wine_quality.m:

function [white_indicators, red_indicators]=wine_quality()
    dwhite=dlmread('../data/winequality-white.csv', ';', 1, 0);
    white_indicators=do_wine_quality(dwhite, 0.0003, 1000)
    dred=dlmread('../data/winequality-red.csv', ';', 1, 0);
    red_indicators=do_wine_quality(dred, 0.005, 1000)
end

function x=do_wine_quality(data, lambda, iters)
    A=data(:, 1:11);
    b=data(:, 12);
    x0=zeros(11, 1);
    % L=norm(A)^2 is the factor of smoothness of g(x)=|Ax-b|^2
    % This sets tau*L=0.9<=1.
    tau=0.9/norm(A)^2;
    x=lasso_fb(A, b, lambda, x0, tau, iters);
end


lasso_fb.m:

function x=lasso_fb(A, b, lambda, x0, tau, iters)
    x=x0;
    for i=1:iters
        % z = x-tau grad g(x)
        x = prox_l1(tau, lambda, x - tau*A'*(A*x-b));
    end
end


prox_l1.m:

function xnext=prox_l1(tau, lambda, z)
    % Soft thresholding
    idx=abs(z)<=lambda;
    xnext=z-lambda*z./abs(z);
    xnext(idx)=0;
end