The code get great performance improvement. My original version cost 133 s
and about 166 G memories, while your version cost 61 s and about 423M
memories!
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
>
>
>
>
