# Finite differences with Julia
**URL:** https://discourse.julialang.org/t/finite-differences-with-julia/20591
**Category:** Performance
**Created:** [February 8, 2019, 5:37pm UTC](https://discourse.julialang.org/t/finite-differences-with-julia/20591 "2019-02-08T17:37:22Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@pnavaro](https://discourse.julialang.org/u/pnavaro)
#### Post date: [February 8, 2019, 5:37pm UTC](https://discourse.julialang.org/t/finite-differences-with-julia/20591/1 "2019-02-08T17:37:23Z")
Dear Julia users,
Is there a way to improve performance of this kind of code without devectorizing (use loops). All variables are 2d arrays. I solve a PDE problem with finite differences method. Thanks for your help
```julia
996988748 divV .= diff(Vx,dims=1)/dx
992096000 divV .+= diff(Vy,dims=2)/dy
-
992096000 Exxc .= diff(Vx,dims=1)/dx
495600000 Exxc .-= 1/2*divV
992096000 Eyyc .= diff(Vy,dims=2)/dy
495600000 Eyyc .-= 1/2*divV
-
507248000 Exyv .= diff(Vx_exp,dims=2)
0 Exyv ./= dy
507248000 Exyv .+= diff(Vy_exp,dims=1)
0 Exyv ./= dx
0 Exyv .*= 0.5
-
1984192000 @views Exyc .= 0.25 * ( Exyv[1:end-1,1:end-1]
- + Exyv[2:end ,1:end-1]
- + Exyv[1:end-1,2:end]
- + Exyv[2:end ,2:end])
```
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [February 8, 2019, 7:43pm UTC](https://discourse.julialang.org/t/finite-differences-with-julia/20591/2 "2019-02-08T19:43:04Z")
Don’t use `diff`, that creates temporary arrays. Don’t use multiple lines of `.+=`, `./=`, etcetera — you want a single fused loop for cache efficiency. Don’t use `*` and `+` and `/` when you want `.*` and `.+` and `./` in order to fuse the loops.
(But honestly, this is the sort of thing that is probably more readable if you just write a loop, and there is no performance reason not to do so in Julia.)
---
### Author:  [@pnavaro](https://discourse.julialang.org/u/pnavaro)
#### Post date: [February 8, 2019, 8:36pm UTC](https://discourse.julialang.org/t/finite-differences-with-julia/20591/3 "2019-02-08T20:36:04Z")
Thanks for your answer, i rewrite the code following your advices and it is better. With loops the code is faster. If i understood well, in julia the fortran-like syntax is better than the
matlab-like syntax. Unfortunately, the code i wanted to translate is in matlab 🙂
I really like Julia as a language but fortran is still faster for what i am doing (for now).
```nohighlight
1024000 @views divV .= ((f.Vx[2:end,:] .- f.Vx[1:end-1,:])./dx
- .+(f.Vy[:,2:end] .- f.Vy[:,1:end-1])./dy)
-
1024000 @views Exyv .= 0.5 .*( (Vx_exp[:,2:end] .- Vx_exp[:,1:end-1])./dy
- .+ (Vy_exp[2:end,:] .- Vy_exp[1:end-1,:])./dx)
-
1024000 @views Exyc .= 0.25 .* ( Exyv[1:end-1,1:end-1]
- .+ Exyv[2:end ,1:end-1]
- .+ Exyv[1:end-1,2:end]
- .+ Exyv[2:end ,2:end])
-
0 Eii2 .= 0.5 .* (Exxc.^2 .+ Eyyc.^2) .+ Exyc.^2
```
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [February 9, 2019, 1:50pm UTC](https://discourse.julialang.org/t/finite-differences-with-julia/20591/4 "2019-02-09T13:50:23Z")
Check out this for more information. One example is on a reaction-diffusion equation.
[https://nbviewer.jupyter.org/github/JuliaDiffEq/DiffEqTutorials.jl/blob/master/Introduction/OptimizingDiffEqCode.ipynb](https://nbviewer.jupyter.org/github/JuliaDiffEq/DiffEqTutorials.jl/blob/master/Introduction/OptimizingDiffEqCode.ipynb)
---
### Author:  [@pnavaro](https://discourse.julialang.org/u/pnavaro)
#### Post date: [February 9, 2019, 3:43pm UTC](https://discourse.julialang.org/t/finite-differences-with-julia/20591/5 "2019-02-09T15:43:07Z")
Thank you very much for help, the last link will help
My code is here [GitHub - pnavaro/M2Dpt.jl](https://github.com/pnavaro/M2Dpt.jl)
I will try to beat fortran and matlab during next few days.
---
### Author:  [@improbable22](https://discourse.julialang.org/u/improbable22)
#### Post date: [February 9, 2019, 7:25pm UTC](https://discourse.julialang.org/t/finite-differences-with-julia/20591/6 "2019-02-09T19:25:05Z")
I agree this may be clearer & faster with loops, or functions containing the loops. But sometimes it’s good to have something which matches the old code almost line-for-line.
You may want to try `@uviews` from [UnsafeArrays.jl](https://github.com/oschulz/UnsafeArrays.jl) for creating lots of views you’ll only use once.