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	9.256 ns	×3.3	2.785 ns	×1.0
`A ⊡ a`	3.095 ns	53.888 ns	×17.0	3.095 ns	×1.0
`S ⊡ a`	3.095 ns	53.806 ns	×17.0	3.095 ns	×1.0
Double contraction
`A ⊡₂ A`	3.406 ns	11.111 ns	×3.3	3.706 ns	×1.1
`S ⊡₂ S`	3.095 ns	10.188 ns	×3.3	3.706 ns	×1.2
`AA ⊡₂ A`	7.723 ns	72.107 ns	×9.3	7.722 ns	×1.0
`SS ⊡₂ S`	4.037 ns	67.150 ns	×17.0	4.117 ns	×1.0
Tensor product
`a ⊗ a`	3.706 ns	33.668 ns	×9.1	3.406 ns	×0.92
Cross product
`a × a`	3.706 ns	33.668 ns	×9.1	3.406 ns	×0.92
Determinant
`det(A)`	3.095 ns	168.433 ns	×54.0	3.095 ns	×1.0
`det(S)`	3.095 ns	169.929 ns	×55.0	3.095 ns	×1.0
Inverse
`inv(A)`	6.261 ns	471.949 ns	×75.0	7.400 ns	×1.2
`inv(S)`	4.929 ns	492.528 ns	×100.0	7.400 ns	×1.5
`inv(AA)`	950.478 ns	1.503 μs	×1.6	961.818 ns	×1.0
`inv(SS)`	365.609 ns	958.929 ns	×2.6	368.914 ns	×1.0

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

julia> versioninfo()
Julia Version 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 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)