Question

matlab中nlinfit非线性拟合求参数

x1=[0.4292 0.4269 0.381 0.4015 0.4117 0.3017];
>> x2=[0.00014 0.00059 0.0126 0.0061 0.00425 0.0443];
>> y=[0.517 0.509 0.44 0.466 0.479 0.309];
>> myfunc=inline('2.350176*beta(1)*(1-1/beta(2))*(1-(1-x1^(1/beta(2)))^beta(2))^2*(x1^(-1/beta(2))-1)^(-beta(2))*x1^(-1/beta(2)-0.5)*x2','beta','x1','x2');
>> beta=nlinfit(x1,x2,y,myfunc,[8 0.5]);

y是函数；x1，x2是自变量；要求beta(1)和beta（2）,哪里不对？

出错信息
??? Error using ==> statset
Expected argument 2 to be a parameter name string or an options structure
created with STATSET.

Error in ==> nlinfit at 91
options = statset(statset('nlinfit'), options);
beta=nlinfit(x,y,@myfun,[8 0.5])
我怎么把这句改为beta=nlinfit(x,y,@myfun,[8；0.5])才能运行出结果？我不太懂啊。。。还有，它上面有些警告。Warning: Rank deficient, rank = 1, tol = 5.7039e-013.
> In nlinfit at 192
Warning: The Jacobian at the solution is ill-conditioned, and some
model parameters may not be estimated well (they are not identifiable).
Use caution in making predictions.
> In nlinfit at 272

beta =

1.0e+010 *

-5.6511
0.0000
是不是数据不够好，拟合的有些不好？

Answer 1

补充回答：数据不好
建立函数文件：
function y = myfun(beta,x)
y = 2.350176*beta(1)*(1-1/beta(2))*(1-(1-x(:,1).^(1/beta(2))).^beta(2)).^2.*(x(:,1).^(-1/beta(2))-1).^(-beta(2)).*x(:,1).^(-1/beta(2)-0.5).*x(:,2);

运行代码：
x=[0.4292 0.4269 0.381 0.4015 0.4117 0.3017; 0.00014 0.00059 0.0126 0.0061 0.00425 0.0443];
x = x';
y=[0.517 0.509 0.44 0.466 0.479 0.309];
y = y';
beta=nlinfit(x,y,@myfun,[8 0.5])

运行结果：
beta =
-55262931764.9336 0.0517

Answer 2

clear all;
x1=[0.4292 0.4269 0.381 0.4015 0.4117 0.3017]';
x2=[0.00014 0.00059 0.0126 0.0061 0.00425 0.0443]';
x=[x1 x2];
y=[0.517 0.509 0.44 0.466 0.479 0.309]';
f=@(p,x) 2.350176*p(1)*(1-1/p(2))*(1-(1-x(:,1).^(1/p(2))).^p(2)).^2.*(x(:,1).^(-1/p(2))-1).^(-p(2)).*x(:,1).^(-1/p(2)-0.5).*x(:,2);
p0=[8 0.5]';
opt=optimset('TolFun',1e-3,'TolX',1e-3);
[p R]=nlinfit(x,y,f,p0,opt)