matlab 求拟合直线的斜率_常见的插值和拟合方法

function y=Lagrange(x0,y0,x)
%输入：x0:节点变量数据
%      y0:节点函数值
%      x:插值数据
%输出：y:插值函数值
    n=length(x0);m=length(x);
    for i=1:m
        z=x(i);
        s=0.0;
        for k=1:n
            p=1.0;
            for j=1:n
                if j~=k
                    p=p*(z-x0(j))/(x0(k)-x0(j));
                end
            end
            s=p*y0(k)+s;
        end
        y(i)=s;
    end
end

function [YY,y]=newton_chazhi(X,Y,x,M)
%输入为：X-插值点的x轴向量
%Y-插值点的y轴向量
%需要求解的x变量
%M为多项式次数
%输出YY为差分表
%y是x对应的因变量
m=length(X);
YY=zeros(m);
YY(:,1)=Y;
%求查分表
for i=2:m
    for j=i:m
        YY(j,i)=(YY(j,i-1)-YY(j-1,i-1))/(X(j)-X(j-i+1));
    end
end
y=Y(1);
%计算newton插值公式
for i=1:M
    xl=1;
   for j=1:i
       xl=xl*(x-X(j));
   end
   y=y+xl*YY(i+1,i+1);
end
end


function [YY,y]=main()
X=[0.40,0.55,0.65,0.80,0.90,1.05];
Y=[0.41075,0.57815,0.69675,0.88811,1.02652,1.25382];
x=0.596;
M=4;
[YY,y]=newton_chazhi(X,Y,x,M);
end

function y=hermiter_chazhi(X,Y,x1,x)
%求差分表
m=length(X);
YY=zeros(m);
YY(:,1)=Y;
for i=2:m
    for j=i:m
        YY(j,i)=(YY(j,i-1)-YY(j-1,i-1))/(X(j)-X(j-i+1));
    end
end
%求A
A=x1-YY(2,2)-(X(2)-X(1))*YY(3,3);

%求插值
y=Y(1)+YY(2,2).*(x-X(1))+YY(3,3).*(x-X(1)).*(x-X(2))+A.*(x-X(1)).*(x-X(2)).*(x-X(3));
end

function y=main_her()
x=[1/4:0.01:9/4];
f=x.^(3/2);
X=[1/4,1,9/4];
Y=[1/8,1,27/8];
x1=3/2;
y=hermiter_chazhi(X,Y,x1,x);

plot(x,y,"r")
grid on
hold on 
plot(x,f,"b")
scatter(X,Y)
legend("插值曲线","实际曲线")
end