%% Numerical simulation for the symmetry measure. Uniform distribution
function [s] = sym_measure (matrix)
%%
%Parameters and variables necessary for running this code without external call. Also a loop over the value of a is needed
%n_samples = 10000; %number of matrixes in the sample
%N = 200; %number of neurons
%max_w = 1;
%a = 0:0.1:0.9; %pruning values
%number_points = size(a,2); %number of points in the plot
%sample_mean = zeros(number_points);
%sample_variance = zeros(number_points);
%%
%symm = zeros(1,n_samples);
%for iter = 1:n_samples
%sample_matrix = max_w .* rand(N) .* (rand(N) > a); %generate a random NxN matrix from zero to max_w and introduce pruning a
upper = triu(matrix,1); %extract the upper triangle matrix
lower = tril(matrix,1)'; %extract the lower triangle matrix and transpose it
x = upper(:); %convert the matrix into a vector
y = lower(:); %convert the matrix into a vector
temp = x + y; %sum vector elements==sum the reciprocal elements of the matrix
nonzero_index = find(temp~=0.); %create a vector whoose elements are the index of the non zero elements in temp
K = length(nonzero_index); %counts how many elements of temp are nonzero==counts the number of pairs connections for which at least one direction is nonzero
if K > 0
s = 1  sum ( abs(x(nonzero_index)y(nonzero_index)) ./ (x(nonzero_index)+y(nonzero_index)) ) / K;
else
s = 0;
end
%sprintf('Point number %d iteration number %d',n,iter)
%end
%sample_mean = mean(symm);
%sample_variance = var(symm);
