关于polyfit-函数使用介绍

1、关于polyfit 函数使用介绍文章来源：不详 作者：佚名 -该文章讲述了关于polyfit 函数使用介绍. polyfit函数的使用 MATLAB软件提供了基本的曲线拟合函数的命令 多项式函数拟合：P=polyfit(x,y,n) 其中n表示多项式的最高阶数，x，y为将要拟合的数据，它是用数组的方式输入输出参数P为拟合多项式 P(1)*XN + P(2)*X(N-1) +.+ P(N)*X + P(N+1).的系数 多项式在x处的值y可用下面程序计算 y=polyval(P,x,m) 线性：m=1, 二次：m=2, polyfit的输出是一个多项式系数的行向量。为了计算在xi数据点的多项式值

2、，调用MATLAB的函数polyval。 例： x=0:0.1:1; y=-0.447 1.978 3.28 6.16 7.08 7.34 7.66 9.56 9.48 9.30 11.2; A=polyfit(x,y,2) Z=polyval(A,x); Plot(x,y,r*,x,z,b) polyfit不能保证你每次都能得到最优解，math的答案是使用数值计算。个人认为，对于这种非线性的曲线，尽量不要使用ployfit, ployfit多项式抑合适合线性方程！ 用polyfit（）函数去拟合这么复杂的曲线不太合适，polyfit（）函数对于数据遵循多项式分布是比较好的，一般来说，利用po

3、lyfit（）函数拟合的阶数不要超过5阶。如果是不需要得到拟合曲线的函数，只是把这些点利用一些光滑曲线连接，建议使用三次样条函数spline（）进行插值即可。帮助：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 c

4、oefficients in descending powers, P(1)*XN + 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 Van

5、dermonde 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)*normr2/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

6、(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 sca

7、ling. Class support for inputs X,Y: float: double, singlepolyfit.m 在MATLAB安装目录下 toolboxmatlabpolyfunfunction 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

8、% row vector of length N+1 containing the polynomial coefficients in% descending powers, P(1)*XN + 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 th

9、e 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)*normr2/df,% where Rinv is the inverse of R.% P,S,MU = POLYFIT(X,Y,

10、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 repeate

11、d, 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

12、 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

13、 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 = Vy;warni

14、ng(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 pointsn . 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 structu