Question

麻烦matlab高手用lsqcurvefit函数帮我拟合一组数据。

y=[0.925,0.881,0.8604,0.8604,0.8409,0.8409,0.8409,0.8222,0.8222,0.8222,0.8044,
0.8044,0.8044,0.8044,0.7872,0.7872,0.7872,0.7872,0.7708,0.7708,0.7708,0.7708,
0.7708,0.7551,0.7255,0.7115,0.6727,0.6599,0.6491,0.6379,0.6271,0.6271,0.6167,
0.6167,0.6066,0.6066,0.6066,0.5968,0.5968,0.5968,0.5873,0.5873,0.5873,0.5873]
x=[0.0833,0.1667,0.25,0.3333,0.4167,0.5,0.5833,0.6667,0.75,0.8333,0.9167,1,1.0833
,1.1667,1.25,1.3333,1.4167,1.5,1.5833,1.6667,1.75,1.8333,1.9167,2,6,9,22,34,46, 58,70,82,94,106,118,130,142,154,166,178,190,202,214,226].想用matlab里的lsqcurvefit拟合出下面这个函数，y=1/a+x/b+(1/c)*[1-exp(-c*x/d)]。a,b,c,d要求的大于0的。就这些条件了。麻烦哪位会的同学，帮我解决下，在线等- -哪里看不清的可以说下。谢谢了。。。

Answer 1

我做了一下发现误差比较大，是不是我给的初值有问题，还是给的数据有问题，你可以参考下

function f=curvefun1(x,xdata)

%  y=1/a+x/b+(1/c)*[1-exp(-c*x/d)]

f=1/x(1)+xdata/x(2)+(1/x(3))*(1-exp(-x(3)*xdata/x(4)));

运行：

clear;clc;

xdata=[0.0833,0.1667,0.25,0.3333,0.4167,0.5,0.5833,0.6667,0.75,...

    0.8333,0.9167,1,1.0833,1.1667,1.25,1.3333,1.4167,1.5,1.5833,...

    1.6667,1.75,1.8333,1.9167,2,6,9,22,34,46, 58,70,82,94,106,118,...

    130,142,154,166,178,190,202,214,226];

ydata=[0.925,0.881,0.8604,0.8604,0.8409,0.8409,0.8409,0.8222,0.8222,0.8222,0.8044,...

0.8044,0.8044,0.8044,0.7872,0.7872,0.7872,0.7872,0.7708,0.7708,0.7708,0.7708,...

0.7708,0.7551,0.7255,0.7115,0.6727,0.6599,0.6491,0.6379,0.6271,0.6271,0.6167,...

0.6167,0.6066,0.6066,0.6066,0.5968,0.5968,0.5968,0.5873,0.5873,0.5873,0.5873];

x0=[5,3,5,2];   %初值

x=lsqcurvefit('curvefun1',x0,xdata,ydata)

f=curvefun1(x,xdata);

plot(xdata,ydata,'.')

hold on

plot(xdata,f,'.')

运行结果：

x =

  1.0e+002 *

  Columns 1 through 3

   0.036322600853330   2.664204064307804   0.038239112150553

  Column 4

   0.000104652408479

追问

对不起，我的错，我给的Y值有问题，Y值是：y=[0.0123,0.0129,0.0132,0.0132,0.0135,0.0135,0.0135,0.0138,0.0138,0.0138,0.0141,0.0141,0.0141,0.0141,0.0144,0.0144,0.0144,0.0144,0.0148,0.0148,0.0148,0.0148,0.0148,0.0151,0.0157,0.016,0.0169,0.0172,0.0175,0.0178,0.0181,0.018,0.0184,0.0184,0.0188,0.0188,0.0188,0.0191,0.0191,0.0191,0.0194,0.0194,0.0194,0.0194]
X值不变。麻烦你再看看，耽误你时间了，不好意思。

Answer 2

你确定你的数据和方程有联系吗，我用其他方程拟合的，用你原来的方程拟合效果极差，我用的方程式y=a*exp(b*x)+c*exp(d*x)

追问

不是用CFTOOL拟合的，你应该不是用的lsqcurvefit拟合的吧，这个需要初始值的- -

追答

用cftool可以自定义拟合方程，我把你的原始方程设成自定义拟合方程了，拟合之后完全不搭边，所以我换了指数拟合，感觉还好，所以我很怀疑你的数据和方程有联系吗。
我一般用lsqcurvefit拟合时，都是先用cftool拟合把初值找到，再编程的，但是发现完全不搭边，所以直接编程我感觉也拟合不出来，数据真没问题吗

追问

不好意思，初始数据中的X是有点问题，应该是它的倒数，x=[1.0811,1.1351,1.1623,1.1623,1.1892,1.1892,1.1892,1.2162,1.2162,1.2162,1.2432,1.2432,
1.2432,1.2432,1.2703,1.2703,1.2703,1.2703,1.2974,1.2974,1.2974,1.2974,1.2974,1.3243,
1.3784,1.4055,1.4865,1.5154,1.5406,1.5676,1.5946,1.5946,1.6215,1.6215,1.6485,1.6485,
1.6485,1.6756,1.6756,1.6756,1.7027,1.7027,1.7027,1.7027]。麻烦再帮忙看看- -

追答

还有问题，或者说你的原始方程根本就是错的，按你的方程拟合结果

追问

对不起，是我糊涂了，没想好就发上来了，是把y变了。x不变，还是0.0083到226。
y=[0.0123,0.0129,0.0132,0.0132,0.0135,0.0135,0.0135,0.0138,0.0138,0.0138,0.0141,0.0141,0.0141,0.0141,0.0144,0.0144,0.0144,0.0144,0.0148,0.0148,0.0148,0.0148,0.0148,0.0151,0.0157,0.016,0.0169,0.0172,0.0175,0.0178,0.0181,0.018,0.0184,0.0184,0.0188,0.0188,0.0188,0.0191,0.0191,0.0191,0.0194,0.0194,0.0194,0.0194]
麻烦了- -

追答

我的天啊，你真有才

追问

我的错，麻烦大侠再来一次- -CFTOOL中的自编公式，刚才我试了，好像不行。方程应该没什么问题吧，是burgers模型方程。对不住大家- -

追答

不好意思，还是不行，我就不传图片了，你再仔细检查检查
还是用指数拟合