Fitting to 4D data
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The fit() function allows fitting a surface to 3D data, where regularly spaced x,y data values specify a "grid" location and the z value specifies a surface "height". The fitted surface can be expressed as a polynomial of up to degree 5 in x and y.
Is there a means of fitting a model (polynomial or otherwise) to 4D data? In this case, the x,y,z data values specify a location (regularly spaced, within a unit cube for example), and w specifies a value at that location. Such data expresses a 3D "field" rather than a surface.
Thanks, mitch
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Matt J
2023-9-13
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Do you know of any multi-dimensional fitting examples I can look at?
Here's an example I just made up. The unknown parameter vector to be recovered is w:
xyz=rand(100,3); %fake x,y,z data
w=[1,2,3]; %ground truth parameters
F=vecnorm(xyz.*w,2,2); %fake dependent data
F=F+randn(size(F))*0.05; %add noise
wfit=lsqcurvefit(@modelFcn,[1,1,1], xyz,F)
function Fpred=modelFcn(w,xyz)
Fpred=vecnorm(xyz.*w,2,2);
end
Anyway, the point is that lsqcurvefit doesn't care about the dimensions of the data xyz and F. It only cares that your modelFcn returns a prediction Fpred of F as an array the same size as F.
Mitch
2023-9-14
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