Additionally, the allocation problem is not solved. I guess this http://julia-programming-language.2336112.n4.nabble.com/How-to-avoid-temporary-arrays-being-created-in-a-function-td14492.html might be helpful, but I just don't know how to change my code.
在 2016年3月30日星期三 UTC+8上午1:15:07，Yichao Yu写道： > > > > On Tue, Mar 29, 2016 at 12:43 PM, 博陈 <chenph...@gmail.com <javascript:>> > wrote: > >> I tried the built-in profiler, and find that the problem lies in lines I >> end with ******, the result is shown below: >> that proved my guess, how can I pre-allocate these arrays? If I don't >> want to divide this code into several parts that calculate these arrays >> separately. >> > > I don't understand what you mean by `divide this code into several parts > that calculate these arrays separately` > > >> | lines | backtrace | >> >> | 169 | 9011 | *********** >> >> | 173 | 1552 | >> >> | 175 | 2604 | >> >> | 179 | 2906 | >> >> | 181 | 1541 | >> >> | 192 | 4458 | >> >> | 211 | 13332 ************| >> >> | 214 | 8431 |************ >> >> | 218 | 15871 |*********** >> >> | 221 | 2538 | >> >> >> 在 2016年3月29日星期二 UTC+8下午9:27:27，Stefan Karpinski写道： >>> >>> Have you tried: >>> >>> (a) calling @code_typewarn on your function >>> (b) using the built-in profiler? >>> >>> >>> On Tue, Mar 29, 2016 at 9:23 AM, 博陈 <chenph...@gmail.com> wrote: >>> >>>> First of all, have a look at the result. >>>> >>>> >>>> <https://lh3.googleusercontent.com/-anNt-E4P1vM/Vvp-TybegZI/AAAAAAAAABE/ZvDO2xarndMSgKVOXy_hcPd5NTh-7QcEA/s1600/QQ%25E5%259B%25BE%25E7%2589%258720160329210732.png> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> My code calculates the evolution of 1-d 2-electron system in the >>>> electric field, some variables are calculated during the evolution. >>>> According to the result of @time evolution, my code must have a >>>> pre-allocation problem. Before you see the long code, i suggest that the >>>> hotspot might be around the Arrays prop_e, \phio, pp. I have learnt that I >>>> can use m = Array(Float64, 1) outside a "for" loop and empty!(m) and >>>> push!(m, new_m) inside the loop to pre-allocate the variable m, but in my >>>> situations, I don't know how to pre-allocate these arrays. >>>> >>>> Below is the script (precisely, the main function) itself. >>>> >>>> function evolution(ϕ::Array{Complex{Float64}, 2}, >>>> ele::Array{Float64, 1}, dx::Float64, dt::Float64, >>>> flags::Tuple{Int64, Int64, Int64, Int64}) >>>> ϕg = copy(ϕ) >>>> FFTW.set_num_threads(8) >>>> ns = length( ϕ[:, 1] ) >>>> x = get_x(ns, dx) >>>> p = get_p(ns, dx) >>>> if flags[4] == 1 >>>> pp = similar(p) >>>> A = -cumsum(ele) * dt >>>> A² = A.*A >>>> ##### splitting >>>> r_sp = 150.0 >>>> δ_sp = 5.0 >>>> splitter = Array(Float64, ns, ns) >>>> end >>>> nt = length( ele ) >>>> >>>> # ##### Pre-allocate result and temporary arrays >>>> #if flags[1] == 1 >>>> σ = zeros(Complex128, nt) >>>> #end >>>> #if flags[2] == 1 >>>> a = zeros(Float64, nt) >>>> #end >>>> #if flags[3] == 1 >>>> r_ionization = 20.0 >>>> n1 = round(Int, ns/2 - r_ionization/dx) >>>> n2 = round(Int, ns/2 + r_ionization/dx) >>>> ip = zeros(Float64, nt) >>>> #end >>>> >>>> ##### FFT plan >>>> p_fft! = plan_fft!( similar(ϕ), flags=FFTW.MEASURE ) >>>> >>>> prop_x = similar( ϕ ) >>>> prop_p = similar( prop_x ) >>>> prop_e = similar( prop_x ) >>>> # this two versions just cost the same time >>>> xplusy = Array(Float64, ns, ns) >>>> #xplusy = Array( Float64, ns^2) >>>> >>>> ##### absorb boundary >>>> r_a = ns * dx /2 - 50.0 >>>> δ = 10.0 >>>> absorb = Array(Float64, ns, ns) >>>> >>>> k0 = 2π / (ns * dx) >>>> >>>> @inbounds for j in 1:ns >>>> @inbounds for i in 1:ns >>>> prop_x[i, j] = exp( -im * get_potential(x[i], x[j]) * dt / >>>> 2 ) >>>> prop_p[i, j] = exp( -im * (p[i]^2 + p[j]^2)/2 * dt ) >>>> >>>> xplusy[i, j] = x[i] + x[j] >>>> >>>> absorb[i, j] = (1.0 - get_out(x[i], r_a, δ ))* (1.0 - >>>> get_out(x[j], >>>> r_a, δ)) >>>> end >>>> end >>>> >>>> if flags[2] == 1 >>>> pvpx = Array(Float64, ns, ns) >>>> @inbounds for j in 1:ns >>>> @inbounds for i in 1:ns >>>> pvpx[i, j] = get_pvpx(x[i], x[j]) >>>> end >>>> end >>>> end >>>> >>>> if flags[4] == 1 >>>> ϕo = zeros(Complex128, ns, ns) >>>> ϕp = zeros(Complex128, ns, ns) >>>> @inbounds for j in 1:ns >>>> @inbounds for i in 1:ns >>>> splitter[i, j] = get_out(x[i], r_sp, δ_sp) * >>>> get_out(x[j], r_sp, δ_sp) >>>> end >>>> end >>>> end >>>> >>>> for i in 1:nt >>>> for j in eachindex(ϕ) >>>> prop_e[j] = exp( -im * ele[i] * xplusy[j] * dt/2.0) >>>> ************************************169 >>>> >>>> > You might be hitting a stupid inlining issue here, try adding parenthesis > to the multiplication > (i.e. instead of `a * b * c * d` do `(a * b) * (c * d)`) > > >> end >>>> >>>> for j in eachindex(ϕ) >>>> ϕ[j] *= prop_x[j] * prop_e[j] >>>> end >>>> p_fft! * ϕ >>>> for j in eachindex(ϕ) >>>> ϕ[j] *= prop_p[j] >>>> end >>>> p_fft! \ ϕ >>>> for j in eachindex(ϕ) >>>> ϕ[j] *= prop_x[j] * prop_e[j] >>>> end >>>> ########## autocorrelation function σ(t) >>>> if flags[1] == 1 >>>> for j in eachindex(ϕ) >>>> σ[i] += conj(ϕg[j]) * ϕ[j] >>>> end >>>> end >>>> ########## dipole acceleration a(t) >>>> if flags[2] == 1 >>>> for j in eachindex(ϕ) >>>> a[i] += abs(ϕ[j])^2 * (pvpx[j] + 2ele[i]) >>>> end >>>> end >>>> ########## ionization probability ip(t) >>>> if flags[3] == 1 >>>> for j1 in n1:n2 >>>> for j2 in 1:ns >>>> ip[i] += abs( ϕ[j2+ns*(j1-1)] )^2 >>>> end >>>> end >>>> for j1 in [1:n1-1; n2+1:ns] >>>> for j2 in n1:n2 >>>> ip[i] += abs( ϕ[j2+ns*(j1-1)] )^2 >>>> end >>>> end >>>> end >>>> ########## get momentum >>>> if flags[4] == 1 >>>> for j in eachindex(ϕo) >>>> ϕo[j] = ϕ[j] * splitter[j] * exp( -im * A[i]*xplusy[j] >>>> ) **********************************211 >>>> >>>> > Same with above > > >> end >>>> for j in eachindex(p) >>>> pp[j] = p[j]^2 /2 * (nt-i) - p[j] *sum( A[i:nt] ) + >>>> sum( A²[1:nt] ) /2 ******************214 >>>> >>>> > write out the sum directly, you can do with a helper function > Using subarray would also eliminate the data copy but is still suboptimum > as it is now. > > >> end >>>> for j2 in 1:ns >>>> for j1 in 1:ns >>>> ϕo[j1, j2] = ϕo[j1, j2] * exp( -im * (pp[j1] + >>>> pp[j2]) * dt)************************218 >>>> >>>> > I don't see any obvious problem, (apart from the potential inlining issue > as above) but it does look like a keep loop with c function call so it > won't be surprising if most of the time is spent here. > > >> end >>>> end >>>> p_fft! * ϕo >>>> for j in eachindex(ϕp) >>>> ϕp[j] += ϕo[j] >>>> end >>>> end >>>> >>>> ########## absorb boundary >>>> if mod(i, 300) == 0 >>>> for j in eachindex(ϕ) >>>> ϕ[j] *= absorb[j] >>>> end >>>> end >>>> >>>> if (mod(i, 500) == 0) >>>> println("i = $i") >>>> flush(STDOUT) >>>> end >>>> end >>>> σ *= dx^2 >>>> a *= dx^2 >>>> ip *= dx^2 >>>> >>>> save("data/fs.jld", "ϕ", ϕ) >>>> if flags[1] == 1 >>>> save("data/sigma.jld", "σ", σ) >>>> end >>>> if flags[2] == 1 >>>> save("data/a.jld", "a", a) >>>> end >>>> if flags[3] == 1 >>>> save("data/ip.jld", "ip", ip) >>>> end >>>> if flags[4] == 1 >>>> save("data/pf.jld", "ϕp", ϕp) >>>> end >>>> >>>> #return σ, a, ip, ϕ >>>> nothing >>>> end >>>> >>>> >>>> >>> >
