fitqr.rar_QR分解算法_fit$qr_qr分解_总体最小二乘

function [c,R2,rout] = fitqr(x,y,basefun) % fitqr Least-squares fit via solution of overdetermined system with QR % Given ordered pairs of data, (x_i,y_i), i=1,...,m, fitqr % returns the vector of coefficients, c_1,...,c_n, such that % F(x) = c_1*f_1(x) + c_2*f_2(x) + ... + c_n*f_n(x) % minimizes the L2 norm of y_i - F(x_i). % % Synopsis: c = fitqr(x,y,basefun) % [c,R2] = fitqr(x,y,basefun) % [c,R2,r] = fitqr(x,y,basefun) % % Input: x,y = vectors of data to be fit % basefun = (string) name of user-supplied m-file that computes % matrix A. The columns of A are the values of the % basis functions evaluated at the x data points. % % Output: c = vector of coefficients obtained from the fit % R2 = (optional) adjusted coefficient of determination; 0 <= R2 <= 1 % R2 close to 1 indicates a strong relationship between y and x % r = (optional) residuals of the fit if length(y)~= length(x); error('x and y are not compatible'); end A = feval(basefun,x(); % Coefficient matrix of overdetermined system c = A\y(; % Solve overdetermined system with QR factorization if nargout>1 r = y - A*c; % Residuals at data points used to obtain the fit [m,n] = size(A); R2 = 1 - (m-1)/(m-n-1)*(norm(r)/norm(y-mean(y)))^2; if nargout>2, rout = r; end end