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	3.095 ns	×1.1
`A ⊡ a`	3.406 ns	49.028 ns	×14.0	3.095 ns	×0.91
`S ⊡ a`	3.105 ns	49.050 ns	×16.0	3.095 ns	×1.0
Double contraction
`A ⊡₂ A`	3.406 ns	10.811 ns	×3.2	3.707 ns	×1.1
`S ⊡₂ S`	3.406 ns	9.878 ns	×2.9	3.707 ns	×1.1
`AA ⊡₂ A`	7.722 ns	67.442 ns	×8.7	7.732 ns	×1.0
`SS ⊡₂ S`	4.137 ns	58.972 ns	×14.0	4.067 ns	×0.98
Tensor product
`a ⊗ a`	3.105 ns	28.093 ns	×9.0	3.105 ns	×1.0
Cross product
`a × a`	3.105 ns	28.093 ns	×9.0	3.105 ns	×1.0
Determinant
`det(A)`	3.095 ns	165.145 ns	×53.0	3.406 ns	×1.1
`det(S)`	3.095 ns	165.250 ns	×53.0	3.406 ns	×1.1
Inverse
`inv(A)`	6.201 ns	434.601 ns	×70.0	7.582 ns	×1.2
`inv(S)`	4.949 ns	437.227 ns	×88.0	7.401 ns	×1.5
`inv(AA)`	988.286 ns	1.522 μs	×1.5	972.500 ns	×0.98
`inv(SS)`	386.635 ns	933.316 ns	×2.4	368.790 ns	×0.95

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

julia> versioninfo()
Julia Version 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 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)