Fit surface from Two vectors and a matrix

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Drew Mitchell
Drew Mitchell 2016-2-11
编辑： Matt J 2016-2-12
I have two vectors (of different length) that correspond to x and y locations in the x-y plane. I also have the corresponding matrix, z, that gives the hight above the x-y plane for all combinations of x and y( If size(x)=10,1 size(y)=7,1 then size(z)=10,7). I can plot a surface of the data by using surf(x,y,z) and it will work. What I want to do is to be able to fit this surface with a polynomial function of x and y. I am attempting to use fit([x,y],z,'fittype') however this function takes x y and z in the form of vectors only. How do I get the polynomial surface fit from the data I have?
Thanks

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Matt J
Matt J 2016-2-11
编辑：Matt J 2016-2-11
[X,Y]=ndgrid(1:10,1:7);
fit([X(:),Y(:)],z(:),'fittype')
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Drew Mitchell
Drew Mitchell 2016-2-12
That was what I needed thanks! Is it possible to get a higher order than poly55? I.e. 5th order for x and 5th order for y? So something 9th order for x and 8th order for y. I get an error when I attempt to go to a greater order than 55. Im atempting to use fit([x y],z,'poly98) Thanks again
Drew
Matt J
Matt J 2016-2-12
编辑：Matt J 2016-2-12
I expect that that will be a highly ill-conditioned fitting problem. However, if the Curve Fitting Toolbox won't even attempt it for you, then one of these might:
http://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn
http://www.mathworks.com/matlabcentral/fileexchange/13719-2d-weighted-polynomial-fitting-and-evaluation

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