function summa=integrate_inverse_nonlinearity(y)
    % the main idea: to summarize the area under the 'unity-line' between
    % theta and every coordinate of y
    
    % theta can be arbitrary between -1 and 1, so the sake of simplicity
    % please choose theta = -1
    theta=-1;
    summa=0;
    
    % here iterate over every coordinate of y and compute the value of the
    % integral
    
    for 
    
end
