# Problem with addition and contraction of QN preserving tensors with \`delta\`

**URL:** <https://itensor.discourse.group/t/problem-with-addition-and-contraction-of-qn-preserving-tensors-with-delta/982>\
**Category:** ITensor Julia Questions\
**Tags:** julia\
**Created:** [June 27, 2023, 3:58pm UTC](https://itensor.discourse.group/t/problem-with-addition-and-contraction-of-qn-preserving-tensors-with-delta/982 "2023-06-27T15:58:49Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![matuser2](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/matuser2/32/318_2.png) [@matuser2](https://itensor.discourse.group/u/matuser2)\
**Post date:** [June 27, 2023, 3:58pm UTC](https://itensor.discourse.group/t/problem-with-addition-and-contraction-of-qn-preserving-tensors-with-delta/982/1 "2023-06-27T15:58:49Z")

</div>

Hi everyone,

I encountered some errors with addition and multiplication of seemingly innocent tensors.  
I created in julia a simple ITensor `A` with QN-perserving indices, and tried to calculate the sum- `A*A' + delta([i,j], [i`,j`]):

```julia

using ITensors

# initializing
i = Index([QN(0) => 2, QN(1) => 3], "i")
j = Index([QN(0) => 2, QN(1) => 3], "j")
A = randomITensor(i, j)

A_squared = dag(A)*A'
A_delta = delta([dag(i), dag(j)], [i', j'])
# Here A_squared and A_delta have the same indices with the same order, the same flux ect.

# trying to sum them together
@show A_squared + A_delta

```

At this point I got the following error message:

> ERROR: `perutedims!(output_tensor::Tensor, tensor::Tensor, perm, f::Function=(r, t) -> t)` not implemented for `typeof(output_tensor) = NDTensors.BlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{Float64, Vector{Float64}, 4}}`, `typeof(tensor) = NDTensors.DiagBlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 4}}`, `perm = (1, 2, 3, 4)`, and `f = #281`.  
> Stacktrace:  
> [1] error(s::String)  
> @ Base ./error.jl:35  
> [2] permutedims!(output\_tensor::NDTensors.BlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{Float64, Vector{Float64}, 4}}, tensor::NDTensors.DiagBlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 4}}, perm::NTuple{4, Int64}, f::Function)  
> @ NDTensors ~/.julia/packages/NDTensors/oXCSC/src/tensoralgebra/generic\_tensor\_operations.jl:20  
> [3] permutedims!!(output\_tensor::NDTensors.BlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{Float64, Vector{Float64}, 4}}, tensor::NDTensors.DiagBlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 4}}, perm::NTuple{4, Int64}, f::Function)  
> @ NDTensors ~/.julia/packages/NDTensors/oXCSC/src/tensoralgebra/generic\_tensor\_operations.jl:14  
> [4] \_map!!(f::Function, R::NDTensors.BlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{Float64, Vector{Float64}, 4}}, T1::NDTensors.BlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{Float64, Vector{Float64}, 4}}, T2::NDTensors.DiagBlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 4}})  
> @ ITensors ~/.julia/packages/ITensors/HjjU3/src/itensor.jl:1921  
> [5] map!(f::Function, R::ITensor, T1::ITensor, T2::ITensor)  
> @ ITensors ~/.julia/packages/ITensors/HjjU3/src/itensor.jl:1926  
> [6] copyto!  
> @ ~/.julia/packages/ITensors/HjjU3/src/broadcast.jl:301 [inlined]  
> [7] materialize!  
> @ ./broadcast.jl:884 [inlined]  
> [8] materialize!  
> @ ./broadcast.jl:881 [inlined]  
> [9] \_add(A::NDTensors.BlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{Float64, Vector{Float64}, 4}}, B::NDTensors.DiagBlockSparseTensor{Float64, 4, NTuple{4, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 4}})  
> @ ITensors ~/.julia/packages/ITensors/HjjU3/src/itensor.jl:1822  
> [10] +(A::ITensor, B::ITensor)  
> @ ITensors ~/.julia/packages/ITensors/HjjU3/src/itensor.jl:1830  
> [11] top-level scope  
> @ REPL[267]:1

I don’t know what went wrong. Notice that the permutation to perform is (1,2,3,4)- meaning everything is already in order.

The other problem with delta I encountered is when I tried to multiply them together-

```julia
# as before:
i = Index([QN(0) => 2, QN(1) => 3], "i")
j = Index([QN(0) => 2, QN(1) => 3], "j")

@show delta(i,i')*delta(j,j')

```

Here I get another angry error message:

> ERROR: UndefVarError: `IndsR` not defined  
> Stacktrace:  
> [1] contraction\_output\_type(TensorT1::Type{NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}}, TensorT2::Type{NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}}, indsR::NTuple{4, Index{Vector{Pair{QN, Int64}}}})  
> @ NDTensors ~/.julia/packages/NDTensors/oXCSC/src/blocksparse/diagblocksparse.jl:278  
> [2] zero\_contraction\_output  
> @ ~/.julia/packages/NDTensors/oXCSC/src/tensor/tensor.jl:389 [inlined]  
> [3] contraction\_output  
> @ ~/.julia/packages/NDTensors/oXCSC/src/blocksparse/diagblocksparse.jl:295 [inlined]  
> [4] contraction\_output  
> @ ~/.julia/packages/NDTensors/oXCSC/src/tensoralgebra/generic\_tensor\_operations.jl:47 [inlined]  
> [5] contract(tensor1::NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}, labelstensor1::Tuple{Int64, Int64}, tensor2::NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}, labelstensor2::Tuple{Int64, Int64}, labelsoutput\_tensor::NTuple{4, Int64})  
> @ NDTensors ~/.julia/packages/NDTensors/oXCSC/src/tensoralgebra/generic\_tensor\_operations.jl:93  
> [6] contract(::Type{NDTensors.CanContract{NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}, NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}}}, tensor1::NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}, labels\_tensor1::Tuple{Int64, Int64}, tensor2::NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}, labels\_tensor2::Tuple{Int64, Int64})  
> @ NDTensors ~/.julia/packages/NDTensors/oXCSC/src/tensoralgebra/generic\_tensor\_operations.jl:76  
> [7] contract  
> @ ~/.julia/packages/SimpleTraits/l1ZsK/src/SimpleTraits.jl:331 [inlined]  
> [8] \_contract(A::NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}}, B::NDTensors.DiagBlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.DiagBlockSparse{Float64, Float64, 2}})  
> @ ITensors ~/.julia/packages/ITensors/HjjU3/src/tensor\_operations/tensor\_algebra.jl:3  
> [9] \_contract(A::ITensor, B::ITensor)  
> @ ITensors ~/.julia/packages/ITensors/HjjU3/src/tensor\_operations/tensor\_algebra.jl:9  
> [10] contract(A::ITensor, B::ITensor)  
> @ ITensors ~/.julia/packages/ITensors/HjjU3/src/tensor\_operations/tensor\_algebra.jl:104  
> [11] \*(A::ITensor, B::ITensor)  
> @ ITensors ~/.julia/packages/ITensors/HjjU3/src/tensor\_operations/tensor\_algebra.jl:91  
> [12] top-level scope  
> @ REPL[268]:1

What went wrong?  
I use ITensors v0.3.34 in julia 1.9.1

Thank you in advance:)

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**Author:** ![miles](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/miles/32/6_2.png) [@miles](https://itensor.discourse.group/u/miles)\
**Post date:** [July 23, 2023, 3:03am UTC](https://itensor.discourse.group/t/problem-with-addition-and-contraction-of-qn-preserving-tensors-with-delta/982/2 "2023-07-23T03:03:50Z")

</div>

The delta type of tensor was originally created primarily for contracting with other tensors, so we have not defined addition of QN-conserving delta tensors at this time.

If it is an important operation for your code, I would suggest making a small function which creates the equivalent of a delta tensor by making a QN-conserving ITensor (just making an ITensor from your QN-labeled indices) then setting the diagonal elements equal to one in a for-loop, then returning that tensor to use instead of a delta. (As a technical note, delta tensors use a special internal storage type that is different from regular QN-conserving ITensors, so addition has to be implemented specially for that type. We might do so in the future, but for now please use the workaround described above if it is important.)

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**Author:** ![JanReimers](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/janreimers/32/171_2.png) [@JanReimers](https://itensor.discourse.group/u/JanReimers)\
**Post date:** [July 23, 2023, 1:20pm UTC](https://itensor.discourse.group/t/problem-with-addition-and-contraction-of-qn-preserving-tensors-with-delta/982/3 "2023-07-23T13:20:19Z")

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Hi Guys, FYI the denseblocks() function will convert the delta ITensor from DiagBlockSparse to BlockSparse storage and allow addition operation to proceed.

```auto
A_delta = denseblocks(delta([dag(i), dag(j)], [i', j']))

```

Obviously it wastes some memory so use with caution.  
Regards  
Jan

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<div class="post-metadata">

**Author:** ![matuser2](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/matuser2/32/318_2.png) [@matuser2](https://itensor.discourse.group/u/matuser2)\
**Post date:** [July 31, 2023, 8:58am UTC](https://itensor.discourse.group/t/problem-with-addition-and-contraction-of-qn-preserving-tensors-with-delta/982/4 "2023-07-31T08:58:26Z")

</div>

Thank you very much!  
I thought the question had been long forgotten, `denseblocks` is an elegant workaround.