
 -0.479196  -0.38026

[:, :, 4] =
 -0.480049  0.0857029
 -0.669551  0.560276