/local_convex_test.jl
Last active Mar 6, 2019
A test for local convexity
| 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 | |
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