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function fe=fitfun() 
%连续函数的最佳逼近 
%取基{1, x, ...} 
%fitfun.m 
 
%默认算例为课本：P60，例3.1 
%原函数f(x)=x^(1/2)， 定义域 [1/4, 1] 
%结果：P(x) = 10/27 + 88/135x		平方误差=0.00010803 
 
fs=input('<连续函数的最佳逼近>\n输入原函数f(x)：[直接回车表示：f(x)=x^(1/2)]\nf(x)=', 's'); 
if isempty(fs) 
	fs='x^(1/2)'; 
end 
f=sym(fs); 
a=input('定义域([a, b]) 上界a:'); 
b=input('Domain ([a, b]) edge b:'); 
n=input('{1, x, x^2, ..., x^n}\nInput the maximum index n: '); 
 
v=vv(n); 
h=vh(n); 
G=int(v*h, a, b); 
B=int(f*v, a, b); 
C=inv(G)*B; 
fe=h*C; 
 
%Error delta 
SError=vpa(int(f*f, a, b)-int(f*h, a, b)*C, 6) 
 
%Diagram 
x=a:(b-a)/100:b; 
y=subs(f,x); 
plot(x,y,'r') 
hold on 
y=subs(fe,x); 
plot(x,y) 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
function v=vv(n) 
%Create vector in vertical style, such as  
% 				1 
% 				x 
% 		v =   x^2 
% 				x^3 
% 				... 
% 				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)); 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
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)); 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%