matlab三次样条插值函数完整代码

以下是 MATLAB 中的三次样条插值代码：

function [spline_x, spline_y] = cubic_spline(x, y, num_points)
% x: x坐标集合
% y: y坐标集合
% num_points: 插值点数目

n = length(x);
h = zeros(1, n-1);
for i = 1:n-1
    h(i) = x(i+1) - x(i);
end

alpha = zeros(1, n-1);
for i = 2:n-1
    alpha(i) = 3/h(i) * (y(i+1)-y(i)) - 3/h(i-1) * (y(i)-y(i-1));
end

l = zeros(1, n);
mu = zeros(1, n);
z = zeros(1, n);
l(1) = 1;
mu(1) = z(1) = 0;

for i = 2:n-1
    l(i) = 2 * (x(i+1)-x(i-1)) - h(i-1) * mu(i-1);
    mu(i) = h(i) / l(i);
    z(i) = (alpha(i) - h(i-1) * z(i-1)) / l(i);
end
l(n) = 1;
z(n) = 0;
c = zeros(1, n);
b = zeros(1, n);
d = zeros(1, n);
c(n) = 0;

for j = n-1:-1:1
    c(j) = z(j) - mu(j) * c(j+1);
    b(j) = (y(j+1)-y(j))/h(j) - h(j)*(c(j+1)+2*c(j))/3;
    d(j) = (c(j+1)-c(j))/(3*h(j));
end

spline_x = linspace(x(1), x(n), num_points);
spline_y = zeros(1, num_points);
for i = 1:num_points
    for j = 1:n-1
        if spline_x(i) >= x(j) && spline_x(i) <= x(j+1)
            spline_y(i) = y(j) + b(j)*(spline_x(i)-x(j)) + c(j)*(spline_x(i)-x(j))^2 + d(j)*(spline_x(i)-x(j))^3;
        end
    end
end
end

其中，`x` 和 `y` 分别是样本点的横纵坐标，`num_points` 是插值点的数量。函数返回两个数组 `spline_x` 和 `spline_y`，它们分别表示插值后的点的横纵坐标。