matlab三次平滑模型的预测函数

function y_pred = cubic_smoothing(x, y, lambda, x_pred)
% x: vector of independent variable
% y: vector of dependent variable
% lambda: smoothing parameter
% x_pred: vector of independent variable for prediction
% y_pred: vector of predicted values

n = length(x);
W = zeros(n, n);
for i = 2:n-1
W(i, i-1:i+1) = [1 2 1];
end
W(1,1:2) = [2 1];
W(n,n-1:n) = [1 2];
D = diag(ones(n, 1));
S = D + lambda*W;
S_inv = inv(S);

y_pred = zeros(size(x_pred));
for i = 1:length(x_pred)
K = zeros(n, 1);
for j = 1:n
K(j) = exp(-0.5*(x(j)-x_pred(i))^2);
end
y_pred(i) = K' * S_inv * y / sum(K' * S_inv);
end

end