最小二乘法拟合曲面。

代码如下

x=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8];

x2=x.^2;

y=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6];

y2=y.^2;

z=[0.85 0.85 0.85 0.861 0.87 0.885 0.893 0.925 0.948 0.971 0.993 1.016 1.035 1.062 1.085 1.106 1.13 1.148

0.855 0.855 0.855 0.864 0.874 0.888 0.907 0.93 0.954 0.977 1.001 1.026 1.05 1.074 1.096 1.12 1.142 1.159

0.864 0.864 0.864 0.868 0.879 0.884 0.913 0.936 0.961 0.986 1.011 1.037 1.061 1.085 1.11 1.132 1.152 1.169

0.873 0.873 0.873 0.874 0.885 0.901 0.92 0.945 0.969 0.995 1.021 1.047 1.072 1.097 1.122 1.144 1.163 1.18

0.882 0.882 0.882 0.883 0.894 0.908 0.929 0.959 0.978 1.005 1.022 1.057 1.083 1.109 1.133 1.154 1.173 1.188

0.892 0.892 0.892 0.894 0.904 0.92 0.941 0.964 0.99 1.016 1.043 1.067 1.094 1.12 1.143 1.164 1.182 1.196

0.901 0.901 0.901 0.906 0.916 0.93 0.952 0.975 1 1.026 1.052 1.077 1.104 1.129 1.152 1.171 1.188 1.203

0.911 0.911 0.911 0.916 0.926 0.942 0.962 0.985 1.01 1.036 1.062 1.086 1.112 1.136 1.158 1.176 1.194 1.209

0.921 0.921 0.921 0.928 0.935 0.952 0.972 0.996 1.021 1.046 1.072 1.096 1.12 1.143 1.163 1.181 1.199 1.214

0.929 0.929 0.931 0.936 0.946 0.962 0.982 1.006 1.031 1.056 1.081 1.106 1.128 1.15 1.169 1.187 1.204 1.22

0.935 0.937 0.94 0.946 0.956 0.972 0.993 1.017 1.042 1.066 1.092 1.116 1.138 1.159 1.177 1.195 1.212 1.228

0.941 0.944 0.949 0.956 0.966 0.982 1.004 1.028 1.053 1.077 1.103 1.126 1.148 1.168 1.186 1.204 1.222 1.237

0.946 0.951 0.957 0.966 0.977 0.993 1.016 1.04 1.063 1.089 1.114 1.136 1.158 1.178 1.196 1.214 1.232 1.25

0.953 0.959 0.967 0.975 0.986 1.005 1.028 1.05 1.075 1.101 1.124 1.147 1.168 1.187 1.206 1.224 1.244 1.266

0.961 0.988 0.975 0.984 0.997 1.018 1.04 1.061 1.086 1.111 1.134 1.156 1.176 1.196 1.215 1.235 1.258 1.277

0.972 0.978 0.985 0.994 1.01 1.03 1.05 1.073 1.096 1.119 1.142 1.164 1.184 1.204 1.224 1.245 1.268 1.289

];

n=length(x); X=[x2 y2 ones(n,1)];

a = regress(z,X);

c=a(3);

b=a(2);

a=a(1);

错误显示

错误使用 horzcat

串联的矩阵的维度不一致。

出错 zxecfnh (line 22)

n=length(x); X=[x2 y2 ones(n,1)];

求大神解答~

Answer 1

[sedor]

也许可用下列模型拟合(y=y-.8)：

fx=(b(1)+b(2)*x1+b(3)*x2+b(4)*x1.^2+b(5)*x2.^2+b(6)*x1.*x2+b(7)*x1.^3+b(8)*x2.^3+b(9)*x1.*x2.^2+b(10)*x1.^2.*x2)./(1+b(11)*x1+b(12)*x2+b(13)*x1.^2+b(14)*x2.^2);

b =[0.04592294559 -0.03901414484 0.068398893 0.09567766717 -0.04613171904 -0.1331041884 0.1423630308 0.03154915609 0.06671164437 0.06088959563 -0.8034532625 -0.6256762205 1.066828227 0.3648534856]

RSS = 0.0028752156241

MSe = 1.0493e-05

R^2 = 0.99922