matlab_拟合zernike波面与原始波面的偏差_QR分解_Householder分解_检验Gram-Schm的计算是否正确

function clas_GS = clgs(A) % compute the reduced QR decomposition of A using the % classical Gram-Schmidt % algorithm % compute m and n, the number of rows and columns of A m = size(A,1); n = size(A,2); % initialize the program: normalize the first column of A % to get the first orthogonal vector of Q Q = zeros(m,n); R(1,1) = norm(A(:,1)); Q(:,1) = A(:,1)/R(1,1); for j = 2:n v = A(:,j); % inner loop of the classical GS; orthogonalize % the j-th column of A on the space with respect to the % first j-1 orthogonal vectors from Q for i = 1:(j-1) R(i,j) = conj(Q(:,i))'*A(:,j); v = v - R(i,j) * Q(:,i); end R(j,j) = norm(v); Q(:,j) = v/R(j,j); % set the j-th orthogonal vector of Q clear v end R = [ R zeros(m-n,n) ]; clas_GS = [ Q R ]; % RECOVER Q AND R: % cQR = clgs(A); % m = size(cQR,1); n = size(cQR,2)/2; % Qclgs = cQR(:,1:n); Rclgs = cQR(1:n,n+1:2*n);