interp.txt

实现拉朗日插值、线性插值、样条插值

function p=jie1(x,xdata)
p=x(1)+x(2)*exp(-x(3)*xdata+x(4));

x0=[1   2   3   4   5   6   7   8   9   10];
y0=[2615 1943 1494 1087 765 538 484 290 226 204];
plot(x0,y0,'*');
hold on;
xi=[0.5:0.5:10];
yi=interp1(x0,y0,xi,'spline');
plot(xi,yi);hold on;
y4=interp1(x0,y0,4.5,'spline')
t0=[2.3,1,2.0,2.0];
x=lsqcurvefit(@jie1,t0,x0,y0)
y=x(1)+x(2)*exp(-x(3)*xi+x(4));
plot(xi,y,'r');hold off;


高维插值
x0=-1:0.4:1;y0=-1:0.4:1;a=1.2;z0=zeros(6,6);
for i=1:6
    for j=1:6           z0(i,j)=0.3+sin(16/15*x0(i)-a)+sin(16/15*x0(i)-a).^2+sin(16/15*y0(j)-a)+sin(16/15*y0(j)-a).^2;
    end
end
xi=-1:0.1:1;yi=-1:0.1:1;zi1=interp2(x0,y0,z0,xi,yi','nearest');
mesh(xi,yi,zi1);
zi2=interp2(x0,y0,z0,xi,yi','linear');figure(2);
mesh(xi,yi,zi2);
zi3=interp2(x0,y0,z0,xi,yi','spline');figure(3);
mesh(xi,yi,zi3);
zi4=interp2(x0,y0,z0,xi,yi','cubic');figure(4);
mesh(xi,yi,zi4);