Benchmarks

Here are some benchmark timings for tensors in 3 dimensions. For comparison the timings for the same operations using standard Julia Arrays are also presented.

In the table below, a denotes a vector, A, As denotes second order non-symmetric and symmetric tensors and AA, AAs denotes fourth order non-symmetric and symmetric tensors respectively.

Operation	`Tensor`	`Array`	speed-up
Single contraction
`a ⋅ a`	1.241 ns	9.795 ns	×7.9
`A ⋅ a`	2.161 ns	58.769 ns	×27.2
`A ⋅ A`	3.117 ns	44.395 ns	×14.2
`As ⋅ As`	5.125 ns	44.498 ns	×8.7
Double contraction
`A ⊡ A`	1.927 ns	12.189 ns	×6.3
`As ⊡ As`	1.927 ns	12.187 ns	×6.3
`AA ⊡ A`	6.087 ns	78.554 ns	×12.9
`AA ⊡ AA`	60.820 ns	280.502 ns	×4.6
`AAs ⊡ AAs`	22.104 ns	281.003 ns	×12.7
`As ⊡ AAs ⊡ As`	9.466 ns	89.747 ns	×9.5
Outer product
`a ⊗ a`	2.167 ns	32.447 ns	×15.0
`A ⊗ A`	9.801 ns	86.568 ns	×8.8
`As ⊗ As`	4.311 ns	87.830 ns	×20.4
Other operations
`det(A)`	1.924 ns	177.134 ns	×92.1
`det(As)`	1.924 ns	182.831 ns	×95.0
`inv(A)`	6.099 ns	595.591 ns	×97.7
`inv(As)`	4.587 ns	635.858 ns	×138.6
`norm(a)`	1.494 ns	9.838 ns	×6.6
`norm(A)`	1.990 ns	16.752 ns	×8.4
`norm(As)`	2.011 ns	16.757 ns	×8.3
`norm(AA)`	9.283 ns	28.125 ns	×3.0
`norm(AAs)`	5.422 ns	28.134 ns	×5.2
`a × a`	1.921 ns	32.736 ns	×17.0

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

julia> versioninfo()

Julia Version 0.6.0-pre.beta.297
Commit 2a61131* (2017-04-24 23:57 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: Intel(R) Core(TM) i5-7600K CPU @ 3.80GHz
  WORD_SIZE: 64
  BLAS: libopenblas (USE64BITINT NO_AFFINITY HASWELL)
  LAPACK: libopenblas64_
  LIBM: libopenlibm
  LLVM: libLLVM-3.9.1 (ORCJIT, broadwell)