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2D Weighted Polynomial Fitting and Evaluation

by

 

19 Jan 2007 (Updated )

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

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File Information
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
---
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 file inspired 2 D Polynomial Fitting With Svd and Poly Val2 D And Poly Fit2 D.

MATLAB release MATLAB 7.3 (R2006b)
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Comments and Ratings (8)
03 Oct 2011 milad babaei

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

14 Jan 2011 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.

04 Aug 2009 K E

Very useful. Matlab should build it in.

25 Jun 2009 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));

16 Jun 2009 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).

12 Dec 2007 Feng Liu

Good work!

20 Nov 2007 Eric Lin

Thank you!

11 Feb 2007 Ron Abileah  

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