clear;

n = 1000;
p = 20;
gamma = 0.02;
m = 200;

A = randn(m, n);
A = A - repmat(mean(A, 1), m, 1);
scale = norm(A, 2);
A = A / scale;
A1 = A;   
AtA = A' * A;

Xinit = randn(n, p);
[Xinit, ~] = qr(Xinit, 0);


opts.dim = [n, p];
% opts0.maxit = 8000;
% opts0.gtol = 1e-8;
opts.gamma = gamma;
% opts0.X = Xinit;

obj_fun = @fun_PCA_l1_lr;



tic
[out] = stop_slpg(obj_fun, opts, A, opts.gamma);
t_PenC = toc;
feas_penc = norm(out.X' * out.X - eye(p), 'fro');

semilogy(1:out.iter, out.kkts, 1:out.iter, out.feas, 1:out.iter, out.feas_subs)



function [fvalue,grad] = fun_PCA_l1_lr(X,A,gamma)
% min -0.5*(X^TA^TAX) + gamma* ||X||_1 
% low-rank version
% 
[n, p] = size(X);
AX = A * X;
AAX = A' * AX;
grad = -AAX;
fvalue = 0.5 * sum(sum(X .* grad)) + gamma * sum(sum(abs(X))) + 2 * norm(X' * X - eye(p), 'fro');
end