离散试验数据点的正交多项式最小二乘拟合
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%离散试验数据点的正交多项式最小二乘拟合
function a=ZJZXEC(x,y,m)
if(length(x) == length(y))
n = length(x);
else
disp('x和y的维数不相等！');
return;
end
syms v;
d = zeros(1,m+1);
q = zeros(1,m+1);
alpha = zeros(1,m+1);
for k=0:m
px(k+1)=power(v,k);
end
B2 = [1];
d(1) = n;
for l=1:n
q(1) = q(1) + y(l);
alpha(1) = alpha(1) + x(l);
end
q(1) = q(1)/d(1);
alpha(1) = alpha(1)/d(1);
a(1) = q(1);
B1 = [-alpha(1) 1];
for l=1:n
d(2) = d(2) + (x(l)-alpha(1))^2;
q(2) = q(2) + y(l)*(x(l)-alpha(1));
alpha(2) = alpha(2) + x(l)*(x(l)-alpha(1))^2; end
q(2) = q(2)/d(2);
alpha(2) = alpha(2)/d(2);
a(1) = a(1)+q(2)*(-alpha(1));
a(2) = q(2);
beta = d(2)/d(1);
for i=3:(m+1)
B = zeros(1,i);
B(i) = B1(i-1);
B(i-1) = -alpha(i-1)*B1(i-1)+B1(i-2);
for j=2:i-2
B(j) = -alpha(i-1)*B1(j)+B1(j-1)-beta*B2(j);
end
B(1) = -alpha(i-1)*B1(1)-beta*B2(1); BF = B*transpose(px(1:i));
for l=1:n
Qx = subs(BF,'v',x(l));
d(i) = d(i) + (Qx)^2;
q(i) = q(i) + y(l)*Qx;
alpha(i) = alpha(i) + x(l)*(Qx)^2; end
alpha(i) = alpha(i)/d(i);
q(i) = q(i)/d(i);
beta = d(i)/d(i-1);
for k=1:i-1
a(k) = a(k)+q(i)*B(k);
end
a(i) = q(i)*B(i);
B2 = B1;
B1 = B;
end
function a=ZJZXEC(x,y,m)
if(length(x) == length(y))
n = length(x);
else
disp('x和y的维数不相等！');
return;
end %维数检查
syms v;
d = zeros(1,m+1);
q = zeros(1,m+1);
alpha = zeros(1,m+1);
for k=0:m
px(k+1)=power(v,k);
end %x的幂多项式
B2 = [1];
d(1) = n;
for l=1:n
q(1) = q(1) + y(l);
alpha(1) = alpha(1) + x(l);
end
q(1) = q(1)/d(1);
alpha(1) = alpha(1)/d(1);
a(1) = q(1);
B1 = [-alpha(1) 1];
for l=1:n
d(2) = d(2) + (x(l)-alpha(1))^2;
q(2) = q(2) + y(l)*(x(l)-alpha(1));
alpha(2) = alpha(2) + x(l)*(x(l)-alpha(1))^2; end
q(2) = q(2)/d(2);
alpha(2) = alpha(2)/d(2);
a(1) = a(1)+q(2)*(-alpha(1));
a(2) = q(2);
beta = d(2)/d(1);
for i=3:(m+1)
B = zeros(1,i);
B(i) = B1(i-1);
B(i-1) = -alpha(i-1)*B1(i-1)+B1(i-2);
for j=2:i-2
B(j) = -alpha(i-1)*B1(j)+B1(j-1)-beta*B2(j); end
B(1) = -alpha(i-1)*B1(1)-beta*B2(1); BF = B*transpose(px(1:i));
for l=1:n
Qx = subs(BF,'v',x(l));
d(i) = d(i) + (Qx)^2;
q(i) = q(i) + y(l)*Qx;
alpha(i) = alpha(i) + x(l)*(Qx)^2; end
alpha(i) = alpha(i)/d(i);
q(i) = q(i)/d(i);
beta = d(i)/d(i-1);
for k=1:i-1
a(k) = a(k)+q(i)*B(k);
end
a(i) = q(i)*B(i);
B2 = B1;
B1 = B;
end