MATLAB: Fit surface from Two vectors and a matrix

cftoolfitfit surfacepolyfitsurf

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

Best Answer

[X,Y]=ndgrid(1:10,1:7);
   fit([X(:),Y(:)],z(:),'fittype')

Related Solutions

MATLAB: How to get fitting parameter in sftool.

The generated code should look something like this:

%%Initialization.
% Convert all inputs to column vectors.
x = x(:);
y = y(:);
z = z(:);
%%Fit: 'untitled fit 1'.
ft = fittype( 'poly11' );
opts = fitoptions( ft );
opts.Weights = zeros(1,0);
[fitresult, gof] = fit( [x, y], z, ft, opts );
% Plot fit with data.
figure( 'Name', 'untitled fit 1' );
h = plot( fitresult, [x, y], z );
legend( h, 'untitled fit 1', 'z vs. x, y', 'Location', 'NorthEast' );
% Label axes
xlabel( 'x' );
ylabel( 'y' );
zlabel( 'z' );
grid on

And fitting parameters are stored in fitresult:

fitresult.p00
fitresult.p01
fitresult.p10

MATLAB: How to plot 3d line on fit function

You need to use hold on. For example,

x  = rand(100,1);
y  = rand(100,1);
z  = x.^2 + y;
sf = fit([x, y],z,'poly23')
plot(sf); hold on;
X=x(10:15)
Y=y(10:15)
Z=z(10:15)
plot3(X,Y,Z,'mo')
grid on;

Best Answer

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MATLAB: How to get fitting parameter in sftool.

MATLAB: How to plot 3d line on fit function

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