写一个matlab实现拉格朗日插值的算法

以下是MATLAB实现拉格朗日插值的代码：

function [p] = LagrangeInterpolation(x, y, xi)
% x: interpolation nodes
% y: interpolation values
% xi: evaluation points
% p: interpolated values at xi

n = length(x);
m = length(xi);

% initialize result
p = zeros(m, 1);

% loop over evaluation points
for i = 1:m
    % loop over interpolation nodes
    for j = 1:n
        % calculate Lagrange basis polynomial
        L = 1;
        for k = 1:n
            if k ~= j
                L = L .* (xi(i) - x(k)) ./ (x(j) - x(k));
            end
        end
        % add contribution of current node to interpolated value
        p(i) = p(i) + y(j) .* L;
    end
end

end

使用方法示例：

% define interpolation nodes and values
x = [0 1 2 3];
y = [1 0 2 1];

% define evaluation points
xi = linspace(0, 3, 101);

% interpolate at evaluation points
p = LagrangeInterpolation(x, y, xi);

% plot original function and interpolated function
plot(x, y, 'o', xi, p, '-')