如何寻找最好的拟合曲线？以及matlab中Polyfit的用法？...

优质解答

【1】用cftool

>>cftool

回车,出现一个对话框.【1】Data输入相应的x,y,然后create data set；【2】fitting,选择提供的各种模型,逐个试试,总能找到残差最小的,相关系数最大的一种模型.

【2】给个例子.

clc;clear

x=-1:0.1:1

for k=1:length(x)

y(k)=x(k)^2+0.1*rand

end

[p,s]=polyfit(x,y,2)

s.R

plot(x,y,'o',x,polyval(p,x))

结果：

p =

1.0072 0.0091 0.0439

s =

R:[3x3 double]

df:18

normr:0.1153

ans =

-2.2509 -0.0000 -3.4208

0 2.7749 0.0000

0 0 -3.0492

s是个结构数组.

S contains fields for the triangular factor (R) from a QR decomposition of the Vandermonde matrix 【范德蒙特矩阵】of X,the degrees of freedom (df)【自由度】,and the norm of the residuals (normr)【范数】.

其他类似问题

问题1：用matlab求最小二乘法（polyfit）曲线拟合用最小二乘（polyfit）曲线拟合下列数据,并画出多项式曲线x 0.5 1 1.5 2 2.5 3y 1.75 2.45 3.81 4.8 8 8.6 用matlab要怎么做啊,求程序解法[数学科目]

clc

%原数据节点

x=[0.5 1 1.5 2 2.5 3];

y=[1.75 2.45 3.81 4.8 8 8.6];

plot(x,y,'*');

hold on;

%求最小二乘意义下拟合多项式的系数

n=3;%待拟合多项式的次数；

p=polyfit(x,y,n);

%新的插值节点

xx=0:0.01:3;

yy=polyval(p,xx);

plot(xx,yy);

你可以再Matlab帮助文件下,搜索polyfit和polyval这两个命令的含义和用法.

这样,这个问题是很容易实现的.

问题2：matlab中polyfit与polyval的功能?

polyfit用于多项式曲线拟合

p=polyfit(x,y,m)

其中,x,y为已知数据点向量,分别表示横,纵坐标,m为拟合多项式的次数,结果返回m次拟合多项式系数,从高次到低次存放在向量p中.

y0=polyval(p,x0)

可求得多项式在x0处的值y0

问题3：matlab polyfit拟合出来的函数怎样分析其精确程度?用误差分析怎么算?结果具体怎样分析?

Year=[1625 1830 1930 1960 1974 1987 1999];

Population=[5 10 20 30 40 50 60];

Year1=1625:2020;

Year2=2000:2020;

[P2 S2]=polyfit(Year,Population,3);

Population1=polyval(P2,Year1);

Population2=polyval(P2,Year2);

plot(Year,Population,'*',Year2,Population2,'X',Year1,Population1);

这里的S2是误差的大小~

问题4：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*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)];

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.'])

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);

问题5：matlab中使用polyfit函数报错试用了几个例子,执行polyfit函数时无一例外报错：Attempt to execute SCRIPT polyfit as a function.不知道有没有人可以指点下这错误到底是因为什么?matlab使用一直正常,执行其

>> x=[2138 2150 2177 2204 2241]

y=[825 834 853 873 900]

x =

2138 2150 2177 2204 2241

y =

825 834 853 873 900

>> p1=polyfit(x,y,1)

p1 =

0.7271 -729.4239

%%---------------------

你的语句没有问题.检查一下你是不是自己编了一个polyfit.m的脚本文件,删掉它.或者改个名字.

open polyfit试试