[BUG] Outer product tensor contractions are broken

[mtfishman]

Currently, outer product tensor contractions are broken:

julia> using TensorAlgebra: contract

julia> contract(randn(2, 2), ("i", "j"), randn(2, 2), ("k", "l"))
MethodError: no method matching output_axes(::typeof(contract), ::TensorAlgebra.BlockedPermutation{2, (2, 2), NTuple{4, Int64}}, ::Matrix{Float64}, ::TensorAlgebra.BlockedPermutation{1, (2,), Tuple{Int64, Int64}}, ::Matrix{Float64}, ::TensorAlgebra.BlockedPermutation{1, (2,), Tuple{Int64, Int64}}, ::Bool)
The function `output_axes` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  output_axes(::typeof(contract), ::TensorAlgebra.BlockedPermutation{0}, ::AbstractArray, ::TensorAlgebra.BlockedPermutation{1}, ::AbstractArray, ::TensorAlgebra.BlockedPermutation{1}, ::Number)
   @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/allocate_output.jl:23
  output_axes(::typeof(contract), ::TensorAlgebra.BlockedPermutation{1}, ::AbstractArray, ::TensorAlgebra.BlockedPermutation{2}, ::AbstractArray, ::TensorAlgebra.BlockedPermutation{1}, ::Number)
   @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/allocate_output.jl:55
  output_axes(::typeof(contract), ::TensorAlgebra.BlockedPermutation{2}, ::AbstractArray, ::TensorAlgebra.BlockedPermutation{2}, ::AbstractArray, ::TensorAlgebra.BlockedPermutation{2}, ::Number)
   @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/allocate_output.jl:5
  ...

Stacktrace:
  [1] allocate_output(::typeof(contract), biperm_dest::TensorAlgebra.BlockedPermutation{2, (2, 2), NTuple{4, Int64}}, a1::Matrix{Float64}, biperm1::TensorAlgebra.BlockedPermutation{1, (2,), Tuple{Int64, Int64}}, a2::Matrix{Float64}, biperm2::TensorAlgebra.BlockedPermutation{1, (2,), Tuple{Int64, Int64}}, α::Bool)
    @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/allocate_output.jl:81
  [2] contract(alg::TensorAlgebra.Matricize, biperm_dest::TensorAlgebra.BlockedPermutation{2, (2, 2), NTuple{4, Int64}}, a1::Matrix{Float64}, biperm1::TensorAlgebra.BlockedPermutation{1, (2,), Tuple{Int64, Int64}}, a2::Matrix{Float64}, biperm2::TensorAlgebra.BlockedPermutation{1, (2,), Tuple{Int64, Int64}}, α::Bool; kwargs::@Kwargs{})
    @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:121
  [3] contract(alg::TensorAlgebra.Matricize, biperm_dest::TensorAlgebra.BlockedPermutation{2, (2, 2), NTuple{4, Int64}}, a1::Matrix{Float64}, biperm1::TensorAlgebra.BlockedPermutation{1, (2,), Tuple{Int64, Int64}}, a2::Matrix{Float64}, biperm2::TensorAlgebra.BlockedPermutation{1, (2,), Tuple{Int64, Int64}}, α::Bool)
    @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:111
  [4] contract(alg::TensorAlgebra.Matricize, labels_dest::NTuple{4, String}, a1::Matrix{Float64}, labels1::Tuple{String, String}, a2::Matrix{Float64}, labels2::Tuple{String, String}, α::Bool; kwargs::@Kwargs{})
    @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:92
  [5] contract(alg::TensorAlgebra.Matricize, labels_dest::NTuple{4, String}, a1::Matrix{Float64}, labels1::Tuple{String, String}, a2::Matrix{Float64}, labels2::Tuple{String, String}, α::Bool)
    @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:81
  [6] contract(alg::TensorAlgebra.Matricize, a1::Matrix{Float64}, labels1::Tuple{String, String}, a2::Matrix{Float64}, labels2::Tuple{String, String}, α::Bool; kwargs::@Kwargs{})
    @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:49
  [7] contract
    @ ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:39 [inlined]
  [8] #contract#27
    @ ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:36 [inlined]
  [9] contract
    @ ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:27 [inlined]
 [10] contract(a1::Matrix{Float64}, labels1::Tuple{String, String}, a2::Matrix{Float64}, labels2::Tuple{String, String})
    @ TensorAlgebra ~/.julia/packages/TensorAlgebra/WrWQd/src/contract/contract.jl:27
 [11] top-level scope
    @ REPL[4]:1

(as mentioned in #1 but I'm starting a new issue for visibility and discussion).

This should probably be written in terms of a lower level function devoted to performing tensor/outer products.

TensorOperations.jl calls this tensorproduct(...), and TensorCore.jl calls this tensor(...), with a unicode alias ⊗. In NDTensors.jl, we call it outer(...).

Right now, I'm torn between the names tensorproduct, outerproduct, and outer.

[mtfishman]

For whatever it is worth, Python's numpy calls this outer(...), though it is limited to vectors, so is more like x * y' in Julia. ufunc.outer(...) is a generalization to arrays.

[ogauthe]

We already define tensor_product in GradedUnitRanges.jl for a different operation. I would go for outerproduct.