matlab三次样条插值原代码
时间: 2023-11-08 13:06:50 浏览: 45
以下是 MATLAB 的三次样条插值的原代码:
```matlab
function [spline] = cubic_spline(x, y)
% x: 自变量向量
% y: 因变量向量
% spline: 三次样条插值函数
n = length(x);
h = zeros(n-1, 1);
for i = 1:n-1
h(i) = x(i+1) - x(i);
end
% 构造三对角矩阵
A = zeros(n);
A(1, 1) = 1;
A(n, n) = 1;
for i = 2:n-1
A(i, i-1) = h(i-1);
A(i, i) = 2*(h(i-1) + h(i));
A(i, i+1) = h(i);
end
% 构造右端向量
b = zeros(n, 1);
for i = 2:n-1
b(i) = 3/h(i)*(y(i+1)-y(i)) - 3/h(i-1)*(y(i)-y(i-1));
end
% 解方程组
c = A \ b;
% 计算 a 和 b
a = zeros(n-1, 1);
b = zeros(n-1,1);
for i = 1:n-1
a(i) = y(i);
b(i) = (y(i+1)-y(i))/h(i) - h(i)/3*(2*c(i)+c(i+1));
end
% 构造三次样条插值函数
spline = @(xq) interp_spline(xq, x, a, b, c);
end
function [yq] = interp_spline(xq, x, a, b, c)
% xq: 待插值的自变量
% x: 自变量向量
% a, b, c: 三次样条插值函数的系数
% yq: 插值结果
n = length(x);
yq = zeros(size(xq));
for i = 1:length(xq)
j = find(xq(i) >= x, 1, 'last');
if j == n
j = n-1;
end
dx = xq(i) - x(j);
yq(i) = a(j) + b(j)*dx + c(j)*dx^2 + (c(j+1)-c(j))/(3*(x(j+1)-x(j)))*dx^3;
end
end
```
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