DPCP_IRLS_modified.m

function [f, distances, time] = DPCP_IRLS_modified(X_tilde, delta, T, epsilon_J, C)
    %%DPCP-IRLS's implementation
    %%Solve min_f ||X^T f||_{1,2} s.t ||f||_2 == 1 's problem.

    % display([D,N]);
    %% init parameters.
    tic;
    [D, N] = size(X_tilde);
    %display(size(X_tilde));
    Delta_J = Inf;
    k = 0;
    w = ones(N, 1);
    J_old = zeros(N, 1);
    J_new = zeros(N, 1);
    resIter = 0;

    %% Get the f.
    while (Delta_J > epsilon_J) 
        if (T ~= -1 && k > T)
            break;
        end
        resIter = resIter + 1;
        R_X = X_tilde * diag(w) * X_tilde';
        [U, S, V] = svd(R_X);
        % display(U);
        f = U(:,D - C + 1:D);

        for j = 1:N
            w(j) = 1 / max(delta, norm(f' * X_tilde(:, j)));
            % display(f' * X_tilde(:, j));
            % display(norm(f' * X_tilde(:, j)));
            J_new(j) = norm(f' * X_tilde(:, j));
        end

        k = k + 1;
        Delta_J = abs(sum(J_old) - sum(J_new)) / (sum(J_old) + 10^(-9));
        J_old = J_new;
    end

    %% Get some experiements's result
    distances = zeros(1, N);
    for j = 1:N
        distances(j) = norm(f' * X_tilde(:, j));
    end
    time = toc;
end