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] =
 -0.291333  -0.64942
 -0.568165  -0.412998

[:, :, 2] =
  0.915735   0.0223202
 -0.309864  -0.254785

[:, :, 3] =
 0.23575    -0.613823
 0.0336105   0.752671

[:, :, 4] =
 -0.144831  0.448303
 -0.761606  0.444977
julia> s4-element Tensor{Float64, 1, Vector{Float64}}:
 2.0922519886959807
 0.9258359072228243
 0.21450673050213467
 0.09635861141253553
julia> v2×2×4 Tensor{Float64, 3, Base.ReshapedArray{Float64, 3, LinearAlgebra.Transpose{Float64, Matrix{Float64}}, Tuple{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64}}}}:
[:, :, 1] =
 -0.572246  -0.300512
 -0.198957  -0.736643

[:, :, 2] =
 -0.349542    0.930807
 -0.0490428  -0.0949409

[:, :, 3] =
 -0.28405   -0.100633
 -0.821747   0.483653

[:, :, 4] =
 -0.685325  -0.18211
  0.531736   0.463058