woodbury timings

gistfile1.txt

#
# woodburysolve
#
using ApproxFun, SingularIntegralEquations, PyPlot

d = 8
t1,t2 = Array(Float64,min(d,6)),Array(Float64,d)

for i = 1:d

    dom = cantor(Interval(),i)
    ⨍ = DefiniteLineIntegral(dom)
    f = Fun(x->logabs(x-5im),dom)

    if i < 7 
        G = GreensFun((x,y)->1/2,CauchyWeight(Space(dom)⊗Space(dom),0);method=:Cholesky)

        gc()
        gc_disable()
        tic()
        u1 = ⨍[G]\transpose(f)
        t1[i] = toc()
        gc_enable()
        gc()

        println("Adaptive QR  forward error norm is: ",norm(⨍[G]*u1-f))
    end
  
    G1 = GreensFun((x,y)->1/2,CauchyWeight(Space(dom)⊗Space(dom),0);method=:hierarchical)
    H = ⨍[G1]

    gc()
    gc_disable()
    tic()
    u2 = H\f
    t2[i] = toc()
    gc_enable()
    gc()
    gc_disable()
    tic()
    u2 = H\f
    t2[i] = toc()
    gc_enable()
    gc()


    if i < 7 println("The Woodbury forward error norm is: ",norm(⨍[G]*u2-f)) end

end


d1 = 2.0.^(1:length(t1))
d2 = 2.0.^(1:length(t2))

clf();loglog(d1,t1,"-r",d1,(d1/2).^3.*t1[1],"--b")
loglog(d2,t2,"-g",d2,(d2/2).^2*t2[1],"--k")
grid()
xlabel("Number of domains")
ylabel("Execution time")
savefig("timingtestsLaplace.png",dpi=300)