On Tue, Mar 29, 2016 at 1:50 PM, 博陈 <[email protected]> wrote:
> 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. > > The only places you create temporary arrays according to your profile is the `sum(A[1:n])` and you just need to loop from 1:n manually instead of creating an subarray > > > 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 <[email protected]> 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 <[email protected]> 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 >>>>> >>>>> >>>>> >>>> >>
