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	9.266 ns	×3.3	2.785 ns	×1.0
`A ⊡ a`	3.095 ns	55.766 ns	×18.0	3.095 ns	×1.0
`S ⊡ a`	3.406 ns	55.806 ns	×16.0	3.095 ns	×0.91
Double contraction
`A ⊡₂ A`	3.406 ns	11.121 ns	×3.3	3.707 ns	×1.1
`S ⊡₂ S`	3.095 ns	10.189 ns	×3.3	3.706 ns	×1.2
`AA ⊡₂ A`	7.732 ns	77.452 ns	×10.0	7.732 ns	×1.0
`SS ⊡₂ S`	4.067 ns	70.933 ns	×17.0	4.258 ns	×1.0
Tensor product
`a ⊗ a`	3.406 ns	32.841 ns	×9.6	3.416 ns	×1.0
Cross product
`a × a`	3.406 ns	32.841 ns	×9.6	3.416 ns	×1.0
Determinant
`det(A)`	3.396 ns	173.918 ns	×51.0	3.095 ns	×0.91
`det(S)`	3.095 ns	174.391 ns	×56.0	3.095 ns	×1.0
Inverse
`inv(A)`	6.582 ns	496.368 ns	×75.0	7.410 ns	×1.1
`inv(S)`	4.929 ns	496.731 ns	×100.0	7.411 ns	×1.5
`inv(AA)`	944.333 ns	1.514 μs	×1.6	946.960 ns	×1.0
`inv(SS)`	358.014 ns	990.900 ns	×2.8	356.048 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)