关于非线形最小二乘法求解。
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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？
采纳的回答
bidag
2022-11-20
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
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