在matlab中使用矩阵拟合2维函数

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最近要解决用2维矩阵拟合2维函数的问题，貌似在中文网站中没有找到方法，最后在stack overflow才问到了答案，解答如下。

假设有5*5数组：

d=    [0.0177104427823448,0.00246661459209512,0.0399831543374395,0.0615494164555707,0.0476204124707652;0.0275276152854314,0.0219153841813084,0.0581144391404502,0.144890028400954,0.157839631316098;0.0622883972729130,0.0716157303159909,0.245482781674067,0.123999612575059,0.177495187746408;0.0200735764542146,0.0573087934038160,0.0636451189717613,0.0160810084568415,0.0484992279558924;0.0185180386159227,0.00841167700273800,0.0372017422726281,0.0173721095082637,0.0459520362441099]

想用最小均方法拟合2维函数：

r = alfa*sin(pi*(n1+delta1))*sin(pi*(n2+delta2)) / (25*sin(pi/5*(n1+delta1))*sin(pi/5*(n2+delta2)))

可以在matlab中这样实现：

[n,m]=size(d);%assumes that d is a n x m matrix[X,Y]=meshgrid(1:n,1:m);%your x-y coordinatesx(:,1)=X(:); % x= first columnx(:,2)=Y(:); % y= second columnf=d(:); % your data f(x,y) (in column vector)%--- now define the function in terms of x%--- where you use x(:,1)=X and x(:,2)=Yfun = @(c,x) c(1)*sin(pi*(x(:,1)+c(2))).*sin(pi*(x(:,2)+c(3))) ./ (25*sin(pi/5*(x(:,1)+c(2))).*sin(pi/5*(x(:,2)+c(3))));%--- now solve with lsqcurvefitoptions=optimset('TolX',1e-6);c0=[1 0 0];%start-guess herecc=lsqcurvefit(fun,c0,x,f,[],[],options);Ifit=fun(cc,x); Ifit=reshape(Ifit,[n m]);%fitting data reshaped as matrixsurf(X,Y,Ifit);hold on;plot3(X, Y, dataArray);