2D Weighted Polynomial Fitting and Evaluation

Two scripts: polyfitweighted2 fits 2D data with weights, and polyval2 evaluates the 2D polynomial

Description

polyfitweighted2.m and polyval2.m
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polyfitweighted2.m: Find a least-squares fit of 2D data z(x,y) with an n th order polynomial, weighted by w(x,y).

polyval2.m: Evaluate 2D polynomial produced by polyfitweighted2.m.

Usage polyfitweighted2
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P = polyfitweighted2(X,Y,Z,N,W) finds the coefficients of a polynomial P(X,Y) of degree N that fits the data Z best in a least-squares sense. P is a row vector of length (N+1)*(N+2)/2 containing the polynomial coefficients in ascending powers, 0th order first.

 P = [p00 p10 p01 p20 p11 p02 p30 p21 p12 p03...]

where pNM is the polynomial coefficient of the Nth power of X times the Mth power of Y.

based on polyfit.m by The Mathworks Inc.

For more information see HTML-published M-file included.

Note: P is not in the format of standard Matlab 1D polynomials. Use polval2.m to evaluate the polynomial in this format, at given values of x,y.

Usage polyval2
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Z = POLYVAL2(P,X,Y) returns the value of a 2D polynomial P evaluated at (X,Y). P is a vector of length (N+1)*(N+2)/2 containing the polynomial coefficients in ascending powers as above.

• Acknowledgements: This submission has inspired the following:; 2D polynomial fitting with SVD
• MATLAB release: MATLAB 7.3 (R2006b)

[Ron Abileah]

 

[Eric Lin]

Thank you!

[Feng Liu]

Good work!

[Andrey Rubshtein]

Dear Salman, first of all thank you for your submission.
Nevertheless, I have a minor remark - In many applications (x,y,z) triples are not necessarily measured on a grid. For example: I have:
(1,1,10), (1,2,5) , (2,1,7) , but i have no clue what is the value of z at (2,2).

[Ryan Kruse]

This is great! Thanks!

I made a slight modification to deal with NaN values. I changed this:
x = x(:);
y = y(:);
z = z(:);
w = w(:);

to this:
x = x(~isnan(z));
y = y(~isnan(z));
z = z(~isnan(z));
w = w(~isnan(z));

[K E]

Very useful. Matlab should build it in.

[David Holdaway]

Very useful program, only a few issues with memory usage creating the very large grid of zeros length(x)*length(y) by length(p). Could possibly be improved with a catch routine to check if the memory usage is too high and split the (x,y) grid into 4 or 9 etc and apply the program multiple times.
This is just nitpicking though it's a very good program.

[milad babaei]

would somebody plz explain me on that those script algorithm??how does code work (does the least square )???