2D Weighted Polynomial Fitting and Evaluation

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

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.