Add benchmark script

Author: YingboMa

README.md

@@ -10,3 +10,28 @@
 #### Implemented Algorithms:
 
 - Sivan Toledo's recursive left-looking LU algorithm. DOI: [10.1137/S0895479896297744](https://epubs.siam.org/doi/10.1137/S0895479896297744)
+
+#### Performance:
+
+For medium sized mat
+```julia
+julia> using BenchmarkTools
+
+julia> import LinearAlgebra, RecursiveFactorization
+
+julia> A = rand(40, 40);
+
+julia> @btime RecursiveFactorization.lu($A);
+  23.762 μs (19 allocations: 26.50 KiB)
+
+julia> @btime LinearAlgebra.lu($A);
+  63.846 μs (3 allocations: 13.05 KiB)
+
+julia> A = rand(80, 80);
+
+julia> @btime RecursiveFactorization.lu($A);
+  91.609 μs (42 allocations: 102.95 KiB)
+
+julia> @btime LinearAlgebra.lu($A);
+  420.470 μs (4 allocations: 50.83 KiB)
+```

perf/lu.jl

@@ -0,0 +1,26 @@
+using BenchmarkTools
+import LinearAlgebra, RecursiveFactorization
+
+BenchmarkTools.DEFAULT_PARAMETERS.seconds = 0.5
+
+luflop(m, n) = n^3÷3 - n÷3 + m*n^2
+luflop(n) = luflop(n, n)
+
+bas_mflops = Float64[]
+rec_mflops = Float64[]
+ns = 50:50:800
+for n in ns
+    A = rand(n, n)
+    bt = @belapsed LinearAlgebra.lu!($(copy(A)))
+    rt = @belapsed RecursiveFactorization.lu!($(copy(A)))
+    push!(bas_mflops, luflop(n)/bt/1e9)
+    push!(rec_mflops, luflop(n)/rt/1e9)
+end
+
+using Plots
+plt = plot(ns, bas_mflops, legend=:bottomright, lab="OpenBLAS", title="LU Factorization Benchmark", marker=:auto, dpi=150)
+plot!(plt, ns, rec_mflops, lab="RecursiveFactorization", marker=:auto)
+xaxis!(plt, "size (N x N)")
+yaxis!(plt, "GFLOPS")
+savefig("lubench.png")
+savefig("lubench.pdf")