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function fp=fitpt() 
%最小二乘 
%基取{1, x, ...} 
%fitpt.m 
 
%默认算例为课本：P65，例3.2 
%	x=[0,1,2,3,4,5,6,7] 
%	y=[3.95,6.82,9.78,12.91,15.74,19.26,21.73,24.07] 
%结果：P(x) = 4.005 + 2.936x		平方误差=0.6162 
 
%MatLab函数：polyfit(x,y,n) 
 
s=input('<最小二乘>\n输入已知点的x坐标：（回车表示[0,1,2,3,4,5,6,7]）\n', 's'); 
if isempty(s) 
	s='[0,1,2,3,4,5,6,7]'; 
else 
	if (s(1)~='[') 
		s=strcat('[', s); 
		s=strcat(s, ']'); 
	end 
end 
x=sym(s); 
 
s=input('输入已知点的y坐标：（回车表示[3.95,6.82,9.78,12.91,15.74,19.26,21.73,24.07]）\n', 's'); 
if isempty(s) 
	s='[3.95,6.82,9.78,12.91,15.74,19.26,21.73,24.07]'; 
else 
	if (s(1)~='[') 
		s=strcat('[', s); 
		s=strcat(s, ']'); 
	end 
end 
y=sym(s); 
sz=size(x); 
sz=sz(2); 
n=input('输入多项式次数n：'); 
if (n+1>sz) 
    n=input('多项式次数需要小于已知点个数，请重新输入n：'); 
end 
if (n+1>sz) 
    error('多项式次数不能小于已知点个数！'); 
end 
fp=s_fitpt_p(x,y,n); 
 
%Diagram 
plot(double(x),double(y),'r*') 
hold on 
a=double(x(1)); 
b=double(x(sz)); 
x=a:abs(b-1)/100:b; 
y=subs(fp,x); 
plot(x,y) 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
function f=s_fitpt_p(x,y,n) 
%用n次多项式实现的最小二乘法 
 
sz=size(x); 
sz=sz(2); 
A=zeros(sz, n+1); 
v=vh(n); 
for i=1:sz 
    A(i,:)=subs(v, double(x(i))); 
end 
f=linsolve(A'*A, A'*y'); 
f=vpa(f,4); 
f=v*f; 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
function v=vh(n) 
%Create vector in horizontal style, such as  
%		v=[1, x, x^2, ..., x^n] 
 
if (n<0 | n>9) 
	error('Make sure ''n'' is in range of [0, 9]') 
end 
s=''; 
for i=0:n 
	s=strcat(s, ',x^'); 
	s=strcat(s, num2str(i)); 
end 
s(1)='['; 
sz=size(s); 
s(sz(2)+1)=']'; 
 
v=simplify(sym(s)); 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%