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\polyfun

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. 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*por

%

% 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)]

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 uniquedegree >= 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.'])

end

end

r = 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)

1、首先需要知道polyfit是多项式曲线拟合函数，polyval是多项式计算求值函数。

2、可以在命令行窗口中输入“help polyval”,按回车键之后，掘缺查看一下polyval函数的使用方铅散卖法。

3、在命令行窗口中输入“help polyfit”，可槐逗以查看polyfit函数的使用方法。

4、如果想求多项式p(x)=4*x^2+2*x+1在x=[5 6 7]的值，输入“

p = [4 2 1]

x=[5 6 7]

polyval(p,x)。

5、按回车键之后，可以看到多项式p(x)=4*x^2+2*x+1在x=[5 6 7]的值分别为111，157，211。

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