polyfits-ls.m

matlab线性拟合程序

function [th,err,yi]=polyfits(x,y,N,xi,r)
M=length(x);
x=x(:);
y=y(:);
if nargin==4
    if length(xi)==M
        r=xi;
        xi=x;
    else r=1;
    end
elseif nargin==3
    xi=x;
    r=1;
end
A(:,N+1)=ones(M,1);
for n=N:-1:1
    A(:,n)=A(:,n+1).*x;
end
if length(r)==M
    for m=1:M
        A(m,:)=A(m,:)/r(m);
        y(m)=y(m)/r(m);
    end
end
th=(A\y)';
ye=polyval(th,x);
err=norm(y-ye)/norm(y);
yi=polyval(th,xi);

%Ls
x=[1 3 5 7 9 11 13 15 17 19 21 23 25]';
y=[87035 97288 119893 132642 284586 198859 133937 178275 158586 99844 96291 102252 103273]';
for i=1:7
N=2*i-1;
[p,s]=polyfit(x,y,N);
yi=polyval(p,x,s);
subplot(220+i);
plot(x,y,'k*')
hold on
plot(x,yi,'g:','LineWidth',1.5);
title(['The',num2str(N),'th Polynomial curve Fitting'])
grid on
end