基于矩阵QR分解的最小二乘拟合MATLAB源程序

suffer

1. function [c,R2,rout] = fitqr(x,y,basefun)
   
2. % fitqr  Least-squares fit via solution of overdetermined system with QR
   
3. %        Given ordered pairs of data, (x_i,y_i), i=1,...,m, fitqr
   
4. %        returns the vector of coefficients, c_1,...,c_n, such that
   
5. %            F(x) = c_1*f_1(x) + c_2*f_2(x) + ... + c_n*f_n(x)
   
6. %        minimizes the L2 norm of y_i - F(x_i).
   
7. %
   
8. % Synopsis:  c       = fitqr(x,y,basefun)
   
9. %           [c,R2]   = fitqr(x,y,basefun)
   
10. %           [c,R2,r] = fitqr(x,y,basefun)
    
11. %
    
12. % Input:   x,y     = vectors of data to be fit
    
13. %          basefun = (string) name of user-supplied m-file that computes
    
14. %                    matrix A.  The columns of A are the values of the
    
15. %                    basis functions evaluated at the x data points.
    
16. %
    
17. % Output:  c = vector of coefficients obtained from the fit
    
18. %          R2 = (optional) adjusted coefficient of determination; 0 <= R2 <= 1
    
19. %               R2 close to 1 indicates a strong relationship between y and x
    
20. %          r  = (optional) residuals of the fit
    
21. 
    
22. if length(y)~= length(x);  error('x and y are not compatible');  end
    
23. 
    
24. A = feval(basefun,x(:)); %  Coefficient matrix of overdetermined system
    
25. c = A\y(:);              %  Solve overdetermined system with QR factorization
    
26. if nargout>1
    
27.   r = y - A*c;           %  Residuals at data points used to obtain the fit
    
28.   [m,n] = size(A);
    
29.   R2 = 1 - (m-1)/(m-n-1)*(norm(r)/norm(y-mean(y)))^2;
    
30.   if nargout>2,  rout = r;  end
    
31. end

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xtw1128

顶

zhaoym_0413

不错的程序,不知楼主有没做过时间序列的非线性最小二乘拟合

happy

原帖由 zhaoym_0413 于 2007-1-18 17:26 发表
不错的程序,不知楼主有没做过时间序列的非线性最小二乘拟合

matlab中有现成的函数

lym

看得懂一点点
不知道楼主是否有LQG控制振动的程序啊