Matlab:拟合(2)

非线性最小二乘拟合：

解法一：用命令lsqcurvefit

 function f = curvefun(x, tdata)
 f = x() + x()*exp(0.02 * x() * tdata);
 %其中x() = a; x() = b; x() = c;

 %数据输入
 tdata = ::;
 cdata = 1e- * [4.54, 4.99, 5.35, 5.65, 5.90, 6.10, 6.26, 6.39, 6.50, 6.59];
 %设定预测值
 x0 = [0.2 0.05 0.05];
 %非线性拟合函数
 x = lsqcurvefit('curvefun', x0, tdata, cdata)
 %作图
 f = curvefun(x, tdata)
 plot(tdata, cdata, 'k+')
 hold on
 plot(tdata, f, 'r')

结果：
x =

-0.0074    0.0116    0.0118

f =

Columns 1 through 8

0.0044    0.0047    0.0050    0.0053    0.0056    0.0059    0.0062    0.0066

Columns 9 through 10

0.0069    0.0072

解法二：用命令lsqnonlin

 function f = curvefun1(x)
 %curvefun1的自变量是x，cdata和tdata是已知参数，故应将cdata,tdata的值卸载curvefun1中
 tdata = ::;
 cdata = 1e- * [4.54, 4.99, 5.35, 5.65, 5.90, 6.10, 6.26, 6.39, 6.50, 6.59];
 f = x() + x()*exp(0.02 * x() * tdata) - cdata;%注意

 tdata = ::;
 cdata = 1e- * [4.54, 4.99, 5.35, 5.65, 5.90, 6.10, 6.26, 6.39, 6.50, 6.59];
 %预测值
 x0 = [0.2 0.05 0.05];
 x = lsqnonlin('curvefun1', x0)
 f = curvefun1(x)
 plot(tdata, cdata, 'k+')
 hold on
 plot(tdata, f+cdata, 'r')

结果：

x =

-0.0074    0.0116    0.0118

f =

1.0e-003 *

Columns 1 through 8

-0.1168   -0.2835   -0.3534   -0.3564   -0.3022   -0.1908   -0.0320    0.1645

Columns 9 through 10

0.3888    0.6411