function coef = poly_fit(m,data)
%計算最小二乘法的系數方程
%輸入參數：m為擬合多項式的次數，data為擬合數據，格式為二維列向量,第一列為自變量，第二列為因變量.
%輸出參數：擬合多項式的系數行向量.
%調用關系：調用行向量內積函數inner_product(vector1,vector2)和高斯列主元消元法函數Gauss_solve(A).

x = data(:,1)';
y = data(:,2)';

for i = 1:(m+1)
    phi(i,:) = x.^(i-1);
end

for i = 1:(m+1)
    for j = i:(m+1)
        A(i,j) = inner_product(phi(i,:),phi(j,:));
        A(j,i) = A(i,j);
    end
    A(i,j+1) = inner_product(y,phi(i,:));
end
coef = Gauss_solve(A);