# \[ANN\] Tensorial.jl: Statically sized tensors and related operations for Julia

**URL:** <https://discourse.julialang.org/t/ann-tensorial-jl-statically-sized-tensors-and-related-operations-for-julia/121588>\
**Category:** Package Announcements\
**Tags:** package, announcement, tensors\
**Created:** [October 22, 2024, 12:24pm UTC](https://discourse.julialang.org/t/ann-tensorial-jl-statically-sized-tensors-and-related-operations-for-julia/121588 "2024-10-22T12:24:06Z")\
**Posts on this page:** 6\
**Page:** 2

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**Author:** ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)\
**Post date:** [October 23, 2024, 6:21pm UTC](https://discourse.julialang.org/t/ann-tensorial-jl-statically-sized-tensors-and-related-operations-for-julia/121588/21 "2024-10-23T18:21:33Z")

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> [@danielwe](#):
>
> `dot` is semantically equivalent to `sum(dot(vx,vy) for (vx,vy) in zip(x, y))`

This is arguably a slightly strange choice, maybe the only function in LinearAlgebra which regards arrays as a bag of numbers, ignoring their structure. And begin recursive seems the wrong behaviour on e.g. vectors of matrices, to me (and wasn’t seriously discussed when added?). Nevertheless, it’s too late to change this, and least confusing if the entire ecosystem agrees.

> [@KeitaNakamura](#):
>
> `⊡₂` for double contraction, what do you think? Is it too fancy?

That seems fine to me. It’s typed `\boxdot<tab>\_2<tab>`. We could add this to TensorCore.jl too… like the single contraction it’s always reshape-then-`*`, i.e. it allows `rand(2,3,4) ⊡₂ rand(3,4,5)` but not `rand(2,3,4) ⊡₂ rand(4,3,5)`:

```julia
julia> x, y = Tensorial.@Tensor(rand(2,3,4)), Tensorial.@Tensor(rand(3,4,5));

julia> Tensorial.contract2(x, y)
2×5 Mat{2, 5, Float64, 10}:
 2.38424 1.98448 4.23119 2.87129 2.06991
 2.73175 2.26099 4.28346 3.05636 2.02472

julia> ans ≈ reshape(x, 2,:) * reshape(y, :,5)
true

```

> [@ExpandingMan](#):
>
> since DI has no way of knowing how to deal with Tensorial arrays rather than to create `Array`, particularly becuase, lacking `MArray`, there is no viable `similar`.

Maybe worth noting that Enzyme appears to just work, by understanding that these are just tuples, without ever calling `similar`. DI seems able to use that:

```julia
julia> Base.similar(_::typeof(Vec(5.0,6.0)), ::Type{Float64}, ::Base.Dims) = error("similar not defined")

julia> Enzyme.gradient(Reverse, v -> dot(v, Mat{2,2}(1,2,3,4), v), Vec(5.0,6.0))[1]
2-element Vec{2, Float64}:
 40.0
 73.0

julia> DifferentiationInterface.gradient(v -> dot(v, Mat{2,2}(1,2,3,4), v), AutoEnzyme(), Vec(5.0,6.0))
2-element Vec{2, Float64}:
 40.0
 73.0

```

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**Author:** ![KeitaNakamura](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/keitanakamura/32/211562_2.png) [@KeitaNakamura](https://discourse.julialang.org/u/KeitaNakamura)\
**Post date:** [October 24, 2024, 1:21am UTC](https://discourse.julialang.org/t/ann-tensorial-jl-statically-sized-tensors-and-related-operations-for-julia/121588/22 "2024-10-24T01:21:03Z")

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Yes, very long time ago, I tried to develop `Tensor` as a subtype of `StaticArray`. But, if I remember correctly, I couldn’t account for tensor symmetries without modifying the internal code of StaticArrays.jl, so I eventually gave up. I understand your situation, but may I ask why your function needs to handle both StaticArrays.jl and Tensors.jl in the first place?

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**Author:** ![KeitaNakamura](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/keitanakamura/32/211562_2.png) [@KeitaNakamura](https://discourse.julialang.org/u/KeitaNakamura)\
**Post date:** [October 24, 2024, 1:29am UTC](https://discourse.julialang.org/t/ann-tensorial-jl-statically-sized-tensors-and-related-operations-for-julia/121588/23 "2024-10-24T01:29:40Z")

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> [@mcabbott](#):
>
> like the single contraction it’s always reshape-then-`*`, i.e. it allows `rand(2,3,4) ⊡₂ rand(3,4,5)` but not `rand(2,3,4) ⊡₂ rand(4,3,5)`:

Yes, this is exactly what I’m doing in Tensorial.jl. Maybe we should handle the `n`-th contraction as `boxdot(A, B, nth)` in TensorCore.jl. If you agree, I’ll submit a PR.

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**Author:** ![tverho](https://avatars.discourse-cdn.com/v4/letter/t/839c29/32.png) [@tverho](https://discourse.julialang.org/u/tverho)\
**Post date:** [October 25, 2024, 7:50am UTC](https://discourse.julialang.org/t/ann-tensorial-jl-statically-sized-tensors-and-related-operations-for-julia/121588/24 "2024-10-25T07:50:12Z")

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I’m writing a FEM code, where it makes sense to store vectors as `Vec`s to make use of `Tensors.jl` for constitutive models. However, there are parts of the code which are specialized algorithms (polygon clipping) which could be used in other contexts as well. It would make sense to make these functions agnostic of whether the input is `SVectors` or `Vec`s, as long as they are static and support the same basic operations.

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**Author:** ![KeitaNakamura](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/keitanakamura/32/211562_2.png) [@KeitaNakamura](https://discourse.julialang.org/u/KeitaNakamura)\
**Post date:** [October 25, 2024, 11:30am UTC](https://discourse.julialang.org/t/ann-tensorial-jl-statically-sized-tensors-and-related-operations-for-julia/121588/25 "2024-10-25T11:30:18Z")

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I think you can define a `Union` type once and then use it across all functions.

```Julia
const SVectorOrVec{L,T} = Union{SVector{L,T}, Vec{L,T}}

```

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**Author:** ![gdalle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gdalle/32/224680_2.png) [@gdalle](https://discourse.julialang.org/u/gdalle)\
**Post date:** [October 27, 2024, 7:33am UTC](https://discourse.julialang.org/t/ann-tensorial-jl-statically-sized-tensors-and-related-operations-for-julia/121588/26 "2024-10-27T07:33:04Z")

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Split this topic on October 27, 2024, 7:33am UTC

A post was split to a new topic: [Compile FastDifferentiation derivatives one time only](https://discourse.julialang.org/t/compile-fastdifferentiation-derivatives-one-time-only/121816)

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