Reducing memory allocation in DifferentialEquations.jl

user_14758201 0
Viewed 268

I'm using DifferentialEquations.jl to solve an ODE system as shown below. The result is not really relevant since p only contains test parameters for the purpose of producing a MWE, but the key is that I am seeing a lot of memory allocation despite using an in-place ODE function.

using DifferentialEquations

function ode_fun!(du,u,p,t)
    a,b,c,d,e = p

    X = @. u[1] * a * ((b-c)/b)
    Y = @. u[2] * d * ((b-e)/b)

    du[1] = -sum(X) + sum(Y) - u[1]*u[2]
    du[2] = sum(X) - sum(Y) - u[1]*u[2]
end

#exemplary parameters 
a = collect(10:-0.1:0.1)
b = a.^2
c = b*0.7
d = collect(0.01:0.01:1)
e = b*0.3

u0 = [1.0, 0.5]
p = [a,b,c,d,e]
tspan = [0.0, 100.0]
t = collect(0:0.01:100) 

prob = ODEProblem(ode_fun!,u0,tspan,p,saveat=t) 
@time sol = solve(prob)

1.837609 seconds (5.17 M allocations: 240.331 MiB, 2.31% gc time) #Julia 1.5.2

Since I need to solve this ODE system repeatedly I would like to reduce allocations as much as possible and am wondering if there is anything that can be done about them. I have been wondering if the issue lies with X and Y and have tried to preallocate these outside the ODE function, but have unfortunately not succeeded in reducing allocations that way.

differentialequations.jl julia
1 Answers

I'm pretty sure this should be faster and half the allocations

function ode_fun!(du,u,p,t)
    a,b,c,d,e = p
    XmY = @. u[1] * a * (1-c/b) - u[2] * d * (1-e/b)
    sXmY = sum(XmY)
    du[1] = -sXmY - u[1]*u[2]
    du[2] = sXmY - u[1]*u[2]
end

There's probably a way to get rid of all of them, but I'm not a DifferentialEquations expert.

user_51413280
Related