用MATLAB写一个函数，使用者给出节点的数据，选用拉格朗日插值方法分别作出x_k,y_k的插值，平均增加到121个节点，并计算出这些点的数值，在xoy平面上上画出较光滑的曲线图

以下是使用拉格朗日插值方法实现的MATLAB代码：

function [x_interp, y_interp] = lagrange_interpolation(x_k, y_k, num_interp_points)
% x_k: vector of x-coordinates of known data points
% y_k: vector of y-coordinates of known data points
% num_interp_points: number of interpolation points to add between known data points

% Add interpolation points between known data points
x_interp = linspace(min(x_k), max(x_k), (num_interp_points+1)*length(x_k)-num_interp_points);
y_interp = zeros(size(x_interp));

% Calculate interpolated y-coordinates using Lagrange interpolation
for i = 1:length(y_interp)
    for j = 1:length(x_k)
        term = y_k(j);
        for k = 1:length(x_k)
            if k ~= j
                term = term * (x_interp(i) - x_k(k)) / (x_k(j) - x_k(k));
            end
        end
        y_interp(i) = y_interp(i) + term;
    end
end

% Plot interpolated curve
plot(x_interp, y_interp);
end

使用示例：

% Define known data points
x_k = [1, 2, 4, 5];
y_k = [2, 3, 1, 7];

% Perform Lagrange interpolation with 120 additional points
[x_interp, y_interp] = lagrange_interpolation(x_k, y_k, 120);

这将在xoy平面上绘制出一个平滑的插值曲线，其中包括原始数据点和121个插值点。