%拉格朗日插值法
%x=[1 3 2]; x=[0.1 0.15 0.25 0.40 0.50 0.57 0.70 0.85 0.93 1.0];
%y=[1 2 -1];y=[0.904837 0.860708 0.778801 0.670320 0.606531 0.565525
%0.496585 0.427415 0.394554 0.367879];
%p=1.5;p=0.63
function Lagelangrichazhifa(x,y,p)
z=0;
s=1;
A=size(x);
n=A(2);
for i=2:n
    s=s*(p-x(i))/(x(1)-x(i));
end
L(1)=s*y(1);
L(1);
for k=2:n
    s=1;
for i=1:k-1 
     s=s*(p-x(i))/(x(k)-x(i));
end
s;
for i=k+1:n
      s=s*(p-x(i))/(x(k)-x(i));
end
L(k)=s*y(k);
end
for i=1:n
z=z+L(i);
end
display('該處應用拉格朗日插值法得到插值為：')
z


%調用函數Lagelangrichazhifa(x,y,p)：

x=[0.1 0.15 0.25 0.40 0.50 0.57 0.70 0.85 0.93 1.0];
y=[0.904837 0.860708 0.778801 0.670320 0.606531 0.565525 0.496585 0.427415 0.394554 0.367879];
p=0.63;
Lagelangrichazhifa(x,y,p)