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chriselrod/LinearAlgebraBenchmarks.jl

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LAPACK vs LinearAlgebra.jl
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LinearAlgebraBenchmarks.jl
using BenchmarkTools, LinearAlgebra
#LinearAlgebra code at: https://github.com/andreasnoack/LinearAlgebra.jl
#Install LinearAlgebra via Pkg.clone("https://github.com/andreasnoack/LinearAlgebra.jl")
function gen_pos_def(p::Int)
X = randn( div(3p, 2), p)
S = X' * X
S, Hermitian(S, :L)
end
S20, H20 = gen_pos_def(20);
S35, H35 = gen_pos_def(33);
S40, H40 = gen_pos_def(40);
S100, H100 = gen_pos_def(100);
S133, H133 = gen_pos_def(133);
S150, H150 = gen_pos_def(150);
S300, H300 = gen_pos_def(300);
S1000, H1000 = gen_pos_def(1000);
#"Julia_eig" is actually identical to simply "eig" when "using LinearAlgebra"
#When not using LinearAlgebra, "eig" on a Symmetric or Hermitian matrix A will default to syevr!(copy(A))
#Just want to make it clear what code both are running.
Julia_eig(A) = LinearAlgebra.EigenSelfAdjoint.eig!(copy(A))
LAPACK_eig(A) = Base.LinAlg.LAPACK.syevr!('V', 'A', 'L', copy(A), 1.0, 1.0, 1, 1, eps())
vals_j, vecs_j = Julia_eig(H40)
vals_L, vecs_L = LAPACK_eig(S40)
#Eigenvalues are approximately equal.
vals_j ≈ vals_L
#Eigenvectors are orthogonal.
vecs_j' * vecs_j ≈ eye(40)
vecs_L' * vecs_L ≈ eye(40)
@benchmark Julia_eig($H20)
@benchmark LAPACK_eig($S20)
@benchmark Julia_eig($H35)
@benchmark LAPACK_eig($S35)
@benchmark Julia_eig($H40)
@benchmark LAPACK_eig($S40)
@benchmark Julia_eig($H100)
@benchmark LAPACK_eig($S100)
@benchmark Julia_eig($H133)
@benchmark LAPACK_eig($S133)
@benchmark Julia_eig($H150)
@benchmark LAPACK_eig($S150)
@benchmark Julia_eig($H300)
@benchmark LAPACK_eig($S300)
@benchmark Julia_eig($H1000)
@benchmark LAPACK_eig($S1000)
############################################################################
############################# Windows & Intel ##############################
############################################################################
julia> versioninfo()
Julia Version 0.6.0
Commit 903644385b* (2017-06-19 13:05 UTC)
Platform Info:
OS: Windows (x86_64-w64-mingw32)
CPU: Intel(R) Core(TM) i7-4790 CPU @ 3.60GHz
WORD_SIZE: 64
BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Haswell)
LAPACK: libopenblas64_
LIBM: libopenlibm
LLVM: libLLVM-3.9.1 (ORCJIT, haswell)
julia> vals_j, vecs_j = Julia_eig(H40)
([2.06457, 3.43887, 4.20197, 5.41251, 6.52628, 8.68195, 9.86435, 12.4965, 15.997
7, 16.4481 . 99.4326, 99.9603, 109.002, 117.18, 120.139, 135.266, 147.287, 159
.937, 163.705, 186.442], [0.175411 -0.0157983 . -0.0729909 0.345485; -0.122313 -
0.0702725 . 0.0162747 -0.0864244; . ; 0.267428 0.137832 . -0.0641975 0.171393; 0
.0037438 -0.1076 . -0.0869933 -0.0728508])
julia> vals_L, vecs_L = LAPACK_eig(S40)
([2.06457, 3.43887, 4.20197, 5.41251, 6.52628, 8.68195, 9.86435, 12.4965, 15.997
7, 16.4481 . 99.4326, 99.9603, 109.002, 117.18, 120.139, 135.266, 147.287, 159
.937, 163.705, 186.442], [0.175411 -0.0157983 . 0.0729909 -0.345485; -0.122313 -
0.0702725 . -0.0162747 0.0864244; . ; 0.267428 0.137832 . 0.0641975 -0.171393; 0
.0037438 -0.1076 . 0.0869933 0.0728508])
julia> #Eigenvalues are approximately equal.
julia> vals_j ≈ vals_L
true
julia> #Eigenvectors are orthogonal.
julia> vecs_j' * vecs_j ≈ eye(40)
true
julia> vecs_L' * vecs_L ≈ eye(40)
true
julia> @benchmark Julia_eig($H20)
BenchmarkTools.Trial:
memory estimate: 11.56 KiB
allocs estimate: 24
--------------
minimum time: 35.067 µs (0.00% GC)
median time: 35.923 µs (0.00% GC)
mean time: 38.622 µs (2.49% GC)
maximum time: 2.641 ms (97.42% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark LAPACK_eig($S20)
BenchmarkTools.Trial:
memory estimate: 18.03 KiB
allocs estimate: 15
--------------
minimum time: 157.375 µs (0.00% GC)
median time: 174.195 µs (0.00% GC)
mean time: 180.103 µs (1.01% GC)
maximum time: 2.608 ms (88.99% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark Julia_eig($H35)
BenchmarkTools.Trial:
memory estimate: 32.00 KiB
allocs estimate: 24
--------------
minimum time: 140.554 µs (0.00% GC)
median time: 145.686 µs (0.00% GC)
mean time: 151.807 µs (2.10% GC)
maximum time: 2.576 ms (91.45% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark LAPACK_eig($S35)
BenchmarkTools.Trial:
memory estimate: 43.05 KiB
allocs estimate: 15
--------------
minimum time: 450.457 µs (0.00% GC)
median time: 469.273 µs (0.00% GC)
mean time: 479.217 µs (0.89% GC)
maximum time: 2.953 ms (76.93% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark Julia_eig($H40)
BenchmarkTools.Trial:
memory estimate: 40.91 KiB
allocs estimate: 24
--------------
minimum time: 191.302 µs (0.00% GC)
median time: 197.289 µs (0.00% GC)
mean time: 204.647 µs (1.85% GC)
maximum time: 2.536 ms (90.58% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark LAPACK_eig($S40)
BenchmarkTools.Trial:
memory estimate: 53.45 KiB
allocs estimate: 15
--------------
minimum time: 560.221 µs (0.00% GC)
median time: 583.313 µs (0.00% GC)
mean time: 594.813 µs (0.85% GC)
maximum time: 3.257 ms (81.24% GC)
--------------
samples: 8383
evals/sample: 1
julia> @benchmark Julia_eig($H100)
BenchmarkTools.Trial:
memory estimate: 240.27 KiB
allocs estimate: 27
--------------
minimum time: 2.275 ms (0.00% GC)
median time: 2.316 ms (0.00% GC)
mean time: 2.367 ms (1.04% GC)
maximum time: 5.070 ms (52.26% GC)
--------------
samples: 2111
evals/sample: 1
julia> @benchmark LAPACK_eig($S100)
BenchmarkTools.Trial:
memory estimate: 272.25 KiB
allocs estimate: 19
--------------
minimum time: 2.939 ms (0.00% GC)
median time: 3.049 ms (0.00% GC)
mean time: 3.100 ms (0.82% GC)
maximum time: 7.278 ms (0.00% GC)
--------------
samples: 1605
evals/sample: 1
julia> @benchmark Julia_eig($H133)
BenchmarkTools.Trial:
memory estimate: 422.23 KiB
allocs estimate: 27
--------------
minimum time: 5.075 ms (0.00% GC)
median time: 5.169 ms (0.00% GC)
mean time: 5.244 ms (0.70% GC)
maximum time: 7.835 ms (25.84% GC)
--------------
samples: 953
evals/sample: 1
julia> @benchmark LAPACK_eig($S133)
BenchmarkTools.Trial:
memory estimate: 464.77 KiB
allocs estimate: 19
--------------
minimum time: 6.019 ms (0.00% GC)
median time: 6.160 ms (0.00% GC)
mean time: 6.232 ms (0.58% GC)
maximum time: 9.568 ms (18.64% GC)
--------------
samples: 800
evals/sample: 1
julia> @benchmark Julia_eig($H150)
BenchmarkTools.Trial:
memory estimate: 536.05 KiB
allocs estimate: 27
--------------
minimum time: 7.029 ms (0.00% GC)
median time: 7.273 ms (0.00% GC)
mean time: 7.373 ms (0.67% GC)
maximum time: 10.220 ms (20.95% GC)
--------------
samples: 678
evals/sample: 1
julia> @benchmark LAPACK_eig($S150)
BenchmarkTools.Trial:
memory estimate: 583.77 KiB
allocs estimate: 19
--------------
minimum time: 5.118 ms (0.00% GC)
median time: 5.526 ms (0.00% GC)
mean time: 5.640 ms (0.86% GC)
maximum time: 9.927 ms (0.00% GC)
--------------
samples: 887
evals/sample: 1
julia> @benchmark Julia_eig($H300)
BenchmarkTools.Trial:
memory estimate: 2.08 MiB
allocs estimate: 27
--------------
minimum time: 52.009 ms (0.00% GC)
median time: 53.261 ms (0.00% GC)
mean time: 53.488 ms (0.35% GC)
maximum time: 56.266 ms (3.95% GC)
--------------
samples: 94
evals/sample: 1
julia> @benchmark LAPACK_eig($S300)
BenchmarkTools.Trial:
memory estimate: 2.17 MiB
allocs estimate: 20
--------------
minimum time: 16.236 ms (0.00% GC)
median time: 17.151 ms (0.00% GC)
mean time: 17.474 ms (1.09% GC)
maximum time: 27.921 ms (0.00% GC)
--------------
samples: 286
evals/sample: 1
julia> @benchmark Julia_eig($H1000)
BenchmarkTools.Trial:
memory estimate: 22.94 MiB
allocs estimate: 27
--------------
minimum time: 1.848 s (0.52% GC)
median time: 1.884 s (0.51% GC)
mean time: 1.882 s (1.16% GC)
maximum time: 1.915 s (2.88% GC)
--------------
samples: 3
evals/sample: 1
julia> @benchmark LAPACK_eig($S1000)
BenchmarkTools.Trial:
memory estimate: 23.25 MiB
allocs estimate: 20
--------------
minimum time: 224.482 ms (0.93% GC)
median time: 231.353 ms (0.92% GC)
mean time: 234.625 ms (2.08% GC)
maximum time: 290.533 ms (19.53% GC)
--------------
samples: 22
evals/sample: 1
############################################################################
############################## Linux & AMD #################################
############################################################################
### cat /proc/cpuinfo gave 2.0 GHz for one core, and 1.4 GHz for the remaining 5.
### The cpu fan had failed at one point in this processor's life, possibly damaging it.
julia> versioninfo()
Julia Version 0.6.0
Commit 9036443 (2017-06-19 13:05 UTC)
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: AMD FX(tm)-6300 Six-Core Processor
WORD_SIZE: 64
BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Piledriver)
LAPACK: libopenblas64_
LIBM: libopenlibm
LLVM: libLLVM-3.9.1 (ORCJIT, bdver1)
julia> vals_j, vecs_j = Julia_eig(H40)
([2.74341, 4.00335, 5.0059, 8.16496, 9.08941, 11.9694, 12.1274, 12.7644, 14.2789, 18.5737 … 99.6323, 109.549, 110.885, 120.946, 125.619, 129.633, 140.819, 156.037, 162.288, 186.041], [-0.274927 0.261569 … -0.259847 -0.0474208; 0.0962548 -0.389692 … -0.0260467 0.103609; … ; -0.278481 -0.0513077 … 0.0454802 0.0979261; 0.197902 -0.0335611 … 0.053795 0.00835505])
julia> vals_L, vecs_L = LAPACK_eig(S40)
([2.74341, 4.00335, 5.0059, 8.16496, 9.08941, 11.9694, 12.1274, 12.7644, 14.2789, 18.5737 … 99.6323, 109.549, 110.885, 120.946, 125.619, 129.633, 140.819, 156.037, 162.288, 186.041], [-0.274927 -0.261569 … -0.259847 -0.0474208; 0.0962548 0.389692 … -0.0260467 0.103609; … ; -0.278481 0.0513077 … 0.0454802 0.0979261; 0.197902 0.0335611 … 0.053795 0.00835505])
julia> #Eigenvalues are approximately equal.
vals_j ≈ vals_L
true
julia> #Eigenvectors are orthogonal.
vecs_j' * vecs_j ≈ eye(40)
true
julia> vecs_L' * vecs_L ≈ eye(40)
true
julia> @benchmark Julia_eig($H20)
BenchmarkTools.Trial:
memory estimate: 11.56 KiB
allocs estimate: 24
--------------
minimum time: 88.706 μs (0.00% GC)
median time: 89.681 μs (0.00% GC)
mean time: 91.207 μs (0.73% GC)
maximum time: 1.850 ms (91.26% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark LAPACK_eig($S20)
BenchmarkTools.Trial:
memory estimate: 18.03 KiB
allocs estimate: 15
--------------
minimum time: 120.944 μs (0.00% GC)
median time: 132.230 μs (0.00% GC)
mean time: 133.704 μs (0.93% GC)
maximum time: 1.908 ms (87.35% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark Julia_eig($H35)
BenchmarkTools.Trial:
memory estimate: 32.00 KiB
allocs estimate: 24
--------------
minimum time: 351.276 μs (0.00% GC)
median time: 353.887 μs (0.00% GC)
mean time: 358.823 μs (0.44% GC)
maximum time: 1.582 ms (72.70% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark LAPACK_eig($S35)
BenchmarkTools.Trial:
memory estimate: 43.05 KiB
allocs estimate: 15
--------------
minimum time: 319.903 μs (0.00% GC)
median time: 353.628 μs (0.00% GC)
mean time: 362.566 μs (0.65% GC)
maximum time: 27.133 ms (0.00% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark Julia_eig($H40)
BenchmarkTools.Trial:
memory estimate: 40.91 KiB
allocs estimate: 24
--------------
minimum time: 493.866 μs (0.00% GC)
median time: 496.545 μs (0.00% GC)
mean time: 501.775 μs (0.34% GC)
maximum time: 1.646 ms (62.11% GC)
--------------
samples: 9925
evals/sample: 1
julia> @benchmark LAPACK_eig($S40)
BenchmarkTools.Trial:
memory estimate: 53.45 KiB
allocs estimate: 15
--------------
minimum time: 405.791 μs (0.00% GC)
median time: 441.776 μs (0.00% GC)
mean time: 452.478 μs (0.54% GC)
maximum time: 20.474 ms (0.00% GC)
--------------
samples: 10000
evals/sample: 1
julia> @benchmark Julia_eig($H100)
BenchmarkTools.Trial:
memory estimate: 240.27 KiB
allocs estimate: 27
--------------
minimum time: 6.449 ms (0.00% GC)
median time: 6.473 ms (0.00% GC)
mean time: 6.529 ms (0.10% GC)
maximum time: 7.701 ms (0.00% GC)
--------------
samples: 766
evals/sample: 1
julia> @benchmark LAPACK_eig($S100)
BenchmarkTools.Trial:
memory estimate: 272.25 KiB
allocs estimate: 19
--------------
minimum time: 2.381 ms (0.00% GC)
median time: 2.520 ms (0.00% GC)
mean time: 2.703 ms (0.33% GC)
maximum time: 36.480 ms (0.00% GC)
--------------
samples: 1850
evals/sample: 1
julia> @benchmark Julia_eig($H133)
BenchmarkTools.Trial:
memory estimate: 422.23 KiB
allocs estimate: 27
--------------
minimum time: 14.639 ms (0.00% GC)
median time: 14.827 ms (0.00% GC)
mean time: 14.924 ms (0.07% GC)
maximum time: 16.660 ms (0.00% GC)
--------------
samples: 335
evals/sample: 1
julia> @benchmark LAPACK_eig($S133)
BenchmarkTools.Trial:
memory estimate: 464.77 KiB
allocs estimate: 19
--------------
minimum time: 3.815 ms (0.00% GC)
median time: 3.965 ms (0.00% GC)
mean time: 4.187 ms (0.35% GC)
maximum time: 29.175 ms (0.00% GC)
--------------
samples: 1194
evals/sample: 1
julia> @benchmark Julia_eig($H150)
BenchmarkTools.Trial:
memory estimate: 536.05 KiB
allocs estimate: 27
--------------
minimum time: 20.064 ms (0.00% GC)
median time: 20.214 ms (0.00% GC)
mean time: 20.315 ms (0.06% GC)
maximum time: 22.388 ms (0.00% GC)
--------------
samples: 247
evals/sample: 1
julia> @benchmark LAPACK_eig($S150)
BenchmarkTools.Trial:
memory estimate: 583.77 KiB
allocs estimate: 19
--------------
minimum time: 4.974 ms (0.00% GC)
median time: 5.421 ms (0.00% GC)
mean time: 5.649 ms (0.31% GC)
maximum time: 33.376 ms (0.00% GC)
--------------
samples: 885
evals/sample: 1
julia> @benchmark Julia_eig($H300)
BenchmarkTools.Trial:
memory estimate: 2.08 MiB
allocs estimate: 27
--------------
minimum time: 151.875 ms (0.00% GC)
median time: 152.833 ms (0.00% GC)
mean time: 153.114 ms (0.03% GC)
maximum time: 157.302 ms (0.00% GC)
--------------
samples: 33
evals/sample: 1
julia> @benchmark LAPACK_eig($S300)
BenchmarkTools.Trial:
memory estimate: 2.17 MiB
allocs estimate: 20
--------------
minimum time: 17.447 ms (0.00% GC)
median time: 17.557 ms (0.00% GC)
mean time: 18.319 ms (0.34% GC)
maximum time: 51.399 ms (0.00% GC)
--------------
samples: 273
evals/sample: 1
julia> @benchmark Julia_eig($H1000)
BenchmarkTools.Trial:
memory estimate: 22.94 MiB
allocs estimate: 27
--------------
minimum time: 5.424 s (0.01% GC)
median time: 5.424 s (0.01% GC)
mean time: 5.424 s (0.01% GC)
maximum time: 5.424 s (0.01% GC)
--------------
samples: 1
evals/sample: 1
julia> @benchmark LAPACK_eig($S1000)
BenchmarkTools.Trial:
memory estimate: 23.25 MiB
allocs estimate: 20
--------------
minimum time: 254.586 ms (0.25% GC)
median time: 257.614 ms (0.25% GC)
mean time: 269.437 ms (2.17% GC)
maximum time: 341.979 ms (24.85% GC)
--------------
samples: 19
evals/sample: 1
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