# Accessing the solution of differential equations: understanding alloc
**URL:** https://discourse.julialang.org/t/accessing-the-solution-of-differential-equations-understanding-alloc/31364
**Category:** General Usage
**Created:** [November 21, 2019, 11:44pm UTC](https://discourse.julialang.org/t/accessing-the-solution-of-differential-equations-understanding-alloc/31364 "2019-11-21T23:44:02Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Egwene\_al\_Vere](https://discourse.julialang.org/u/Egwene_al_Vere)
#### Post date: [November 21, 2019, 11:44pm UTC](https://discourse.julialang.org/t/accessing-the-solution-of-differential-equations-understanding-alloc/31364/1 "2019-11-21T23:44:02Z")
I’m preallocating an array for the solution of an ODE at each time step, for post-processing. However, `julia --track-allocation=user foo.jl` still reports large allocations. To simplify with `@btime`:
```julia
using DifferentialEquations
using BenchmarkTools
function f(du,u,p,t)
for i = 1:10
du[i] = -u[i]*sin(i) + 1*im
end
end
u0 = [cos(i)+im*sin(i) for i = 1:10]
tf = 10.0
tspan = (0.0, tf)
prob = ODEProblem(f, u0, tspan)
sol = solve(
prob,
Vern8(),
saveat = 0.0:.01:tf,
)
sol_tmp = similar(u0)
ns = Int(tf/.01)
@btime for sol_i in sol.u
copyto!(sol_tmp, sol_i)
end
@btime for i in 1:length(sol.u)
copyto!(sol_tmp, sol.u[i])
end
@btime copyto!(sol_tmp, sol.u[1])
```
returns
```julia
66.102 μs (1492 allocations: 38.95 KiB)
110.124 μs (1983 allocations: 46.64 KiB)
65.983 ns (0 allocations: 0 bytes)
```
note that accessing via iterator (1st approach) is ~1.6x faster here than accessing by index (2nd approach); a difficult thing for me to understand is why `@btime copyto!(sol_tmp, sol.u[1])` does not allocate while it allocates in loop. Note that in loops, normal arrays do not allocate with `copyto!`:
```julia
a = [rand(3,3) for i = 1:1000];
b = rand(3,3)
@btime for i in 1:1000
copyto!($b,$a[i])
end
```
gives
```julia
4.603 μs (0 allocations: 0 bytes)
```
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [November 22, 2019, 4:34am UTC](https://discourse.julialang.org/t/accessing-the-solution-of-differential-equations-understanding-alloc/31364/2 "2019-11-22T04:34:15Z")
your bechmarking is using global variables, allocations will be caused by this.
Also, if you’re using `@btime`, you do not need to write a loop yourself
---
### Author:  [@Vasily\_Pisarev](https://discourse.julialang.org/u/Vasily_Pisarev)
#### Post date: [November 22, 2019, 5:50am UTC](https://discourse.julialang.org/t/accessing-the-solution-of-differential-equations-understanding-alloc/31364/3 "2019-11-22T05:50:36Z")
> [@Egwene\_al\_Vere](#):
>
> note that accessing via iterator (1st approach) is ~1.6x faster here than accessing by index (2nd approach)
Would it be the same with `@inbounds` on index iteration?
---
### Author:  [@Egwene\_al\_Vere](https://discourse.julialang.org/u/Egwene_al_Vere)
#### Post date: [November 22, 2019, 2:30pm UTC](https://discourse.julialang.org/t/accessing-the-solution-of-differential-equations-understanding-alloc/31364/4 "2019-11-22T14:30:41Z")
thanks! i’ll look into global var. effects, but the for loop is not to do repeated measurements but to iterate through the sol.u array, in real program there’s post processing after that, the minimum example’s just to illustrate the allocations.