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注册: 2012-11-01
专业: 安全科学与工程

[求助] 二元非线性拟合，请大神帮忙看下程序哪有问题，谢谢！已有1人参与

两个自变量x1、x2，一个因变量y。通过绘图可以看出各个自变量和因变量的关系分布类似于正态分布，因此选用二维正太分布模型拟合。

下面是二维正态分布模型：

http://baike.baidu.com/view/9306579.htm
可详见 http://baike.baidu.com/view/9306579.htm 百度百科

下面是数据：

y       x1                x2
0 1000          2
0 1200          5
1 1400          15
1 1570          20
2 1720             30
2 1790          40
3 1860          60
4 1880          90
6 1980          172
7 2250          200
7 2530          250
8 2850          350
9 3100          450
10 3300          550
11 3500          650
12 3600          800
13 3800          1100
14 4000          1440
14 4200          1501
14 4500          1563
14 4800          1637
6 6800          2863

下面是函数代码：
function yy=fun(beta,x)
b1 = beta(1);
b2 = beta(2);
b3 = beta(3);
b4 = beta(4);
b5 = beta(5);
yy=(2*pi*b3*b4*(1-b5^2)^(1/2))^(-1)*exp(-1/2*(1-b5^2)^(-1)*((x(:,1)-b1)^2*b3^(-2)-2*b5*(x(:,1)-b1)*(x(:,2)-b2)*(b3*b4)^(-1)+(x(:,2)-b2)^2*b4^(-2)));

下面是程序运行代码：
clc
clear
data=load('data.txt');
y=data(:,1);
x=data(:,2:3);
beta=[1,0.1,3,1,0.5];
[beta_out,r,J,COVB,mse]=nlinfit(x,y,@fun,beta);
beta_out;
mse;
betaci=nlparci(beta_out,r,'Jacobian',J);
betaa=[beta_out',betaci];
[yy,delta]=nlpredci(@fun,x,beta_out,r,'Jacobian',J);
alpha=0.05;
nlintool(x,y,'fun',beta,alpha)
r=corrcoef(y,yy);
plotregression(y,yy)
regstats(y,yy)

运行结果：
Warning: Rank deficient, rank = 0, tol =  0.000000e+00.
> In nlinfit>LMfit at 351
  In nlinfit at 184
  In nihe at 7
Warning: Some columns of the Jacobian are effectively zero at the solution, indicating that the
model is insensitive to some of its parameters.  That may be because those parameters are not
present in the model, or otherwise do not affect the predicted values.  It may also be due to
numerical underflow in the model function, which can sometimes be avoided by choosing better
initial parameter values, or by rescaling or recentering.  Parameter estimates may be unreliable.
> In nlinfit at 253
  In nihe at 7
Warning: Matrix is singular to working precision.
> In nlinfit at 274
  In nihe at 7
Warning: Matrix is singular to working precision.
> In nlparci at 104
  In nihe at 10
Warning: Matrix is singular to working precision.
> In nlpredci at 181
  In nihe at 12
Warning: Matrix is singular to working precision.
> In nlintool>PredictionsPlusError at 409
  In nlintool at 257
  In nihe at 14
Warning: Matrix is singular to working precision.
> In nlintool>PredictionsPlusError at 409
  In nlintool at 257
  In nihe at 14
Warning: Matrix is singular to working precision.
> In nlintool>PredictionsPlusError at 409
  In nlintool at 271
  In nihe at 14
Warning: Matrix is singular to working precision.
> In regstats at 193
  In regstats at 155
  In nihe at 17
Warning: Matrix is singular to working precision.
> In regstats at 208
  In regstats at 155
  In nihe at 17

出现很多错误，拟合度很低或者出现NaN。
求大神看是什么问题。

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