Benchmarks

The performance for some typical operators is summarized below. For fourth-order tensors, both Array and SArray use the classical Voigt form to correctly handle symmetries. The benchmakrs show that Tensor offers performance comparable to SArray without the hassle of using the Voigt form.

a = rand(Vec{3})
A = rand(SecondOrderTensor{3})
S = rand(SymmetricSecondOrderTensor{3})
AA = rand(FourthOrderTensor{3})
SS = rand(SymmetricFourthOrderTensor{3})

Operation	`Tensor`	`Array`	Speedup	`SArray`	Speedup
Single contraction
`a ⊡ a`	2.785 ns	9.276 ns	×3.3	3.095 ns	×1.1
`A ⊡ a`	3.406 ns	53.776 ns	×16.0	3.406 ns	×1.0
`S ⊡ a`	3.406 ns	53.755 ns	×16.0	3.406 ns	×1.0
Double contraction
`A ⊡₂ A`	3.706 ns	11.121 ns	×3.0	3.406 ns	×0.92
`S ⊡₂ S`	3.095 ns	10.198 ns	×3.3	3.406 ns	×1.1
`AA ⊡₂ A`	7.733 ns	72.356 ns	×9.4	7.742 ns	×1.0
`SS ⊡₂ S`	4.087 ns	67.801 ns	×17.0	4.088 ns	×1.0
Tensor product
`a ⊗ a`	3.406 ns	33.193 ns	×9.7	3.716 ns	×1.1
Cross product
`a × a`	3.406 ns	33.193 ns	×9.7	3.716 ns	×1.1
Determinant
`det(A)`	3.406 ns	170.157 ns	×50.0	3.095 ns	×0.91
`det(S)`	3.396 ns	173.630 ns	×51.0	3.095 ns	×0.91
Inverse
`inv(A)`	6.191 ns	478.379 ns	×77.0	7.410 ns	×1.2
`inv(S)`	4.939 ns	487.768 ns	×99.0	7.410 ns	×1.5
`inv(AA)`	957.524 ns	1.493 μs	×1.6	949.545 ns	×0.99
`inv(SS)`	368.855 ns	954.312 ns	×2.6	364.555 ns	×0.99

The benchmarks are generated by runbenchmarks.jl on the following system:

julia> versioninfo()
Julia Version 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)