matlab polyfit源码,MATLAB的拟合函数polyfit 的程序代码是什么啊

polyfit函数的MATLAB程序代码如下：

function [p, S, mu] = polyfit(x, y, n)
%POLYFIT Fit polynomial to data.
%   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(X)
%   is a row vector of length N+1 containing the polynomial coefficients
%   in descending powers.
%
%   [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:
%      S.normr   -- 2-norm of the residual: norm(Y - PVAL)./sqrt(length(Y))
%      S.resid   -- vector of residuals:  Y - PVAL
%      S.df      -- degrees of freedom
%      S.normr^2 -- S.normr squared
%      S.R       -- the triangular factor from a QR decomposition of the
%                   Vandermonde matrix of X
%      S.coeff   -- vector of coefficients in a model that is orthogonal
%                   to the constant term:  X - repmat(mean(X),size(X,1),1)
%                   = Q*R,  Y - repmat(mean(Y),size(Y,1),1) = Q*[Rc;rest]
%                   where Rc is a vector of regression coefficients for
%                   the orthogonal polynomial terms, and rest is a vector
%                   of coefficients for the null space of X - ones(n,1)*[1
%                   mean(X)].
%
%   [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.
%
%   Class support for inputs X,Y:
%      float: double, single
%
%   See also POLY, POLYVAL, ROOTS, LSCOV, VANDER.

%   Copyright 1984-2004 The MathWorks, Inc.
%   $Revision: 5.26.4.8 $  $Date: 2004/12/06 16:38:03 $

if ~isequal(size(x),size(y))
    error('X and Y vectors must be the same size.')
end

x = x(:);
y = y(:);

if nargin < 3, n = 1; end

if n > length(x)-1
    error('N must be less than the length of X.')
end

if length(x) ~= length(y)
    error('X and Y vectors must be the same length.')
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

% Compute coefficients.
[Q,R] = qr(V,0);
ws = warning('off','MATLAB:rankDeficientMatrix');
p = R\(Q'*y);    % Same as p = V\y;
warning(ws);

% Remove trailing zeros.
p = p.'; % Polynomial coefficients are row vectors by convention.
if length(p) > n
    p = p(1:n+1);
end

% Compute error structure vector.
if nargout > 1
    r = y - V*p.';
    normr = norm(r);
    df = length(y) - (n+1);
    S.normr = normr;
    S.resid = r;
    S.df = df;
    S.normr2 = normr^2;
    S.R = R;
    S.coeff = p;
end

% Undo scaling and centering.
if nargout > 2
    mu = [mean(x); std(x)];
else
    mu = [];
end
if length(p) > 1
    p = polyfix(p,mu);
end

% ------------------------------------------------------------------
function c = polyfix(c,mu)
%POLYFIX  Fix polynomial coefficients for new data.
%   C = POLYFIX(C,MU) fixes the polynomial coefficients C for a
%   change of variable XHAT = (X-MU(1))/MU(2).  MU(1) is the mean of
%   the original data and MU(2) is the standard deviation.  C is a
%   row vector of polynomial coefficients in descending powers.

if isempty(c), return, end
m = length(c) - 1;
if m == 0, return, end

c = c(:);
% Scale coefficients.
scal = cumprod([1 repmat(mu(2),1,m)]./[1:m+1]);
c = c.*scal;

% Shift coefficients.
c(1:m) = c(1:m) - c(m+1:-1:2).'*mu(1)./mu(2).^(1:m);

% Remove scale factors.
c = c./mu(2).^max(0,(0:m));

c = c.';  % Polynomial coefficients are row vectors by convention.