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自定义非线性人口普查拟合

此示例说明如何对人口普查数据进行自定义方程拟合,指定边界、系数和问题相关参数。

加载 census.mat 中的数据并绘图:

load census
plot(cdate,pop,'o')
hold on

为自定义非线性模型 y = a(x-b)n 创建一个拟合 options 结构体和一个 fittype 对象,其中 a 和 b 是系数,n 是与问题相关的参数。有关与问题相关的参数的更多详细信息,请参阅 fittype 函数页。

s = fitoptions('Method','NonlinearLeastSquares',...
               'Lower',[0,0],...
               'Upper',[Inf,max(cdate)],...
               'Startpoint',[1 1]);
f = fittype('a*(x-b)^n','problem','n','options',s);

使用拟合选项和值 n = 2 拟合数据:

[c2,gof2] = fit(cdate,pop,f,'problem',2)
c2 = 
     General model:
     c2(x) = a*(x-b)^n
     Coefficients (with 95% confidence bounds):
       a =    0.006092  (0.005743, 0.006441)
       b =        1789  (1784, 1793)
     Problem parameters:
       n =           2
gof2 = struct with fields:
           sse: 246.1543
       rsquare: 0.9980
           dfe: 19
    adjrsquare: 0.9979
          rmse: 3.5994

使用拟合选项和值 n = 3 拟合数据:

[c3,gof3] = fit(cdate,pop,f,'problem',3)
c3 = 
     General model:
     c3(x) = a*(x-b)^n
     Coefficients (with 95% confidence bounds):
       a =   1.359e-05  (1.245e-05, 1.474e-05)
       b =        1725  (1718, 1731)
     Problem parameters:
       n =           3
gof3 = struct with fields:
           sse: 232.0058
       rsquare: 0.9981
           dfe: 19
    adjrsquare: 0.9980
          rmse: 3.4944

绘制拟合结果和数据:

plot(c2,'m')
plot(c3,'c')
legend('data','fit with n=2','fit with n=3')