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Matlab polyfit函数程序.docx
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function [p,S,mu] = polyfit(x,y,n)
%POLYFIT Fit polynomial to data.
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P = POLYFIT(X,Y,N) finds the coefficients of a polynomial P(X) of
degree N that fits the data Y best in a least-squares sense. P is a
row vector of length N+1 containing the polynomial coefficients in
descending powers, P(1)*X^N + P(2)*X^(N-1) +...+ P(N)*X + P(N+1).
[P,S] = POLYFIT(X,Y,N) returns the polynomial coefficients P and a
structure S for use with POLYVAL to obtain error estimates for
predictions. Scontains fields for the triangular factor (R) from a QR
decomposition of the Vandermonde matrix of X, the degrees of freedom
(df), and the norm of the residuals (normr). If the data Y are random,
an estimate of the covariance matrix of P is (Rinv*Rinv')*normr^2/df,
where Rinv is the inverse of R.
[P,S,MU] = POLYFIT(X,Y,N) finds the coefficients of a polynomial in
XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X). This
centering and scaling transformation improves the numerical properties
of both the polynomial and the fitting algorithm.
Warning messages result if N is >= length(X), if X has repeated, or
nearly repeated, points, or if X might need centering and scaling.
Class support for inputs X,Y:
float: double, single
See also POLY, POLYVAL, ROOTS.
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Copyright 1984-2005 The MathWorks, Inc.
$Revision: 5.17.4.7 $ $Date: 2005/12/12 23:26:23 $
% The regression problem is formulated in matrix format as:
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y = V*p
or
3 2
y = [x x x 1] [p3
p2
p1
p0]
% where the vector p contains the coefficients to be found. For a
% 7th order polynomial, matrix V would be:
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% V = [x.^7 x.^6 x.^5 x.^4 x.^3 x.^2 x ones(size(x))];
if ~isequal(size(x),size(y))
error('MATLAB:polyfit:XYSizeMismatch',...
'X and Y vectors must be the same size.')
end
x = x(:);
y = y(:);
if nargout > 2
mu = [mean(x); std(x)];
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