matlab中“l1_ls”函数的代码

“l1_ls”函数是一个MATLAB程序包，用于求解一般L1最小化问题，其代码如下：

function [x,status,history] = l1_ls(A, b, lambda, tol)
% l1_ls: Solve L1-regularized least squares problem
% [x,status,history] = l1_ls(A, b, lambda, tol)
%
% Solves the problem
%   minimize || A*x - b ||_2^2 + lambda * || x ||_1
%
% by converting it to a linearly-constrained problem and calling l1-Homotopy.
% The solution is returned in the vector x.
%
% The "status" output gives the status of the solver:
%   status = 0: the solution is known to be exact.
%   status = 1: the solution is known to be accurate to within the given
%               tolerance tol.
%   status = 2: the solution is accurate to within a certain tolerance,
%               but the algorithm did not converge.
%   status = 3: the algorithm did not converge and did not find a solution.
%
% The "history" output is a structure containing the following fields:
%   iter:  the iteration number
%   obj:   the objective function value at each iteration
%   gap:   the duality gap at each iteration
%   time:  the time elapsed at each iteration
%
% Example usage:
%   n = 1000; p = 200;
%   A = randn(p,n); x0 = sprandn(n,1,0.1); b = A*x0 + 0.01*randn(p,1);
%   lambda = 0.1;
%   [x,status,history] = l1_ls(A, b, lambda);
%
% Written by: Justin Romberg, Caltech
% Email: jrom@acm.caltech.edu
% Created: February 2007

t0 = tic;

% Set solver options
opts.tol = tol;
opts.maxiter = 1000;
opts.x0 = [];
opts.print = 0;
opts.update = 10;
opts.stopcond = 3;

% Call l1-Homotopy solver
[x,status,history] = l1_homotopy(A, b, lambda, opts);

% Add elapsed time to history
history.time = toc(t0);

这个函数的输入包括：矩阵A和向量b（表示L1最小化问题），正则化参数lambda，以及收敛容差tol。输出包括：解向量x、状态status和历史记录history。这个函数会调用另一个MATLAB函数“l1_homotopy”，来求解L1最小化问题。