function y=lagrange(x0,y0,x)

%n个数据以数组x0,y0输入，m个插值点以数组x输入，输出数组y为m个插值。
n=length(x0);m=length(x);
for i=m;z=x(i);s=0.0;for k=1:np=1.0;for j=1:n;if j~=kp=p*(z-x0(j))/(x0(k)-x0(j));endends=p*y0(k)+s;endy(i)=s;
end

function y-hermite(x0,y0,y1,x);
%x0,y0为样本点数据，y1为导数指，m个插值点以数组x输入，输出数组y为m个插值
n=length(x0);m=length(x);
for k=1:m;yy=0.0;for i=1:nh=1.0;a=0.0;for j=i:nif j~=ih=h*((x(k)-x0(j))/(x0(i)-x0(j)))^2; a=1/(x0(i)-x0(j))+a;endendyy=yy+h*((x0(i)-x0(k))*(2*a*y0(i)-y(i))+y0(i));endy(k)=yy;
end

%转载= =

clear,clc
x0=[0,3,5,7,9,11,12,13,14,15];
y0=[0,1.2,1.7,2.0,2.1,2.0,1.8,1.2,1.0,1.6];
t=0:0.05:15;
%拉格朗日插值函数
y1=lagrange(x0,y0,t);%调用编写的lagrange函数
dy1=(lagrange(x0,y0,0.0001)-lagrange(x0,y0,0))/0.0001%x=0处斜率
min1=min(lagrange(x0,y0,13:0.001:15))%13到15最小值
subplot(2,2,1);
plot(x0,y0,'ro',t,y1);%画出曲线
title('拉格朗日插值函数');
%分段线性插值
y2=interp1(x0,y0,t,'spline');%注意区分spline与linear
Y2=interp1(x0,y0,t);%默认linear
dy2=(interp1(x0,y0,0.0001,'spline')-interp1(x0,y0,0,'spline'))/0.0001%x=0处斜率
min2=min(interp1(x0,y0,13:0.001:15,'spline'))%13到15最小值
subplot(2,2,2);
plot(t,y2,'b',t,Y2,'r',x0,y0,'ro');%画出曲线
title('分段线性插值');
legend('边条','线性');%显示图形图例
%三次线条插值A
y3=spline(x0,y0,t);
dy3=(spline(x0,y0,0.0001)-spline(x0,y0,0))/0.0001%x=0处斜率
min3=min(spline(x0,y0,13:0.001:15))%13到15最小值
subplot(2,2,3);
plot(x0,y0,'ro',t,y3);%画出曲线
title('三次线条插值A');
%三次线条插值B
pp1=csape(x0,y0);%默认的边界条件,即给定边界一阶导数
pp2=csape(x0,y0,'second');%给定边界二阶导数
y4=ppval(pp1,t);
Y4=ppval(pp2,t);
dy4=(ppval(pp1,0.0001)-ppval(pp1,0))/0.0001%x=0处斜率
min4=min(ppval(pp1,13:0.001:15))%13到15最小值
subplot(2,2,4);
plot(t,y4,'b',t,Y4,'r',x0,y0,'ro');%画出曲线
title('三次线条插值B');
legend('一阶','二阶');

z=interp2(x0,y0,z0,x,y,'method')

pp=csape({x0,y0},z0,conds,valconds),z=fnval(pp,{x,y})

clear,clc%样本点信息
x=100:100:500;
y=100:100:400;z=[636   697   624  478   450698   712   630  478   420680   674   598  412   400662   626   552  334   310];%录入样本点信息
pp=csape({x,y},z');  %注意z矩阵的行列所对应的向量
xi=100:10:500;
yi=100:10:400;
cz1=fnval(pp,{xi,yi});cz2=interp2(x,y,z,xi,yi','spline');
[i,j]=find(cz1==max(max(cz1)))subplot(1,2,1);
surf(xi,yi,cz1');
shading interp;   %插入颜色插值
axis equal;
title('cz1');subplot(1,2,2);
surf(xi,yi,cz2);
shading interp;
axis equal;
title('cz2');

zi=griddata(x,y,z,xi,yi)

clear,clc%样本点信息
x=[129,140,103.5,88,185.5  195  105  157.5  107.5   77   81  162   162   117.5];
y=[7.5   141.5  23  147   22.5   137.5  85.5   -6.5   -81   3  56.5   -66.5  84  -33.5];
z=-[4   8  6 8  6  8  8  9  9  8  8  9  4  9];xi=75:200;
yi=-50:150;
zi=griddata(x,y,z,xi,yi','cubic');subplot(1,2,1);
plot(x,y,'*');
title('xy');subplot(1,2,2);
mesh(xi,yi,zi);
shading interp;
axis equal;
title('xyz');