MATLAB的拟合函数polyfit 的程序代码是什么啊

MATLAB的拟合函数polyfit 的程序代码是什么啊

polyfit.m 在MATLAB安装目录下 \toolbox\matlab\polyfunfunction [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. S contains 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 1984-2004 The MathWorks, Inc.% $Revision: 5.17.4.5 $ $Date: 2004/07/05 17:01:37 $% 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.')endx = x(:);y = y(:);if nargout > 2 mu = [mean(x); std(x)]; x = (x - mu(1))/mu(2);end% Construct Vandermonde matrix.V(:,n+1) = ones(length(x),1,class(x));for j = n:-1:1 V(:,j) = x.*V(:,j+1);end% Solve least squares problem.[Q,R] = qr(V,0);ws = warning('off','all'); p = R\(Q'*y); % Same as p = V\y;warning(ws);if size(R,2) > size(R,1) warning('MATLAB:polyfit:PolyNotUnique', ... 'Polynomial is not unique; degree >= number of data points.')elseif condest(R) > 1.0e10 if nargout > 2 warning('MATLAB:polyfit:RepeatedPoints', ... 'Polynomial is badly conditioned. Remove repeated data points.') else warning('MATLAB:polyfit:RepeatedPointsOrRescale', ... ['Polynomial is badly conditioned. Remove repeated data points\n' ... ' or try centering and scaling as described in HELP POLYFIT.']) endendr = y - V*p;p = p.'; % Polynomial coefficients are row vectors by convention.% S is a structure containing three elements: the triangular factor from a% QR decomposition of the Vandermonde matrix, the degrees of freedom and% the norm of the residuals.S.R = R;S.df = length(y) - (n+1);S.normr = norm(r);