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benchmarks for LU-based matrix functions (det, inv, expm, solve)
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‎perf/bench_matrix_ops.txt

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Julia Version 0.6.2
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Commit d386e40c17* (2017-12-13 18:08 UTC)
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Platform Info:
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OS: Linux (x86_64-linux-gnu)
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CPU: AMD Ryzen 7 1800X Eight-Core Processor
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WORD_SIZE: 64
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BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Barcelona)
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LAPACK: libopenblas64_
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LIBM: libopenlibm
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LLVM: libLLVM-3.9.1 (ORCJIT, generic)
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80×6 DataFrames.DataFrame
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│ Row │ SIZE │ STAT │ det │ inv │ expm │ \\ │
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├─────┼──────┼───────────────────┼─────────────┼─────────────┼─────────────┼─────────────┤
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│ 1 │ 1 │ compile time (s) │ 0.0358709 │ 0.00410504 │ 0.029984 │ 0.0932384 │
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│ 2 │ │ StaticArrays (μs) │ 0.001813 │ 0.001813 │ 0.0106907 │ 0.004648 │
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│ 3 │ │ Base (μs) │ 0.0548293 │ 0.221979 │ 0.77535 │ 0.0877129 │
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│ 4 │ │ max error │ 0.0 │ 0.0 │ 0.0 │ 0.0 │
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│ 5 │ 2 │ compile time (s) │ 0.00551981 │ 0.00544899 │ 0.0109721 │ 0.109253 │
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│ 6 │ │ StaticArrays (μs) │ 0.001813 │ 0.002064 │ 0.0479443 │ 0.0349496 │
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│ 7 │ │ Base (μs) │ 0.192087 │ 0.554522 │ 2.60044 │ 1.4488 │
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│ 8 │ │ max error │ 2.22045e-16 │ 1.31167e-9 │ 3.17919e-15 │ 2.27485e-13 │
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│ 9 │ 3 │ compile time (s) │ 0.0810862 │ 0.0491976 │ 1.11676 │ 0.0138903 │
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│ 10 │ │ StaticArrays (μs) │ 0.001853 │ 0.00998799 │ 0.148526 │ 0.0606544 │
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│ 11 │ │ Base (μs) │ 0.244762 │ 0.671916 │ 3.19611 │ 1.8104 │
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│ 12 │ │ max error │ 2.22045e-16 │ 3.40212e-7 │ 5.55049e-15 │ 8.41688e-11 │
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│ 13 │ 4 │ compile time (s) │ 0.0180314 │ 0.846753 │ 1.10441 │ 0.0243759 │
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│ 14 │ │ StaticArrays (μs) │ 0.0104805 │ 0.0403582 │ 0.30312 │ 0.113047 │
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│ 15 │ │ Base (μs) │ 0.295459 │ 0.92675 │ 5.10971 │ 2.09289 │
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│ 16 │ │ max error │ 2.77556e-16 │ 2.62963e-10 │ 1.16735e-14 │ 2.01389e-9 │
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│ 17 │ 5 │ compile time (s) │ 2.92353 │ 0.41665 │ 1.58469 │ 0.0376695 │
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│ 18 │ │ StaticArrays (μs) │ 0.105874 │ 0.204571 │ 0.519827 │ 0.198071 │
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│ 19 │ │ Base (μs) │ 0.373642 │ 1.047 │ 5.89783 │ 2.2522 │
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│ 20 │ │ max error │ 1.66533e-16 │ 2.15962e-9 │ 1.84223e-14 │ 5.0253e-10 │
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│ 21 │ 6 │ compile time (s) │ 0.594495 │ 0.26922 │ 2.571 │ 0.0567599 │
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│ 22 │ │ StaticArrays (μs) │ 0.20246 │ 0.331432 │ 0.83373 │ 0.321775 │
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│ 23 │ │ Base (μs) │ 0.442449 │ 1.2143 │ 6.5424 │ 2.3995 │
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│ 24 │ │ max error │ 1.66533e-16 │ 1.53235e-8 │ 4.67587e-14 │ 6.4429e-9 │
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│ 25 │ 7 │ compile time (s) │ 0.679751 │ 0.367467 │ 4.41147 │ 0.0837663 │
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│ 26 │ │ StaticArrays (μs) │ 0.285484 │ 0.479979 │ 1.3115 │ 0.481318 │
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│ 27 │ │ Base (μs) │ 0.533771 │ 1.4007 │ 7.57425 │ 2.65178 │
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│ 28 │ │ max error │ 1.66533e-16 │ 1.54685e-7 │ 1.13318e-13 │ 3.0299e-9 │
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│ 29 │ 8 │ compile time (s) │ 0.798822 │ 0.501215 │ 7.42485 │ 0.125385 │
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│ 30 │ │ StaticArrays (μs) │ 0.400655 │ 0.672679 │ 1.7624 │ 0.678955 │
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│ 31 │ │ Base (μs) │ 0.613287 │ 1.603 │ 8.035 │ 2.94444 │
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│ 32 │ │ max error │ 2.77556e-16 │ 4.73129e-9 │ 1.46772e-13 │ 2.61726e-9 │
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│ 33 │ 9 │ compile time (s) │ 0.91446 │ 0.677859 │ 3.29461 │ 0.188982 │
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│ 34 │ │ StaticArrays (μs) │ 0.574361 │ 0.9838 │ 2.81078 │ 0.965474 │
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│ 35 │ │ Base (μs) │ 0.7649 │ 1.8765 │ 9.128 │ 3.17475 │
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│ 36 │ │ max error │ 3.46945e-16 │ 6.68251e-9 │ 3.30702e-13 │ 2.04139e-9 │
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│ 37 │ 10 │ compile time (s) │ 1.09413 │ 0.923797 │ 4.16234 │ 0.258198 │
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│ 38 │ │ StaticArrays (μs) │ 0.770716 │ 1.3145 │ 4.16643 │ 1.3064 │
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│ 39 │ │ Base (μs) │ 2.82311 │ 4.12057 │ 12.835 │ 5.3835 │
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│ 40 │ │ max error │ 1.94289e-16 │ 1.7691e-9 │ 2.42841e-13 │ 1.97784e-9 │
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│ 41 │ 11 │ compile time (s) │ 1.30448 │ 1.21905 │ 5.35341 │ 0.396076 │
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│ 42 │ │ StaticArrays (μs) │ 1.037 │ 1.7583 │ 5.43033 │ 1.7323 │
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│ 43 │ │ Base (μs) │ 3.24737 │ 4.82417 │ 16.481 │ 6.83967 │
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│ 44 │ │ max error │ 2.42861e-16 │ 1.91576e-9 │ 5.14422e-13 │ 3.63391e-9 │
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│ 45 │ 12 │ compile time (s) │ 1.55567 │ 1.66793 │ 6.75529 │ 0.601386 │
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│ 46 │ │ StaticArrays (μs) │ 1.3044 │ 2.203 │ 6.8148 │ 2.18522 │
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│ 47 │ │ Base (μs) │ 3.3915 │ 5.04783 │ 15.549 │ 6.2778 │
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│ 48 │ │ max error │ 2.77556e-16 │ 6.40505e-10 │ 7.41502e-13 │ 9.72575e-10 │
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│ 49 │ 13 │ compile time (s) │ 1.93222 │ 2.21769 │ 8.61503 │ 0.847173 │
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│ 50 │ │ StaticArrays (μs) │ 1.6922 │ 2.83978 │ 8.623 │ 2.812 │
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│ 51 │ │ Base (μs) │ 3.841 │ 5.813 │ 25.147 │ 6.2298 │
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│ 52 │ │ max error │ 2.22045e-16 │ 3.45741e-8 │ 1.43535e-12 │ 3.7065e-10 │
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│ 53 │ 14 │ compile time (s) │ 2.26075 │ 2.94048 │ 10.9119 │ 1.22455 │
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│ 54 │ │ StaticArrays (μs) │ 2.11289 │ 3.49162 │ 10.63 │ 3.43775 │
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│ 55 │ │ Base (μs) │ 6.0394 │ 8.1555 │ 29.706 │ 8.3256 │
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│ 56 │ │ max error │ 5.55112e-16 │ 2.75214e-8 │ 2.81287e-12 │ 1.23022e-8 │
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│ 57 │ 15 │ compile time (s) │ 0.0109467 │ 0.0650982 │ 16.0084 │ 0.059017 │
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│ 58 │ │ StaticArrays (μs) │ 6.788 │ 8.787 │ 37.942 │ 11.321 │
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│ 59 │ │ Base (μs) │ 6.6 │ 8.43933 │ 24.837 │ 9.819 │
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│ 60 │ │ max error │ 0.0 │ 0.0 │ 6.88512e-12 │ 0.0 │
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│ 61 │ 16 │ compile time (s) │ 0.0108788 │ 0.0883042 │ 18.8852 │ 0.0656792 │
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│ 62 │ │ StaticArrays (μs) │ 7.4815 │ 10.4963 │ 44.585 │ 11.091 │
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│ 63 │ │ Base (μs) │ 7.116 │ 9.638 │ 36.8 │ 12.223 │
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│ 64 │ │ max error │ 0.0 │ 0.0 │ 8.35981e-12 │ 0.0 │
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│ 65 │ 17 │ compile time (s) │ 0.0110253 │ 0.103676 │ 23.3029 │ 0.0761904 │
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│ 66 │ │ StaticArrays (μs) │ 8.656 │ 11.402 │ 53.001 │ 10.37 │
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│ 67 │ │ Base (μs) │ 8.386 │ 11.592 │ 47.86 │ 12.814 │
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│ 68 │ │ max error │ 0.0 │ 0.0 │ 2.26813e-11 │ 0.0 │
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│ 69 │ 18 │ compile time (s) │ 0.0128607 │ 0.0897007 │ 27.215 │ 0.0820536 │
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│ 70 │ │ StaticArrays (μs) │ 11.061 │ 13.706 │ 62.048 │ 17.152 │
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│ 71 │ │ Base (μs) │ 12.584 │ 14.096 │ 55.174 │ 14.878 │
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│ 72 │ │ max error │ 0.0 │ 0.0 │ 1.89276e-11 │ 0.0 │
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│ 73 │ 19 │ compile time (s) │ 0.0110386 │ 0.113333 │ 32.6636 │ 0.090609 │
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│ 74 │ │ StaticArrays (μs) │ 10.48 │ 14.387 │ 71.615 │ 17.143 │
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│ 75 │ │ Base (μs) │ 13.325 │ 13.636 │ 60.074 │ 12.513 │
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│ 76 │ │ max error │ 0.0 │ 0.0 │ 2.97618e-11 │ 0.0 │
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│ 77 │ 20 │ compile time (s) │ 0.0111067 │ 0.110741 │ 39.7384 │ 0.0973694 │
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│ 78 │ │ StaticArrays (μs) │ 11.2547 │ 14.768 │ 69.351 │ 13.365 │
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│ 79 │ │ Base (μs) │ 10.59 │ 13.887 │ 62.789 │ 17.813 │
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│ 80 │ │ max error │ 0.0 │ 0.0 │ 1.64377e-11 │ 0.0 │

‎perf/benchmark_matrix_ops.jl

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using StaticArrays, BenchmarkTools, DataFrames, DataStructures
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Nmax = 20
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unary = (det, inv, expm)
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binary = (\,)
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data = OrderedDict{Symbol,Any}()
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data[:SIZE] = vcat(([i, "", "", ""] for i in 1:Nmax)...)
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data[:STAT] = [stat for sz in 1:Nmax for stat in ("compile time (s)", "StaticArrays (μs)", "Base (μs)", "max error")]
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for f in unary
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f_data = Float64[]
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for N in 1:Nmax
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print("\r$((f,N))")
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SA = @SMatrix rand(N,N)
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A = Array(SA)
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push!(f_data, @elapsed f(SA))
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push!(f_data, 1e6*@belapsed $f($SA))
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push!(f_data, 1e6*@belapsed $f($A))
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push!(f_data, maximum([begin
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SA = @SMatrix rand(N,N)
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A = Array(SA)
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norm(f(A) - f(SA))
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end for i in 1:1000]))
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end
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data[Symbol(f)] = f_data
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end
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for f in binary
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f_data = Float64[]
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for N in 1:Nmax
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print("\r$((f,N))")
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SA = @SMatrix rand(N,N)
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A = Array(SA)
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SB = @SMatrix rand(N,N)
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B = Array(SB)
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push!(f_data, @elapsed f(SA,SB))
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push!(f_data, 1e6*@belapsed $f($SA,$SB))
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push!(f_data, 1e6*@belapsed $f($A,$B))
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push!(f_data, maximum([begin
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SA = @SMatrix rand(N,N)
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A = Array(SA)
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SB = @SMatrix rand(N,N)
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B = Array(SB)
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norm(f(A,B) - f(SA,SB))
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end for i in 1:1000]))
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end
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data[Symbol(f)] = f_data
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end
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df = DataFrame(data...)
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open("bench_matrix_ops.txt", "w") do f
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versioninfo(f)
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showall(f, df)
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end

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