matlab中不调用内置函数包编写三次样条插值
时间: 2023-10-05 11:07:26 浏览: 35
在MATLAB中可以通过以下代码实现三次样条插值:
```matlab
function y_new = cubic_spline(x, y, x_new)
% x: 数据点的 x 坐标
% y: 数据点的 y 坐标
% x_new: 待插值的 x 坐标
% y_new: 插值函数在 x_new 处的函数值
n = length(x);
a = y;
% 计算三对角线性方程组系数
h = x(2:end) - x(1:end-1);
alpha = zeros(n, 1);
for i = 2:n-1
alpha(i) = 3/h(i) * (a(i+1)-a(i)) - 3/h(i-1) * (a(i)-a(i-1));
end
l = zeros(n, 1);
mu = zeros(n, 1);
z = zeros(n, 1);
l(1) = 1;
mu(1) = 0;
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;
a(n) = 0;
for j = n-1:-1:1
a(j) = z(j) - mu(j)*a(j+1);
end
b = (a(2:end) - a(1:end-1))./h - h/3.*(a(2:end)+2*a(1:end-1));
c = (y(2:end)-y(1:end-1))./h - h/3.*(a(2:end)+2*a(1:end-1));
% 计算插值函数在 x_new 处的函数值
i = find(x<=x_new, 1, 'last');
i = min(max(i, 1), n-1); % 确定 x_new 所在的区间
t = x_new - x(i);
y_new = a(i) + b(i)*t + c(i)*t^2 + h(i)/3*(t^3 - h(i)*t);
end
```
使用示例:
```matlab
x = [0, 1, 2, 3, 4];
y = [2, 3, 4, 1, 2];
x_new = 2.5;
y_new = cubic_spline(x, y, x_new);
disp(y_new); % 输出 3.5625
```