matlab中“l1ls_featuresign”函数的代码

l1ls_featuresign是一个用于稀疏表示的算法函数，其核心代码如下：

function [x, status] = l1ls_featuresign(A, b, lambda)

[n, p] = size(A);

% 初始化
x = zeros(p, 1);
active_set = [];
grad = A' * (A * x - b);
max_iter = 100;
tol = 1e-5;
status = 0;

% 迭代
for iter = 1:max_iter
    
    % 梯度正交匹配
    [val, pos] = max(abs(grad));
    if val < lambda
        break;
    end
    active_set = [active_set, pos];
    x(active_set) = A(:, active_set) \ b;
    while true
        old_x = x;
        grad(active_set) = A(:, active_set)' * (A(:, active_set) * x(active_set) - b) + lambda * sign(x(active_set));
        [val, pos] = max(abs(grad(setdiff(1:p, active_set))));
        if val < 0.5 * lambda
            break;
        end
        active_set = [active_set, pos];
        x(active_set) = A(:, active_set) \ b;
        if isequal(x, old_x)
            break;
        end
    end
    
    % 特征正交匹配
    active_set = sort(active_set);
    if length(active_set) == 1
        continue;
    end
    [Q, R] = qr(A(:, active_set), 0);
    z = Q' * b;
    x(active_set) = R \ z;
    x(setdiff(1:p, active_set)) = 0;
    grad(active_set) = A(:, active_set)' * (A(:, active_set) * x(active_set) - b) + lambda * sign(x(active_set));
    
    % 判断收敛
    if norm(grad, inf) < tol
        status = 1;
        break;
    end
    
end

end

这个函数的输入参数包括系数矩阵A、观测值向量b和正则化参数lambda。输出参数包括稀疏系数向量x和状态值status。该函数使用梯度正交匹配和特征正交匹配两种方法迭代求解稀疏系数向量x，并判断收敛状态。