拟合练习:
function f = curvefun(x, tdata)
f = (x()*x()*x()) / (x()-x()) * ( exp(-x()*tdata)/(x()-x()) + exp(-x()*tdata)/(x()-x()) - (/(x()-x())+/(x()-x()))*exp(-x()*tdata) );
%数据输入
tdata = [0.25 0.5 0.75 1.5 2.5 3.5 4.5 ];
vdata = [ ];
%拟定估计值
x0 = [ ];
x = lsqcurvefit('curvefun', x0, tdata, vdata)
f = curvefun(x, tdata)
%作散点图和你和图
plot(tdata, vdata, 'k+')
hold on
plot(tdata, f, 'r')
结果: x =
256.2035 0.1512 0.2422 1.9506
f =
Columns 1 through 8
39.7501 62.2565 74.2700 79.9309 81.3616 77.1765 71.3312 65.2712
Columns 9 through 16
59.5001 54.1706 49.3072 44.8893 37.2494 30.9669 25.7925 21.5224
Columns 17 through 23
17.9914 15.0658 12.6370 10.6167 8.9330 7.5272 6.3515
方法一：解超定方程组
x = :0.1:;
y = [-0.447 1.978 3.28 6.16 7.08 7.34 7.66 9.56 9.48 9.30 11.2];
R = [(x.^)', x', ones(, )];
A = R\y'
结果：
A =
-9.8108 20.1293 -0.0317
即为系数a1, a2, a3
方法二：用多项式拟合
x = :0.1:;
y = [-0.447 1.978 3.28 6.16 7.08 7.34 7.66 9.56 9.48 9.30 11.2];
%二次多项式拟合
A = polyfit(x, y, )
%计算拟合之后的原始数据点的函数值
Y = polyval(A, x);
%作出数据点和拟合曲线的图形
plot(x, y, 'k+')
hold on
plot(x, Y, 'r')
结果：
A =
-9.8108 20.1293 -0.0317
拟合曲线