# Ewald summation in Julia

I am writing a small MD (molecular dynamics) engine in Julia and I noticed that 67% of the time spent running the following Ewald summation function (to calculate coulomb energy of an infinite crystal lattice in reciprocal space) is spent in garbage collection. Besides algorithmic improvements, which can certainly be made here, what can I do to make it faster in terms of Julia tricks / good practices?

function getEwaldEnergy(top::Topology, xyz::Array{Float64})::Float64
# cubic box only for now
tolerance::Float64 = 1.0e-24
tryUntil::Int64 = 4  # 5 box sizes gets it to five decimal places
L::Float64 = top.box[1]
rc::Float64 = L / 2.0

α::Float64 = 3.5 / (top.box[1] / 2)
σ::Float64 = 1 / (sqrt(2) * α)

λ::Float64 = 1.0
ns::Array{Int64} = getCombinations(-tryUntil, tryUntil, 3)

# self-energy corrections
selfEnergy::Float64 = 0.0
for i::Int64 in 1:top.nAtoms
selfEnergy += (1 / (sqrt(2 * pi) * σ)) * (top.charges[i] * top.charges[i])
end

# short-range energy
shortRangeEnergy::Float64 = 0.0
shortRangeEnergyBefore::Float64 = 0.0
for l::Int64 in 1:size(ns)[1]
shortRangeEnergyBefore = shortRangeEnergy
for i in 1:top.nAtoms
for j::Int64 in 1:top.nAtoms
ci::Float64 = top.charges[i]
cj::Float64 = top.charges[j]

idx::Array{Array{Int64}} = top.bondIdx
bonded::Bool = false

# check if i/j pair is bonded
for k::Int64 in 1:length(idx)
if (i == idx[k][1] && j == idx[k][2]) || (j == idx[k][1] && i == idx[k][2])
bonded = true
break
end
end

if bonded == false && !(i == j && ns[l, :] == [0.0, 0.0, 0.0])
r::Float64 = norm(xyz[i, :] - xyz[j, :] + L * ns[l, :])
if r < rc - λ
shortRangeEnergy += 0.5 * ((ci * cj) / r) * erfc(r / (sqrt(2) * σ))
elseif r < rc && r > rc - λ
# switching function turns on
shortRangeEnergy += 0.5 * ((ci * cj) * (rc - r)^2 * (-2 * rc + 2 * r + 3 * λ) * erfc(r / (sqrt(2) * σ))) / (2 * r * λ^3)
end
end
end
end
end

# long-range energy
longRangeEnergy::Float64 = 0.0
longRangeEnergyBefore::Float64 = 0.0
volume::Float64 = L^3
ms = ns

longRangeEnergyBefore = copy(longRangeEnergy)
for l in 1:size(ms)[1]  # no k = [0, 0, 0]
if ms[l, :] == [0.0, 0.0, 0.0]
continue
end

# define reciprocal space vectors
kVector::Array{Float64} = (2 * pi) * (ms[l, :] / L)
k::Float64 = norm(kVector)

# check this equal 1 good
# println(exp(-im * dot(kVector, L * [ms[l, 1], ms[l, 2], ms[l, 3]])))
strucFactor::ComplexF64 = 0.0
for i in 1:top.nAtoms
strucFactor += top.charges[i] * exp(im * dot(kVector, xyz[i, :]))
end

longRangeEnergy += ((4 * pi) / (volume)) * ((exp(-σ^2 * k^2 / 2) / k^2) * (abs(strucFactor)^2))
end

# this roughly cancels out long range energy due to bonded interactions (Tuckerman pg. 663)
bondEnergy::Float64 = 0.0
idx = top.bondIdx
for b::Int64 in 1:size(idx)[1]
for i in 1:top.nAtoms
for j in 1:top.nAtoms
if ((idx[b][1] == i && idx[b][2] == j) || (idx[b][1] == j && idx[b][2] == i)) # && !(i in isdone)
# println("firing j: ", j)
ci::Float64 = top.charges[i]
cj::Float64 = top.charges[j]
# rx::Float64 = xyz[i, 1] - xyz[j, 1]
# ry::Float64 = xyz[i, 2] - xyz[j, 2]
# rz::Float64 = xyz[i, 3] - xyz[j, 3]
rij::Float64 = norm(xyz[i, :] - xyz[j, :])
bondEnergy += (ci * cj * erf(rij / (sqrt(2) * σ))) / rij
end
end
end
end

ewaldEnergy = shortRangeEnergy + longRangeEnergy - selfEnergy - bondEnergy

return ewaldEnergy
end

• Welcome to Code Review! The title is not very descriptive of what the code achieves. Please update it as well as providing more of a description in the body of the post by clicking the edit link. For more information see when asking your question. May 10 at 5:13
• Can you include the definition of the Topology type? It is very likely that performance issues are hiding there, and it is also impossible to test your code without that definition.
– DNF
May 10 at 7:07
• Code review does not seem to be very active. You are likely to get more help if you post your question on discourse.julialang.org , which is the main forum for Julia users, moreso than stackoverflow. This is exactly the sort of question users there like to answer. (But remember to link to your stackoverflow/code review posts as a courtesy.)
– DNF
May 10 at 7:12