matlab多参数指数拟合如何实现

sophialll

我有一组数据
x=[5 6 7 8 9 .....30]
y=[0.07187  0.05888 0.04987 0.04324 0.03815 0.03417 0.03093 0.02824 0.02598 0.02406 0.02241 0.02096 0.0197 0.01857 0.01757 0.01667 0.01585 0.01511 0.01444  0.01383 0.01326 0.01275 0.01226 0.01182 0.0114 0.01101]
绘出来像个指数函数。我猜想它是指数函数，用matlab进行拟合，但是指数的底不知道，还有N多其他参数也不知道，应该如何拟合啊，求高手帮忙，要具体程序过程。我编了好几个程序都运行不成功。

sophialll

初始回归系数也不清楚。

qibbxxt

1. General model Exp2:
   
2.      f(x) = a*exp(b*x) + c*exp(d*x)
   
3. Coefficients (with 95% confidence bounds):
   
4.        a =      0.1916  (0.1792, 0.204)
   
5.        b =      -0.319  (-0.3373, -0.3006)
   
6.        c =     0.04072  (0.03814, 0.04329)
   
7.             d =    -0.04487  (-0.0476, -0.04214)
   
8. 
   
9. Goodness of fit:
   
10.   SSE: 1.669e-006
    
11.   R-square: 0.9997
    
12.   Adjusted R-square: 0.9997
    
13.   RMSE: 0.0002754

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1. function createFit(x,y)
   
2. %CREATEFIT Create plot of data sets and fits
   
3. %   CREATEFIT(X,Y)
   
4. %   Creates a plot, similar to the plot in the main Curve Fitting Tool,
   
5. %   using the data that you provide as input.  You can
   
6. %   use this function with the same data you used with CFTOOL
   
7. %   or with different data.  You may want to edit the function to
   
8. %   customize the code and this help message.
   
9. %
   
10. %   Number of data sets:  1
    
11. %   Number of fits:  1% Data from data set "y vs. x":
    
12. %     X = x:
    
13. %     Y = y:
    
14. %     Unweighted% Auto-generated by MATLAB on 18-Apr-2011 10:56:55% Set up figure to receive data sets and fits
    
15. f_ = clf;
    
16. figure(f_);
    
17. set(f_,'Units','Pixels','Position',[578 254 688 485]);
    
18. % Line handles and text for the legend.
    
19. legh_ = [];
    
20. legt_ = {};
    
21. % Limits of the x-axis.
    
22. xlim_ = [Inf -Inf];
    
23. % Axes for the plot.
    
24. ax_ = axes;
    
25. set(ax_,'Units','normalized','OuterPosition',[0 0 1 1]);
    
26. set(ax_,'Box','on');
    
27. axes(ax_);
    
28. hold on;% --- Plot data that was originally in data set "y vs. x"
    
29. x = x(:);
    
30. y = y(:);
    
31. h_ = line(x,y,'Parent',ax_,'Color',[0.333333 0 0.666667],...
    
32.     'LineStyle','none', 'LineWidth',1,...
    
33.     'Marker','.', 'MarkerSize',12);
    
34. xlim_(1) = min(xlim_(1),min(x));
    
35. xlim_(2) = max(xlim_(2),max(x));
    
36. legh_(end+1) = h_;
    
37. legt_{end+1} = 'y vs. x';% Nudge axis limits beyond data limits
    
38. if all(isfinite(xlim_))
    
39.     xlim_ = xlim_ + [-1 1] * 0.01 * diff(xlim_);
    
40.     set(ax_,'XLim',xlim_)
    
41. else
    
42.     set(ax_, 'XLim',[4.75, 30.25]);
    
43. end% --- Create fit "fit 1"
    
44. ok_ = isfinite(x) & isfinite(y);
    
45. if ~all( ok_ )
    
46.     warning( 'GenerateMFile:IgnoringNansAndInfs',...
    
47.         'Ignoring NaNs and Infs in data.' );
    
48. end
    
49. st_ = [0.15243570612980811 -0.25709456653830987 0.033745642790019854 -0.038489626682204618 ];
    
50. ft_ = fittype('exp2');% Fit this model using new data
    
51. cf_ = fit(x(ok_),y(ok_),ft_,'Startpoint',st_);
    
52. % Alternatively uncomment the following lines to use coefficients from the
    
53. % original fit. You can use this choice to plot the original fit against new
    
54. % data.
    
55. %    cv_ = { 0.19159877789258178, -0.31895949786907274, 0.040716429909295873, -0.044867078417144955};
    
56. %    cf_ = cfit(ft_,cv_{:});% Plot this fit
    
57. h_ = plot(cf_,'fit',0.95);
    
58. set(h_(1),'Color',[1 0 0],...
    
59.     'LineStyle','-', 'LineWidth',2,...
    
60.     'Marker','none', 'MarkerSize',6);
    
61. % Turn off legend created by plot method.
    
62. legend off;
    
63. % Store line handle and fit name for legend.
    
64. legh_(end+1) = h_(1);
    
65. legt_{end+1} = 'fit 1';% --- Finished fitting and plotting data. Clean up.
    
66. hold off;
    
67. % Display legend
    
68. leginfo_ = {'Orientation', 'vertical', 'Location', 'NorthEast'};
    
69. h_ = legend(ax_,legh_,legt_,leginfo_{:});
    
70. set(h_,'Interpreter','none');
    
71. % Remove labels from x- and y-axes.
    
72. xlabel(ax_,'');
    
73. ylabel(ax_,'');
    

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sophialll

回复 3 # qibbxxt 的帖子

不好意思啊，求教高手，前面的系数是怎么求出来的？直接用的matlab的工具箱吗？还是程序运行的结果啊？

sophialll

回复 3 # qibbxxt 的帖子

另外，您怎么这么厉害，不知道有什么学习经验可以传授一下吗？

meiyongyuandeze

1. x=[5:30];
   
2. >> y=[0.07187 0.05888 0.04987 0.04324 0.03815 0.03417 0.03093 0.02824 0.02598 0.02406 0.02241 0.02096 0.0197 0.01857 0.01757 0.01667 0.01585 0.01511 0.01444 0.01383 0.01326 0.01275 0.01226 0.01182 0.0114 0.01101];
   
3. >> f=fittype('a*exp(b*x)+c*exp(d*x)','coeff',{'a','b','c','d'});
   
4. >> [c,gof2]=fit(x',y',f)
   
5. Warning: Start point not provided, choosing random start point.
   
6. > In fit>handlewarn at 705
   
7. In fit at 321
   
8. 
   
9. c =
   
10. 
    
11. General model:
    
12. c(x) = a*exp(b*x)+c*exp(d*x)
    
13. Coefficients (with 95% confidence bounds):
    
14. a = 0.00362 (-0.02079, 0.02803)
    
15. b = 0.1983 (-0.107, 0.5036)
    
16. c = -3.244e-010 (-1.577e-008, 1.512e-008)
    
17. d = 0.7468 (-0.7801, 2.274)
    
18. 
    
19. 
    
20. gof2 =
    
21. 
    
22. sse: 1.7698
    
23. rsquare: -282.6509
    
24. dfe: 22
    
25. adjrsquare: -321.3306
    
26. rmse: 0.2836

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请教主任，我用的上面的指数函数进行拟合，为什么和你给出的系数差别如此大呢！请指教！

ChaChing

回复 4 # sophialll 的帖子

这有些也是跟qibbxxt学的, 我来补充下
1.command window下cftool
2.>> data %% 输入x,y
3.>> Fitting >> New fit
4. Type of fit >> Exponential >> 选a*exp(b*x) + c*exp(d*x) >> apply
5. File >> Generate M-file

meiyongyuandeze

回复 7 # ChaChing 的帖子

用cftool工具和我自己用代码操作（代码在6楼），选择的函数都是指数函数，为什么拟合的系数差别比较大呢！
个人感觉应该和warning有关，是不是应该给定初值，如果是这样的话，请教您初值一般应该如何给才能保证精度呢?

sophialll

回复 7 # ChaChing 的帖子

:handshake太感谢了，都是高手

ChaChing

回复 8 # meiyongyuandeze 的帖子

最近回帖都没刷新下, 所以都没注意到有新回帖!
以前自己没使用过Curve Fitting Toolbox, 来此为了回帖才稍微看下的
试下你的写法, 的确不同, 但也与你的不同, 我的是R2009a

1. >> f=fittype('a*exp(b*x)+c*exp(d*x)','coeff',{'a','b','c','d'});
   
2. 
   
3. >> [c,gof2]=fit(x',y',f)
   
4. Warning: Start point not provided, choosing random start point.
   
5. > In fit>handlewarn at 817
   
6.   In fit at 380
   
7. Maximum number of function evaluations exceeded. Increasing
   
8. MaxFunEvals (in fit options) may allow for a better fit, or
   
9. the current equation may not be a good model for the data.
   
10. 
    
11. c =
    
12. 
    
13.      General model:
    
14.        c(x) = a*exp(b*x)+c*exp(d*x)
    
15.      Coefficients (with 95% confidence bounds):
    
16.        a =     -0.0237  (-3.612e+004, 3.612e+004)
    
17.        b =      0.9074  (-234.8, 236.6)
    
18.        c =     0.02348  (-3.612e+004, 3.612e+004)
    
19.        d =      0.9077  (-235.7, 237.5)
    
20. 
    
21. gof2 =
    
22. 
    
23.            sse: 6.5381e+012
    
24.        rsquare: -1.0479e+015
    
25.            dfe: 22
    
26.     adjrsquare: -1.1907e+015
    
27.           rmse: 5.4515e+005

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ChaChing

比较下与3F的差异, 不难发现是fittype的差异
至於两者的差异, 有空再看看help说明了, 汗, 还没详看

1. >> f=fittype('exp2');
   
2. >> [c,gof2]=fit(x',y',f)
   
3. 
   
4. c =
   
5. 
   
6.      General model Exp2:
   
7.        c(x) = a*exp(b*x) + c*exp(d*x)
   
8.      Coefficients (with 95% confidence bounds):
   
9.        a =      0.1916  (0.1792, 0.204)
   
10.        b =      -0.319  (-0.3373, -0.3006)
    
11.        c =     0.04072  (0.03814, 0.04329)
    
12.        d =    -0.04487  (-0.0476, -0.04214)
    
13. 
    
14. gof2 =
    
15. 
    
16.            sse: 1.6686e-006
    
17.        rsquare: 0.9997
    
18.            dfe: 22
    
19.     adjrsquare: 0.9997
    
20.           rmse: 2.7540e-004

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ChaChing

回复 8 # meiyongyuandeze 的帖子

我也没发现问题的所在!
无编辑权限了, 不然真想从10F开始分割成另一帖, 因已是另一个问题

meiyongyuandeze

回复 12 # ChaChing 的帖子

我已经将问题抽来，重新分割成另外的一个帖子，请关注讨论！

tre

就那么实现呗！！！