2d polynomial fitting to table data MATLAB

Question

I am trying to use 2D polynomial fitting for my table data, my data format is exactly like the link below: http://www.mathworks.de/help/toolbox/curvefit/brx2ldg-1.html#bso46rp-1

I mean I have vector X with length n, Y with length m and m*n Matrix Z, I would like to fit 5 degree 2d polynomial to my data,

I am wondering that is there any syntax in MATLAB for solving this problem? like SFIT command in IDL, http://star.pst.qub.ac.uk/idl/SFIT.html

I have cftool and sftool, but it seems that they don't work for this purpose or most probably I don't know how to employ them.

and I know that there some m.file which people share in MATLAB Mathworks file exchange, please if you know one works properly, suggest me.

I'd appreciate any help and comment.

Answer 1

You can use polyfitn from file exchange and re-format your data in order to have 3 MxN x,y,z vectors.

Example:

Assume you have a table data of the form

N = 100; M = 80;
x = linspace(0, 1, M);
y = linspace(0, 1, N).';
z = bsxfun(@franke, x, y);

Create meshgrid for x, and y instead

N = 100; M = 80;
[x, y] = meshgrid(0:1:N, 0:1:M);
z = bsxfun(@franke, x, y);

(Note that unique(x) and unique(y) will give you the original linspace values of your table rows and columns.)

Use polyfitn to get the 5-degree polynomial coefficients

p = polyfitn([x(:),y(:)], z(:), 5);

You can additionally convert the result into a symbolic form to view the polynomial using the provided polyn2sym(p)

>> pretty(polyn2sym(p))

                      5                           4                             4                         3   2
     90264379051097 X1         2537627280433653 X1  X2       7778045812403061 X1       6982058230382053 X1  X2
- ------------------------- - -------------------------- + ------------------------ - -------------------------- + ...
  2417851639229258349412352   38685626227668133590597632   604462909807314587353088   77371252455336267181195264