# 2D Weighted Polynomial Fitting and Evaluation 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Sep 14, 2007

Downloads : 10

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## polyfitweighted2.m: Find a least-squares fit of 2D ...

weighted. 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

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 format 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).

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

Usage polyfitweighted2

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 format 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).

**2D Weighted Polynomial Fitting and Evaluation 1.0 scripting tags:**coefficients, polynomial, powers, order, polynomial fitting, length, weighted, leastsquares, ascending, format, statistics probability.

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