A test for local convexity

local_convex_test.jl

using LinearAlgebra
using Random

function local_convex_test(N)

	#srand(1234)

	sum = 0.0

	for i=1:100

        
		beta = rand()
	
		## the input signal
		X = rand(3,1)*2 .-1.0

		Z_1 = rand(3,3)*sqrt(2/3)
		Z_2 = rand(3,3)*sqrt(2/3)

		out_1 = (beta*Z_1 + (1-beta)*Z_2)*X .+ 0.1

		out_2 = Z_1*X .+ 0.1

		out_3 = Z_2*X .+ 0.1

		## the main calculation 
		for j=1:N-1

			## two sets of matrices:
			W_1 = rand(3,3)*sqrt(2/3)
			W_2 = rand(3,3)*sqrt(2/3)

			out_1 = (beta*W_1 + (1-beta)*W_2)*out_1 .+ 0.1

			out_2 = W_1*out_2 .+ 0.1

			out_3 = W_2*out_3 .+ 0.1

		end
			## the infinity norm is actually a much weaker convexity test: 
			sum += minimum(beta*out_2 + (1-beta)*out_3 .- out_1 .+ 1e-10 .> 0.0)*1.0

	end

	return sum/100

end