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[TensorAlgebra] [Feature request] TensorAlgebra.contract to accept biperm #1507

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@ogauthe

Description

@ogauthe

For a FusionTensor, a permutation is not enough to specify the structure, a biperm is needed. Currently, TensorAlgebra.contract does not allow this.

using NDTensors.FusionTensors: FusionTensor
using NDTensors.GradedAxes
using NDTensors.Sectors: U1

  g1 = GradedAxes.gradedrange([U1(0) => 1])
  ft1 = FusionTensor(Float64, (GradedAxes.dual(g1),), (g1,))
  ft2 = FusionTensor(Float64, (GradedAxes.dual(g1),), (g1,g1))

  ft3, legs = TensorAlgebra.contract(ft1, (1,2), ft2, (2, 3, 4))  # Ok
  ft4 = TensorAlgebra.contract((1,4, 3), ft1, (1,2), ft2, (2, 3, 4))  # Ok
  ft5 = TensorAlgebra.contract(((1,4),(3,)), ft1, (1,2), ft2, (2, 3, 4))   # MethodError
ERROR: MethodError: no method matching blockedperm(::Tuple{Nothing}, ::Tuple{Nothing, Nothing})

Closest candidates are:
blockedperm(::NDTensors.NamedDimsArrays.AbstractNamedDimsArray, ::Tuple...)
 @ NDTensors ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/NamedDimsArrays/ext/NamedDimsArraysTensorAlgebraExt/src/fusedims.jl:4

Stacktrace:
[1] blockedperms(::typeof(NDTensors.TensorAlgebra.contract), dimnames_dest::Tuple{…}, dimnames1::Tuple{…}, dimnames2::Tuple{…})
 @ NDTensors.TensorAlgebra ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/blockedperms.jl:26
[2] contract(alg::NDTensors.BackendSelection.Algorithm{…}, labels_dest::Tuple{…}, a1::FusionTensor{…}, labels1::Tuple{…}, a2::FusionTensor{…}, labels2::Tuple{…}, α::Bool; kwargs::@Kwargs{})
 @ NDTensors.TensorAlgebra ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/contract.jl:87
[3] contract
 @ ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/contract.jl:77 [inlined]
[4] #contract#33
 @ ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/contract.jl:58 [inlined]
[5] contract
 @ ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/contract.jl:48 [inlined]
[6] contract(labels_dest::Tuple{…}, a1::FusionTensor{…}, labels1::Tuple{…}, a2::FusionTensor{…}, labels2::Tuple{…})
 @ NDTensors.TensorAlgebra ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/contract.jl:48
[7] top-level scope
 @ REPL[65]:1
Some type information was truncated. Use `show(err)` to see complete types.

Note that it is not possible to construct a BlockedPermutation from ((1,4), (3,)):

julia> TensorAlgebra.blockedperm((1,4), (3,))
ERROR: AssertionError: isperm(blockedperm)
Stacktrace:
[1] blockedperm
 @ ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/blockedpermutation.jl:166 [inlined]
[2] blockedperm
 @ ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/blockedpermutation.jl:110 [inlined]
[3] #blockedperm#13
 @ ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/blockedpermutation.jl:106 [inlined]
[4] blockedperm(::Tuple{Int64, Int64}, ::Tuple{Int64})
 @ NDTensors.TensorAlgebra ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/blockedpermutation.jl:105
[5] top-level scope
 @ REPL[66]:1

but even a correct BlockedPermutation fails:

biperm = TensorAlgebra.blockedperm((1,3),(2,))
ft5 = TensorAlgebra.contract(biperm, ft1, (1,4), ft2, (4, 2, 3))   # MethodError
ERROR: MethodError: no method matching contract(::NDTensors.TensorAlgebra.BlockedPermutation{…}, ::FusionTensor{…}, ::Tuple{…}, ::FusionTensor{…}, ::Tuple{…})

Closest candidates are:
  contract(::NDTensors.BackendSelection.Algorithm, ::AbstractArray, ::Tuple, ::AbstractArray, ::Tuple; ...)
   @ NDTensors ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/contract.jl:35
  contract(::NDTensors.BackendSelection.Algorithm, ::AbstractArray, ::Tuple, ::AbstractArray, ::Tuple, ::Number; kwargs...)
   @ NDTensors ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/contract.jl:35
  contract(::Tuple, ::AbstractArray, ::Tuple, ::AbstractArray, ::Tuple; ...)
   @ NDTensors ~/Documents/itensor/ITensors.jl/NDTensors/src/lib/TensorAlgebra/src/contract/contract.jl:48
  ...

Stacktrace:
 [1] top-level scope
   @ REPL[84]:1
Some type information was truncated. Use `show(err)` to see complete types.

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