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1、function p = polyfit2d(x,y,z,n,m)% P= POLYFIT2D(x,y,z,n,m) finds the coefficients of a % polynomial function of 2 variables formed from the% data in vectors x and y of degrees n and m, respectively,% that fitthe data in vector z in a least-squares sense. % The regression problem is formulated in mat
2、rix format as:%z = A*P So that if the polynomial is cubic in % x and linear in y, the problem becomes:%z = y.*x.3 y.*x.2 y.*x y x.3 x.2 x ones(length(x),1)*% p31 p21 p11 p01 p30 p20 p10 p00 % Note that the various xy products are column vectors of length(x).% The coefficents of the output p % matrix
3、 are arranged as shown:% p31 p30 % p21 p20 % p11 p10 % p01 p00% The indices on the elements of p correspond to the % order of x and y associated with that element.% For a solution to exist, the number of ordered % triples x,y,z must equal or exceed (n+1)*(m+1).% Note that m or n may be zero.% To eva
4、luate the resulting polynominal function,% use POLYVAL2D.% Perry W. Stout June 29, 1995% 4829 Rockland Way% Fair Oaks, CA 95628% (916) 966-0236% Based on the Matlab function polyfit.if any(size(x) = size(y) | (size(z) = size(y)error(X, Y,and Z vectors must be the same size)endx = x(:); y = y(:); z=
5、z(:); % Switches vectors to columns-matrices, tooif length(x) (n+1)*(m+1) error(Number of points must equal or exceed order of polynomial function.)endn = n + 1;m = m + 1; % Increments n and m to equal row, col numbers of p.a = zeros(max(size(x),n*m);% Construct the extended Vandermonde matrix, containing all xy products. for i1= 1:m for j1=1:n a(:,j1+(i1-1)*n) = (x.(n-j1).*(y.(m-i1); end endp1 = (az);% Reform p as a matrix.p=;for i1=1:mp=p, p1(n*(i1-1)+1):(n*i1);end