Fitting a surface over a mxn matrix

2011 10 3
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Hi,
I have a function u(x,y) which I wish to fit using the 'poly11' option within the 'fit' funtion The problem is that x, y, and u are all m x n matrices with m not equal to n. I can fit the data using the sftool but I would like to do it in a programmatic way. Any help will be greatly appreciated.
Thanks, Andy

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Walter Roberson
Walter Roberson 2011-10-3

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Poking around a bit, poly11 appears to fit a polynomial of the form a*x + b*y + c. I could be wrong on that, perhaps there is an x*y term as well, but my interpretation of the documentation is that there is no x*y term.
If your equation to fit is indeed of the form a * x + b * y + c, then it can be rewritten as being of the form
U = [x y 1] * [a;b;c]
where [a;b;c] are unknowns to determine.
This can then be rewritten as a simple mldivide ('\') operation:
U(:) \ [x(:) y(:) ones(numel(x),1)]
or some close relative thereof (I keep forgetting the order of the components)

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Andres
Andres 2011-10-3
In fact poly11 fits a function of the form f(x,y) = a + b*x + c*y. By using your method wouldn't I get the coefficients a, b, and c which are each m x n matrices since x and y are both m x n?
Walter Roberson
Walter Roberson 2011-10-3
Notice the (:) that I used: that turns the arrays in to column vectors. U(:) will be an n*m x 1 column vector, the part to the right will be an n*m x 3 array, and the result of fitting will be a 3 x 1 array (provided I got the terms in the right order: see mldivide for examples.)

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