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	8.955 ns	×3.2	3.085 ns	×1.1
`A ⊡ a`	3.095 ns	49.313 ns	×16.0	3.396 ns	×1.1
`S ⊡ a`	3.095 ns	49.403 ns	×16.0	3.396 ns	×1.1
Double contraction
`A ⊡₂ A`	3.396 ns	10.801 ns	×3.2	3.396 ns	×1.0
`S ⊡₂ S`	3.095 ns	9.878 ns	×3.2	3.396 ns	×1.1
`AA ⊡₂ A`	7.722 ns	67.691 ns	×8.8	7.722 ns	×1.0
`SS ⊡₂ S`	4.277 ns	59.134 ns	×14.0	4.308 ns	×1.0
Tensor product
`a ⊗ a`	3.406 ns	28.536 ns	×8.4	3.396 ns	×1.0
Cross product
`a × a`	3.406 ns	28.536 ns	×8.4	3.396 ns	×1.0
Determinant
`det(A)`	3.095 ns	162.834 ns	×53.0	3.095 ns	×1.0
`det(S)`	3.095 ns	168.708 ns	×55.0	3.095 ns	×1.0
Inverse
`inv(A)`	6.241 ns	431.616 ns	×69.0	7.410 ns	×1.2
`inv(S)`	4.939 ns	459.949 ns	×93.0	7.410 ns	×1.5
`inv(AA)`	979.611 ns	1.521 μs	×1.6	972.842 ns	×0.99
`inv(SS)`	397.591 ns	969.091 ns	×2.4	367.551 ns	×0.92

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

julia> versioninfo()
Julia Version 1.12.6
Commit 15346901f00 (2026-04-09 19:20 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-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)