关于非线形最小二乘法求解。

我在文件中写了个函数：function F = myfun(z,xdata)F = exp(z(1))./(exp(z(1))+exp(-z(1))).*exp(-(xdata./exp(z(3))).^exp(z(2)))+(1-exp(z(1))./(exp(z(1))+exp(-z(1)))).*exp(-(xdata./exp(z(5))).^exp(z(4)));

%%其实就是混合威布尔做了个变换，

z(0)=[1.7380;0.9555;-1.3863;2.0149;-2.5257];

[z,resnorm] = lsqcurvefit(@ercheng,z0,xdata,ydata1);

其中xdata=0.0580000000000000

0.0710000000000000

0.0760000000000000

0.0790000000000000

0.0830000000000000

0.0870000000000000

0.0980000000000000

0.111000000000000

0.117000000000000

0.122000000000000

0.122000000000000

0.133000000000000

0.134000000000000

0.138000000000000

0.140000000000000

0.142000000000000

0.150000000000000

0.155000000000000

0.160000000000000

0.160000000000000

0.168000000000000

0.173000000000000

0.173000000000000

0.173000000000000

0.175000000000000

0.176000000000000

0.177000000000000

0.181000000000000

0.182000000000000

0.183000000000000

0.194000000000000

0.203000000000000

0.214000000000000

0.218000000000000

0.222100000000000

0.223000000000000

0.225000000000000

0.247000000000000

0.253000000000000

0.256000000000000

0.257000000000000

0.258000000000000

0.262000000000000

0.263000000000000

0.264000000000000

0.266000000000000

0.267000000000000

0.276000000000000

0.278000000000000

0.280000000000000

0.288000000000000

0.289000000000000

0.306000000000000

0.315000000000000

0.333000000000000

0.335000000000000

0.353000000000000

0.389000000000000

0.404000000000000

0.418000000000000

0.456000000000000

0.489000000000000；

ydata1=0.983870967741936

0.967741935483871

0.951612903225807

0.935483870967742

0.919354838709677

0.903225806451613

0.887096774193548

0.870967741935484

0.854838709677419

0.838709677419355

0.822580645161290

0.806451612903226

0.790322580645161

0.774193548387097

0.758064516129032

0.741935483870968

0.725806451612903

0.709677419354839

0.693548387096774

0.677419354838710

0.661290322580645

0.645161290322581

0.629032258064516

0.612903225806452

0.596774193548387

0.580645161290322

0.564516129032258

0.548387096774193

0.532258064516129

0.516129032258064

0.500000000000000

0.483870967741935

0.467741935483871

0.451612903225806

0.435483870967742

0.419354838709677

0.403225806451613

0.387096774193548

0.370967741935484

0.354838709677419

0.338709677419355

0.322580645161290

0.306451612903226

0.290322580645161

0.274193548387097

0.258064516129032

0.241935483870968

0.225806451612903

0.209677419354839

0.193548387096774

0.177419354838710

0.161290322580645

0.145161290322581

0.129032258064516

0.112903225806452

0.0967741935483870

0.0806451612903230

0.0645161290322580

0.0483870967741930

0.0322580645161290

0.0161290322580639

0;

然后迭代停止了，原因如下：

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to

its initial value is less than the default value of the function tolerance.

<stopping criteria details>

Optimization stopped because the relative sum of squares (r) is changing

by less than options.TolFun = 1.000000e-06.

Optimization Metric Options

relative change r = 8.13e-07 TolFun = 1e-06 (default)

我看了应该是每次迭代值得变化量太小了

请教怎么修改？

Answer 1

[bidag]

用1stOpt试试，不需初值：

Parameter z(5);
Variable xdata,ydata;
function ydata=exp(z1)/(exp(z1)+exp(-z1))*exp(-(xdata/exp(z3))^exp(z2))+(1-exp(z1)/(exp(z1)+exp(-z1)))*exp(-(xdata/exp(z5))^exp(z4));
Data;
//xdata        ydata
0.0580000000000000        0.983870967741936
0.0710000000000000        0.967741935483871
0.0760000000000000        0.951612903225807
0.0790000000000000        0.935483870967742
0.0830000000000000        0.919354838709677
....

均方差(RMSE):0.0219986879583782

残差平方和(SSE):0.0300044208571858

相关系数(R): 0.997096801446503

相关系数之平方(R^2): 0.994202031454848

确定系数(DC): 0.994191181598297

卡方系数(Chi-Square): 0.0586246925239279

F统计(F-Statistic): 2453.16672248202

参数 最佳估算

---------- -------------

z1 -1.41618646065971

z2 4.78561688232175

z3 -1.74873503367802

z4 0.839853042838169

z5 -1.42063299481894