www.pudn.com > geometric.rar > polysurf.m, change:2004-08-13,size:2874b


function c=polysurf(x,y,z,order,w)  % fit a 2-D polynomial surface to the data % % c=polysurf(x,y,z,order,w) % c=polysurf(x,y,z,order) % % x = vector containing the x coordinates of the data %			  % y = vector containing the y coordinates of the data %				   % z = vector containing the z coordinates of the data %				 % c= vector of 2-D polynomial coefficients % % w = vector of weights for the data points %   ****** default = ones(size(z)) ******* % % by G.F. Margrave, March 1993 % % NOTE: It is illegal for you to use this software for a purpose other % than non-profit education or research UNLESS you are employed by a CREWES % Project sponsor. By using this software, you are agreeing to the terms % detailed in this software's Matlab source file.   % BEGIN TERMS OF USE LICENSE % % This SOFTWARE is maintained by the CREWES Project at the Department % of Geology and Geophysics of the University of Calgary, Calgary, % Alberta, Canada.  The copyright and ownership is jointly held by  % its author (identified above) and the CREWES Project.  The CREWES  % project may be contacted via email at:  crewesinfo@crewes.org %  % The term 'SOFTWARE' refers to the Matlab source code, translations to % any other computer language, or object code % % Terms of use of this SOFTWARE % % 1) Use of this SOFTWARE by any for-profit commercial organization is %    expressly forbidden unless said organization is a CREWES Project %    Sponsor. % % 2) A CREWES Project sponsor may use this SOFTWARE under the terms of the  %    CREWES Project Sponsorship agreement. % % 3) A student or employee of a non-profit educational institution may  %    use this SOFTWARE subject to the following terms and conditions: %    - this SOFTWARE is for teaching or research purposes only. %    - this SOFTWARE may be distributed to other students or researchers  %      provided that these license terms are included. %    - reselling the SOFTWARE, or including it or any portion of it, in any %      software that will be resold is expressly forbidden. %    - transfering the SOFTWARE in any form to a commercial firm or any  %      other for-profit organization is expressly forbidden. % % END TERMS OF USE LICENSE  %generate the 2-D Vandermonde matrix of order=order numcols = sum( 1:order+1 );  V = zeros(length(z),numcols);    colcount = 1; for n=order:-1:0    for m=0:n          V(:,colcount) = (x(:).^(n-m)).*(y(:).^m);          colcount=colcount+1;    end end  % generate a matrix of weights and apply them to the Vandermonde matrix  if( nargin > 4 ) 	[nr,nc]=size(V); 	[wr,wc]=size(w); 	if(wr==1) w=w';end 	z = z.*w; 	w=w*ones(1,nc);% each row gets a constant weight 	V=V.*w; % apply with array multiply end  % now we have generated the matrix V necessary for the equation % Vc=z where c is the unknown vector of 2-d polynomial coefficients % The solution is: % z=z.';  c = V\z;