added

git-svn-id: http://moon:8086/svn/matlab/trunk@99 801c6759-fa7c-4059-a304-17956f83a07c
2018-08-30 18:06:49 +00:00
parent 07c78cd992
commit 1ab94a4bea
24 changed files with 988 additions and 0 deletions
@@ -0,0 +1,88 @@
+function [p,S,mu] = myPolyfit(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, P(X(I))~=Y(I), in a least-squares sense. 
+% 
+%   [P,S] = POLYFIT(X,Y,N) returns the polynomial coefficients P and a 
+%   structure S for use with POLYVAL to obtain error estimates on 
+%   predictions.  If the errors in the data, Y, are independent normal 
+%   with constant variance, POLYVAL will produce error bounds which 
+%   contain at least 50% of the predictions. 
+% 
+%   The structure S contains the Cholesky factor of the Vandermonde 
+%   matrix (R), the degrees of freedom (df), and the norm of the 
+%   residuals (normr) as fields.    
+% 
+%   [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. 
+% 
+%   See also POLY, POLYVAL, ROOTS. 
+ 
+%   Copyright 1984-2002 The MathWorks, Inc. 
+%   $Revision: 5.17 $  $Date: 2002/04/09 00:14:25 $ 
+ 
+% 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('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); 
+for j = n:-1:1 
+   V(:,j) = x.*V(:,j+1); 
+end 
+ 
+% Solve least squares problem, and save the Cholesky factor. 
+[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 Cholesky factor 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);