julia> t = Tensor(rand(2,2,2,2), [:i,:j,:k,:l]);
julia> q, r = tensor_qr_thin(
t;
inds_q = Index.([:i, :k]),
inds_r = Index.([:j, :l]),
ind_virtual = Index(:x)
);
julia> q2×2×4 Tensor{Float64, 3, Array{Float64, 3}}:
[:, :, 1] =
-0.668873 -0.153963
-0.647854 -0.33044
[:, :, 2] =
0.27999 0.775449
-0.204135 -0.527838
[:, :, 3] =
0.270886 -0.549341
0.235716 -0.754509
[:, :, 4] =
0.633116 -0.270553
-0.69502 0.207155
julia> r4×2×2 Tensor{Float64, 3, Array{Float64, 3}}:
[:, :, 1] =
-1.21742 -0.982754
0.0 0.51828
0.0 0.0
0.0 0.0
[:, :, 2] =
-0.984218 -0.597685
-0.179305 0.135688
-0.427365 -0.726178
0.0 0.055193