Counter-example for continuous time.

examples/example10.jl

@@ -0,0 +1,30 @@
+using EllZeroTrendFiltering
+
+N = 10
+t = [0.0:N-1...]
+I_g = rand(N)
+I_g2 = rand(N)
+I_tg = rand(N)
+
+ℓ = EllZeroTrendFiltering.TransitionCostContinuous{Float64}(t, I_g, I_g2, I_tg)
+
+#ℓ = compute_transition_costs(x -> exp(2^x), linspace(0,2,N))
+
+ℓ = compute_transition_costs(x -> exp(x^2), linspace(0,1,20))
+
+V_N = QuadraticPolynomial(0.0, 0.0, 0.0)
+
+M = 10
+
+@time Λ =  pwq_dp_constrained(ℓ, V_N, M)
+
+
+unique_polys(Λ) = length(unique([λ.π for λ in Λ]))
+
+sizes = [(isassigned(Λ,i,j) ? unique_polys(Λ[i,j]) : 0) for i = 1:size(Λ,1), j = 1:size(Λ,2)]
+sizes = [(isassigned(Λ,i,j) ? length(Λ[i,j]) : 0) for i = 1:size(Λ,1), j = 1:size(Λ,2)]
+
+# Check compared to bound R <= N
+nom_sizes = fill(1, M, 1)*(20-1:-1:0)'
+
+println(maximum(sizes - nom_sizes))