Oh, thank you very very much. I am quite a green hand. Before following
advises from you and Yichao, my code cost 133 s, but now, your version only
cost 61 s!
Although Yichao has pointed out almost all the optimization strategies and
make things clear enough, I don't really know how to follow his advice.
Your answer has helped me a lot! Before asking for help in this
julia-users' group, I felt depressed for the inefficiency of my julia code,
but now I feel great passion again.
在 2015年12月15日星期二 UTC+8下午7:34:55，Pablo Zubieta写道：
>
> Stefan said that your code is well type (type stable). Have you tried
> Yichao's suggestions?
>
> Here is the function ground() taking them into account:
>
> function ground()
> R = 320.
> Ks = 2^11 - 1
> x = linspace(-R, R, Ks+1)
> dx = 2R/Ks
> dt = 0.1
> pm = 2π/2dx
> px = circshift( linspace(-pm, pm, Ks+1), round(Int64, Ks/2) )
> FFTW.set_num_threads(8)
>
>
> V = Float64[Potential(ix, iy) for ix in x, iy in x]
> ko = Float64[e^(-dt/4* (Ko(ipx,ipy))) for ipx in px, ipy in px]
> ko2 = ko.^2
> vo = Float64[e^(-dt* (Potential(ix,iy))) for ix in x, iy in x]
> ϕ = Array(Complex128,(Ks+1,Ks+1))
> Pl = plan_fft!(ϕ; flags=FFTW.MEASURE)
> for i in eachindex(ϕ); ϕ[i] = V[i]; end # Conversion is automatic here
>
>
> invnormphi = 1. / (sqrt(sumabs2(ϕ))*dx)
> scale!(ϕ, invnormphi)
>
>
> Pl * ϕ # No need to assign to ϕ
> for i in eachindex(ϕ); ϕ[i] *= ko[i]; end
> Pl \ ϕ
>
> ϕ′ = similar(ϕ)
>
> Δϕ = 1.
> nstep = 0
> println("start loop")
> while Δϕ > 1.e-15
> copy!(ϕ′, ϕ)
> for i in eachindex(ϕ), ϕ[i] *= vo[i]; end
>
> invnormphi = 1. / (sqrt(sumabs2(ϕ))*dx)
> scale!(ϕ, invnormphi)
>
>
> Pl * ϕ
> for i in eachindex(ϕ); ϕ[i] *= ko2[i]; end
> Pl \ ϕ
> # if check Δϕ for every step, 35s is needed.
> if nstep>500
> Δϕ = maxabs(ϕ-ϕ′)
> end
> nstep += 1
> if mod(nstep,200)==0
> print(nstep," ")
> println("Δϕ=",Δϕ)
> end
>
> end
> for i in eachindex(ϕ); ϕ[i] *= vo[i]; end
>
> Pl * ϕ
> for i in eachindex(ϕ); ϕ[i] *= ko[i]; end
> Pl \ ϕ
>
>
> invnormphi = 1. / (sqrt(sumabs2(ϕ))*dx)
> scale!(ϕ, invnormphi)
> end
>
>
>
>
