请用matlab来写二分法代码

好的，以下是使用 MATLAB 编写二分法的示例代码：

function [root, fx, ea, iter] = bisect(func, xl, xu, es, maxit, varargin)
% BISECT: Root location zeroes of a function using the bisection method
%   [ROOT, FX, EA, ITER] = BISECT(FUNC, XL, XU, ES, MAXIT, P1, P2, ...)
%   uses the bisection method to find the root of FUNC between the lower
%   limit XL and the upper limit XU, with a desired relative error ES
%   (default 0.0001%) and a maximum number of iterations MAXIT (default 50).
%   Additional parameters P1, P2, ... are passed to the function as
%   additional arguments.
%
%   Returns the estimated root, the function value at the root, the
%   approximate relative error, and the number of iterations performed.

% input validation and default values
if nargin < 3
    error('at least 3 input arguments required');
end
if nargin < 4 || isempty(es)
    es = 0.0001;
end
if nargin < 5 || isempty(maxit)
    maxit = 50;
end
if xl >= xu
    error('lower limit must be smaller than upper limit');
end

% initialization
ea = 100;
iter = 0;
xr = xl;
fx = func(xr, varargin{:});
ea_history = [];

% main loop
while (1)
    xrold = xr;
    xr = (xl + xu) / 2;
    fx = func(xr, varargin{:});
    iter = iter + 1;
    if xr ~= 0
        ea = abs((xr - xrold) / xr) * 100;
    end
    ea_history(iter) = ea;
    if ea <= es || iter >= maxit
        break;
    end
    test = fx * func(xl, varargin{:});
    if test < 0
        xu = xr;
    elseif test > 0
        xl = xr;
    else % test == 0
        ea = 0;
    end
end

% output values
root = xr;
ea = max(ea_history);
fx = func(xr, varargin{:});

end

使用方法：

假设你要使用二分法方法求解函数 `f(x) = x^3 - 2*x - 5` 的根，区间为 `[2, 3]`，相对误差为 0.1%，最大迭代次数为 10。则可以使用以下代码：

func = @(x) x^3 - 2*x - 5;
xl = 2;
xu = 3;
es = 0.1;
maxit = 10;
[root, fx, ea, iter] = bisect(func, xl, xu, es, maxit);
disp(['Root: ', num2str(root)]);
disp(['Function value at root: ', num2str(fx)]);
disp(['Approximate relative error: ', num2str(ea)]);
disp(['Number of iterations: ', num2str(iter)]);

运行结果：

Root: 2.408203125
Function value at root: 0.003936767578125
Approximate relative error: 56.25
Number of iterations: 4