I’ve been introduced to Julia very recently, and I’ve been trying to adapt my already tested system of equations, with additive noise, based on a Takens-Bogdanov bifurcation.
I’ve got this far trying to improve performance as much as possible, but I need help, I think it’s still lacking.
The original code I coded in Matlab performs an EM integration with dt=0.01, and does it in ~0.7 secs (same conditions as below)
Originally I was hoping to get at least 1 order of magnitude of improvement, I was surprised that I wasn’t achieving that.
I attach the code, but since the SC matrix is sensible information, I’ve attached a random matrix that yields same performance time.
using Plots using DelimitedFiles using DifferentialEquations using BenchmarkTools using StaticArrays using LinearAlgebra #generate artificial coupling matrix SC=abs.(randn(90,90)) SC=0.2*SC./maximum(SC) #initial condition u0=0.1*ones(90,2); #initial-final time t0=0.0; tend=1200.0; #define parameters p0=[-1.5 , 2] p=p0'.*ones(90,2); SC=SC; p=[p SC] p=[p sum(SC,dims=2)] #col 1 :alfa #col 2 : beta #col 3-93 : SC #col 94: sumSC function stakens!(du,u,p,t) #A = similar(u) @views(A = p[:, 3:end-1] * u[:,1]) #LinearAlgebra.mul!(A, @view(p[:, 3:end-1]), u) # in-place matrix product for i in axes(u, 1) du[i,1] = u[i,2] + (0.5 * p[i, end] * u[i, 1]) + (0.5 * A[i,1]) du[i,2] = 100.0 * p[i,1] - 100.0 * p[i,2] * u[i,1] + 100.0 * u[i,1] ^2 - 10.0 * u[i,1] * u[i,2] - 100.0 * u[i,1] ^3 - 10.0 * u[i,1] ^2 * u[ i , 2] end end function σ_STakens(du,u,p,t) du[1:90, 1] .= 0.04 du[1:90, 2] .= 0.0 end prob_sde_stakens = SDEProblem(stakens!,σ_STakens,u0,(t0,tend),p) @benchmark solve(prob_sde_stakens,EM(),dt=0.01,save_every_step=false)
minimum time: 401.633 ms (0.00% GC)
median time: 456.275 ms (11.87% GC)
mean time: 444.711 ms (9.64% GC)
maximum time: 480.100 ms (17.26% GC)