% uses the last column as the target and randomly holds
% out test_frac of the rows for evaluating solution robustness
function compare_qlsqr(A, epsilon, test_frac)
    if(nargin < 2), epsilon = 0.01; end
    if(nargin < 3), test_frac = 0.2; end
 
    [baseX, baseY, testX, testY] = split_data(A, test_frac);
   
    % time the qlsqr solution
    tic;
    bQ = qlsqr(baseX, baseY, epsilon);
    qTime = toc;
    % eval error of qlsqr solution on held-out rows
    errQ = norm(testY - testX*bQ, 'fro') / sqrt(length(testY));
    fprintf('\tqlsqr: %.4f sec, error on held-out rows: %.4f rmse\n', qTime, errQ);
    
    % time the exact solution
    tic;
    bEx = baseX \ baseY;
    exactTime = toc;
    % eval error of exact solution on held-out rows
    errEx = norm(testY - testX*bEx, 'fro') / sqrt(length(testY));
    fprintf('\tmatlab: %.4f sec, error on held-out rows: %.4f rmse\n', exactTime, errEx);

    fprintf('\tqlsqr speedup: %.2f\n', exactTime/qTime);
end

% randomly splits rows into fractions f and 1-f,
% then splits final column from each for use as a linear system target
function [base_x, base_y, test_x, test_y] = split_data(A, test_frac)
    [m,n] = size(A);
    perm_i = randperm(m); % permute rows
    test_size = ceil(test_frac*m);
    base_i = perm_i(1:(m-test_size));
    test_i = perm_i((m-test_size+1):m);
    
    base_x = A(base_i, 1:(n-1));
    base_y = A(base_i, n);
    test_x = A(test_i, 1:(n-1));
    test_y = A(test_i, n);
end