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Matlab polyfit函数程序.pdf
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2021-09-14
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function [p,S,mu] = polyfit(x,y,n)
%POLYFIT Fit polynomial to data.
% 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.
% 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:
%
% 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:
%
% 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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