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	3.095 ns	×1.1
`A ⊡ a`	3.396 ns	53.716 ns	×16.0	3.396 ns	×1.0
`S ⊡ a`	3.396 ns	53.694 ns	×16.0	3.396 ns	×1.0
Double contraction
`A ⊡₂ A`	3.706 ns	11.111 ns	×3.0	3.406 ns	×0.92
`S ⊡₂ S`	3.095 ns	10.189 ns	×3.3	3.406 ns	×1.1
`AA ⊡₂ A`	7.742 ns	71.562 ns	×9.2	7.732 ns	×1.0
`SS ⊡₂ S`	4.097 ns	63.507 ns	×16.0	4.257 ns	×1.0
Tensor product
`a ⊗ a`	3.406 ns	33.466 ns	×9.8	3.716 ns	×1.1
Cross product
`a × a`	3.406 ns	33.466 ns	×9.8	3.716 ns	×1.1
Determinant
`det(A)`	3.095 ns	165.120 ns	×53.0	3.095 ns	×1.0
`det(S)`	3.396 ns	165.198 ns	×49.0	3.095 ns	×0.91
Inverse
`inv(A)`	6.201 ns	483.882 ns	×78.0	7.410 ns	×1.2
`inv(S)`	4.929 ns	487.738 ns	×99.0	7.400 ns	×1.5
`inv(AA)`	958.000 ns	1.547 μs	×1.6	968.300 ns	×1.0
`inv(SS)`	364.341 ns	992.900 ns	×2.7	356.072 ns	×0.98

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)