test continuous GD

experiments/tests_period_8/lineareq_ode.jl

@@ -0,0 +1,62 @@
+using Plots
+using Random
+using GLM, DataFrames
+using Plots.PlotMeasures
+
+function Yplot(t, sig, A::Function, f::Function, y0)
+ (s = -log(rand()) / sig; sol = y0)
+ path = []
+ while s < t
+ push!(path, (s, sol))
+ sol += (A(s) * sol .+ f(s)) ./ sig
+ s -= log(rand()) / sig
+ end
+ if length(path) > 0
+ push!(paths, path)
+ end
+ sol
+end
+
+a = 1.5
+AA = [2 1; 0 -1]
+b = [1, 0]
+A(s) = -a * AA' * AA .+ (rand() - 0.5) / 3
+q = [0.55, -0.05]
+f(s) = a * AA' * b
+sol(s) = AA \ b
+print(sol(1))
+
+Random.seed!(2234)
+paths = []
+t = 6
+sigs = [5.0, 100.0]
+nsim1 = 20
+
+markers = [:circle, :square, :diamond, :cross, :xcross, :utriangle, :dtriangle, :rtriangle, :ltriangle, :pentagon, :hexagon, :heptagon, :octagon, :star4, :star5, :star6, :star7, :star8, :vline, :hline]
+colors = [:red, :green, :blue, :orange, :purple, :brown, :black, :grey]
+pl = plot(layout=(2, 3), size=(1300, 800),
+ bottom_margin=5mm, left_margin=5mm, right_margin=4mm) # Change layout to 2 rows and 3 columns
+for i in [1, 2]
+ paths = []
+ sig = sigs[i]
+ y = sum(Yplot(t, sig, A, f, q) for _ in 1:nsim1) / nsim1
+ for c in [1, 2]
+ Random.seed!(6421)
+ for path in paths
+ marker = rand(markers)
+ color = rand(colors)
+ if i == 1
+ for p in path
+ scatter!(pl[(i-1)*3+c], [p[1]], [p[2][c] - sol(p[1])[c]], label="", marker=marker, color=color, alpha=0.5)
+ end
+ end
+ plot!(pl[(i-1)*3+c], [p[1] for p in path], [p[2][c] - sol(p[1])[c] for p in path], label="", alpha=0.5, color=color, linewidth=2)
+ xlabel!(pl[(i-1)*3+c], "time")
+ ylabel!(pl[(i-1)*3+c], "error")
+ end
+ hline!(pl[(i-1)*3+c], [0], label="0 error", color=:black, linewidth=3)
+ title!(pl[(i-1)*3+c], "error, sig=$sig, component=$c", titiefontsize=10)
+ end
+end
+
+display(pl)

latex/main paper/plots_julia_code/main_poisson_convergence.jl

@@ -14,8 +14,8 @@ end
 
 a = 1
 A(s) = [a 0; 1 a]
-q = [1, 0]
-f(s) = zero(q)
+q = [1.0, 0.0]
+f(s) = 0.0
 sol(s) = [exp(a * s), s * exp(a * s)]
 sig = 1.0
 t = 1.0