MATLAB怎么求二次曲线拟合系数 运用MATLAB拟合二次曲线后，怎么做误差分析？
\u5982\u4f55\u8fd0\u7528MATLAB\u62df\u5408\u4e8c\u6b21\u66f2\u7ebf\u65b9\u6cd51\uff1a
x=0:0.1:1;
y=[-0.447 1.978 3.28 6.16 7.08 7.34 7.66 9.56 9.48 9.30 11.2];
A=polyfit(x,y,2)
z=polyval(A,x);
plot(x,y,'k+',x,z,'r') %\u4f5c\u51fa\u6570\u636e\u70b9\u548c\u62df\u5408\u66f2\u7ebf\u7684\u56fe\u5f62
\u4ee5\u4e0a\u53ea\u662f\u7ebf\u6027\u7684\u6700\u5c0f\u4e8c\u4e58\u62df\u5408\u3002
\u65b9\u6cd52\uff1a\u76f4\u63a5\u7528matlab\u7684CFtool\u5de5\u5177
\u5229\u7528cftool\u66f2\u7ebf\u62df\u5408\u5de5\u5177\u7bb1\uff1a
Linear model Poly2:
f(x) = p1*x^2 + p2*x + p3
Coefficients (with 95% confidence bounds):
p1 = -0.03816 (-0.05458, -0.02173)
p2 = 13.56 (12.62, 14.51)
p3 = -1.28 (-8.511, 5.952)
Goodness of fit:
SSE: 248
R-square: 0.9993
Adjusted R-square: 0.9992
RMSE: 5.952
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1.\u8bef\u5dee\u5e73\u65b9\u548c\uff08SSE\uff09
2. R-Square\uff08\u590d\u76f8\u5173\u7cfb\u6570\u6216\u590d\u6d4b\u5b9a\u7cfb\u6570\uff09
3. Adjusted R-Square\uff08\u8c03\u6574\u81ea\u7531\u5ea6\u590d\u76f8\u5173\u7cfb\u6570\uff09
4.Root mearn squared error(RMSE),(\u5747\u65b9\u6839\u8bef\u5dee)
clear;clc
x=rand(1,12)%自己改
y=rand(1,12)%自己改
z=3+5*x+7*y+11*x.^2+13*y.^2+17*x.*y+rand(1,12)%自己改
%%以下为最小二乘法拟合二次曲面系数
A=z/[ones(size(z));x;y;x.^2;y.^2;x.*y];
s=sprintf('F(x,y)=%.5g%+.5gx%+.5gy%+.5gx^2%+.5gy^2%+.5gxy',A);
disp(s)
%%以下为图形验证
[X,Y]=meshgrid(linspace(min(x),max(x)),linspace(min(y),max(y)));
surf(X,Y,A(1)+A(2)*X+A(3)*Y+A(4)*X.^2+A(5)*Y.^2+A(6)*X.*Y);
shading interp
alpha .5
hold on
plot3(x,y,z,'o');
title(['$',s,'$'],'interpreter','latex')
根据问题要求，可用regress（）函数来拟合ai系数。
x=[。。。]';
y=[。。。]';
n=length(x);
X=[ones(n,1) x y x.^2 y.^2 x.*y];
y=zeros(n,1);
a= regress(y,X)
《看不透》：真阿绣，假阿绣，痴情郎儿看不透；多情郎，好糊涂，落得笑骂留千秋。
你要求的是xy的关系还是F(x,y)、x、y的关系？
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绛旓細>> plot(c,i.^2,'r.',c,polyval(f,c))
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绛旓細clear;clc x=rand(1,12)%鑷繁鏀 y=rand(1,12)%鑷繁鏀 z=3+5*x+7*y+11*x.^2+13*y.^2+17*x.*y+rand(1,12)%鑷繁鏀 浠ヤ笅涓烘渶灏忎簩涔樻硶鎷熷悎浜屾鏇查潰绯绘暟 A=z/[ones(size(z));x;y;x.^2;y.^2;x.*y];s=sprintf('F(x,y)=%.5g%+.5gx%+.5gy%+.5gx^2%+.5gy^...
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绛旓細81,32.38,37.99,40.81,43.62,46.45,49.28,52.13,54.88,57.83,60.84,63.57,66.40];a = polyfit(x,y,2);%杩涜2娆℃嫙鍚锛宎鏄椤瑰紡鍓嶉潰鐨勫笺俛1 = polyval(a,x);%寰楀埌鎷熷悎鍚庣殑鏂板 plot(x,a1,'r');grid on 鎴戣瘯杩囦簡锛岃兘鐢紝涓嶇煡閬撴槸涓嶆槸浣犺鐨勩傝繖鏄浜屾鎷熷悎鏇茬嚎 ...
绛旓細y=a+b.*x.^2 ;%浜х敓y plot(x,y,'o')%鐢诲浘锛岃摑鑹插湀鍦 pp=polyfit(x,y,2)%2娆℃嫙鍚锛宲p涓哄洖褰掔郴鏁 xx=-10:0.1:10; %鍐嶄骇鐢熸柊鐨剎x yy=polyval(pp,xx);%閫氳繃鍥炲綊绯绘暟鍜寈x寰楀埌yy hold on% 鍦ㄥ悓涓涓湴鏂圭敾鍥 plot(xx,yy,'r')%鐢ㄥ洖褰掔郴鏁板拰xx浣滃浘锛岀孩鑹 缁撴灉锛歱p = 5.4762 ...
绛旓細A=polyfit(x,y,3)z=polyval(A,x)plot(x,y,'k+',x,z,'r') %浣滃嚭鏁版嵁鐐瑰拰鎷熷悎鏇茬嚎鐨勫浘褰紝绾挎х殑鏈灏忎簩涔樻嫙鍚堛倅=a(x-h)²+k(a鈮0,a銆乭銆乲涓哄父鏁),椤剁偣鍧愭爣涓猴紙h,k) [4] 锛屽绉拌酱涓虹洿绾縳=h锛岄《鐐圭殑浣嶇疆鐗瑰緛鍜屽浘鍍忕殑寮鍙ｆ柟鍚戜笌鍑芥暟y=ax²鐨勫浘鍍忕浉鍚岋紝褰搙=h鏃...
绛旓細鎹㈠厓娉 a=0:0.01:2*pi;p=1.94/(1.1*sqrt(0.7225)).*sin(a);q=1.94/1.1.*cos(a)-1/1.1;plot(q,p,'-')
