lagrange3.m

MatLab的拉格朗日插值法

% 分段三次Lagrange插值
% 命令格式：y=lagrange3(x0,y0,x)
% x0为节点向量，y0为对应的函数值向量，
% x为插值点向量，返回值y为x处的函数近似值向量。
function y=lagrange3(x0,y0,x)
[n1,n]=size(x0);
[n1,m]=size(x);
for i=1:m
   u=x(i);
   if u<=x0(3)
      y(i)=y0(1)*(u-x0(2))*(u-x0(3))*(u-x0(4))/(x0(1)-x0(2))/(x0(1)-x0(3))/(x0(1)-x0(4))+...
         y0(2)*(u-x0(1))*(u-x0(3))*(u-x0(4))/(x0(2)-x0(1))/(x0(2)-x0(3))/(x0(2)-x0(4))+...
         y0(3)*(u-x0(1))*(u-x0(2))*(u-x0(4))/(x0(3)-x0(1))/(x0(3)-x0(2))*(x0(3)-x0(4))+...
         y0(4)*(u-x0(1))*(u-x0(2))*(u-x0(3))/(x0(4)-x0(1))/(x0(4)-x0(2))*(x0(4)-x0(3));
   elseif u>=x0(n-2)
      y(i)=y0(n-3)*(u-x0(n-2))*(u-x0(n-1))*(u-x0(n))/(x0(n-3)-x0(n-2))/(x0(n-3)-x0(n-1))/(x0(n-3)-x0(n))+...
         y0(n-2)*(u-x0(n-3))*(u-x0(n-1))*(u-x0(n))/(x0(n-2)-x0(n-3))/(x0(n-2)-x0(n-1))/(x0(n-2)-x0(n))+...
         y0(n-1)*(u-x0(n-3))*(u-x0(n-2))*(u-x0(n))/(x0(n-1)-x0(n-3))/(x0(n-1)-x0(n-2))/(x0(n-1)-x0(n))+...
         y0(n)*(u-x0(n-3))*(u-x0(n-2))*(u-x0(n-1))/(x0(n)-x0(n-3))/(x0(n)-x0(n-2))/(x0(n)-x0(n-1));
   else
      for k=3:n-2
         if u>x0(k) & u<=x0(k+1)
            y(i)=y0(k-1)*(u-x0(k))*(u-x0(k+1))*(u-x0(k+2))/(x0(k-1)-x0(k))/(x0(k-1)-x0(k+1))/(x0(k-1)-x0(k+2))+...
               y0(k)*(u-x0(k-1))*(u-x0(k+1))*(u-x0(k+2))/(x0(k)-x0(k-1))/(x0(k)-x0(k+1))/(x0(k)-x0(k+2))+...
               y0(k+1)*(u-x0(k-1))*(u-x0(k))*(u-x0(k+2))/(x0(k+1)-x0(k-1))/(x0(k+1)-x0(k))/(x0(k+1)-x0(k+2))+...
               y0(k+2)*(u-x0(k-1))*(u-x0(k))*(u-x0(k+1))/(x0(k+2)-x0(k-1))/(x0(k+2)-x0(k))/(x0(k+2)-x0(k+1));
         end         
      end
   end
end
y;